Perry's chemical engineers' handjob 9th edition 2021 [9 ed.] 9780071834094, 0071834095, 9780071834087, 0071834087

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Perry’s Chemical Engineers’ Handbook

ABOUT THE EDITORS Dr. Don W. Green is Emeritus Distinguished Professor of Chemical and Petroleum Engineering at the University of Kansas (KU). He holds a B.S. in petroleum engineering from the University of Tulsa, and M.S. and Ph.D. degrees in chemical engineering from the University of Oklahoma. He is the coeditor of the sixth edition of Perry’s Chemical Engineers’ Handbook, and editor of the seventh and eighth editions. He has authored/coauthored 70 refereed publications, over 100 technical meeting presentations, and is coauthor of the first and second editions of the SPE textbook Enhanced Oil Recovery. Dr. Green has won numerous teaching awards at KU, including the Honors for Outstanding Progressive Educator (HOPE) Award and the Chancellor’s Club Career Teaching Award, the highest teaching recognitions awarded at the University. He has also been featured as an outstanding educator in ASEE’s Chemical Engineering Education Journal. He received the KU School of Engineering Distinguished Engineering Service Award (DESA), and has been designated an Honorary Member of both SPE and AIME and a Fellow of the AIChE. Dr. Marylee Z. Southard is Associate Professor of Chemical and Petroleum Engineering at the University of Kansas. She holds B.S., M.S., and Ph.D. degrees in chemical engineering from the University of Kansas. Dr. Southard’s research deals with small molecule drug formulations; but her industrial background is in production and process development of inorganic chemical intermediates. Dr. Southard’s work in inorganic chemicals production has included process engineering, design, and product development. She has consulted for industrial and pharmaceutical chemical production and research companies. She teaches process design and project economics, and has won several university-wide teaching awards, including the Honors for Outstanding Progressive Educator (HOPE) Award and the Kemper Teaching Fellowship. She has authored 1 patent, 15 refereed publications, and numerous technical presentations. Her research interests are in biological and pharmaceutical mass transport. She is a senior member of AIChE and ASEE.

PERRY’S CHEMICAL ENGINEERS’ HANDBOOK NINTH EDITION New York Chicago San Francisco Athens London Madrid Mexico City Milan New Delhi Singapore Sydney Toronto

Editor-in-Chief Don W. Green Emeritus Distinguished Professor of Chemical and Petroleum Engineering, University of Kansas

Associate Editor Marylee Z. Southard Associate Professor of Chemical & Petroleum Engineering, University of Kansas

Copyright © 2019 by McGraw-Hill Education. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. ISBN: 978-0-07-183409-4 MHID: 0-07-183409-5 The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-183408-7, MHID: 0-07-183408-7. eBook conversion by codeMantra Version 1.0 All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill Education eBooks are available at special quantity discounts to use as premiums and sales promotions or for use in corporate training programs. To contact a representative, please visit the Contact Us page at www.mhprofessional.com. Neither McGraw-Hill nor its authors make any representation(s), warranties or guarantees, expressed or implied, as to the fitness or relevance of the ideas, suggestions, or recommendations presented herein, for any purpose or use, or the suitability, accuracy, reliability or completeness of the information or procedures contained herein. Neither McGraw-Hill nor its authors shall be responsible for any errors, omissions, damages or liabilities arising from use of this information. Use of such equations, instructions, and descriptions shall, therefore, be at the user’s sole decision and risk. Company or organization affiliation for authors is shown for information only and does not imply ideas approval by the Company or Organization. The information contained in this Handbook is provided with the understanding that neither McGraw-Hill nor its authors are providing engineering or other professional services or advice. This work is published with the understanding that McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. TERMS OF USE This is a copyrighted work and McGraw-Hill Education and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill Education’s prior consent. You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms. THE WORK IS PROVIDED “AS IS.” McGRAW-HILL EDUCATION AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill Education and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill Education nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill Education has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill Education and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise.

Contents

For the detailed contents of any section, consult the title page of that section. See also the alphabetical index in the back of the handbook.

Section Unit Conversion Factors and Symbols

Marylee Z. Southard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Marylee Z. Southard, Richard L. Rowley. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Physical and Chemical Data

Bruce A. Finlayson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Mathematics

J. Richard Elliott, Carl T. Lira, Timothy C. Frank, Paul M. Mathias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Thermodynamics

Geoffrey D. Silcox, James J. Noble, Phillip C. Wankat, Kent S. Knaebel . . . . . . . . . . . . . . . . . . . . . . . . 5

Heat and Mass Transfer

James N. Tilton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Fluid and Particle Dynamics

Tiberiu M. Leib, Carmo J. Pereira . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Reaction Kinetics

Thomas F. Edgar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Process Control Process Economics

James R. Couper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Transport and Storage of Fluids Heat-Transfer Equipment

Meherwan P. Boyce, Victor H. Edwards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Richard L. Shilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Psychrometry, Evaporative Cooling, and Solids Drying

John P. Hecht . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Michael F. Doherty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Distillation

Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation Liquid-Liquid Extraction and Other Liquid-Liquid Operations and Equipment

Timothy C. Frank . . . . . . . . . . . . . . . . . 15

M. Douglas LeVan, Giorgio Carta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Adsorption and Ion Exchange

Gas–Solid Operations and Equipment Liquid-Solid Operations and Equipment Reactors

Henry Z. Kister . . . . . . . . . . . . . 14

Ted M. Knowlton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Wayne J. Genck. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Carmo J. Pereira, Tiberiu M. Leib . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Bioreactions and Bioprocessing

Gregory Frank, Jeffrey Chalmers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Solids Processing and Particle Technology Waste Management Process Safety

Karl V. Jacob . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Louis Theodore, Paul S. Farber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Daniel A. Crowl, Robert W. Johnson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Energy Resources, Conversion, and Utilization Materials of Construction

Shabbir Ahmed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Lindell R. Hurst, Jr., Edward R. Naylor, Emory A. Ford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Index follows Section 25 v

This page intentionally left blank

Contributors

D. Shabbir Ahmed, Ph.D. Chemical Engineer, Chemical Sciences and Engineering Division, Argonne National Laboratory (Section Editor, Sec. 24, Energy Resources, Conversion, and Utilization) Brooke Albin, M.S.E. Chemical Engineer, MATRIC (Mid-Atlantic Technology, Research and Innovation Center), Charleston, WV; Member, American Institute of Chemical Engineers, American Filtration Society (Crystallization from the Melt) (Sec. 18, Liquid-Solid Operations and Equipment) John Alderman, M.S., P.E., C.S.P. Managing Partner, Hazard and Risk Analysis, LLC (Electrical Area Classification, Fire Protection Systems) (Sec. 23, Process Safety) Paul Amyotte, Ph.D., P.Eng. Professor of Chemical Engineering and C.D. Howe Chair in Process Safety, Dalhousie University; Fellow, Chemical Institute of Canada; Fellow, Canadian Academy of Engineering (Dust Explosions) (Sec. 23, Process Safety) Frank A. Baczek, B.S. Sr. Research Advisor, FLSmidth USA, Inc. (Gravity Sedimentation Operations) (Sec. 18, LiquidSolid Operations and Equipment) Wayne E. Beimesch, Ph.D. Technical Associate Director (Retired), Corporate Engineering, The Procter & Gamble Company (Drying Equipment, Operation and Troubleshooting) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying) Ray Bennett, Ph.D., P.E., CEFEI Senior Principal Engineer, Baker Engineering and Risk Consultants, Inc.; Member, American Petroleum Institute 752, 753, and 756 (Estimation of Damage Effects) (Sec. 23, Process Safety) B. Wayne Bequette, Ph.D. Professor of Chemical and Biological Engineering, Rensselaer Polytechnic Institute (Unit Operations Control, Advanced Control Systems) (Sec. 8, Process Control) Patrick M. Bernhagen, P.E., B.S. Director of Sales—Fired Heater, Amec Foster Wheeler North America Corp.; API Subcommittee on Heat Transfer Equipment API 530, 536, 560, and 561 (Compact and Nontubular Heat Exchangers) (Sec. 11, Heat-Transfer Equipment) Michael J. Betenbaugh, Ph.D. Professor of Chemical and Biomolecular Engineering, Johns Hopkins University; Member, American Institute of Chemical Engineers (Emerging Biopharmaceutical and Bioprocessing Technologies and Trends) (Sec. 20, Bioreactions and Bioprocessing) Lorenz T. Biegler, Ph.D. Bayer Professor of Chemical Engineering, Carnegie Mellon University; Member, National Academy of Engineering (Sec. 3, Mathematics) Meherwan P. Boyce, Ph.D., P.E. (Deceased) Chairman and Principal Consultant, The Boyce Consultancy Group, LLC; Fellow, American Society of Mechanical Engineers (U.S.); Fellow, National Academy Forensic Engineers (U.S.); Fellow, Institution of Mechanical Engineers (U.K.); Fellow, Institution of Diesel and Gas Turbine Engineers (U.K.); Registered Professional Engineer (Texas), Chartered Engineer (U.K.); Sigma Xi, Tau Beta Pi, Phi Kappa Phi. (Section Coeditor, Sec. 10, Transport and Storage of Fluids) Jeffrey Breit, Ph.D. Principal Scientist, Capsugel; Member, American Association of Pharmaceutical Scientists (Product Attribute Control) (Sec. 20, Bioreactions and Bioprocessing)

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COnTRIBUTORS

Laurence G. Britton, Ph.D. Process Safety Consultant; Fellow, American Institute of Chemical Engineers; Fellow, Energy Institute; Member, Institute of Physics (U.K.) (Flame Arresters) (Sec. 23, Process Safety) nathan Calzadilla, M.S.E. Research Program Assistant, Johns Hopkins Medicine, Chemical and Biomolecular Engineering, Johns Hopkins University; Member, American Institute of Chemical Engineers (Emerging Biopharmaceutical and Bioprocessing Technologies and Trends) (Sec. 20, Bioreactions and Bioprocessing) John W. Carson, Ph.D. President, Jenike & Johanson, Inc., Founding member and past chair of ASTM Subcommittee D18.24, “Characterization and Handling of Powders and Bulk Solids” (Bulk Solids Flow and Hopper Design) (Sec. 21, Solids Processing and Particle Technology) Giorgio Carta, Ph.D. Lawrence R. Quarles Professor, Department of Chemical Engineering, University of Virginia; Member, American Institute of Chemical Engineers, American Chemical Society (Section Coeditor, Sec. 16, Adsorption and Ion Exchange) Jeffrey Chalmers, Ph.D. Professor of Chemical and Biomolecular Engineering, The Ohio State University; Member, American Institute of Chemical Engineers; American Chemical Society; Fellow, American Institute for Medical and Biological Engineering (Section Coeditor, Sec. 20, Bioreactions and Bioprocessing) J. Wayne Chastain, B.S., P.E., CCPSC Engineering Associate, Eastman Chemical Company; Member, American Institute of Chemical Engineers (Layer of Protection Analysis) (Sec. 23, Process Safety) Wu Chen, Ph.D. Principal Research Scientist, The Dow Chemical Company; Fellow, American Filtration and Separations Society (Expression) (Sec. 18, Liquid-Solid Operations and Equipment) Martin P. Clouthier, M.Sc., P.Eng. Director, Jensen Hughes Consulting Canada Ltd. (Dust Explosions) (Sec. 23, Process Safety) James R. Couper, D.Sc. Professor Emeritus, The Ralph E. Martin Department of Chemical Engineering, University of Arkansas—Fayetteville (Section Editor, Sec. 9, Process Economics) Daniel A. Crowl, Ph.D., CCPSC AIChE/CCPS Staff Consultant; Adjunct Professor, University of Utah; Professor Emeritus of Chemical Engineering, Michigan Technological University; Fellow, American Institute of Chemical Engineers; Fellow, AIChE Center for Chemical Process Safety (Section Coeditor, Sec. 23, Process Safety) Rita D’Aquino, M.E. Consultant, Member, American Institute of Chemical Engineers (Pollution Prevention) (Sec. 22, Waste Management) Michael Davies, Ph.D. President and CEO, Braunschweiger Flammenfilter GmbH (PROTEGO), Member, American Institute of Chemical Engineers; Member, National Fire Protection Association (Flame Arresters) (Sec. 23, Process Safety) Sheldon W. Dean, Jr., ScD, P.E. President, Dean Corrosion Technology, Inc.; Fellow, Air Products and Chemicals, Inc., Retired; Fellow, ASTM; Fellow, NACE; Fellow, AIChE; Fellow, Materials Technology Institute (Corrosion Fundamentals, Corrosion Prevention) (Sec. 25, Materials of Construction) Dennis W. Dees, Ph.D. Senior Electrochemical Engineer, Chemical Sciences and Engineering Division, Argonne National Laboratory (Electrochemical Energy Storage) (Sec. 24, Energy Resources, Conversion, and Utilization) Vinay P. Deodeshmukh, Ph.D. Sr. Applications Development Manager—High Temperature and Corrosion Resistant Alloys, Haynes International Inc. (Corrosion Fundamentals, High-Temperature Corrosion, Nickel Alloys) (Sec. 25, Materials of Construction) Shrikant Dhodapkar, Ph.D. Fellow, The Dow Chemical Company; Fellow, American Institute of Chemical Engineers (Gas–Solids Separations) (Sec. 17, Gas–Solid Operations and Equipment); (Feeding, Metering, and Dosing) (Sec. 21, Solids Processing and Particle Technology) David S. Dickey, Ph.D. Consultant, MixTech, Inc.; Fellow, American Institute of Chemical Engineers; Member, North American Mixing Forum (NAMF); Member, American Chemical Society; Member, American Society of Mechanical Engineers; Member, Institute of Food Technology (Mixing and Processing of Liquids and Solids & Mixing of Viscous Fluids, Pastes, and Doughs) (Sec. 18, Liquid-Solid Operations and Equipment) Michael F. Doherty, Ph.D. Professor of Chemical Engineering, University of California—Santa Barbara (Section Editor, Sec. 13, Distillation) Arthur M. Dowell, III, P.E., B.S. President, A M Dowell III PLLC; Fellow, American Institute of Chemical Engineers; Senior Member, Instrumentation, Systems and Automation Society (Risk Analysis) (Sec. 23, Process Safety) Brandon Downey, B.A.Sc. Principal Engineer, R&D, Lonza; Member, American Institute of Chemical Engineers (Product Attribute Control) (Sec. 20, Bioreactions and Bioprocessing) Karin nordström Dyvelkov, Ph.D. GEA Process Engineering A/S Denmark (Drying Equipment, Fluidized Bed Dryers, Spray Dryers) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying)

COnTRIBUTORS

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Thomas F. Edgar, Ph.D. Professor of Chemical Engineering, University of Texas—Austin (Section Editor, Sec. 8, Process Control) Victor H. Edwards, Ph.D., P.E. Principal, VHE Technical Analysis; Fellow and Life Member, American Institute of Chemical Engineers; Member, American Association for the Advancement of Science, American Chemical Society, National Society of Professional Engineers; Life Member, New York Academy of Sciences; Registered Professional Engineer (Texas), Phi Lambda Upsilon, Sigma Tau (Section Coeditor, Sec. 10, Transport and Storage of Fluids) J. Richard Elliott, Ph.D. Professor, Department of Chemical and Biomolecular Engineering, University of Akron; Member, American Institute of Chemical Engineers; Member, American Chemical Society; Member, American Society of Engineering Educators (Section Coeditor, Sec. 4, Thermodynamics) Dirk T. Van Essendelft, Ph.D. Chemical Engineer, National Energy Technology Laboratory, U.S. Department of Energy (Coal) (Sec. 24, Energy Resources, Conversion, and Utilization) James R. Fair, Ph.D., P.E. (Deceased) Professor of Chemical Engineering, University of Texas; Fellow, American Institute of Chemical Engineers; Member, American Chemical Society, American Society for Engineering Education, National Society of Professional Engineers (Section Editor of the 7th edition and major contributor to the 5th, 6th, and 7th editions) (Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation) Yi Fan, Ph.D. Associate Research Scientist, The Dow Chemical Company (Solids Mixing) (Sec. 21, Solids Processing and Particle Technology) Paul S. Farber, P.E., M.S. Principal, P. Farber & Associates, LLC, Willowbrook, Illinois; Member, American Institute of Chemical Engineers, Air & Waste Management Association (Section Coeditor, Sec. 22, Waste Management) Hans K. Fauske, D.Sc. Emeritus President and Regent Advisor, Fauske and Associates, LLC; Fellow, American Institute of Chemical Engineers; Fellow, American Nuclear Society; Member, National Academy of Engineering (Pressure Relief Systems) (Sec. 23, Process Safety) Zbigniew T. Fidkowski, Ph.D. (Sec. 13, Distillation)

Process Engineer, Evonik Industries (Distillation Systems, Batch Distillation)

Bruce A. Finlayson, Ph.D. Rehnberg Professor Emeritus, Department of Chemical Engineering, University of Washington; Member, National Academy of Engineering (Section Editor, Sec. 3, Mathematics) Emory A. Ford, Ph.D. Associate Director, Materials Technology Institute, Chief Scientist and Director of Research, Lyondell/Bassel Retired, Fellow Materials Technology Institute (Section Coeditor, Sec. 25, Materials of Construction) Gregory Frank, Ph.D. Principal Engineer, Amgen Inc.; Fellow, American Institute of Chemical Engineers; Member, Society of Biological Engineering; North American Mixing Forum; Pharmaceutical Discovery, Development, and Manufacturing Forum (Section Coeditor, Sec. 20, Bioreactions and Bioprocessing) Timothy C. Frank, Ph.D. Fellow, The Dow Chemical Company; Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 4, Thermodynamics; Sec. 15, Liquid-Liquid Extraction and Other Liquid-Liquid Operations and Equipment) Walter L. Frank, B.S., P.E., CCPSC President, Frank Risk Solutions, Inc.; AIChE/CCPS Staff Consultant; Fellow, American Institute of Chemical Engineers; Fellow, AIChE Center for Chemical Process Safety (Hazards of Vacuum, Hazards of Inerts) (Sec. 23, Process Safety) Ben J. Freireich, Ph.D. Technical Director, Particulate Solid Research, Inc. (Solids Mixing, Size Enlargement) (Sec. 21, Solids Processing and Particle Technology) James D. Fritz, Ph.D. Consultant, NACE International certified Material Selection Design Specialist; Member of the Metallic Materials and Materials Joining Subcommittees of the ASME Bioprocessing Equipment Standard, the Ferrous Specifications Subcommittee of the ASME Boiler & Pressure Vessel Code, and ASM International (Stainless Steels) (Sec. 25, Materials of Construction) Kevin L. Ganschow, B.S., P.E. Senior Staff Materials Engineer, Chevron Corporation; Registered Professional Mechanical Engineer (California) (Ferritic Steels) (Sec. 25, Materials of Construction) Wayne J. Genck, Ph.D. President, Genck International; consultant on crystallization and precipitation; Member, American Chemical Society, American Institute of Chemical Engineers, Association for Crystallization Technology, International Society of Pharmaceutical Engineers (ISPE) (Section Editor, Sec. 18, Liquid-Solid Operations and Equipment) Craig G. Gilbert, B.Sc. Global Product Manager-Paste, FLSmidth USA, Inc.; Member, Society for Mining, Metallurgy, and Exploration; Mining and Metallurgical Society of America; Registered Professional Engineer (Gravity Sedimentation Operations) (Sec. 18, Liquid-Solid Operations and Equipment)

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COnTRIBUTORS

Roy A. Grichuk, P.E. Piping Director, Fluor, BSME, P.E.; Member, American Society of Mechanical Engineers, B31 Main Committee, B31MTC Committee, and B31.3 Committee; Registered Professional Engineer (Texas) (Piping) (Sec. 10, Transport and Storage of Fluids) Juergen Hahn, Ph.D. Professor of Biomedical Engineering, Rensselaer Polytechnic Institute (Advanced Control Systems, Bioprocess Control) (Sec. 8, Process Control) Roger G. Harrison, Ph.D. Professor of Chemical, Biological, and Materials Engineering and Professor of Biomedical Engineering, University of Oklahoma; Member, American Institute of Chemical Engineers, American Chemical Society, American Society for Engineering Education, Oklahoma Higher Education Hall of Fame; Fellow, American Institute for Medical and Biological Engineering (Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions and Bioprocessing) John P. Hecht, Ph.D. Technical Section Head, Drying and Particle Processing, The Procter & Gamble Company; Member, American Institute of Chemical Engineers (Section Editor, Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying) Matthew K. Heermann, P.E., B.S. Consultant—Fossil Power Environmental Technologies, Sargent & Lundy LLC, Chicago, Illinois (Introduction to Waste Management and Regulatory Overview) (Sec. 22, Waste Management) Dennis C. Hendershot, M.S. Process Safety Consultant; Fellow, American Institute of Chemical Engineers (Inherently Safer Design and Related Concepts, Hazard Analysis, Key Procedures) (Sec. 23, Process Safety) Taryn Herrera, B.S. Process Engineer, Manager Separations Laboratory, FLSmidth USA, Inc. (Gravity Sedimentation Operations) (Sec. 18, Liquid-Solid Operations and Equipment) Darryl W. Hertz, B.S. Senior Manager, Value Improvement Group, KBR, Houston, Texas (Front-End Loading, Value-Improving Practices) (Sec. 9, Process Economics) Bruce S. Holden, M.S. Principal Research Scientist, The Dow Chemical Company; Fellow, American Institute of Chemical Engineers (Sec. 15, Liquid-Liquid Extraction and Other Liquid-Liquid Operations and Equipment) Predrag S. Hrnjak, Ph.D. Will Stoecker Res. Professor of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign; Principal Investigator—U of I Air Conditioning and Refrigeration Center; Assistant Professor, University of Belgrade; International Institute of Chemical Engineers; American Society of Heat, Refrigerating, and Air Conditioning Engineers (Refrigeration) (Sec. 11, Heat-Transfer Equipment) Lindell R. Hurst, Jr., M.S., P.E. Senior Materials and Corrosion Engineer, Shell Global Solutions (US) Inc. Retired, Registered Professional Metallurgical Engineer (Alabama, Ohio, North Dakota) (Section Coeditor, Sec. 25, Materials of Construction) Karl V. Jacob, B.S. Fellow, The Dow Chemical Company; Lecturer, University of Michigan; Fellow, American Institute of Chemical Engineers (Section Editor, Sec. 21, Solids Processing and Particle Technology) Pradeep Jain, M.S. Senior Fellow, The Dow Chemical Company (Feeding, Metering, and Dosing) (Sec. 21, Solids Processing and Particle Technology) David Johnson, P.E., M.Ch.E. (Sec. 11, Heat-Transfer Equipment)

Retired (Thermal Design of Heat Exchangers, Condensers, Reboilers)

Robert W. Johnson, M.S.Ch.E. President, Unwin Company; Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 23, Process Safety) Hugh D. Kaiser, P.E., B.S., M.B.A. Principal Engineer, WSP USA; Fellow, American Institute of Chemical Engineers; Registered Professional Engineer (Indiana, Nebraska, Oklahoma, and Texas) (Storage and Process Vessels) (Sec. 10, Transport and Storage of Fluids) Ian C. Kemp, M.A. (Cantab) Scientific Leader, GlaxoSmithKline; Fellow, Institution of Chemical Engineers; Associate Member, Institution of Mechanical Engineers (Psychrometry, Solids-Drying Fundamentals, Freeze Dryers) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying); (Pinch Analysis) (Sec. 24, Energy Resources, Conversion, and Utilization) Pradip R. Khaladkar, M.S., P.E. Principal Consultant, Materials Engineering Group, Dupont Company (Retired), Registered Professional Engineer (Delaware), Fellow, Materials Technology Institute, St. Louis (Nonmetallic Materials) (Sec. 25, Materials of Construction) Henry Z. Kister, M.E., C.Eng., C.Sc. Senior Fellow and Director of Fractionation Technology, Fluor Corporation; Member, National Academy of Engineering (NAE); Fellow, American Institute of Chemical Engineers; Fellow, Institution of Chemical Engineers (U.K.); Member, Institute of Energy (Section Editor, Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation) Kent S. Knaebel, Ph.D. President, Adsorption Research, Inc.; Member, American Institute of Chemical Engineers, International Adsorption Society; Professional Engineer (Ohio) (Mass Transfer Coeditor, Sec. 5, Heat and Mass Transfer)

COnTRIBUTORS

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Ted M. Knowlton, Ph.D. Technical Consultant and Fellow, Particulate Solid Research, Inc.; Member, American Institute of Chemical Engineers (Section Editor, Sec. 17, Gas–Solid Operations and Equipment) James F. Koch, M.S. Senior Process Engineering Specialist, The Dow Chemical Company (Size Reduction, Screening) (Sec. 21, Solids Processing and Particle Technology) Tim Langrish, D. Phil. School of Chemical and Biomolecular Engineering, The University of Sydney, Australia (Solids-Drying Fundamentals, Cascading Rotary Dryers) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying) Tim J. Laros, M.S. Owner, Filtration Technologies, LLC, Park City, UT; Member, Society for Mining, Metallurgy, and Exploration (Filtration) (Sec. 18, Liquid-Solid Operations and Equipment) Tiberiu M. Leib, Ph.D. Principal Consultant, The Chemours Company (retired); Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 7, Reaction Kinetics; Sec. 19, Reactors) M. Douglas LeVan, Ph.D. J. Lawrence Wilson Professor of Engineering Emeritus, Department of Chemical and Biomolecular Engineering, Vanderbilt University; Member, American Institute of Chemical Engineers, American Chemical Society, International Adsorption Society (Section Coeditor, Sec. 16, Adsorption and Ion Exchange) Wenping Li, Ph.D. R&D Director, Agrilectric Research Company; Member, American Filtration and Separations Society, American Institute of Chemical Engineers (Expression) (Sec. 18, Liquid-Solid Operations and Equipment) Eugene L. Liening, M.S., P.E. Manufacturing & Engineering Technology Fellow, The Dow Chemical Company Retired; Fellow, Materials Technology Institute; Registered Professional Metallurgical Engineer (Michigan) (Corrosion Testing) (Sec. 25, Materials of Construction) Dirk Link, Ph.D. Chemist, National Energy Technology Laboratory, U.S. Department of Energy (Nonpetroleum Liquid Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization) Carl T. Lira, Ph.D. Associate Professor, Department of Chemical and Materials Engineering, Michigan State University; Member, American Institute of Chemical Engineers; Member, American Chemical Society; Member, American Society of Engineering Educators (Section Coeditor, Sec. 4, Thermodynamics) Peter J. Loftus, D. Phil. Chief Scientist, Primaira LLC, Member, American Society of Mechanical Engineers (Heat Generation) (Sec. 24, Energy Resources, Conversion, and Utilization) Michael F. Malone, Ph.D. Professor of Chemical Engineering and Vice-Chancellor for Research and Engagement, University of Massachusetts—Amherst (Batch Distillation, Enhanced Distillation) (Sec. 13, Distillation) Paul E. Manning, Ph.D. Director CRA Marketing and Business Development, Haynes International (Nickel Alloys) (Sec. 25, Materials of Construction) Chad V. Mashuga, Ph.D., P.E. Assistant Professor of Chemical Engineering, Texas A&M University (Flammability, Combustion and Flammability Hazards, Explosions, Vapor Cloud Explosions, Boiling-Liquid Expanding-Vapor Explosions) (Sec. 23, Process Safety) Paul M. Mathias, Ph.D. Senior Fellow and Technical Director, Fluor Corporation; Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 4, Thermodynamics); (Design of Gas Absorption Systems) (Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation) Paul McCurdie, B.S. Product Manager-Vacuum Filtration, FLSmidth USA, Inc. (Filtration) (Sec. 18, Liquid-Solid Operations and Equipment) James K. McGillicuddy, B.S. Product Specialist, Centrifuges, Andritz Separation Inc.; Member, American Institute of Chemical Engineers (Centrifuges) (Sec. 18, Liquid-Solid Operations and Equipment) John D. McKenna, Ph.D. Principal, ETS, Inc.; Member, American Institute of Chemical Engineers, Air and Waste Management Association (Air Pollution Management of Stationary Sources) (Sec. 22, Waste Management) Terence P. Mcnulty, Ph.D. President, T. P. McNulty and Associates, Inc.; consultants in mineral processing and extractive metallurgy; Member, National Academy of Engineering; Member, American Institute of Mining, Metallurgical, and Petroleum Engineers; Member, Society for Mining, Metallurgy, and Exploration; Member, The Metallurgical Society; Member Mining and Metallurgical Society of America (Leaching) (Sec. 18, Liquid-Solid Operations and Equipment) Greg Mehos, Ph.D., P.E. Senior Project Engineer, Jenike & Johanson, Inc. (Bulk Solids Flow and Hopper Design) (Sec. 21, Solids Processing and Particle Technology) Georges A. Melhem, Ph.D. President and CEO, IoMosaic; Fellow, American Institute of Chemical Engineers (Emergency Relief Device Effluent Collection and Handling) (Sec. 23, Process Safety) Valerie S. Monical, B.S. Fellow, Ascend Performance Materials, Inc. (Phase Separation) (Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation)

xii

COnTRIBUTORS

Ronnie Montgomery Technical Manager, Process Control Systems, IHI Engineering and Construction International Corporation; Member, Process Industries Practices, Process Controls Function Team; Member, International Society of Automation (Flow Measurement) (Sec. 10, Transport and Storage of Fluids) David A. Moore, B.Sc., M.B.A., P.E., C.S.P. President, AcuTech Consulting Group; Member, ASSE, ASIS, NFPA (Security) (Sec. 23, Process Safety) Charles G. Moyers, Ph.D. Senior Chemical Engineering Consultant, MATRIC (Mid-Atlantic Technology, Research and Innovation Center), Charleston, WV; Fellow, American Institute of Chemical Engineers (Crystallization from the Melt) (Sec. 18, Liquid-Solid Operations and Equipment) William E. Murphy, Ph.D., P.E. Professor of Mechanical Engineering, University of Kentucky; American Society of Heating, Refrigerating, and Air-Conditioning Engineers; American Society of Mechanical Engineers; International Institute of Refrigeration (Air Conditioning) (Sec. 11, Heat-Transfer Equipment) Edward R. naylor, B.S., M.S. Senior Materials Engineering Associate, AkzoNobel; Certified API 510, 570, 653 and Fixed Equipment Source Inspector (Section Coeditor, Sec. 25, Materials of Construction) James J. noble, Ph.D., P.E., Ch.E. [U.K.] Research Affiliate, Department of Chemical Engineering, Massachusetts Institute of Technology; Fellow, American Institute of Chemical Engineers; Member, New York Academy of Sciences (Heat Transfer Coeditor, Sec. 5, Heat and Mass Transfer) W. Roy Penney, Ph.D., P.E. Professor Emeritus, Department of Chemical Engineering, University of Arkansas; Fellow, American Institute of Chemical Engineers (Gas-in-Liquid Dispersions) (Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation) Clint Pepper, Ph.D. Director, Lonza; Member, American Institute of Chemical Engineers (Product Attribute Control) (Sec. 20, Bioreactions and Bioprocessing) Carmo J. Pereira, Ph.D., M.B.A. DuPont Fellow, E. I. du Pont de Nemours and Company; Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 7, Reaction Kinetics; Sec. 19, Reactors) Demetri P. Petrides, Ph.D. President, Intelligen, Inc.; Member, American Institute of Chemical Engineers, American Chemical Society (Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions and Bioprocessing) Thomas H. Pratt, Ph.D., P.E., C.S.P. Retired; Emeritus Member, NFPA 77 (Static Electricity) (Sec. 23, Process Safety) Richard W. Prugh, M.S., P.E., C.S.P. Principal Process Safety Consultant, Chilworth Technology, Inc., a Dekra Company; Fellow, American Institute of Chemical Engineers; Member, National Fire Protection Association (Toxicity) (Sec. 23, Process Safety) Massood Ramezan, Ph.D., P.E. Sr. Technical Advisor, KeyLogic Systems, Inc. (Coal Conversion) (Sec. 24, Energy Resources, Conversion, and Utilization) George A. Richards, Ph.D. Mechanical Engineer, National Energy Technology Laboratory, U.S. Department of Energy (Natural Gas, Liquefied Petroleum Gas, Other Gaseous Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization) John R. Richards, Ph.D. Research Fellow, E. I. du Pont de Nemours and Company (retired); Fellow, American Institute of Chemical Engineers (Polymerization Reactions) (Sec. 7, Reaction Kinetics) James A. Ritter, Ph.D. L. M. Weisiger Professor of Engineering and Carolina Distinguished Professor, Department of Chemical Engineering, University of South Carolina; Member, American Institute of Chemical Engineers, American Chemical Society, International Adsorption Society (Sorption Equilibrium, Process Cycles, Equipment) (Sec. 16, Adsorption and Ion Exchange) Richard L. Rowley, Ph.D. Professor Emeritus of Chemical Engineering, Brigham Young University (Section Coeditor, Sec. 2, Physical and Chemical Data) Scott R. Rudge, Ph.D. Chief Operating Officer and Chairman, RMC Pharmaceutical Solutions, Inc.; Adjunct Professor, Chemical and Biological Engineering, University of Colorado; Vice President, Margaux Biologics, Scientific Advisory Board, Sundhin Biopharma (Downstream Processing: Primary Recovery and Purification); Member, American Chemical Society, International Society of Pharmaceutical Engineers, American Association for the Advancement of Science, Parenteral Drug Association (Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions and Bioprocessing) Adel F. Sarofim, Sc.D. Deceased; Presidential Professor of Chemical Engineering, Combustion, and Reactors, University of Utah; Member, American Institute of Chemical Engineers, American Chemical Society, Combustion Institute (Radiation) (Sec. 5, Heat and Mass Transfer) David K. Schmalzer, Ph.D., P.E. Argonne National Laboratory (Retired), Member, American Chemical Society, American Institute of Chemical Engineers (Resources and Reserves, Liquid Petroleum Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization)

COnTRIBUTORS

xiii

Fred Schoenbrunn, B.S. Director-Sedimentation Products, Member, Society of Metallurgical and Exploration Engineers of the American Institute of Minting, Metallurgical and Petroleum Engineers; Registered Professional Engineer (Gravity Sedimentation Operations) (Sec. 18, Liquid-Solid Operations and Equipment) A. Frank Seibert, Ph.D., P.E. Technical Manager, Separations Research Program, The University of Texas at Austin; Fellow, American Institute of Chemical Engineers (Sec. 15, Liquid-Liquid Extraction and Other Liquid-Liquid Operations and Equipment) Yongkoo Seol, Ph.D. Geologist, National Energy Technology Laboratory, U.S. Department of Energy (Natural Gas) (Sec. 24, Energy Resources, Conversion, and Utilization) Lawrence J. Shadle, Ph.D. Mechanical Engineer, National Energy Technology Laboratory, U.S. Department of Energy (Coke) (Sec. 24, Energy Resources, Conversion, and Utilization) Robert R. Sharp, P.E., Ph.D. Environmental Consultant; Professor of Environmental Engineering, Manhattan College; Member, American Water Works Association; Water Environment Federation Section Director (Wastewater Management) (Sec. 22, Waste Management) Dushyant Shekhawat, Ph.D., P.E. Chemical Engineer, National Energy Technology Laboratory, U.S. Department of Energy (Natural Gas, Fuel and Energy Costs) (Sec. 24, Energy Resources, Conversion, and Utilization) Richard L. Shilling, P.E., B.E.M.E. Senior Engineering Consultant, Heat Transfer Research, Inc.; American Society of Mechanical Engineers (Section Editor, Sec. 11, Heat-Transfer Equipment) nicholas S. Siefert, Ph.D., P.E. Mechanical Engineer, National Energy Technology Laboratory, U.S. Department of Energy (Other Solid Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization) Geoffrey D. Silcox, Ph.D. Professor of Chemical Engineering, University of Utah; Member, American Institute of Chemical Engineers, American Chemical Society (Heat Transfer Section Coeditor, Sec. 5, Heat and Mass Transfer) Cecil L. Smith, Ph.D. Principal, Cecil L. Smith Inc. (Batch Process Control, Telemetering and Transmission, Digital Technology for Process Control, Process Control and Plant Safety) (Sec. 8, Process Control) (Francis) Lee Smith, Ph.D. Principal, Wilcrest Consulting Associates, LLC, Katy, Texas; Partner and General Manager, Albutran USA, LLC, Katy, Texas (Front-End Loading, Value-Improving Practices) (Sec. 9, Process Economics); (Evaporative Cooling) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying); (Energy Recovery) (Sec. 24, Energy Resources, Conversion, and Utilization) Joseph D. Smith, Ph.D. Professor of Chemical and Biochemical Engineering, Missouri University of Science and Technology (Thermal Energy Conversion and Utilization) (Sec. 24, Energy Resources, Conversion, and Utilization) Daniel J. Soeder, M.S. Director, Energy Resources Initiative, South Dakota School of Mines & Technology (Gaseous Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization) Marylee Z. Southard, Ph.D. Associate Professor of Chemical and Petroleum Engineering, University of Kansas; Senior Member, American Institute of Chemical Engineers; Member, American Society for Engineering Education (Section Editor, Sec. 1, Unit Conversion Factors and Symbols); (Section Editor, Sec. 2, Physical and Chemical Data) Thomas O. Spicer III, Ph.D., P.E. Professor; Maurice E. Barker Chair in Chemical Engineering, Chemical Hazards Research Center Director, Ralph E. Martin Department of Chemical Engineering, University of Arkansas; Fellow, American Institute of Chemical Engineers (Atmospheric Dispersion) (Sec. 23, Process Safety) Jason A. Stamper, M. Eng. Technology Leader, Drying and Particle Processing, The Procter & Gamble Company; Member, Institute for Liquid Atomization and Spray Systems (Drying Equipment, Fluidized Bed Dryers, Spray Dryers) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying) Daniel E. Steinmeyer, P.E., M.S. Distinguished Science Fellow, Monsanto Company (retired); Fellow, American Institute of Chemical Engineers; Member, American Chemical Society (Phase Dispersion, Liquid in Gas Systems) (Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation) Gary J. Stiegel, P.E., M.S. Technology Manager (Retired), National Energy Technology Laboratory, U.S. Department of Energy (Coal Conversion) (Sec. 24, Energy Resources, Conversion, and Utilization) Angela Summers, Ph.D., P.E. President, SIS-TECH; Adjunct Professor, Department of Environmental Management, University of Houston–Clear Lake; Fellow, International Society of Automation; Fellow, American Institute of Chemical Engineers; Fellow, AIChE Center for Chemical Process Safety (Safety Instrumented Systems) (Sec. 23, Process Safety) Richard C. Sutherlin, B.S., P.E. Richard Sutherlin, PE, Consulting, LLC; Registered Professional Metallurgical Engineer (Oregon) (Reactive Metals) (Sec. 25, Materials of Construction) Ross Taylor, Ph.D. Distinguished Professor of Chemical Engineering, Clarkson University (Simulation of Distillation Processes) (Sec. 13, Distillation)

xiv

COnTRIBUTORS

Louis Theodore, Eng.Sc.D. Consultant, Theodore Tutorials, Professor of Chemical Engineering, Manhattan College; Member, Air and Waste Management Association (Section Coeditor, Sec. 22, Waste Management) Susan A. Thorneloe, M.S. U.S. EPA/Office of Research & Development, National Risk Management Research Laboratory; Member, Air and Waste Management Association, International Waste Working Group (Sec. 22, Waste Management) James n. Tilton, Ph.D., P.E. DuPont Fellow, Chemical and Bioprocess Engineering, E. I. du Pont de Nemours & Co.; Member, American Institute of Chemical Engineers; Registered Professional Engineer (Delaware) (Section Editor, Sec. 6, Fluid and Particle Dynamics) Paul W. Todd, Ph.D. Chief Scientist Emeritus, Techshot, Inc.; Member, American Institute of Chemical Engineers (Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions and Bioprocessing) Krista S. Walton, Ph.D. Professor and Robert “Bud” Moeller Faculty Fellow, School of Chemical & Biomolecular Engineering, Georgia Institute of Technology; Member, American Institute of Chemical Engineers, American Chemical Society, International Adsorption Society (Adsorbents) (Sec. 16, Adsorption and Ion Exchange) Phillip C. Wankat, Ph.D. Clifton L. Lovell Distinguished Professor of Chemical Engineering Emeritus, Purdue University; Member, American Institute of Chemical Engineers (Mass Transfer Coeditor, Sec. 5, Heat and Mass Transfer) Kenneth n. Weiss, P.E., BCEE, B.Ch.E, M.B.A. Managing Partner, ERM; Member, Air and Waste Management Association (Introduction to Waste Management and Regulatory Overview) (Sec. 22, Waste Management) W. Vincent Wilding, Ph.D. Professor of Chemical Engineering, Brigham Young University; Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 2, Physical and Chemical Data) Ronald J. Willey, Ph.D., P.E. Professor, Department of Chemical Engineering, Northeastern University; Fellow, American Institute of Chemical Engineers (Case Histories) (Sec. 23, Process Safety) Todd W. Wisdom, M.S. Director-Separations Technology, FLSmidth USA, Inc.; Member, American Institute of Chemical Engineers (Filtration) (Sec. 18, Liquid-Solid Operations and Equipment) John L. Woodward, Ph.D. Senior Principal Consultant, Baker Engineering and Risk Consultants, Inc.; Fellow, American Institute of Chemical Engineers (Discharge Rates from Punctured Lines and Vessels) (Sec. 23, Process Safety)

Preface to the ninth Edition

“This handbook is intended to supply both the practicing engineer and the student with an authoritative reference work that covers comprehensively the field of chemical engineering as well as important related fields.” —John H. Perry, 1934

Chemical engineering is generally accepted to have had its origin in the United Kingdom (U.K.) during the latter part of the nineteenth century, largely in response to the industrial revolution and growth in the demand for industrial chemicals. To answer this demand, chemical companies began to mass-produce their products, which meant moving from batch processing to continuous operation. New processes and equipment, in turn, called for new methods. Initially, continuous reactions and processing were implemented largely by plant operators, mechanical engineers, and industrial chemists. Chemical engineering evolved from this advancement of the chemical industry, creating engineers who were trained in chemistry as well as the fundamentals of engineering, physics, and thermodynamics. As an academic discipline, the earliest reported chemical engineering lectures were given in the United Kingdom. George Davis is generally recognized as the first chemical engineer, lecturing at the Manchester Technical School (later the University of Manchester) in 1887. The first American chemical engineering courses were taught at MIT in 1888. Davis also proposed an appropriate professional society that evolved with the industrial and academic profession, ultimately called the Society of Chemical Industry (1881). His initial proposal was for a society of chemical engineers but the name was changed because so few chemical engineers existed at that time. From there, the American Institute of Chemical Engineers, AIChE (1908), and the U.K.-origin Institution of Chemical Engineers, IChemE (1922), were created. As the discipline advanced, important approaches to describing and designing chemical and physical processes developed. George Davis is credited with an early description of what came to be termed “unit operations,” although he did not use that specific term. Arthur D. Little coined the phrase in 1908 in a report to the president of MIT and developed the concept and applications with William H. Walker. Walker later defined “unit operations” in his 1923 seminal textbook published by McGraw-Hill, Principles of Chemical Engineering, coauthored with Warren K. Lewis and William H. McAdams. Other concepts developed over time, including chemical reactor engineering, transport phenomena, and use of computers to enhance mathematical simulation, have increased our ability to understand and design chemical/physical industrial processes. Chemical engineering concepts and methods have been applied in increasingly diverse fields, including environmental engineering, pharmaceutical processing, microelectronics, and biological/biosimilar engineering. The first known handbook of chemical engineering was in two volumes, written by George Davis, and published in the United Kingdom in 1901. A second edition followed in 1904. The emphasis was on materials and their properties; laboratory equipment and techniques; steam production and distribution; power and its applications; moving solids, liquids, and gases; and solids handling. In the preface, Davis acknowledged the advances in industrial chemistry made in Germany, especially in commercial organic chemistry. He also noted the “severe competition” coming from America “in the ammoniasoda industry.” The first US handbook was edited by Donald M. Liddell and published by McGraw-Hill in 1922. It was a two-volume book with thirty-one contributing writers. It dealt with many of the same topics as in the Davis handbook, but also had significantly more emphasis on operations such as leaching, crystallization, evaporation, and drying. Perry’s Chemical Engineers’ Handbook originated from a decision by McGraw-Hill in 1930 (during the Great Depression) to develop a new handbook of chemical engineering. Receiving support for the project from DuPont Company, they selected John H. Perry to be the editor. Perry had earned a Ph.D. from MIT in 1922 in Physical Chemistry and Chemical Engineering. He subsequently worked for the US Bureau of Mines, next as a chemist for a DuPont subsidiary in Cleveland, OH, then moved to Wilmington, DE, to work for DuPont as a chemist in the company’s experimental station, and back to xv

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Cleveland, still with DuPont. Family lore says that Perry was a very hard worker, dedicated to chemical engineering, and willing to basically live two lives: one as a full-time engineer for DuPont and the other as editor of the handbook. On weekends he would hitchhike to New York, go to the Chemist’s Club with a packet of galley proofs and a carton of cigarettes, and work all weekend, sometimes for 24 hours at a time. His work on the book extended through 1933, leading to publication of the first edition in January 1934. There were 63 contributors, 14 from the DuPont Company and 21 from different universities, all experts in their respective technical areas. The first sentence in the preface was applicable then as well as for this ninth edition: “This handbook is intended to supply both the practicing engineer and the student with an authoritative reference work that covers comprehensively the field of chemical engineering as well as important related fields.” Several chemical engineers, serving as editor or coeditor, have guided the preparation of the different editions over the years. John H. Perry was editor of the first (1934), second (1941), and third (1950) editions before his untimely death in 1953. The position of editor passed to his only child, Robert H. Perry (Bob), a notable chemical engineer in his own right. Bob had a Ph.D. in chemical engineering from the University of Delaware and was working in industry at the time of his father’s death. In 1958, he took a position as professor and later chair of the Department of Chemical Engineering at the University of Oklahoma. He was the editor of the fourth (1963) edition, coedited with Cecil H. Chilton and assisted by Sidney D. Kirkpatrick, and the fifth (1973) edition, coedited with Chilton. For the sixth edition, Bob asked Don W. Green, his first Ph.D. student and now a professor of Chemical and Petroleum Engineering at the University of Kansas, to assist him. Tragically, Bob Perry’s work on the handbook ceased when he was killed in an accident south of London in November 1978. Green assumed responsibility as editor and completed the sixth edition (1984), assisted by a colleague at KU, James O. Maloney. The first five editions were titled The Chemical Engineers’ Handbook. Beginning with the sixth edition, the book was renamed Perry’s Chemical Engineers’ Handbook in honor of the father and son. Green was also editor of the seventh (1997) and eighth (2008) editions, with Maloney assisting on the seventh edition. Robert H. Perry was listed as the “late editor” for the seventh and eighth editions; honoring his ideas that carried over to these recent editions. To create the ninth edition, Green brought on Marylee Z. Southard, a colleague with industrial, consulting, and academic experience in chemical engineering. The organization of this ninth edition replicates the logic of the eighth edition, although content changes are extensive. The first group of sections includes comprehensive tables with unit conversions and fundamental constants, physical and chemical data, methods to predict properties, and basics of mathematics most useful to engineers. The second group, comprising the fourth through the ninth sections, covers fundamentals of chemical engineering. The third and largest group of sections deals with processes, including heat transfer operations, distillation, gas–liquid processes, chemical reactors, and liquid–liquid processes. The last group of sections covers auxiliary information, including waste management, safety and handling of hazardous materials, energy sources, and materials of construction. In 2012, McGraw-Hill launched Access Engineering (ACE), an electronic engineering reference tool for professionals, academics, and students. This edition of Perry’s Chemical Engineers’ Handbook is a part of ACE, as was the eighth edition. Beyond the complete text of the handbook, ACE provides: • Interactive graphs • Video tutorials for example problems given in the handbook • Excel spreadsheets to solve guided and user-defined problems in different areas, such as heat transfer or fluid flow • Curriculum maps for use in complementing engineering course content All 25 sections have been updated to cover the latest advances in technology related to chemical engineering. Notable updates and completely new materials include: • Sec. 2 includes new and updated chemical property data produced by the Design Institute for Physical Properties (DIPPR) of AIChE • Sec. 4 on thermodynamics fundamentals has been redesigned to be more practical, and less theoretical than in earlier editions, to suit the practicing engineer and student pursuing applications • A new Sec. 20, “Bioreactions and Bioprocessing,” has been added in response to the significant, large-scale growth of commercial processes for nonfood products since the end of the twentieth century • Sec. 21 on solids handling operations and equipment has been rewritten by industrial experts in their field A group of 147 professionals, serving as section editors and contributors, has worked on this ninth edition. Their names, affiliations, and writing responsibilities are listed herein as part of the front material and on the title page of their respective sections. These authors are known experts in their field, with many having received professional awards and named as Fellows of their professional societies. Since the publication of the eighth edition, we have lost two major contributors to Perry’s Chemical Engineers’ Handbook. Dr. Adel F. Sarofim died in December 2011. He was a section coeditor/contributor in the radiation subsection from the fifth edition (1973) through this current ninth edition. Dr. Sarofim, a Professor Emeritus at MIT, was a recognized pioneer in the development of combustion science and radiation heat transfer. He received numerous U.S. and international prizes for his work. Dr. Meherwan P. Boyce died in December 2017. He was the editor for the “Transport and Storage of Fluids” section in the seventh edition and co-section editor for the eighth and current editions. Dr. Boyce was founder of Boyce Engineering International. He was also known for his role as the first director of the Turbomachinery Laboratory and founding member of the Turbomachinery Symposium. On this 85th anniversary of Perry’s Chemical Engineers’ Handbook, we celebrate the memory of its creators, Dr. John H. Perry and Dr. Robert H. Perry. Often referred to as “the Bible of Chemical Engineering,” this handbook is the gold standard as a source of valuable information to innumerable chemical engineers. We dedicate this ninth edition to chemical engineers who carry on the profession, creating solutions, products, and processes needed in the challenging world ahead. We hope this edition will provide information and focus for you—to work for the quality and improvement of human life and the earth we inhabit. DON W. GREEN Editor-in-Chief MARYLEE Z. SOUTHARD Associate Editor

Section 1

Unit Conversion Factors and Symbols

Marylee Z. Southard, Ph.D. Associate Professor of Chemical and Petroleum Engineering, University of Kansas; Senior Member, American Institute of Chemical Engineers; Member, American Society for Engineering Education

Table 1-1 Table 1-2a Table 1-2b Table 1-3 Table 1-4 Table 1-5

UnITS AnD SYMBOLS Standard SI Quantities and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common Derived Units of SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Derived Units of SI That Have Special Names . . . . . . . . . . . . . . . . . . . . SI Prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Greek Alphabet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . United States Traditional System of Weights and Measures . . . . . .

1-2 1-2 1-2 1-2 1-2 1-3

Table 1-6 Table 1-7

COnVERSIOn FACTORS Common Units and Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . Alphabetical Listing of Common Unit Conversions . . . . . . . . . . . . . .

1-4 1-5

Table 1-8 Table 1-9 Table 1-10 Table 1-11 Table 1-12 Table 1-13 Table 1-14

Conversion Factors: Commonly Used and Traditional Units to SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Conversion Factors to SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temperature Conversion Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Density Conversion Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kinematic Viscosity Conversion Formulas. . . . . . . . . . . . . . . . . . . . . . . Values of the Ideal Gas Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-7 1-15 1-17 1-17 1-17 1-17 1-18

1-1

1-2

UnIT COnVERSIOn FACTORS AnD SYMBOLS

UnITS AnD SYMBOLS TABLE 1-2b Derived Units of SI That Have Special names

TABLE 1-1 Standard SI Quantities and Units Quantity or “dimension”

SI unit

SI unit symbol (“abbreviation”)

Base quantity or “dimension” m length meter kg kilogram mass s second time A ampere electric current K kelvin thermodynamic temperature mol mole* amount of substance cd candela luminous intensity Supplementary quantity or “dimension” rad radian plane angle sr steradian solid angle *When the mole is used, the elementary entities must be specified; they may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

TABLE 1-2a

Common Derived Units of SI

Quantity

Unit

Symbol

acceleration angular acceleration angular velocity area concentration (mass) concentration (molar) current density density, mass electric charge density electric field strength electric flux density energy density entropy heat capacity heat flux density, irradiance luminance magnetic field strength molar energy molar entropy molar heat capacity moment of force permeability permittivity radiance radiant intensity specific energy specific entropy specific heat capacity specific volume surface tension thermal conductivity velocity viscosity, dynamic viscosity, kinematic volume wave number

meter per second squared radian per second squared radian per second square meter kilogram per cubic meter mole per cubic meter ampere per square meter kilogram per cubic meter coulomb per cubic meter volt per meter coulomb per square meter joule per cubic meter joule per kelvin joule per kelvin watt per square meter candela per square meter ampere per meter joule per mole joule per mole-kelvin joule per mole-kelvin newton-meter henry per meter farad per meter watt per square meter-steradian watt per steradian joule per kilogram joule per kilogram-kelvin joule per kilogram-kelvin cubic meter per kilogram newton per meter watt per meter-kelvin meter per second pascal-second square meter per second cubic meter reciprocal meter

m/s2 rad/s2 rad/s m2 kg/m3 mol/m3 A/m2 kg/m3 C/m3 V/m C/m2 J/m3 J/K J/K W/m2 cd/m2 A/m J/mol J/(mol ⋅ K) J/(mol ⋅ K) N⋅m H/m F/m W/(m2 ⋅ sr) W/sr J/kg J/(kg ⋅ K) J/(kg ⋅ K) m3/kg N/m W/(m ⋅ K) m/s Pa ⋅ s m2/s m3 1/m

Quantity absorbed dose activity (of radionuclides) capacitance conductance electric potential, potential difference, electromotive force electric resistance energy, work, quantity of heat force frequency (of a periodic phenomenon) illuminance inductance luminous flux magnetic flux magnetic flux density power, radiant flux pressure, stress quantity of electricity, electric charge

Unit

Symbol

gray becquerel farad siemens volt

Gy Bq F S V

J/kg l/s C/V A/V W/A

Formula

ohm joule newton hertz lux henry lumen weber tesla watt pascal coulomb

Ω J N Hz lx H lm Wb T W Pa C

V/A N⋅m (kg ⋅ m)/s2 1/s lm/m2 Wb/A Cd ⋅ sr V⋅s Wb/m2 J/s N/m2 A⋅s

TABLE 1-3 SI Prefixes Multiplication factor 1 000 000 000 1 000 000 1 000 1

000 000 000 000 1

000 000 000 000 000 1

18

000 = 10 000 = 1015 000 = 1012 000 = 109 000 = 106 000 = 103 100 = 102 10 = 101 0.1 = 10-1 0.01 = 10-2 0.001 = 10-3 0.000 001 = 10-6 0.000 000 001 = 10-9 0.000 000 000 001 = 10-12 0.000 000 000 000 001 = 10-15 0.000 000 000 000 000 001 = 10-18

Prefix

Symbol

exa peta tera giga mega kilo hecto* deka* deci* centi milli micro nano pico femto atto

E P T G M k h da d c m µ n p f a

*Generally to be avoided.

TABLE 1-4 Greek Alphabet alpha = A, α beta = B, b gamma = Γ, γ delta = Δ, δ epsilon = Ε, ε zeta = Ζ, ζ eta = Η, η theta = Θ, θ iota = Ι, ι kappa = Κ, κ lambda = Λ, λ mu = Μ, µ

nu xi omicron pi rho sigma tau upsilon phi chi psi omega

= Ν, ν = Ξ, ξ = Ο, ο = Π, π = Ρ, ρ = Σ, σ = Τ, τ = Υ, υ = Φ, φ = Χ, χ = Ψ, ψ = Ω, ω

UnITS AnD SYMBOLS TABLE 1-5

United States Traditional System of Weights and Measures Linear Measure 12 inches (in) or (″) = 1 foot ( ft) or (′) 3 feet = 1 yard (yd) 16.5 feet   = 1 rod (rd) 5.5 yards  5280 feet  = 1 mile (mi) 320 rods   1 mil = 0.001 in

Nautical:

6080.2 feet = 1 nautical mile 6 feet = 1 fathom 120 fathoms = 1 cable length 1 knot (kn) = 1 nautical mile per hour 60 nautical miles = 1° of latitude

Square Measure 144 square inches (sq in) or (in2) = 1 sq ft ( ft2) 9 sq ft ( ft2) = 1 sq yd (yd2) 30.25 sq yd = 1 sq rod, pole, or perch  10 sq chains  160 sq rods =   = 1 acre 43.560 sq ft    640 acres = 1 sq mi = 1 section 1 circular in (area of circle of 1-in diameter) = 0.7854 sq in 1 sq in = 1.2732 circular in 1 circular mil = area of circle of 0.001-in diameter 1,000,000 circular mils = 1 circular in Circular Measure 60 seconds (″) = 1 minute or (′) 60 minutes (′) = 1 degree (1°) 90 degrees (90°) = 1 quadrant 360 degrees (360°) = 1 circumference

 1 radian (rad) 57.29578 degrees =   57 17 ′ 44.81′′ Volume Measure Solid:

1728 cubic in (cu in) (in3) = 1 cubic foot (cu ft) ( ft3) 27 cu ft = 1 cubic yard (cu yd) (yd3) Dry Measure: 2 pints = 1 quart 8 quarts = 1 peck 4 pecks = 1 bushel 1 U.S. Winchester bushel = 2150.42 cubic inches (in3) Liquid: 4 gills = 1 pint (pt) 2 pints = 1 quart (qt) 4 quarts = 1 gallon (gal) 7.4805 gallons = 1 cubic foot ( ft3) Apothecaries’ Liquid: 60 minims (min. or ) = 1 fluid dram or drachm 8 drams ( ) = 1 fluid ounce 16 ounces (oz. ) = 1 pint Avoirdupois Weight 16 drams = 437.5 grains (gr) = 1 ounce (oz) 16 ounces = 7000 grains = 1 pound (lb) 100 pounds = 1 hundredweight (cwt) 2000 pounds = 1 short ton; 2240 pounds = 1 long ton Troy Weight 24 grains (gr) = 1 pennyweight (dwt) 20 pennyweights = 1 ounce (oz) 12 ounces = 1 pound (lb) Apothecaries’ Weight 20 grains (gr) = 1 scruple ( ) 3 scruples = 1 dram ( ) 8 drams = 1 ounce ( ) 12 ounces = 1 pound (lb)

1-3

1-4

UnIT COnVERSIOn FACTORS AnD SYMBOLS

COnVERSIOn FACTORS TABLE 1-6 Common Units and Conversion Factors* Mass (M)

Length (L)

Area (L2)

Volume (L3)

Time (θ)

1 pound mass = 453.5924 grams = 0.45359 kilogram = 7000 grains 1 slug = 32.174 pounds mass 1 ton (short) = 2000 pounds mass 1 ton (long) = 2240 pounds mass 1 ton (metric) = 1000 kilograms = 2204.62 pounds mass 1 pound-mole = 453.59 gram-moles 1 foot

= 30.480 centimeters = 0.3048 meter 1 inch = 2.54 centimeters = 0.0254 meter 1 mile (U.S.) = 1.60935 kilometers 1 yard = 0.9144 meter 1 square foot = 929.0304 square centimeters = 0.09290304 square meter 1 square inch = 6.4516 square centimeters 1 square yard = 0.836127 square meter 1 cubic foot = 28,316.85 cubic centimeters = 0.02831685 cubic meter = 28.31685 liters = 7.481 gallons (U.S.) 1 gallon = 3.7853 liters = 231 cubic inches 1 hour (h) = 60 minutes (min) = 3600 seconds (s)

Temperature (T) 1 centigrade or Celsius degree = 1.8 Fahrenheit degrees Temperature, Kelvin = T °C + 273.15 Temperature, Rankine = T °F + 459.7 Temperature, Fahrenheit = 9/5 T °C + 32 Temperature, Celsius or centigrade = 5/9 (T °F - 32) Temperature, Rankine = 1.8T K Force (F) 1 pound force = 444,822.2 dynes = 4.448222 newtons (N) = 32.174 poundals 2 Pressure (F/L ) Normal atmospheric pressure note: U.S. Customary units, or British units, on left and SI units on right. *Adapted from Faust et al., Principles of Unit Operations, John Wiley & Sons, 1980.

1 atm = 760 millimeters of mercury at 0°C (density 13.5951 g/cm3) = 29.921 inches of mercury at 32°F = 14.696 pounds force/square inch = 33.899 feet of water at 39.1°F = 1.01325 × 106 dynes/square centimeter = 1.01325 × 105 newtons/square meter

Density (M/L3) 1 pound mass/cubic foot = 0.01601846 gram/cubic centimeter = 16.01846 kilograms/cubic meter Energy (H or FL) 1 British thermal unit = 251.98 calories = 1054.4 joules = 777.97 foot-pounds force = 10.409 liter-atmospheres = 0.2930 watthour Diffusivity (L2/θ) 1 square foot/hour = 0.258 cm2/s = 2.58 × 10-5 m2/s Viscosity (M/Lθ) 1 pound mass/foot-hour = 0.00413 g/cm s = 0.000413 kg/m s 1 centipoise (cP) = 0.01 poise (P) = 0.01 g/cm s = 0.001 kg/m s = 0.000672 lbm/ft s = 0.0000209 lbf -s/ft2 Thermal conductivity [H/θ L2(T/L)] 1 Btu/h ft2 (°F/ft) = 0.00413 cal/s cm2 (°C/cm) = 1.728 J/s m2 (°C/m) Heat transfer coefficient 1 Btu/h ft2 °F = 5.678 J/s m2 °C Heat capacity (H/MT ) 1 Btu/lbm °F = 1 cal/g °C = 4184 J/kg °C Gas constant 1.987 Btu/lbm mol °R = 1.987 cal/mol K = 82.057 atm cm3/mol K = 0.7302 atm ft3/lbmol °F = 10.73 (lbf /in2) ( ft3)/lb mol °R = 1545 (lbf /ft2) ( ft3)/lb mol °R = 8.314 (N/m2) (m3)/mol K Gravitational acceleration g = 9.8066 m/s2 = 32.174 ft/s2

COnVERSIOn FACTORS

1-5

TABLE 1-7 Alphabetical Listing of Common Unit Conversions To Convert from acres acres acres acre-feet ampere-hours (absolute) angstrom units angstrom units angstrom units atmospheres atmospheres atmospheres atmospheres atmospheres atmospheres atmospheres atmospheres bags (cement) barrels (cement) barrels (oil) barrels (oil) barrels (U.S. liquid) barrels (U.S. liquid) barrels per day bars bars bars board feet boiler horsepower boiler horsepower Btu Btu Btu Btu Btu Btu Btu Btu Btu Btu Btu per cubic foot Btu per hour Btu per minute Btu per pound Btu per pound per degree Fahrenheit Btu per pound per degree Fahrenheit Btu per second Btu per square foot per hour Btu per square foot per minute Btu per square foot per second for a temperature gradient of 1°F per inch Btu (60°F) per degree  Fahrenheit Bushels (U.S. dry) Bushels (U.S. dry) calories, gram calories, gram calories, gram calories, gram calories, gram calories, gram, per gram per degree C

To

Multiply by

square feet square meters square miles cubic meters Coulombs (absolute) inches meters microns or micrometers millimeters of mercury at 32°F dynes per square centimeter newtons per square meter feet of water at 39.1°F grams per square centimeter inches of mercury at 32°F pounds per square foot pounds per square inch pounds (cement) pounds (cement) cubic meters gallons cubic meters gallons gallons per minute atmospheres newtons per square meter pounds per square inch cubic feet Btu per hour kilowatts calories (gram) celsius heat units (chu or pcu) foot-pounds horsepower-hours joules liter-atmospheres pounds carbon to CO2 pounds water evaporated from and at 212°F cubic foot–atmospheres kilowatt-hours joules per cubic meter watts horsepower joules per kilogram calories per gram per degree celsius joules per kilogram per degree kelvin watts joules per square meter per second kilowatts per square foot calories, gram (15°C), per square centimeter per second for a temperature gradient of 1°C per centimeter  calories per degree Celsius

43,560 4074 0.001563 1233 3600 3.937 × 10-9 1 × 10-10 1 × 10-4 760 1.0133 × 106 101,325 33.90 1033.3 29.921 2116.3 14.696 94 376 0.15899 42 0.11924 31.5 0.02917 0.9869 1 × 105 14.504 1 ⁄12 33,480 9.803 252 0.55556 777.9 3.929 × 10-4 1055.1 10.41 6.88 × 10-5 0.001036

cubic feet cubic meters Btu foot-pounds joules liter-atmospheres horsepower-hours joules per kilogram per kelvin

1.2444 0.03524 3.968 × 10-3 3.087 4.1868 4.130 × 10-2 1.5591 × 10-6 4186.8

0.3676 2.930 × 10-4 37,260 0.29307 0.02357 2326 1 4186.8 1054.4 3.1546 0.1758 1.2405

453.6

To Convert from

To

calories, kilogram calories, kilogram per second candle power (spherical) carats (metric) centigrade heat units centimeters centimeters centimeters centimeters centimeters centimeters of mercury at 0°C centimeters of mercury at 0°C centimeters of mercury at 0°C centimeters of mercury at 0°C centimeters of mercury at 0°C centimeters per second centimeters of water at 4°C centistokes circular mils circular mils circular mils cords cubic centimeters cubic centimeters cubic centimeters cubic centimeters cubic feet cubic feet cubic feet cubic feet cubic feet cubic feet cubic foot–atmospheres cubic foot–atmospheres cubic feet of water (60°F) cubic feet per minute cubic feet per minute cubic feet per second cubic feet per second cubic inches cubic yards curies curies degrees drams (apothecaries’ or troy) drams (avoirdupois) dynes ergs Faradays fathoms feet feet per minute feet per minute feet per (second)2 feet of water at 39.2°F foot-poundals foot-poundals foot-poundals foot-pounds foot-pounds foot-pounds foot-pounds foot-pounds foot-pounds foot-pounds force foot-pounds per second foot-pounds per second furlongs gallons (U.S. liquid)

kilowatt-hours kilowatts lumens grams Btu Angstrom units feet inches meters microns or micrometers atmospheres feet of water at 39.1°F newtons per square meter pounds per square foot pounds per square inch feet per minute newtons per square meter square meters per second square centimeters square inches square mils cubic feet cubic feet gallons ounces (U.S. fluid) quarts (U.S. fluid) Bushels (U.S.) cubic centimeters cubic meters cubic yards gallons liters foot-pounds liter-atmospheres pounds cubic centimeters per second gallons per second gallons per minute million gallons per day cubic meters cubic meters disintegrations per minute coulombs per minute radians grams grams newtons joules Coulombs (abs.) feet meters centimeters per second miles per hour meters per (second)2 newtons per square meter Btu joules liter-atmospheres Btu calories, gram foot-poundals horsepower-hours kilowatt-hours liter-atmospheres joules horsepower kilowatts miles barrels (U.S. liquid)

Multiply by 0.0011626 4.185 12.556 0.2 1.8 1 × 108 0.03281 0.3937 0.01 10,000 0.013158 0.4460 1333.2 27.845 0.19337 1.9685 98.064 1 × 10-6 5.067 × 10-6 7.854 × 10-7 0.7854 128 3.532 × 10-5 2.6417 × 10-4 0.03381 0.0010567 0.8036 28,317 0.028317 0.03704 7.481 28.316 2116.3 28.316 62.37 472.0 0.1247 448.8 0.64632 1.6387 × 10-5 0.76456 2.2 × 1012 1.1 × 1012 0.017453 3.888 1.7719 1 × 10-5 1 × 10-7 96,500 6 0.3048 0.5080 0.011364 0.3048 2989 3.995 × 10-5 0.04214 4.159 × 10-4 0.0012856 0.3239 32.174 5.051 × 10-7 3.766 × 10-7 0.013381 1.3558 0.0018182 0.0013558 0.125 0.03175 (Continued )

1-6

UnIT COnVERSIOn FACTORS AnD SYMBOLS

TABLE 1-7 Alphabetical Listing of Common Unit Conversions (Continued ) To Convert from gallons gallons gallons gallons gallons gallons per minute gallons per minute grains grains grains per cubic foot grains per gallon grams grams grams grams grams grams grams per cubic centimeter grams per cubic centimeter grams per liter grams per liter grams per square centimeter grams per square centimeter hectares hectares horsepower (British) horsepower (British) horsepower (British) horsepower (British) horsepower (British) horsepower (British) horsepower (British) horsepower (British) horsepower (metric) horsepower (metric) hours (mean solar) inches inches of mercury at 60°F inches of water at 60°F joules (absolute) joules (absolute) joules (absolute) joules (absolute) joules (absolute) joules (absolute) kilocalories kilograms kilograms force kilograms per square centimeter kilometers kilowatt-hours kilowatt-hours kilowatts knots (international) knots (nautical miles per hour) lamberts liter-atmospheres liter-atmospheres liters liters liters lumens micromicrons microns

To

Multiply by

cubic meters cubic feet gallons (imperial) liters ounces (U.S. fluid) cubic feet per hour cubic feet per second grams pounds grams per cubic meter parts per million drams (avoirdupois) drams (troy) grains kilograms pounds (avoirdupois) pounds (troy) pounds per cubic foot pounds per gallon grains per gallon pounds per cubic foot pounds per square foot pounds per square inch acres square meters btu per minute btu per hour foot-pounds per minute foot-pounds per second watts horsepower (metric) pounds carbon to CO2 per hour pounds water evaporated per hour at 212°F foot-pounds per second kilogram-meters per second seconds meters newtons per square meter newtons per square meter Btu (mean) calories, gram (mean) cubic foot–atmospheres foot-pounds kilowatt-hours liter-atmospheres joules pounds (avoirdupois) newtons pounds per square inch

0.003785 0.13368 0.8327 3.785 128 8.021 0.002228 0.06480 1 ⁄7000 2.2884 17.118 0.5644 0.2572 15.432 0.001 0.0022046 0.002679 62.43 8.345 58.42 0.0624 2.0482 0.014223 2.471 10,000 42.42 2545 33,000 550 745.7 1.0139 0.175

miles Btu foot-pounds horsepower meters per second miles per hour

0.6214 3414 2.6552 × 106 1.3410 0.5144 1.1516

candles per square inch cubic foot–atmospheres foot-pounds cubic feet cubic meters gallons watts microns or micrometers angstrom units

2.054 0.03532 74.74 0.03532 0.001 0.26418 0.001496 1 × 10-6 1 × 104

2.64 542.47 75.0 3600 0.0254 3376.9 248.84 9.480 × 10-4 0.2389 0.3485 0.7376 2.7778 × 10-7 0.009869 4186.8 2.2046 9.807 14.223

To Convert from microns miles (nautical) miles (nautical) miles miles miles per hour miles per hour milliliters millimeters millimeters of mercury at 0°C millimicrons mils mils minims (U.S.) minutes (angle) minutes (mean solar) newtons ounces (avoirdupois) ounces (avoirdupois) ounces (U.S. fluid) ounces (troy) pints (U.S. liquid) poundals pounds (avoirdupois) pounds (avoirdupois) pounds (avoirdupois) pounds per cubic foot pounds per cubic foot pounds per square foot pounds per square foot pounds per square inch pounds per square inch pounds per square inch pounds force pounds force per square foot pounds water evaporated from and at 212°F pound-celsius units (pcu) quarts (U.S. liquid) radians revolutions per minute seconds (angle) slugs slugs slugs square centimeters square feet square feet per hour square inches square inches square yards stokes tons (long) tons (long) tons (metric) tons (metric) tons (metric) tons (short) tons (short) tons (refrigeration) tons (British shipping) tons (U.S. shipping) torr (mm mercury, 0°C) watts watts watts watthours yards

To

Multiply by

meters feet miles (U.S. statute) feet meters feet per second meters per second cubic centimeters meters newtons per square meter microns inches meters cubic centimeters radians seconds kilograms kilograms ounces (troy) cubic meters ounces (apothecaries’) cubic meters newtons grains kilograms pounds (troy) grams per cubic centimeter kilograms per cubic meter atmospheres kilograms per square meter atmospheres kilograms per square centimeter newtons per square meter newtons newtons per square meter horsepower-hours

1 × 10-6 6080 1.1516 5280 1609.3 1.4667 0.4470 1 0.001 133.32 0.001 0.001 2.54 × 10-5 0.06161 2.909 × 10-4 60 0.10197 0.02835 0.9115 2.957 × 10-5 1.000 4.732 × 10-4 0.13826 7000 0.45359 1.2153 0.016018 16.018 4.725 × 10-4 4.882 0.06805 0.07031

Btu cubic meters degrees radians per second radians g pounds kilograms pounds square feet square meters square meters per second square centimeters square meters square meters square meters per second kilograms pounds kilograms pounds tons (short) kilograms pounds Btu per hour cubic feet cubic feet newtons per square meter Btu per hour joules per second kilogram-meters per second joules meters

1.8 9.464 × 10-4 57.30 0.10472 4.848 × 10-6 1 14.594 32.17 0.0010764 0.0929 2.581 × 10-5 6.452 6.452 × 10-4 0.8361 1 × 10-4 1016 2240 1000 2204.6 1.1023 907.18 2000 12,000 42.00 40.00 133.32 3.413 1 0.10197 3600 0.9144

6894.8 4.4482 47.88 0.379

COnVERSIOn FACTORS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units The following unit symbols are used in the table: Unit symbol

Name

A a Bq C cd Ci d °C ° dyn F fc G g gr

Unit symbol

ampere annum (year) becquerel coulomb candela curie day degree Celsius degree dyne farad footcandle gauss gram grain

Name

Gy H h ha Hz J K L, ℓ, l lm lx m min ′ N naut mi

Unit symbol

gray henry hour hectare hertz joule kelvin liter lumen lux meter minute minute newton U.S. nautical mile

Name

Oe Ω Pa rad r S s ″ sr St T t V W Wb

oersted ohm pascal radian revolution siemens second second steradian stokes tesla tonne volt watt weber

note: Copyright SPE-AIME, The SI Metric System of Units and SPE’s Tentative Metric Standard, Society of Petroleum Engineers, Dallas, 1977.

Quantity

Customary or commonly used unit

SI unit

Alternate SI unit

Conversion factor; multiply customary unit by factor to obtain SI unit

Space, time Length

naut mi mi chain link fathom yd ft in in mil

km km m m m m m cm mm cm µm

Length/length

ft/mi

m/km 3

1.852* 1.609 344* 2.011 68* 2.011 68* 1.828 8* 9.144* 3.048* 3.048* 2.54* 2.54 2.54*

E + 00 E + 00 E + 01 E - 01 E + 00 E - 01 E - 01 E + 01 E + 01 E + 00 E + 01

1.893 939

E - 01

Length/volume

ft/U.S. gal ft/ft3 ft/bbl

m/m m/m3 m/m3

8.051 964 1.076 391 1.917 134

E + 01 E + 01 E + 00

Area

mi2 section acre ha yd2 ft2 in2

km2 ha ha m2 m2 m2 mm2 cm2

2.589 988 2.589 988 4.046 856 1.000 000* 8.361 274 9.290 304* 6.451 6* 6.451 6*

E + 00 E + 02 E - 01 E + 04 E - 01 E - 02 E + 02 E + 00

Area/volume

ft2/in3 ft2/ft3

m2/cm3 m2/m3

5.699 291 3.280 840

E - 03 E + 00

Volume

m3 acre ⋅ ft

km3 m3 ha ⋅ m m3 m3 m3 dm3 m3 dm3 m3 dm3 dm3 dm3 dm3 cm3 cm3 cm3

4.168 182 1.233 482 1.233 482 7.645 549 1.589 873 2.831 685 2.831 685 4.546 092 4.546 092 3.785 412 3.785 412 1.136 523 9.463 529 4.731 765 2.841 307 2.957 353 1.638 706

E + 00 E + 03 E - 01 E + 01 E - 01 E - 02 E + 01 E - 03 E + 00 E - 03 E + 00 E + 00 E - 01 E - 01 E + 01 E + 01 E + 01

yd3 bbl (42 U.S. gal) ft3 U.K. gal U.S. gal U.K. qt U.S. qt U.S. pt U.K. fl oz U.S. fl oz in3

L L L L L L

Volume/length (linear displacement)

bbl/in bbl/ft ft3/ft U.S. gal/ft

m3m m3/m m3/m m3/m L/m

6.259 342 5.216 119 9.290 304* 1.241 933 1.241 933

E + 00 E - 01 E - 02 E - 02 E + 01

Plane angle

rad deg (°) min (′) sec (″)

rad rad rad rad

1 1.745 329 2.908 882 4.848 137

E - 02 E - 04 E - 06

Solid angle

sr

sr

1

*An asterisk indicates that the conversion factor is exact.

(Continued )

1-7

1-8

UnIT COnVERSIOn FACTORS AnD SYMBOLS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )

Quantity Time

Customary or commonly used unit

SI unit

Alternate SI unit

a d s min s h

year week h min

Conversion factor; multiply customary unit by factor to obtain SI unit 1 7.0* 3.6* 6.0* 6.0* 1.666 667

E + 00 E + 03 E + 01 E + 01 E - 02

1.016 047 9.071 847 5.080 234 4.535 924 4.535 924 3.110 348 2.834 952 6.479 891

E + 00 E - 01 E + 01 E + 01 E - 01 E + 01 E + 01 E + 01

4.535 924 4.461 58 1.195 30

E - 01 E - 02 E - 03

2.326 000 2.326 000 6.461 112 4.184* 9.224 141

E - 03 E + 00 E - 04 E + 00 E + 00

4.184* 2.326 000

E + 03 E + 00

2.787 163 2.787 163 7.742 119 2.320 800 2.320 800 6.446 667 3.725 895 3.725 895 1.034 971 4.184* 3.581 692

E - 01 E + 02 E - 02 E - 01 E + 02 E - 02 E - 02 E + 01 E - 02 E + 00 E - 01 E + 03 E + 00 E + 01 E - 02

Mass, amount of substance Mass

U.K. ton U.S. ton U.K. cwt U.S. cwt lbm oz (troy) oz (av) gr

Mg Mg kg kg kg g g mg

Amount of substance

lbmmol std m3 (0°C, 1 atm) std ft3 (60°F, 1 atm)

kmol kmol kmol

t t

Enthalpy, calorific value, heat, entropy, heat capacity

cal/g cal/lbm

MJ/kg kJ/kg kWh/kg kJ/kg J/kg

Caloric value, enthalpy (mole basis)

kcal/(g ⋅ mol) Btu/(lb ⋅ mol)

kJ/kmol kJ/kmol

Caloric value (volume basis—solids and liquids)

Btu/U.S. gal

MJ/m3 kJ/m3 kWh/m3 MJ/m3 kJ/m3 kWh/m3 MJ/m3 kJ/m3 kWh/m3 MJ/m3 kJ/m3

kJ/dm3

Caloric value, enthalpy (mass basis)

Btu/lbm

Btu/U.K. gal Btu/ft3

cal/mL ( ft ⋅ lbf)/U.S. gal

J/g J/g

kJ/dm3 kJ/dm3

Caloric value (volume basis—gases)

cal/mL kcal/m3 Btu/ft3

kJ/m3 kJ/m3 kJ/m3 kWh/m3

J/dm3 J/dm3 J/dm3

Specific entropy

Btu/(lbm ⋅ °R) cal/(g ⋅ K) kcal/(kg ⋅ °C)

kJ/(kg ⋅ K) kJ/(kg ⋅ K) kJ/(kg ⋅ K)

J/(g ⋅ K) J/(g ⋅ K) J/(g ⋅ K)

4.184* 4.184* 3.725 895 1.034 971 4.186 8* 4.184* 4.184*

Specific heat capacity (mass basis)

kWh/(kg ⋅ °C) Btu/(lbm ⋅ °F) kcal/(kg ⋅ °C)

kJ/(kg ⋅ K) kJ/(kg ⋅ K) kJ/(kg ⋅ K)

J/(g ⋅ K) J/(g ⋅ K) J/(g ⋅ K)

3.6* 4.186 8* 4.184*

E + 03 E + 00 E + 00

Specific heat capacity (mole basis)

Btu/(lb ⋅ mol ⋅ °F) cal/(g ⋅ mol ⋅ °C)

kJ/(kmol ⋅ K) kJ/(kmol ⋅ K)

4.186 8* 4.184*

E + 00 E + 00

E + 00 E + 00 E + 00

Temperature, pressure, vacuum Temperature (absolute)

°R K

K K

5/9 1

Temperature (traditional)

°F

°C

5/9(°F + 32)

Temperature (difference)

°F

K, °C

5/9

Pressure

atm (760 mmHg at 0°C or 14,696 psi)

MPa kPa bar MPa kPa MPa kPa bar kPa kPa kPa kPa kPa Pa Pa Pa

1.013 250* 1.013 250* 1.013 250* 1.0* 1.0* 6.894 757 6.894 757 6.894 757 3.376 85 2.488 4 1.333 224 9.806 38 4.788 026 1.333 224 1.0* 1.0*

bar mmHg (0°C) = torr µmHg (0°C) µ bar mmHg = torr (0°C) cmH2O (4°C) lbf /ft2 (psf) mHg (0°C) bar dyn/cm2 *An asterisk indicates that the conversion factor is exact.

E - 01 E + 02 E + 00 E + 01 E + 02 E - 03 E + 00 E - 02 E + 00 E - 01 E - 01 E - 02 E - 02 E - 01 E + 05 E - 01

COnVERSIOn FACTORS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )

Customary or commonly used unit

SI unit

Vacuum, draft

inHg (60°F) inH2O (39.2°F) inH2O (60°F) mmHg (0°C) = torr cmH2O (4°C)

kPa kPa kPa kPa kPa

3.376 85 2.490 82 2.488 4 1.333 224 9.806 38

E + 00 E - 01 E - 01 E - 01 E -02

Liquid head

ft in

m mm cm

3.048* 2.54* 2.54*

E - 01 E + 01 E + 00

psi/ft

kPa/m

2.262 059

E + 01

kg/m3 g/m3 kg/m3 g/cm3 kg/m3 kg/m3 g/cm3 kg/m3 kg/m3

1.601 846 1.601 846 1.198 264 1.198 264 9.977 633 1.601 846 1.601 846 1.0* 1.601 846

E + 01 E + 04 E + 02 E - 01 E + 01 E + 01 E - 02 E + 03 E + 01

ft /lbm U.K. gal/lbm U.S. gal/lbm

m3/kg m3/g dm3/kg dm3/kg dm3/kg

6.242 796 6.242 796 6.242 796 1.002 242 8.345 404

E - 02 E - 05 E + 01 E + 01 E + 00

Specific volume (mole basis)

L/(gmol) ft3/(lbmol)

m3/kmol m3/kmol

1 6.242 796

E - 02

Specific volume

bbl/U.S. ton bbl/U.K. ton

m3/t m3/t

1.752 535 1.564 763

E - 01 E - 01

Yield

bbl/U.S. ton bbl/U.K. ton U.S. gal/U.S. ton U.S. gal/U.K. ton

dm3/t dm3/t dm3/t dm3/t

1.752 535 1.564 763 4.172 702 3.725 627

E + 02 E + 02 E + 00 E + 00

Concentration (mass/mass)

wt % wt ppm

kg/kg g/kg mg/kg

1.0* 1.0* 1

E - 02 E + 01

lbm/bbl g/U.S. gal g/U.K. gal lbm/1000 U.S. gal lbm/1000 U.K. gal gr/U.S. gal gr/ft3 lbm/1000 bbl mg/U.S. gal gr/100 ft3

kg/m3 kg/m3 kg/m3 g/m3 g/m3 g/m3 mg/m3 g/m3 g/m3 mg/m3

2.853 010 2.641 720 2.199 692 1.198 264 9.977 633 1.711 806 2.288 351 2.853 010 2.641 720 2.288 351

E + 00 E - 01 E - 01 E + 02 E + 01 E + 01 E + 03 E + 00 E - 01 E + 01

ft3/ft3 bbl/(acreft) vol % U.K. gal/ft3 U.S. gal/ft3 mL/U.S. gal mL/U.K. gal vol ppm U.K. gal/1000 bbl U.S. gal/1000 bbl U.K. pt/1000 bbl

m3/m3 m3/m3 m3/m3 dm3/m3 dm3/m3 dm3/m3 dm3/m3 cm3/m3 dm3/m3 cm3/m3 cm3/m3 cm3/m3

Concentration (mole/volume)

(lbmol)/U.S. gal (lbmol)/U.K. gal (lbmol)/ft3 std ft3 (60°F, 1 atm)/bbl

kmol/m3 kmol/m3 kmol/m3 kmol/m3

Concentration (volume/mole)

U.S. gal/1000 std ft3 (60°F/60°F) bbl/million std ft3 (60°F/60°F)

dm3/kmol

Quantity

Pressure drop/length

Alternate SI unit

Conversion factor; multiply customary unit by factor to obtain SI unit

Density, specific volume, concentration, dosage Density

lbm/ft3 lbm/U.S. gal lbm/U.K. gal lbm/ft3 g/cm3 lbm/ft3

Specific volume

ft3/lbm 3

Concentration (mass/volume)

Concentration (volume/volume)

*An asterisk indicates that the conversion factor is exact.

3

dm /kmol

cm3/g cm3/g

L/t L/t L/t L/t

g/dm3 g/L mg/dm3 mg/dm3 mg/dm3 mg/dm3 mg/dm3

3

L/m L/m3 L/m3 L/m3 L/m3

1 1.288 931 1.0* 1.605 437 1.336 806 2.641 720 2.199 692 1 1.0* 2.859 403 2.380 952 3.574 253

E - 04 E - 02 E + 02 E + 02 E - 01 E - 01 E - 03 E + 01 E + 01 E + 00

1.198 264 9.977 644 1.601 846 7.518 21

E + 02 E + 01 E + 01 E - 03

L/kmol

3.166 91

E + 00

L/kmol

1.330 10

E - 01 (Continued )

1-9

1-10

UnIT COnVERSIOn FACTORS AnD SYMBOLS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )

Quantity

Customary or commonly used unit

SI unit

Alternate SI unit

Conversion factor; multiply customary unit by factor to obtain SI unit

Facility throughput, capacity Throughput (mass basis)

U.K. ton/yr U.S. ton/yr U.K. ton/day U.S. ton/day U.K. ton/h U.S. ton/h lbm/h

Throughput (volume basis)

bbl/day ft3/day bbl/h ft3/h U.K. gal/h U.S. gal/h U.K. gal/min U.S. gal/min

t/a t/a t/d t/h t/d t/h t/h t/h kg/h

1.016 047 9.071 847 1.016 047 4.233 529 9.071 847 3.779 936 1.016 047 9.071 847 4.535 924

E + 00 E - 01 E + 00 E - 02 E - 01 E - 02 E + 00 E - 01 E - 01

t/a m3/d m3/h m3/h m3/h m3/h L/s m3/h L/s m3/h L/s m3/h L/s

5.803 036 1.589 873 1.179 869 1.589 873 2.831 685 4.546 092 1.262 803 3.785 412 1.051 503 2.727 655 7.576 819 2.271 247 6.309 020

E + 01 E - 01 E - 03 E - 01 E - 02 E - 03 E - 03 E - 03 E - 03 E - 01 E - 02 E - 01 E - 02

kmol/h kmol/s

4.535 924 1.259 979

E - 01 E - 04

Throughput (mole basis)

(lbmmol)/h

Flow rate (mass basis)

U.K. ton/min U.S. ton/min U.K. ton/h U.S. ton/h U.K. ton/day U.S. ton/day million lbm/yr U.K. ton/yr U.S. ton/yr lbm/s lbm/min lbm/h

kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s

1.693 412 1.511 974 2.822 353 2.519 958 1.175 980 1.049 982 5.249 912 3.221 864 2.876 664 4.535 924 7.559 873 1.259 979

E + 01 E + 01 E - 01 E - 01 E - 02 E - 02 E + 00 E - 05 E - 05 E - 01 E - 03 E - 04

Flow rate (volume basis)

bbl/day

U.K. gal/h U.S. gal/h U.K. gal/min U.S. gal/min ft3/min ft3/s

m3/d L/s m3/d L/s m3/s L/s m3/s L/s dm3/s dm3/s dm3/s dm3/s dm3/s dm3/s

1.589 873 1.840 131 2.831 685 3.277 413 4.416 314 4.416 314 7.865 791 7.865 791 1.262 803 1.051 503 7.576 820 6.309 020 4.719 474 2.831 685

E - 01 E - 03 E - 02 E - 04 E - 05 E - 02 E - 06 E - 03 E - 03 E - 03 E - 02 E - 02 E - 01 E + 01

Flow rate (mole basis)

(lbmol)/s (lbmol)/h million scf/D

kmol/s kmol/s kmol/s

4.535 924 1.259 979 1.383 45

E - 01 E - 04 E - 02

Flow rate/length (mass basis)

lbm/(sft) lbm/(hft)

kg/(sm) kg/(sm)

1.488 164 4.133 789

E + 00 E - 04

Flow rate/length (volume basis)

U.K. gal/(min ⋅ ft) U.S. gal/(min ⋅ ft) U.K. gal/(h ⋅ in) U.S. gal/(h ⋅ in) U.K. gal/(h ⋅ ft) U.S. gal/(h ⋅ ft)

m2/s m2/s m2/s m2/s m2/s m2/s

2.485 833 2.069 888 4.971 667 4.139 776 4.143 055 3.449 814

E - 04 E - 04 E - 05 E - 05 E - 06 E - 06

Flow rate/area (mass basis)

lbm/(s ⋅ ft2) lbm/(h ⋅ ft2)

kg/(s ⋅ m2) kg/(s ⋅ m2)

4.882 428 1.356 230

E + 00 E - 03

Flow rate/area (volume basis)

ft3/(s ⋅ ft2) ft3/(min ⋅ ft2) U.K. gal/(h ⋅ in2) U.S. gal/(h ⋅ in2) U.K. gal/(min ⋅ ft2) U.S. gal/(min ⋅ ft2) U.K. gal/(h ⋅ ft2) U.S. gal/(h ⋅ ft2)

m/s m/s m/s m/s m/s m/s m/s m/s

3.048* 5.08* 1.957 349 1.629 833 8.155 621 6.790 972 1.359 270 1.131 829

E - 01 E - 03 E - 03 E - 03 E - 04 E - 04 E - 05 E - 05

Flow rate

3

ft /day bbl/h ft3/h

*An asterisk indicates that the conversion factor is exact.

L/s L/s L/s L/s L/s L/s

m3/(s ⋅ m) m3/(s ⋅ m) m3/(s ⋅ m) m3/(s ⋅ m) m3/(s ⋅ m) m3/(s ⋅ m)

m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2)

COnVERSIOn FACTORS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )

Quantity

Customary or commonly used unit

SI unit

Alternate SI unit

Conversion factor; multiply customary unit by factor to obtain SI unit

Energy, work, power

kcal cal ft ⋅ lbf lbf ⋅ ft J (lbf ⋅ ft2)/s2 erg

MJ kJ kWh MJ MJ kJ kWh MJ kJ kWh MJ kJ kJ kWh kJ kWh kJ kJ kJ kJ kJ kJ J

1.055 056 1.055 056 2.930 711 1.431 744 2.684 520 2.684 520 7.456 999 2.647 780 2.647 780 7.354 999 3.6* 3.6* 1.899 101 5.275 280 1.055 056 2.930 711 4.184* 4.184* 1.355 818 1.355 818 1.0* 4.214 011 1.0*

E + 02 E + 05 E + 01 E + 01 E + 00 E + 03 E - 01 E + 00 E + 03 E - 01 E + 00 E + 03 E + 00 E - 04 E + 00 E - 04 E + 00 E - 03 E - 03 E - 03 E - 03 E - 05 E - 07

Impact energy

kgf ⋅ m lbf ⋅ ft

J J

9.806 650* 1.355 818

E + 00 E + 00

Surface energy

erg/cm2

mJ/m2

1.0*

E + 00

J/cm2 J/cm2

9.806 650* 2.101 522

E - 02 E - 03

Energy, work

therm U.S. tonf ⋅ mi hp ⋅ h ch ⋅ h or CV ⋅ h kWh Chu Btu

Specific-impact energy

(kgf ⋅ m)/cm (lbf ⋅ ft)/in2

Power

million Btu/h tons of refrigeration Btu/s kW hydraulic horsepower (hhp) hp (electric) hp [(550 ft ⋅ lbf)/s] ch or CV Btu/min ( ft ⋅ lbf)/s kcal/h Btu/h ( ft ⋅ lbf)/min

MW kW kW kW kW kW kW kW kW kW W W W

2.930 711 3.516 853 1.055 056 1 7.460 43 7.46* 7.456 999 7.354 999 1.758 427 1.355 818 1.162 222 2.930 711 2.259 697

E - 01 E + 00 E + 00

Power/area

Btu/(s ⋅ ft2) cal/(h ⋅ cm2) Btu/(h ⋅ ft2)

kW/m2 kW/m2 kW/m2

1.135 653 1.162 222 3.154 591

E + 01 E - 02 E - 03

Heat-release rate, mixing power

hp/ft3 cal/(h ⋅ cm3) Btu/(s ⋅ ft3) Btu/(h ⋅ ft3)

kW/m3 kW/m3 kW/m3 kW/m3

2.633 414 1.162 222 3.725 895 1.034 971

E + 01 E + 00 E + 01 E - 02

Cooling duty (machinery)

Btu/(bhp ⋅ h)

W/kW

3.930 148

E - 01

Specific fuel consumption (mass basis)

lbm/(hp ⋅ h)

mg/J kg/kWh

kg/MJ

1.689 659 6.082 774

E - 01 E - 01

Specific fuel consumption (volume basis)

m3/kWh U.S. gal/(hp ⋅ h) U.K. pt/(hp ⋅ h)

dm3/MJ dm3/MJ dm3/MJ

mm3/J mm3/J mm3/J

2.777 778 1.410 089 2.116 806

E + 02 E + 00 E - 01

Fuel consumption

U.K. gal/mi U.S. gal/mi mi/U.S. gal mi/U.K. gal

dm3/100 km dm3/100 km km/dm3 km/dm3

L/100 km L/100 km km/L km/L

2.824 807 2.352 146 4.251 437 3.540 064

E + 02 E + 02 E - 01 E - 01

Velocity (linear), speed

knot mi/h ft/s

km/h km/h m/s cm/s m/s mm/s mm/s m/d mm/s mm/s

1.852* 1.609 344* 3.048* 3.048* 5.08* 8.466 667 3.527 778 3.048* 2.54* 4.233 333

E + 00 E + 00 E - 01 E + 01 E - 03 E - 02 E - 03 E - 01 E + 01 E - 01

ft/min ft/h ft/day in/s in/min *An asterisk indicates that the conversion factor is exact.

2

E - 01 E - 01 E - 01 E - 01 E - 02 E - 03 E + 00 E - 01 E - 02

(Continued )

1-11

1-12

UnIT COnVERSIOn FACTORS AnD SYMBOLS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )

Customary or commonly used unit

SI unit

Corrosion rate

in/yr (ipy) mil/yr

mm/a mm/a

2.54* 2.54*

E + 01 E - 02

Rotational frequency

r/min

r/s rad/s

1.666 667 1.047 198

E + 02 E - 01

Acceleration (linear)

ft/s2

m/s2 cm/s2

3.048* 3.048*

E - 01 E + 01

Acceleration (rotational)

rpm/s

rad/s2

1.047 198

E - 01

Momentum

(lbm ⋅ ft)/s

(kg ⋅ m)/s

1.382 550

E - 01

Force

U.K. tonf U.S. tonf kgf lbf dyn

kN kN N N mN

9.964 016 8.896 443 9.806 650* 4.448 222 1.0

E + 00 E + 00 E + 00 E + 00 E - 02

Bending moment, torque

U.S. tonf ⋅ ft kgf ⋅ m lbf ⋅ ft lbf ⋅ in

kN ⋅ m N⋅m N⋅m N⋅m

2.711 636 9.806 650* 1.355 818 1.129 848

E + 00 E + 00 E + 00 E - 01

Bending moment/length

(lbf ⋅ ft)/in (lbf ⋅ in)/in

(N ⋅ m)/m (N ⋅ m)/m

5.337 866 4.448 222

E + 01 E + 00

Moment of inertia

lbm ⋅ ft2

kg ⋅ m2

4.214 011

E - 02

Stress

U.S. tonf/in2 kgf/mm2 U.S. tonf/ft2 lbf/in2 (psi) lbf/ft2 (psf) dyn/cm2

MPa MPa MPa MPa kPa Pa

1.378 951 9.806 650* 9.576 052 6.894 757 4.788 026 1.0*

E + 01 E + 00 E - 02 E - 03 E - 02 E - 01

Quantity

Alternate SI unit

Conversion factor; multiply customary unit by factor to obtain SI unit

N/mm2 N/mm2 N/mm2 N/mm2

Mass/length

lbm/ft

kg/m

1.488 164

E + 00

Mass/area structural loading, bearing capacity (mass basis)

U.S. ton/ft2 lbm/ft2

Mg/m2 kg/m2

9.764 855 4.882 428

E + 00 E + 00

Diffusivity

ft2/s m2/s ft2/h

m2/s mm2/s m2/s

9.290 304* 1.0* 2.580 64*

E - 02 E + 06 E - 05

Thermal resistance

(°C ⋅ m2 ⋅ h)/kcal (°F ⋅ ft2 ⋅ h)/Btu

(K ⋅ m2)/kW (K ⋅ m2)/kW

8.604 208 1.761 102

E + 02 E + 02

Heat flux

Btu/(h ⋅ ft2)

kW/m2

3.154 591

E - 03

W/(m ⋅ K) W/(m ⋅ K) (kJ ⋅ m)/(h ⋅ m2 ⋅ K) W/(m ⋅ K) W/(m ⋅ K) W/(m ⋅ K)

4.184* 1.730 735 6.230 646 1.162 222 1.442 279 1.162 222

E + 02 E + 00 E + 00 E + 00 E - 01 E - 01

Btu/(h ⋅ ft2 ⋅ °R) kcal/(h ⋅ m2 ⋅ °C)

kW/(m2 ⋅ K) kW/(m2 ⋅ K) kW/(m2 ⋅ K) kW/(m2 ⋅ K) kJ/(h ⋅ m2 ⋅ K) kW/(m2 ⋅ K) kW/(m2 ⋅ K)

4.184* 2.044 175 1.162 222 5.678 263 2.044 175 5.678 263 1.162 222

E + 01 E + 01 E - 02 E - 03 E + 01 E - 03 E - 03

Volumetric heat-transfer coefficient

Btu/(s ⋅ ft3 ⋅ °F) Btu/(h ⋅ ft3 ⋅ °F)

kW/(m3 ⋅ K) kW/(m3 ⋅ K)

6.706 611 1.862 947

E + 01 E - 02

Surface tension

dyn/cm

mN/m

Miscellaneous transport properties

Thermal conductivity

2

(cal ⋅ cm)/(s ⋅ cm ⋅ °C) (Btu ⋅ ft)/(h ⋅ ft2 ⋅ °F) (kcal ⋅ m)/(h ⋅ m2 ⋅ °C) (Btu ⋅ in)/(h ⋅ ft2 ⋅ °F) (cal ⋅ cm)/(h ⋅ cm2 ⋅ °C)

Heat-transfer coefficient

Viscosity (dynamic)

cal/(s ⋅ cm2 ⋅ °C) Btu/(s ⋅ ft2 ⋅ °F) cal/(h ⋅ cm2 ⋅ °C) Btu/(h ⋅ ft2 ⋅ °F)

2

(lbf ⋅ s)/in (lbf ⋅ s)/ft2 (kgf ⋅ s)/m2 lbm/( ft ⋅ s) (dyn ⋅ s)/cm2 cP lbm/( ft ⋅ h)

*An asterisk indicates that the conversion factor is exact.

Pa ⋅ s Pa ⋅ s Pa ⋅ s Pa ⋅ s Pa ⋅ s Pa ⋅ s Pa ⋅ s

1 2

(N ⋅ s)/m (N ⋅ s)/m2 (N ⋅ s)/m2 (N ⋅ s)/m2 (N ⋅ s)/m2 (N ⋅ s)/m2 (N ⋅ s)/m2

6.894 757 4.788 026 9.806 650* 1.488 164 1.0* 1.0* 4.133 789

E + 03 E + 01 E + 00 E + 00 E - 01 E - 03 E - 04

COnVERSIOn FACTORS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )

Customary or commonly used unit

SI unit

Viscosity (kinematic)

ft2/s in2/s m2/h ft2/h cSt

m2/s mm2/s mm2/s m2/s mm2/s

9.290 304* 6.451 6* 2.777 778 2.580 64* 1

E - 02 E + 02 E + 02 E - 05

Permeability

darcy millidarcy

µm2 µm2

9.869 233 9.869 233

E - 01 E - 04

Thermal flux

Btu/(h ⋅ ft2) Btu/(s ⋅ ft2) cal/(s ⋅ cm2)

W/m2 W/m2 W/m2

3.152 1.135 4.184

E + 00 E + 04 E + 04

Mass-transfer coefficient

(lbmol)/[h ⋅ ft2(lbmol/ft3)] (gmol)/[s ⋅ m2(gmol/L)]

m/s m/s

8.467 1.0

E - 05 E + 01

Quantity

Alternate SI unit

Conversion factor; multiply customary unit by factor to obtain SI unit

Electricity, magnetism Admittance

S

S

1

Capacitance

µF

µF

1

Charge density

C/mm3

C/mm3

1

Conductance

S

S S

1 1

(mho)

Ω

Conductivity

S/m /m m /m

S/m S/m mS/m

1 1 1

Current density

A/mm2

A/mm2

1 1

Ω

Ω

2

Displacement

C/cm

C/cm2

Electric charge

C

C

1

Electric current

A

A

1

Electric-dipole moment

C⋅m

C⋅m

1

Electric-field strength

V/m

V/m

1

Electric flux

C

C

1

Electric polarization

C/cm2

C/cm2

1

Electric potential

V mV

V mV

1 1

Electromagnetic moment

A ⋅ m2

A ⋅ m2

1

Electromotive force

V

V

1

Flux of displacement

C

C

1

Frequency

cycles/s

Hz

1

Impedance

Ω

Ω

1

Linear-current density

A/mm

A/mm

1

Magnetic-dipole moment

Wb ⋅ m

Wb ⋅ m

1

Magnetic-field strength

A/mm Oe gamma

A/mm A/m A/m

1 7.957 747 7.957 747

Magnetic flux

mWb

mWb

1

Magnetic-flux density

mT G gamma

mT T nT

1 1.0* 1

Magnetic induction

mT

mT

1

Magnetic moment

A ⋅ m2

A ⋅ m2

1

Magnetic polarization

mT

mT

1

Magnetic potential difference

A

A

1

Magnetic-vector potential

Wb/mm

Wb/mm

1

Magnetization

A/mm

A/mm

1

Modulus of admittance

S

S

1

*An asterisk indicates that the conversion factor is exact.

E + 01 E + 04

E - 04

(Continued )

1-13

1-14

UnIT COnVERSIOn FACTORS AnD SYMBOLS

TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )

Customary or commonly used unit

SI unit

Modulus of impedance

Ω

Ω

1

Mutual inductance

H

H

1

Permeability

µH/m

µH/m

1

Permeance

H

H

1

Permittivity

µF/m

µF/m

1

Potential difference

V

V

1

Quantity

Alternate SI unit

Conversion factor; multiply customary unit by factor to obtain SI unit

Quantity of electricity

C

C

1

Reactance

Ω

Ω

1

Reluctance

H-1

H-1

1

Resistance

Ω

Ω

1

Resistivity

Ω ⋅ cm Ω⋅m

Ω ⋅ cm Ω⋅m

1 1

Self-inductance

mH

mH

1

Surface density of change

mC/m2

mC/m2

1

Susceptance

S

S

1

Volume density of charge

C/mm3

C/mm3

1

Absorbed dose

rad

Gy

1.0*

Acoustical energy

J

J

1

Acoustical intensity

W/cm2

W/m2

1.0*

Acoustical power

W

W

1

Sound pressure

N/m2

N/m2

1.0*

Illuminance

fc

lx

1.076 391

E + 01

Illumination

fc

lx

1.076 391

E + 01

Acoustics, light, radiation

2

2

Irradiance

W/m

W/m

1

Light exposure

fc ⋅ s

lx ⋅ s

1.076 391

Luminance

cd/m2

cd/m2

1

Luminous efficacy

lm/W

lm/W

1

2

2

E - 02

E + 04

E + 01

Luminous exitance

lm/m

lm/m

1

Luminous flux

lm

lm

1

Luminous intensity

cd

cd

1

Radiance

W/m2 ⋅ sr

W/m2 ⋅ sr

1

Radiant energy

J

J

1

Radiant flux

W

W

1

Radiant intensity

W/sr

W/sr

1

Radiant power

W

W

1

Wavelength

Å

nm

1.0*

E - 01

Capture unit

10 cm

m

E + 01

m

m

1.0* 1 1

Ci

Bq

3.7*

E + 10

-3

-1

Radioactivity

*An asterisk indicates that the conversion factor is exact.

-1

-1

-1

10-3 cm-1

COnVERSIOn FACTORS TABLE 1-9 Other Conversion Factors to SI Units The first two digits of each numerical entry represent a power of 10. For example, the entry “-02 2.54” expresses the fact that 1 in = 2.54 × 10-2 m. To Convert from abampere abcoulomb abfarad abhenry abmho abohm abvolt acre ampere (international of 1948) angstrom are astronomical unit atmosphere bar barn barrel (petroleum 42 gal) barye British thermal unit (ISO/TC 12) British thermal unit (International Steam Table) British thermal unit (mean) British thermal unit (thermochemical) British thermal unit (39°F) British thermal unit (60°F) bushel (U.S.) cable caliber calorie (International Steam Table) calorie (mean) calorie (thermochemical) calorie (15°C) calorie (20°C) calorie (kilogram, International Steam Table) calorie (kilogram, mean) calorie (kilogram, thermochemical) carat (metric) Celsius (temperature) centimeter of mercury (0°C) centimeter of water (4°C) chain (engineer’s) chain (surveyor’s or Gunter’s) circular mil cord coulomb (international of 1948) cubit cup curie day (mean solar) day (sidereal) degree (angle) denier (international) dram (avoirdupois) dram (troy or apothecary) dram (U.S. fluid) dyne electron volt erg Fahrenheit (temperature) Fahrenheit (temperature) farad (international of 1948) faraday (based on carbon  12) faraday (chemical) faraday (physical) fathom fermi ( femtometer) fluid ounce (U.S.) foot

To

Multiply by

ampere coulomb farad henry mho ohm volt meter2 ampere

+01 1.00 +01 1.00 +09 1.00 -09 1.00 +09 1.00 -09 1.00 -08 1.00 +03 4.046 856 -01 9.998 35

meter meter2 meter newton/meter2 newton/meter2 meter2 meter3 newton/meter2 joule

-10 1.00 +02 1.00 +11 1.495 978 +05 1.013 25 +05 1.00 -28 1.00 -01 1.589 873 -01 1.00 +03 1.055 06

joule

+03 1.055 04

joule joule

+03 1.055 87 +03 1.054 350

joule joule meter3 meter meter joule joule joule joule joule joule

+03 1.059 67 +03 1.054 68 -02 3.523 907 +02 2.194 56 -04 2.54 +00 4.1868 +00 4.190 02 +00 4.184 +00 4.185 80 +00 4.181 90 +03 4.186 8

joule joule

+03 4.190 02 +03 4.184

kilogram kelvin newton/meter2 newton/meter2 meter meter

-04 2.00 tK = tC + 273.15 +03 1.333 22 +01 9.806 38 +01 3.048 +01 2.011 68

meter2 meter3 coulomb

-10 5.067 074 +00 3.624 556 -01 9.998 35

meter meter3 disintegration/second second (mean solar) second (mean solar) radian kilogram/meter kilogram kilogram meter3 newton joule joule kelvin Celsius farad coulomb coulomb coulomb meter meter meter3 meter

-01 4.572 -04 2.365 882 +10 3.70 +04 8.64 +04 8.616 409 -02 1.745 329 -07 1.111 111 -03 1.771 845 -03 3.887 934 -06 3.696 691 -05 1.00 -19 1.602 10 -07 1.00 tK = (5/9)(tF + 459.67) tC = (5/9)(tF - 32) -01 9.995 05 +04 9.648 70 +04 9.649 57 +04 9.652 19 +00 1.828 8 -15 1.00 -05 2.957 352 -01 3.048

To Convert from foot (U.S. survey) foot of water (39.2°F) footcandle footlambert furlong galileo gallon (U.K. liquid) gallon (U.S. dry) gallon (U.S. liquid) gamma gauss gilbert gill (U.K.) gill (U.S.) grad grad grain gram hand hectare henry (international of 1948) hogshead (U.S.) horsepower (550 ft lbf/s) horsepower (boiler) horsepower (electric) horsepower (metric) horsepower (U.K.) horsepower (water) hour (mean solar) hour (sidereal) hundredweight (long) hundredweight (short) inch inch of mercury (32°F) inch of mercury (60°F) inch of water (39.2°F) inch of water (60°F) joule (international of 1948) kayser kilocalorie (International Steam Table) kilocalorie (mean) kilocalorie (thermochemical) kilogram mass kilogram-force (kgf) kilopound-force kip knot (international) lambert lambert langley lbf (pound-force, avoirdupois) lbm (pound-mass, avoirdupois) league (British nautical) league (international nautical) league (statute) light-year link (engineer’s) link (surveyor’s or Gunter’s) liter lux maxwell meter micrometer mil mile (U.S. statute) mile (U.K. nautical) mile (international nautical) mile (U.S. nautical) millibar millimeter of mercury (0°C)

To

Multiply by

meter newton/meter2 lumen/meter2 candela/meter2 meter meter/second2 meter3 meter3 meter3 tesla tesla ampere turn meter3 meter3 degree (angular) radian kilogram kilogram meter meter2 henry meter3 watt watt watt watt watt watt second (mean solar) second (mean solar) kilogram kilogram meter newton/meter2 newton/meter2 newton/meter2 newton/meter2 joule 1/meter joule

-01 3.048 006 +03 2.988 98 +01 1.076 391 +00 3.426 259 +02 2.011 68 -02 1.00 -03 4.546 087 -03 4.404 883 -03 3.785 411 -09 1.00 -04 1.00 -01 7.957 747 -04 1.420 652 -04 1.182 941 -01 9.00 -02 1.570 796 -05 6.479 891 -03 1.00 -01 1.016 +04 1.00 +00 1.000 495 -01 2.384 809 +02 7.456 998 +03 9.809 50 +02 7.46 +02 7.354 99 +02 7.457 +02 7.460 43 +03 3.60 +03 3.590 170 +01 5.080 234 +01 4.535 923 -02 2.54 +03 3.386 389 +03 3.376 85 +02 2.490 82 +02 2.4884 +00 1.000 165 +02 1.00 +03 4.186 74

joule joule kilogram newton newton newton meter/second candela/meter2 candela/meter2 joule/meter2 newton

+03 4.190 02 +03 4.184 +00 1.00 +00 9.806 65 +00 9.806 65 +03 4.448 221 -01 5.144 444 +04 1/π +03 3.183 098 +04 4.184 +00 4.448 221

kilogram

-01 4.535 923

meter meter

+03 5.559 552 +03 5.556

meter meter meter meter meter3 lumen/meter2 weber wavelengths Kr 86 meter meter meter meter meter meter newton/meter2 newton/meter2

+03 4.828 032 +15 9.460 55 -01 3.048 -01 2.011 68 -03 1.00 +00 1.00 -08 1.00 +06 1.650 763 -06 1.00 -05 2.54 +03 1.609 344 +03 1.853 184 +03 1.852 +03 1.852 +02 1.00 +02 1.333 224 (Continued )

1-15

1-16

UnIT COnVERSIOn FACTORS AnD SYMBOLS

TABLE 1-9 Other Conversion Factors to SI Units (Continued ) The first two digits of each numerical entry represent a power of 10. For example, the entry “-02 2.54” expresses the fact that 1 in = 2.54 × 10-2 m. To Convert from minute (angle) minute (mean solar) minute (sidereal) month (mean calendar) nautical mile (international) nautical mile (U.S.) nautical mile (U.K.) oersted ohm (international of 1948) ounce-force (avoirdupois) ounce-mass (avoirdupois) ounce-mass (troy or apothecary) ounce (U.S. fluid) pace parsec pascal peck (U.S.) pennyweight perch phot pica (printer’s) pint (U.S. dry) pint (U.S. liquid) point (printer’s) poise pole pound-force (lbf  avoirdupois) pound-mass (lbm avoirdupois) pound-mass (troy or  apothecary) poundal quart (U.S. dry) quart (U.S. liquid) rad (radiation dose  absorbed) Rankine (temperature) rayleigh (rate of photon  emission) rhe rod roentgen rutherford second (angle)

To

Multiply by

radian second (mean solar) second (mean solar) second (mean solar) meter meter meter ampere/meter ohm newton kilogram kilogram meter3 meter meter newton/meter2 meter3 kilogram meter lumen/meter2 meter meter3 meter3 meter (newton-second)/meter2 meter newton

-04 2.908 882 +01 6.00 +01 5.983 617 +06 2.628 +03 1.852 +03 1.852 +03 1.853 184 +01 7.957 747 +00 1.000 495 -01 2.780 138 -02 2.834 952 -02 3.110 347 -05 2.957 352 -01 7.62 +16 3.083 74 +00 1.00 -03 8.809 767 -03 1.555 173 +00 5.0292 +04 1.00 -03 4.217 517 -04 5.506 104 -04 4.731 764 -04 3.514 598 -01 1.00 +00 5.0292 +00 4.448 221

kilogram

-01 4.535 923

kilogram

-01 3.732 417

newton meter3 meter3 joule/kilogram

-01 1.382 549 -03 1.101 220 -04 9.463 529 -02 1.00

kelvin 1/second-meter2

tK = (5/9)tR +10 1.00

meter2/(newtonsecond) meter coulomb/kilogram disintegration/second radian

+01 1.00 +00 5.0292 -04 2.579 76 +06 1.00 -06 4.848 136

To Convert from

To

Multiply by

second (ephemeris) second (mean solar)

second second (ephemeris)

second (sidereal) section scruple (apothecary) shake skein slug span statampere statcoulomb statfarad stathenry statmho statohm statute mile (U.S.) statvolt stere stilb stoke tablespoon teaspoon ton (assay) ton (long) ton (metric) ton (nuclear equivalent of TNT) ton (register) ton (short, 2000 lb) tonne torr (0°C) township unit pole volt (international of 1948) watt (international of 1948) yard year (calendar) year (sidereal) year (tropical) year 1900, tropical, Jan., day 0, hour 12 year 1900, tropical, Jan., day 0, hour 12

second (mean solar) meter2 kilogram second meter kilogram meter ampere coulomb farad henry mho ohm meter volt meter3 candela/meter2 meter2/second meter3 meter3 kilogram kilogram kilogram joule meter3 kilogram kilogram newton/meter2 meter2 weber volt watt meter second (mean solar) second (mean solar) second (mean solar) second (ephemeris)

+00 1.000 000 Consult American Ephemeris and Nautical Almanac -01 9.972 695 +06 2.589 988 -03 1.295 978 -08 1.00 +02 1.097 28 +01 1.459 390 -01 2.286 -10 3.335 640 -10 3.335 640 -12 1.112 650 +11 8.987 554 -12 1.112 650 +11 8.987 554 +03 1.609 344 +02 2.997 925 +00 1.00 +04 1.00 -04 1.00 -05 1.478 676 -06 4.928 921 -02 2.916 666 +03 1.016 046 +03 1.00 +09 4.20 +00 2.831 684 +02 9.071 847 +03 1.00 +02 1.333 22 +07 9.323 957 -07 1.256 637 +00 1.000 330 +00 1.000 165 -01 9.144 +07 3.1536 +07 3.155 815 +07 3.155 692 +07 3.155 692

second

+07 3.155 692

COnVERSIOn FACTORS TABLE 1-10 Temperature Conversion Formulas °F = (°C × 5/9) + 32 °C = (°F - 32) × 5/9 °R = °F + 459.67 K = °C + 273.15 K = °R × 5/9

TABLE 1-13 Values of the Ideal Gas Constant Temp. scale

Temperature difference ΔT: °F = °C × 9/5

atm atm mmHg bar kg/cm2 atm mmHg

TABLE 1-11 Density Conversion Formulas

lb gal

T,P

lb ft 3

T,P

= sp gr = sp gr

T,P

T,P

Pressure units

Volume units

Kelvin

Bé = 145 − 145 (heavier than H O) 2 sp gr   Tw = sp gr 60 /60 F − 1 0.005 API = 141.5 − 131.5 sp gr

 Bé = 140 − 130 (lighter than H O) 2 sp gr

cm3 liters liters liters liters ft3 ft3

Rankine

atm in Hg mmHg lb/in2 abs lb/ft2 abs

× 8.345406

× 62.42797

ft3 ft3 ft3 ft3 ft3

Viscosity scale Saybolt Universal Saybolt Furol Redwood No. 1

Range of t, s

Kinematic viscosity, stokes*

32 < t < 100 t > 100 25 < t < 40 t > 40 34 < t < 100 t > 100

0.00226t - 1.95/t 0.00220t - 1.35/t 0.0224t - 1.84/t 0.0216t - 0.60/t 0.00260t - 1.79/t 0.00247t - 0.50/t 0.027t - 20/t 0.00147t - 3.74/t

Redwood Admiralty Engler *1 stoke (St) = 1 cm2/s = 10-4 m2/s

R Energy / (Weight ⋅ Temp)

Weight units

Energy units*

g mol g mol g mol g mol g mol g mol g mol g mol lb mol lb mol lb mol

calories joules (abs) joules (int) atm ⋅ cm3 atm ⋅ liters mmHg ⋅ liters bar ⋅ liters kg/(cm2)(liters) atm ⋅ ft3 mmHg ⋅ ft3 chu or pcu

1.9872 8.3144 8.3130 82.057 0.08205 62.361 0.08314 0.08478 1.314 998.9 1.9872

lb mol lb mol lb mol lb mol lb mol lb mol lb mol lb mol

Btu hph kWh atm ⋅ ft3 in Hg ⋅ ft3 mmHg ⋅ ft3 (lb)( ft3)/in2 ft ⋅ lbf

1.9872 0.0007805 0.0005819 0.7302 21.85 555.0 10.73 1545.0

*Energy units are the product of pressure units and volume units.

TABLE 1-12   Kinematic Viscosity Conversion Formulas

1-17

1-18

UnIT COnVERSIOn FACTORS AnD SYMBOLS TABLE 1-14 Fundamental Physical Constants 1 sec = 1.00273791 sidereal seconds g0 = 9.80665 m/s2 1 liter = 0.001 cu m 1 atm = 101,325 newtons/sq m 1 mmHg (pressure) = (1⁄760) atm = 133.3224 newtons/sq m 1 int ohm = 1.000495 ± 0.000015 abs ohm 1 int amp = 0.999835 ± 0.000025 abs amp 1 int coul = 0.999835 ± 0.000025 abs coul 1 int volt = 1.000330 ± 0.000029 abs volt 1 int watt = 1.000165 ± 0.000052 abs watt 1 int joule = 1.000165 ± 0.000052 abs joule T0°C = 273.150 ± 0.010 K (PV)0°CP=0 = (RT)0°C = 2271.16 ± 0.04 abs joule/mole = 22,414.6 ± 0.4 cu cm atm/mole = 22.4146 ± 0.0004 liter atm/mole R = 8.31439 ± 0.00034 abs joule/deg mole = 1.98719 ± 0.00013 cal/deg mole = 82.0567 ± 0.0034 cu cm atm/deg mole = 0.0820567 ± 0.0000034 liter atm/deg mole ln 10 = 2.302585 R ln 10 = 19.14460 ± 0.00078 abs joule/deg mole = 4.57567 ± 0.00030 cal/deg mole N = (6.02283 ± 0.0022) × 1023/mole h = (6.6242 ± 0.0044) × 10-34 joule s c = (2.99776 ± 0.00008) × 108 m/s (h2/8 π2k) = (4.0258 ± 0.0037) × 10-39 g sq cm deg (h/8 π2c) = (2.7986 ± 0.0018) × 10-39 g cm Z = Nhc = 11.9600 ± 0.0036 abs joule cm/mole = 2.85851 ± 0.0009 cal cm/mole Z/R = hc/k = c2 = 1.43847 ± 0.00045 cm deg f = 96,501.2 ± 10.0 int coul/g-equiv or int joule/int volt g-equiv = 96,485.3 ± 10.0 abs coul/g-equiv or abs joule/abs volt g-equiv = 23,068.1 ± 2.4 cal/int volt g-equiv = 23,060.5 ± 2.4 cal/abs volt g-equiv e = (1.60199 ± 0.00060) × 10-19 abs coul = (1.60199 ± 0.00060) × 10-20 abs emu = (4.80239 ± 0.00180) × 10-10 abs esu 1 int electron-volt/molecule = 96,501.2 ± 10 int joule/mole = 23,068.1 ± 2.4 cal/mole 1 abs electron-volt/molecule = 96,485.3 ± 10. abs joule/mole = 23,060.5 ± 2.4 cal/mole 1 int electron-volt = (1.60252 ± 0.00060) × 10-12 erg 1 abs electron-volt = (1.60199 ± 0.00060) × 10-12 erg hc = (1.23916 ± 0.00032) × 10-4 int electron-volt cm = (1.23957 ± 0.00032) × 10-4 abs electron-volt cm k = (8.61442 ± 0.00100) × 10-5 int electron-volt/deg = (8.61727 ± 0.00100) × 10-5 abs electron-volt/deg = R/N = (1.38048 ± 0.00050) × 10-23 joule/deg 1 IT cal = (1⁄860) = 0.00116279 int watt-h = 4.18605 int joule = 4.18674 abs joule = 1.000654 cal 1 cal = 4.1840 abs joule = 4.1833 int joule = 41.2929 ± 0.0020 cu cm atm = 0.0412929 ± 0.0000020 liter atm 1 IT cal/g = 1.8 Btu/lb 1 Btu = 251.996 IT cal = 0.293018 int watt-h = 1054.866 int joule = 1055.040 abs joule = 252.161 cal 1 horsepower = 550 ft-lbf (wt)/s = 745.578 int watt = 745.70 abs watt 1 in = (1/0.3937) = 2.54 cm 1 ft = 0.304800610 m 1 lb = 453.5924277 g 1 gal = 231 cu in = 0.133680555 cu ft = 3.785412 × 10-3 cu m = 3.785412 liter

sec = mean solar second Definition: g0 = standard gravity Definition: atm = standard atmosphere mmHg (pressure) = standard millimeter mercury int = international; abs = absolute amp = ampere coul = coulomb

Absolute temperature of the ice point, 0°C PV = product for ideal gas at 0°C R = gas constant per mole

ln = natural logarithm (base e) N = Avogadro number h = Planck constant c = velocity of light Constant in rotational partition function of gases Constant relating wave number and moment of inertia Z = constant relating wave number and energy per mole c2 = second radiation constant ℱ = Faraday constant e = electronic charge emu = electromagnetic unit of charge esu = electrostatic unit of charge

Constant relating wave number and energy per molecule k = Boltzmann constant Definition of IT cal: IT = International steam tables cal = thermochemical calorie Definition: cal = thermochemical calorie

Definition of Btu: Btu = IT British thermal unit

cal = thermochemical calorie Definition of horsepower (mechanical): lb (wt) = weight of 1 lb at standard gravity Definition of inch: in = U.S. inch ft = U.S. foot (1 ft = 12 in) Definition: lb = avoirdupois pound Definition: gal = U.S. gallon

Section 2

Physical and Chemical Data

Marylee Z. Southard, Ph.D. Associate Professor of Chemical and Petroleum Engineering, University of Kansas; Senior Member, American Institute of Chemical Engineers; Member, American Society for Engineering Education (Section Coeditor, Physical and Chemical Data) Richard L. Rowley, Ph.D. Department of Chemical Engineering, Emeritus, Brigham Young University (Section Coeditor, Prediction and Correlation of Physical Properties) W. Vincent Wilding, Ph.D. Professor of Chemical Engineering, Brigham Young University; Fellow, American Institute of Chemical Engineers (Section Coeditor, Prediction and Correlation of Physical Properties)

GEnERAL REFEREnCES PHYSICAL PROPERTIES OF PURE SUBSTAnCES Tables 2-1 2-2

Physical Properties of the Elements and Inorganic Compounds . . . . . Physical Properties of Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . .

2-5 2-26

VAPOR PRESSURES Tables 2-3 Vapor Pressure of Water Ice from 0 to −40°C . . . . . . . . . . . . . . . . . . . . . . . . 2-4 Vapor Pressure of Supercooled Liquid Water from 0 to −40°C . . . . . . . Vapor Pressures of Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-5 Vapor Pressure (MPa) of Liquid Water from 0 to 100°C . . . . . . . . . . . . . . 2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Sorted by Chemical Family . . . . . . . . . . . 2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 . . . . . . . . . . . . . . . 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K . . . . . . . . . . . . . . . . . . . 2-9 Vapor Pressures of Inorganic Compounds, up to 1 atm . . . . . . . . . . . . . . 2-10 Vapor Pressures of Organic Compounds, up to 1 atm . . . . . . . . . . . . . . . . VAPOR PRESSURES OF SOLUTIOnS Tables 2-11 Partial Pressures of Water over Aqueous Solutions of HCl . . . . . . . . . . . Vapor Pressures of H3PO4 Aqueous: Partial Pressure of H2O Vapor (Fig. 2-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12 Water Partial Pressure, Bar, over Aqueous Sulfuric Acid Solutions . . . 2-13 Partial Vapor Pressure of Sulfur Dioxide over Water, mmHg . . . . . . . . . 2-14 Partial Pressures of HNO3 and H2O over Aqueous Solutions of HNO3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-15 Total Vapor Pressures of Aqueous Solutions of CH3COOH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16 Partial Pressure of H2O over Aqueous Solutions of NH3 (psia) . . . . . . . . 2-17 Partial Pressures of H2O over Aqueous Solutions of Sodium Carbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-46 2-46 2-46 2-46 2-46 2-46 2-47 2-50 2-53 2-59 2-63

2-78 2-78 2-79 2-80 2-80 2-81 2-82 2-83

2-18 Partial Pressures of H2O and CH3OH over Aqueous Solutions of Methyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19 Partial Pressures of H2O over Aqueous Solutions of Sodium Hydroxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Vapor Content in Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Content in Air at Pressures over Atmospheric (Fig. 2-2) . . . . . . . SOLUBILITIES Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-20 Solubilities of Inorganic Compounds in Water at Various Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21 Solubility as a Function of Temperature and Henry’s Constant at 25°C for Gases in Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22 Henry’s Constant H for Various Compounds in Water at 25°C . . . . . . . 2-23 Henry’s Constant H for Various Compounds in Water at 25°C from Infinite Dilution Activity Coefficients . . . . . . . . . . . . . . . . . . . . . . . . 2-24 Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25 Ammonia-Water at 10 and 20°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26 Carbon Dioxide (CO2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27 Chlorine (Cl2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28 Chlorine Dioxide (ClO2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29 Hydrogen Chloride (HCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30 Hydrogen Sulfide (H2S) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DEnSITIES Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References and Comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Densities of Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-31 Density (kg/m3) of Saturated Liquid Water from the Triple Point to the Critical Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) . . . . . . . . . . . . . .

2-83 2-83 2-84 2-84

2-84 2-84 2-85 2-89 2-89 2-90 2-90 2-90 2-90 2-91 2-91 2-91 2-91

2-92 2-92 2-92 2-92 2-93

DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM Tables 2-33 Ammonia (NH3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-100 2-34 Ammonium Chloride (NH4Cl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-100

2-1

2-2

PHYSICAL AnD CHEMICAL DATA

2-35 Calcium Chloride (CaCl2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-36 Ferric Chloride (FeCl3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-37 Ferric Sulfate [Fe2(SO4)3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-38 Ferric Nitrate [Fe(NO3)3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-39 Ferrous Sulfate (FeSO4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-40 Hydrogen Cyanide (HCN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-41 Hydrogen Chloride (HCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42 Hydrogen Peroxide (H2O2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-43 Nitric Acid (HNO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44 Perchloric Acid (HClO4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-45 Phosphoric Acid (H3PO4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-46 Potassium Bicarbonate (KHCO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-47 Potassium Carbonate (K2CO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-48 Potassium Chloride (KCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-49 Potassium Hydroxide (KOH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-50 Potassium Nitrate (KNO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-51 Sodium Acetate (NaC2H3O2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-52 Sodium Carbonate (Na2CO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-53 Sodium Chloride (NaCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-54 Sodium Hydroxide (NaOH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-55 Sulfuric Acid (H2SO4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Densities of Aqueous Organic Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-56 Acetic Acid (CH3COOH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-57 Methyl Alcohol (CH3OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-58 Ethyl Alcohol (C2H5OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-59 n-Propyl Alcohol (C3H7OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-60 Isopropyl Alcohol (C3H7OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-61 Glycerol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-62 Hydrazine (N2H4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-63 Densities of Aqueous Solutions of Miscellaneous Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DEnSITIES OF MISCELLAnEOUS MATERIALS Tables 2-64 Approximate Specific Gravities and Densities of Miscellaneous Solids and Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-65 Density (kg/m3) of Selected Elements as a Function of Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LATEnT HEATS .......................................................

Unit Conversions Tables 2-66 Heats of Fusion and Vaporization of the Elements and Inorganic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-67 Heats of Fusion of Miscellaneous Materials . . . . . . . . . . . . . . . . . . . . . . . . . 2-68 Heats of Fusion of Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SPECIFIC HEATS Specific Heats of Pure Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-70 Heat Capacities of the Elements and Inorganic Compounds . . . . . . . . . 2-71 Specific Heat [kJ/(kg ⋅ K)] of Selected Elements. . . . . . . . . . . . . . . . . . . . . . 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol ⋅ K)] . . . . . 2-73 Specific Heats of Organic Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-74 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to a Polynomial Cp [J/(kmol ⋅ K)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol ⋅ K)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-76 Cp/Cv : Ratios of Specific Heats of Gases at 1 atm Pressure. . . . . . . . . . . . Specific Heats of Aqueous Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-77 Acetic Acid (at 38°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-78 Ammonia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-79 Ethyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-80 Glycerol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-81 Hydrochloric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-82 Methyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-83 Nitric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-84 Phosphoric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-85 Potassium Chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-86 Potassium Hydroxide (at 19°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-87 Normal Propyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-88 Sodium Carbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-89 Sodium Chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-90 Sodium Hydroxide (at 20°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-91 Sulfuric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific Heats of Miscellaneous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-92 Specific Heats of Miscellaneous Liquids and Solids. . . . . . . . . . . . . . . . . . 2-93 Oils (Animal, Vegetable, Mineral Oils) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-100 2-100 2-100 2-100 2-100 2-100 2-100 2-100 2-101 2-102 2-102 2-102 2-102 2-103 2-103 2-103 2-103 2-103 2-103 2-103 2-104 2-106 2-106 2-107 2-108 2-109 2-109 2-110 2-110 2-111

2-113 2-114

2-114 2-115 2-117 2-118 2-120

2-128 2-128 2-128 2-128 2-136 2-137 2-144 2-147 2-149 2-156 2-156 2-156 2-156 2-156 2-156 2-156 2-157 2-157 2-157 2-157 2-157 2-157 2-157 2-157 2-157 2-157 2-157 2-158 2-158 2-158

PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-158 Tables 2-94 Heats and Free Energies of Formation of Inorganic Compounds . . . . . 2-159 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and Net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-167 2-96 Ideal Gas Sensible Enthalpies, hT – h298 (kJ/kmol), of Combustion Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-174 2-97 Ideal Gas Entropies s°, kJ/(kmol ⋅ K), of Combustion Products . . . . . . . 2-175 HEATS OF SOLUTIOn Tables 2-98 Heats of Solution of Inorganic Compounds in Water . . . . . . . . . . . . . . . . 2-99 Heats of Solution of Organic Compounds in Water (at Infinite Dilution and Approximately Room Temperature) . . . . . . . . . . . . . . . . . . THERMAL EXPAnSIOn AnD COMPRESSIBILITY Unit Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Expansion of Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-100 Linear Expansion of the Solid Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-101 Linear Expansion of Miscellaneous Substances . . . . . . . . . . . . . . . . . . . . 2-102 Volume Expansion of Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-103 Volume Expansion of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gas Expansion: Joule-Thomson Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-104 Additional References Available for the Joule-Thomson Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-105 Approximate Inversion-Curve Locus in Reduced Coordinates (Tr = T/Tc ; Pr = P/Pc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Critical Constants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-106 Critical Constants and Acentric Factors of Inorganic and Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compressibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-107 Compressibilities of Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-108 Compressibilities of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . THERMODYnAMIC PROPERTIES Explanation of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-109 Thermodynamic Properties of Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-110 Thermodynamic Properties of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Dry Air (Fig. 2-3) . . . . . . . . . . . . . . . . . . 2-111 Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Air, Moist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-112 Thermodynamic Properties of Ammonia . . . . . . . . . . . . . . . . . . . . . . . . . . 2-113 Thermodynamic Properties of Carbon Dioxide . . . . . . . . . . . . . . . . . . . . 2-114 Thermodynamic Properties of Carbon Monoxide . . . . . . . . . . . . . . . . . . Temperature-Entropy Diagram for Carbon Monoxide (Fig. 2-4) . . . . 2-115 Thermodynamic Properties of Ethanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy-Concentration Diagram for Aqueous Ethyl Alcohol (Fig. 2-5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-116 Thermodynamic Properties of Normal Hydrogen . . . . . . . . . . . . . . . . . . 2-117 Saturated Hydrogen Peroxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-118 Thermodynamic Properties of Hydrogen Sulfide . . . . . . . . . . . . . . . . . . . Enthalpy-Concentration Diagram for Aqueous Hydrogen Chloride at 1 atm (Fig. 2-6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-119 Thermodynamic Properties of Methane . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-120 Thermodynamic Properties of Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . 2-121 Thermodynamic Properties of Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Nitrogen (Fig. 2-7) . . . . . . . . . . . . . . . . . 2-122 Thermodynamic Properties of Oxygen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Oxygen (Fig. 2-8) . . . . . . . . . . . . . . . . . . . Enthalpy-Concentration Diagram for Oxygen-Nitrogen Mixture at 1 atm (Fig. 2-9). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K Values (K = y/x) in Light-Hydrocarbon Systems (Fig. 2-10) . . . . . . . 2-123 Composition of Selected Refrigerant Mixtures . . . . . . . . . . . . . . . . . . . . . 2-124 Thermodynamic Properties of R-22, Chlorodifluoromethane . . . . . . . Pressure-Enthalpy Diagram for Refrigerant 22. (Fig. 2-11) . . . . . . . . . . 2-125 Thermodynamic Properties of R-32, Difluoromethane . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Refrigerant 32. (Fig. 2-12) . . . . . . . . . . 2-126 Thermodynamic Properties of R-125, Pentafluoroethane. . . . . . . . . . . Pressure-Enthalpy Diagram for Refrigerant 125 (Fig. 2-13) . . . . . . . . . 2-127 Thermodynamic Properties of R-134a, 1,1,1,2-Tetrafluoroethane . . . Pressure-Enthalpy Diagram for Refrigerant 134a. (Fig. 2-14). . . . . . . .

2-176 2-178

2-179 2-179 2-179 2-179 2-180 2-181 2-181 2-182 2-182 2-182 2-182 2-182 2-182 2-182 2-183 2-190 2-190 2-190 2-190 2-190

2-191 2-191 2-191 2-191 2-192 2-194 2-198 2-199 2-199 2-200 2-202 2-204 2-206 2-207 2-209 2-210 2-212 2-213 2-215 2-216 2-218 2-220 2-222 2-223 2-225 2-226 2-226 2-227 2-228 2-230 2-231 2-233 2-234 2-236 2-237 2-239

PHYSICAL AnD CHEMICAL DATA 2-128 Thermodynamic Properties of R-143a, 1,1,1-Trifluoroethane . . . . . . . 2-129 Thermodynamic Properties of R-404A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-130 Thermodynamic Properties of R-407C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Refrigerant 407C (Fig. 2-15) . . . . . . . . 2-131 Thermodynamic Properties of R-410A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-132 Opteon YF (R-1234yf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Refrigerant 1234yf (Fig. 2-16) . . . . . . 2-133 Thermophysical Properties of Saturated Seawater . . . . . . . . . . . . . . . . . Enthalpy-Concentration Diagram for Aqueous Sodium Hydroxide at 1 atm (Fig. 2-17) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy-Concentration Diagram for Aqueous Sulfuric Acid at 1 atm (Fig. 2-18) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-134 Saturated Solid/Vapor Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-135 Thermodynamic Properties of Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-136 Thermodynamic Properties of Water Substance along the Melting Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRAnSPORT PROPERTIES Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-137 Surface Tension σ (dyn/cm) of Various Liquids . . . . . . . . . . . . . . . . . . . . 2-138 Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) . . . . . . . . 2-139 Viscosity of Inorganic and Organic Liquids (Pa∙s) . . . . . . . . . . . . . . . . . . 2-140 Viscosities of Liquids: Coordinates for Use with Fig . 2-19 . . . . . . . . . . . Nomograph for Viscosities of Liquids at 1 atm (Fig . 2-19) . . . . . . . . . 2-141 Diffusivities of Pairs of Gases and Vapors (1 atm) . . . . . . . . . . . . . . . . . . 2-142 Diffusivities in Liquids (25°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-143 Transport Properties of Selected Gases at Atmospheric Pressure . . . 2-144 Prandtl Number of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-145 Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m ⋅ K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-146 Thermophysical Properties of Miscellaneous Saturated Liquids . . . . 2-147 Thermal Conductivity of Inorganic and Organic Liquids [W/(m ⋅ K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-148 Nomograph for Thermal Conductivity of Organic Liquids (Fig . 2-20) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-149 Thermal-Conductivity-Temperature Table for Metals and Nonmetals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-150 Thermal Conductivity of Chromium Alloys . . . . . . . . . . . . . . . . . . . . . . . . 2-151 Thermal Conductivity of Some Alloys at High Temperature . . . . . . . . 2-152 Thermophysical Properties of Selected Nonmetallic Solid Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-153 Lower and Upper Flammability Limits, Flash Points, and Autoignition Temperatures for Selected Hydrocarbons . . . . . . . . . . . PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prediction Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Property Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification of Estimation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory and Empirical Extension of Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Corresponding States (CS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Contributions (GCs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computational Chemistry (CC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Empirical QSPR Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molecular Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Critical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-154 Ambrose Group Contributions for Critical Constants . . . . . . . . . . . . . . 2-155 Group Contributions for the Nannoolal et al . Method for Critical Constants and Normal Boiling Point . . . . . . . . . . . . . . . . . . . . . 2-156 Intermolecular Interaction Corrections for the Nannoolal et al . Method for Critical Constants and Normal Boiling Point . . . . . . . . . . 2-157 Wilson-Jasperson First- and Second-Order Contributions for Critical Temperature and Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Melting Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Boiling Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-158 First-Order Groups and Their Contributions for Melting Point . . . . . 2-159 Second-Order Groups and Their Contributions for Melting Point . . . Characterizing and Correlating Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acentric Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radius of Gyration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dipole Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-240 2-242 2-244 2-246 2-247 2-249 2-258 2-259 2-260 2-260 2-261 2-262 2-265

2-266 2-266 2-266 2-266 2-266 2-267 2-274 2-281 2-282 2-283 2-285 2-288 2-288 2-288 2-289 2-296 2-298 2-305 2-306 2-307 2-307 2-307 2-308

2-311 2-311 2-311 2-314 2-314 2-314 2-314 2-315 2-315 2-315 2-315 2-315 2-315 2-315 2-315 2-317 2-318 2-320 2-321 2-321 2-321 2-322 2-322 2-323 2-323 2-324 2-324

Refractive Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dielectric Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-160 Wildman-Crippen Contributions for Refractive Index . . . . . . . . . . . . . . Vapor Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy of Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-161 Domalski-Hearing Group Contribution Values for Standard State Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gibbs Energy of Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Latent Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy of Vaporization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy of Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-162 Cs (C—H) Group Values for Chickos Estimation of ∆Hfus . . . . . . . . . . . 2-163 Ct (Functional) Group Values for Chickos Estimation of ∆H fus . . . . . . Enthalpy of Sublimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-164 Group Contributions and Corrections for ∆Hsub . . . . . . . . . . . . . . . . . . . . Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-165 Benson and CHETAH Group Contributions for Ideal Gas Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-166 Liquid Heat Capacity Group Parameters for Ruzicka-Domalski Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-167 Group Values and Nonlinear Correction Terms for Estimation of Solid Heat Capacity with the Goodman et al . Method . . . . . . . . . . . 2-168 Element Contributions to Solid Heat Capacity for the Modified Kopp’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-169 Simple Fluid Compressibility Factors Z (0) . . . . . . . . . . . . . . . . . . . . . . . . . . 2-170 Acentric Deviations Z (1) from the Simple Fluid Compressibility Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-171 Constants for the Two Reference Fluids Used in Lee-Kesler Method . . . Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-172 Relationships for Eq . (2-70) for Common Cubic EoS . . . . . . . . . . . . . . . . Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-173 Reichenberg Group Contribution Values . . . . . . . . . . . . . . . . . . . . . . . . . . Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-174 Group Contributions for the Hsu et al . Method . . . . . . . . . . . . . . . . . . . . Liquid Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-175 UNIFAC-VISCO Group Interaction Parameters αmn . . . . . . . . . . . . . . . . Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-176 Correlation Parameters for Baroncini et al . Method for Estimation of Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pure Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-177 Knotts Group Contributions for the Parachor in Estimating Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flammability Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flash Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flammability Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-178 Group Contributions for Quantities Used to Estimate Flammability Limits By Rowley et al . Method for Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-179 Ideal Gas Enthalpies of Formation and Average Heat Capacities of Combustion Gases for Use in Eq . (2-125) . . . . . . . . . . . . . . . . . . . . . . . Autoignition Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-180 Group Contributions for Pintar Autoignition Temperature Method for Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-3 2-324 2-325 2-325 2-326 2-326 2-327 2-327 2-327 2-328 2-334 2-334 2-334 2-334 2-335 2-336 2-336 2-336 2-337 2-337 2-337 2-338 2-339 2-343 2-344 2-345 2-345 2-345 2-345 2-345 2-347 2-348 2-349 2-349 2-349 2-350 2-350 2-351 2-351 2-351 2-352 2-353 2-354 2-354 2-355 2-356 2-356 2-357 2-357 2-358 2-358 2-358 2-359 2-360 2-360 2-360

2-361 2-361 2-361 2-362

GEnERAL REFEREnCES Considerations of reader interest, space availability, the system or systems of units employed, copyright issues, etc., have all influenced the revision of material in previous editions for the present edition. Reference is made at numerous places to various specialized works and, when appropriate, to more general works. A listing of general works may be useful to readers in need of further information.

ASHRAE Handbook—Fundamentals, SI edition, ASHRAE, Atlanta, 2005; Benedek, P., and F. Olti, Computer-Aided Chemical Thermodynamics of Gases and Liquids, Wiley, New York, 1985; Brule, M. R., L. L. Lee, and K. E. Starling, Chem. Eng., 86, 25, Nov. 19, 1979, pp. 155–164; Cox, J. D., and G. Pilcher, Thermochemistry of Organic and Organometallic Compounds, Academic Press, New York, 1970; Cox, J. D., D. D. Wagman, and V. A. Medvedev, CODATA Key Values for Thermodynamics, Hemisphere Publishing Corp., New York, 1989; Daubert, T. E., R. P. Danner, H. M. Sibel, and C. C. Stebbins, Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, Taylor & Francis, Washington, 1997; Domalski, E. S., and E. D. Hearing, Heat capacities and entropies of organic compounds in the condensed phase, vol. 3, J. Phys. Chem. Ref. Data 25(1):1–525, Jan-Feb 1996; Dykyj, J., and M. Repas, Saturated vapor pressures of organic compounds, Veda, Bratislava, 1979 (Slovak); Dykyj, J., M. Repas, and J. Svoboda, Saturated vapor pressures of organic compounds, Veda, Bratislava, 1984 (Slovak); Glushko, V. P., ed., Thermal Constants of Compounds, Issues I–X, Moscow, 1965–1982 (Russian only); Gmehling, J., Azeotropic Data, 2 vols., VCH Weinheim, Germany, 1994; Gmehling, J., and U. Onken, Vapor-Liquid Equilibrium Data Collection, Dechema Chemistry Data Series, Frankfurt, 1977–1978; International Data Series, Selected Data on Mixtures, Series A: Thermodynamics Research Center, National Institute of Standards and Technology, Boulder, Colo.; Kaye, S. M., Encyclopedia of Explosives and Related Items, U.S. Army R&D command, Dover, N.J., 1980; King, M. B., Phase Equilibrium in Mixtures, Pergamon, Oxford, 1969; Landolt-Boernstein, Numerical Data and Functional Relationships in Science and Technology (New Series), http://www.springeronline .com/sgw/cda/frontpage/0,11855,4-10113-2-95859-0,00.html; Lide, D. R., CRC Handbook of Chemistry and Physics, 86th ed., CRC Press, Boca Raton, Fla., 2005; Lyman, W. J., W. F. Reehl, and D. H. Rosenblatt, Handbook of Chemical Property Estimation Methods, McGraw-Hill, New York, 1990; Majer, V., and V. Svoboda, Enthalpies of Vaporization of Organic Compounds: A Critical Review and Data Compilation, Blackwell Science, 1985; Majer V., V. Svoboda, and J. Pick, Heats of Vaporization of Fluids, Elsevier, Amsterdam, 1989 (general discussion); Marsh, K. N., Recommended Reference Materials for the Realization of Physicochemical Properties, Blackwell Science, 1987; NIST-IUPAC Solubility Data Series, Pergamon Press, http://www.iupac.org/publications/ ci/1999/march/solubility.html; Ohse, R. W., and H. von Tippelskirch, High Temp.—High Press., 9:367–385, 1977; Ohse, R. W., Handbook of Thermodynamic and Transport Properties of Alkali Metals, Blackwell Science Pubs., Oxford, England, 1985; Pedley, J. B., R. D. Naylor, and S. P. Kirby, Thermochemical Data of Organic Compounds, Chapman and Hall, New York, 1986; Physical Property Data for the Design Engineer, Hemisphere, New York, 1989; Poling, B. E., J. M. Prausnitz, and J. P. O’Connell, The Properties of Gases and

2-4

Liquids, 5th ed., McGraw-Hill, New York, 2001; Rothman, D., et al., Max Planck Inst. f. Stromungsforschung, Ber 6, 1978; Smith, B. D., and R. Srivastava, Thermodynamic Data for Pure Compounds, Part A: Hydrocarbons and Ketones, Elsevier, Amsterdam, 1986, Physical sciences data 25, http://www .elsevier.com/wps/find/bookseriesdescription.librarians/BS_PSD/description; Sterbacek, Z., B. Biskup, and P. Tausk, Calculation of Properties Using Corresponding States Methods, Elsevier, Amsterdam, 1979; Stull, D. R., E. F. Westrum, and G. C. Sink, The Chemical Thermodynamics of Organic Compounds, Wiley, New York, 1969; TRC Thermodynamic Tables—Hydrocarbons, Thermodynamics Research Center, National Institute of Standards and Technology, Boulder, Colo.; TRC Thermodynamic Tables—Non-Hydrocarbons, Thermodynamics Research Center, National Institute of Standards and Technology, Boulder, Colo.; Young, D. A., “Phase Diagrams of the Elements,” UCRL Rep. 51902, 1975 republished in expanded form by the University of California Press, 1991; Zabransky, M., V. Ruzicka, Jr., V. Majer, and E. S. Domalski, Heat Capacity of Liquids: Critical Review and Recommended Values, J. Phys. Chem. Ref. Data, Monograph No. 6, 1996. Critical Data Sources

Ambrose, D., “Vapor-Liquid Critical Properties,” N. P. L. Teddington, Middlesex, Rep. 107, 1980; Kudchaker, A. P., G. H. Alani, and B. J. Zwolinski, Chem. Revs. 68: 659–735, 1968; Matthews, J. F., Chem. Revs. 72: 71–100, 1972; Simmrock, K., R. Janowsky, and A. Ohnsorge, Critical Data of Pure Substances, Parts 1 and 2, Dechema Chemistry Data Series, 1986. Other recent references for critical data can be found in Lide, D. R., CRC Handbook of Chemistry and Physics, 86th ed., CRC Press, Boca Raton, Fla., 2005. Publications on Thermochemistry

Pedley, J. B., Thermochemical Data and Structures of Organic Compounds, 1, Thermodynamic Research Center, Texas A&M Univ., 1994 (976 pp., 3000 cpds.); Frenkel, M., et al., Thermodynamics of Organic Compounds in the Gas State, 2 vols., Thermodynamic Research Center, Texas A&M Univ., 1994 (1825 pp., 2000 cpds.); Barin, I., Thermochemical Data of Pure Substances, 2nd ed., 2 vols., VCH Weinheim, Germany, 1993 (1834 pp., 2400 substances); Gurvich, L. V., et al., Thermodynamic Properties of Individual Substances, 4th ed., 3 vols., Hemisphere, New York, 1989, 1990, and 1993 (2520 pp.); Lide, D. R., and G. W. A. Milne, Handbook of Data on Organic Compounds, 3rd ed., 7 vols., Chemical Rubber, Miami, 1993 (7000 pp.); Daubert, T. E., et al., Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, extant 1995, Taylor & Francis, Bristol, Pa., 1995; Database 11, NIST, Gaithersburg, Md. U.S. Bureau of Mines publications include Bulletins 584, 1960 (232 pp.); 592, 1961 (149 pp.); 595, 1961 (68 pp.); 654, 1970 (26 pp.); Chase, M. W., et al., JANAF Thermochemical Tables, 3d ed., J. Phys. Chem. Ref. Data 14 suppl. 1, 1986 (1896 pp.); Journal of Physical and Chemical Reference Data is available online at http://listserv.nd .edu/cgi-bin/wa?×A2=ind0501&L=pamnet&F=&S=&P=8490 and at http:// www.nist.gov/srd/reprints.htm

PHYSICAL PROPERTIES OF PURE SUBSTAnCES TABLE 2-1

Physical Properties of the Elements and Inorganic Compounds* Abbreviations Used in the Table

a., acid A., specific gravity with reference to air = 1 abs., absolute ac., acetic acid act., acetone al., 95 percent ethyl alcohol alk, alkali (i.e., aq. NaOH or KOH) am., amyl (C5H11) amor., amorphous anh., anhydrous aq., aqueous or water aq. reg., aqua regia

atm., atmosphere or 760 mm. of mercury pressure bk., black brn., brown bz., benzene c., cold cb., cubic cc, cubic centimeter chl., chloroform col., colorless or white conc., concentrated cr., crystals or crystalline d., decomposes D., specific gravity with reference to hydrogen = 1

hyg., hygroscopic i., insoluble ign., ignites lq., liquid lt., light m. al., methyl alcohol mn., monoclinic nd., needles NH3, liquid ammonia NH4OH, ammonium hydroxide solution oct., octahedral or., orange pd., powder

d. 50, decomposes at 50°C; 50 d., melts at 50°C with decomposition delq., deliquescent dil., dilute dk., dark eff., effloresces or efflorescent et., ethyl ether expl., explodes gel., gelatinous gly., glycerol (glycerin) gn., green h., hot hex., hexagonal

Formula weights are based upon the International Atomic Weights in “Atomic Weights of the Elements 2001,” Pure Appl. Chem., 75, 1107, 2003, and are computed to the nearest hundredth . Refractive index, where given for a uniaxial crystal, is for the ordinary (ω) ray; where given for a biaxial crystal, the index given is for the median (β) value . Unless otherwise specified, the index is given for the sodium D-line (λ = 589 .3 µm) . Specific gravity values are given at room temperatures (15 to 20°C) unless otherwise indicated by the small figures which follow the value: thus, 5.6 184° indicates a specific gravity of 5 .6 for the substance at 18°C referred to water at 4°C . In this table the values for the specific gravity of gases are given with reference to air (A) = 1, or hydrogen (D) = 1 . Melting point is recorded in a certain case as 82 d . and in some other case as d . 82, the distinction being made in this manner to indicate that the former is a melting point with decomposition at 82°C, while in the latter decomposition only occurs at 82°C . Where a value such as −2H2O, 82 is given, it indicates loss of 2 moles of water per formula weight of the compound at a temperature of 82°C . Boiling point is given at atmospheric pressure (760 mm of mercury) unless otherwise indicated; thus, 8215 mm indicates the boiling point is 82°C when the pressure is 15 mm .

Name Aluminum acetate, normal acetate, basic bromide bromide carbide chloride

Formula Al Al(C2H3O2)3 Al(OH)(C2H3O2)2 AlBr3 AlBr3⋅6H2O Al4C3 AlCl3

Formula weight 26 .98 204 .11 162 .08 266 .69 374 .78 143 .96 133 .34

Color, crystalline form, and refractive index silv ., cb . wh . pd . wh ., amor . trig . col ., delq . cr . yel ., hex ., 2 .70 wh ., delq ., hex .

Specific gravity 2 .7020° 3 .01 254° 2 .95 2 .44

25 ° 4

pl., plates pr., prisms or prismatic pyr., pyridine rhb., rhombic (orthorhombic) s., soluble satd., saturated sl., slightly soln., solution subl., sublimes sulf., sulfides tart. a., tartaric acid tet., tetragonal tr., transition tri., triclinic

trig., trigonal v., very vac., in vacuo vl., violet volt., volatile or volatilizes wh., white yel., yellow ∞, soluble in all proportions , greater than 42±, about or near 42 −3H2O, 100, loses 3 moles of water per formula weight at 100°C

Solubility is given in parts by weight (of the formula shown at the extreme left) per 100 parts by weight of the solvent; the small superscript indicates the temperature . In the case of gases the solubility is often expressed in some manner as 510° cc which indicates that at 10°C, 5 cc of the gas are soluble in 100 g of the solvent . The symbols of the common mineral acids: H2SO4, HNO3, HCl, etc ., represent dilute aqueous solutions of these acids . See also special tables on Solubility . references: The information given in this table has been collected mainly from the following sources: Mellor, A Comprehensive Treatise on Inorganic and Theoretical Chemistry, Longmans, New York, 1922 . Abegg, Handbuch der anorganischen Chemie, S . Hirzel, Leipzig, 1905 . Gmelin-Kraut, Handbuch der anorganischen Chemie, 7th ed ., Carl Winter, Heidelberg; 8th ed ., Verlag Chemie, Berlin, 1924 . Friend, Textbook of Inorganic Chemistry, Griffin, London, 1914 . Winchell, Microscopic Character of Artificial Inorganic Solid Substances or Artificial Minerals, Wiley, New York, 1931 . International Critical Tables, McGraw-Hill, New York, 1926 . Tables annuelles internationales de constants et donnes numeriques, McGraw-Hill, New York . Annual Tables of Physical Constants and Numerical Data, National Research Council, Princeton, N .J ., 1943 . Comey and Hahn, A Dictionary of Chemical Solubilities, Macmillan, New York, 1921 . Seidell, Solubilities of Inorganic and Metal Organic Compounds, Van Nostrand, New York, 1940 .

Melting point, °C 660 d . 200 d . 97 .5 d . 100 d . >2200 1945 .2atm .

Boiling point, °C 2056 268 752mm

182 .7 ; subl . 178

Solubility in 100 parts Cold water i . s . i . s . s . d . to CH4 69 .8715°

chloride AlCl3⋅6H2O col ., delq ., trig ., 1 .560 400 241 .43 fluoride (fluellite) AlF3⋅H2O col ., rhb ., 1 .490 2 .17 d . sl . s . 101 .99 fluoride Al2F6⋅7H2O wh ., cr . pd . −4H2O, 120 −6H2O, 250 i . 294 .06 hydroxide Al(OH)3 wh ., mn . 2 .42 −2H2O, 300 0 .00010418° 78 .00 nitrate Al(NO3)3⋅9H2O rhb ., delq . 73 d . 134 v . s . 375 .13 4atm . 25 ° nitride Al2N2 yel ., hex . 3 .05 4 2150 d . >1400 d . slowly 81 .98 oxide Al2O3 col ., hex ., 1 .67–8 3 .99 1999 to 2032 i . 101 .96 oxide (corundum) Al2O3 wh ., trig ., 1 .768 4 .00 1999 to 2032 2210 i . 101 .96 phosphate AlPO4 col ., hex . 2 .59 i . 121 .95 ∗By N . A . Lange, Ph .D ., Handbook Publishers, Inc ., Sandusky, Ohio . Abridged from table of Physical Constants of Inorganic Compounds in Lange’s Handbook of Chemistry.

Hot water i . d .

Other reagents s . HCl, H2SO4, alk .

s . d .

s .a .; i . NH4 salts s .al ., act ., CS2 s . al ., CS2 s . a .; i . act . s . et ., chl ., CCl4; i . bz .

v . s .

50 al .; s . et .

s .

sl . s . i . v . s . d . i . i . i .

s . a ., alk .; i . a . s . al ., CS2 s . alk . d . v . sl . s . a ., alk . v . sl . s . a ., alk . s . a ., alk .; i . ac . (Continued )

2-5

2-6 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued )

Name Aluminum (Cont.) potassium silicate (muscovite) potassium silicate (orthoclase) Aluminum potassium tartrate sodium fluoride (cryolite) sodium silicate sulfate Alum, ammonium (tschermigite) ammonium chrome

Formula

Formula weight

3Al2O3⋅K2O⋅6SiO2⋅2H2O Al2O3⋅K2O⋅6SiO2 AlK(C4H4O6)2 AlF3⋅3NaF Al2O3⋅Na2O⋅6SiO2 Al2(SO4)3 Al2(SO4)3⋅(NH4)2SO4⋅ 24H2O Cr2(SO4)3⋅(NH4)2SO4⋅ 24H2O Fe2(SO4)3⋅(NH4)2SO4⋅ 24H2O Al2(SO4)3⋅K2SO4⋅24H2O Cr2(SO4)3⋅K2SO4⋅24H2O Al2(SO4)3⋅Na2SO4⋅24H2O NH3

796 .61 556 .66 362 .22 209 .94 524 .44 342 .15 906 .66 956 .69

Color, crystalline form, and refractive index mn., 1.590 col., mn., 1.524 col. wh., mn., 1.3389 col., tri., 1.529 wh. cr. col., oct., 1.4594 gn . or vl ., oct ., 1 .4842

Specific gravity

Melting point, °C

2.9 2.56

d. 1450 (1150)

2.90 2.61 2.71 1.64 204°

1000 1100 d. 770 93.5

1 .72

Boiling point, °C

−20H2O, 120; −24H2O, 200

100 d .

vl ., oct ., 1 .485

1 .71

40

948 .78 998 .81 916 .56 17 .03

col ., mn ., 1 .4564 red or gn ., cb ., 1 .4814 col ., oct ., 1 .4388 col . gas, 1 .325 (lq .)

92 89 61 −77 .7

−18H2O, 64 .5

77 .08 337 .09 79 .06 97 .94 114 .10 157 .13

wh ., hyg . cr . pl . mn . or rhb ., 1 .5358 col ., cb ., 1 .7108 col . pl . wh . cr .

114 d . 200 d . 35–60 subl . 542 d . 58 subl .

d .

272 .21

wh .

chloride (salammoniac) chloroplatinate chloroplatinite chlorostannate chromate cyanide dichromate ferrocyanide fluoride fluoride, acid formate

NH4C2H3O2 NH4CN⋅Au(CN)3⋅H2O NH4HCO3 NH4Br (NH4)2CO3⋅H2O NH4HCO3⋅ NH2CO2NH4‡ (NH4)2CO3⋅ 2NH4HCO3⋅H2O NH4Cl (NH4)2PtCl6 (NH4)2PtCl4 (NH4)2SnCl6 (NH4)2CrO4 NH4CN (NH4)2Cr2O7 (NH4)4Fe(CN)6⋅6H2O NH4F NH4F⋅HF HCO2NH4

1 .76 264° 1 .83 1 .675 204° 0 .817−79° 0 .5971 (A) 1 .073

53 .49 443 .87 372 .97 367 .50 152 .07 44 .06 252 .06 392 .19 37 .04 57 .04 63 .06

wh ., cb ., 1 .639, 1 .6426 yel ., cb . tet . pink ., cb . yel ., mn . col ., cb . or ., mn . mn . wh ., hex . wh ., rhb ., 1 .390 col ., mn ., delq .

hydrosulfide hydroxide molybdate molybdate, heptanitrate (α), stable −16° to 32° nitrate (β), stable 32° to 84°

NH4HS NH4OH (NH4)2MoO4 (NH4)6Mo7O24⋅4H2O‡ NH4NO3 NH4NO3

51 .11 35 .05 196 .01 1235 .86 80 .04 80 .04

col ., rhb . in soln . only mn . col ., mn . col ., tet ., 1 .611 col ., rhb . or mn .

nitrite osmochloride oxalate oxalate, acid perchlorate persulfate phosphate, monobasic phosphate, dibasic phosphate, meta-

NH4NO2 (NH4)2OsCl6 (NH4)2C2O4⋅H2O NH4HC2O4⋅H2O NH4ClO4 (NH4)2S2O8 NH4H2PO4 (NH4)2HPO4 (NH4)4P4O12

64 .04 439 .02 142 .11 125 .08 117 .49 228 .20 115 .03 132 .06 388 .04

wh . nd . cb . col ., rhb . col ., trimetric col ., rhb ., 1 .4833 wh ., mn ., 1 .5016 col ., tet ., 1 .5246 col ., mn ., 1 .53 col ., mn .

Ammonium acetate auricyanide bicarbonate bromide carbonate carbonate, carbamate carbonate, sesqui-

1 .573 2 .327 154°

124

−33 .4

d . 1 .5317° 3 .065 2 .4 1 .91712° 0 .79100° (A) 2 .15 2 .21 1212° 1 .266

d . 350 d . d .

d . 2 .27

subl . 520

d . 180 36 d . 185 d . 114–116

d . 180; subl . in vac . subl . 120

d . 25 ° 4 25 ° 4

1 .66 1 .725

169 .6

1 .69 2 .93 204° 1 .501 1 .556 1 .95 1 .98 1 .803 194° 1 .619 2 .21

expl .

i. i. s. sl. s. i. 31.30° 3.90° 21 .2

964 .38

ammonium iron potassium (kalinite) potassium chrome sodium Ammonia†

Solubility in 100 parts Cold water

d . 210 d . 210

s. i. 89100° ∞ 100°

25°

Other reagents

i. HCl d. a. i . al . s . al .

25°

i . al .

5 .70° 20 106 .40° 89 .90°

∞93° 50 121 .745° 7 .496°

1484° s . 11 .90° 6810° 10015° 2515°

v . s . 2730° 145 .6100° 6765°

2015°

5049°

29 .40° 0 .715° s . 33 .315° 40 .530° s . 47 .230° s . v . s . v . s . 1020°

77 .3100° 1 .25100° v . s .

s . NH3; sl . s . al ., m . al . 0 .005 al .

d . v . s . v . s . d .

sl . s . act ., NH3; i . al . s . al . s . al .; i . act . i . al . s . al .; i . NH3

53180°

s . al .

v . s . s . d . 4425° 118 .30° 365 .835° s . 2 .5 s . 10 .90° 58 .20° 22 .70° 13115° s .

i . al . i . al . 14 .820° al .; s . et . s . al .; sl . s . act . i . al . i . al . s . al ., et ., act . i . al ., CS2, NH3

s . al . d .

i . al ., NH3 i . al . 30°

241 .8 58080° d .

0°

d . d . d . 120

Hot water

11 .850° 100°

46 .9 d . 173 .2100°

3 .820° al ., 17 .120° m . al .; v . s . NH3 s . al . sl . s . al .; i . NH3 220° al .; s . act .; i . et . i . ac . i . act .

Ammonium phosphomolybdate silicofluoride sulfamate sulfate (mascagnite) sulfate, acid sulfide sulfide, pentasulfite sulfite, acid tartrate thiocyanate vanadate, metaAntimony chloride, tri- (butter of antimony)∗ oxide, tri- (valentinite) oxide, tri- (senarmontite) sulfide, tri- (stibnite)

(NH4)3PO4⋅12MoO3⋅ 3H2O (?) (NH4)2SiF6 NH4⋅SO3NH2 (NH4)2SO4 NH4HSO4 (NH4)2S (NH4)2S5 (NH4)2SO3⋅H2O NH4HSO3 (NH4)2C4H4O6 NH4CNS NH4VO3 Sb

1930 .39 178 .15 114 .12 132 .14 115 .11 68 .14 196 .40 134 .16 99 .11 184 .15 76 .12 116 .98 121 .76

yel. cb., 1.3696 col. pl. col., rhb., 1.5230 col., rhb., 1.480 yel.-wh. or.-red pr. col., mn. rhb. col., mn. col., mn., 1.685± col. cr. tin wh., trig.

d.

0.0315°

i.

s. alk.; i. al., HNO3

55.5 35750° 103.3100°

s. al.; i. act.

8760° 17020° 3.0570° i.

1.769 204° 1.78

132 235 d. 146.9 d.

1.41 2.03 124° 1.60 1.305 2.326 6.68425°

d. d. d. 149.6 d. 630.5

1380

18.517.5° 1340° 70.60° 100 v. s. s. 10012° s. 450° 1200° 0.4418° i.

73.4

220.2

601.60°

∞72°

656 652 550

1570

2.01

SbCl3

228 .12

col., rhb., delq.

3.14

Sb2O3 Sb2O3 Sb2S3

291 .52 291 .52 339 .72

rhb ., 2 .35 cb ., 2 .087 bk ., rhb ., 4 .046

5 .67 5 .2 4 .64

20 ° 4

0°

subl. d. 160 490

d. 170

i. al., act., CS2 v. sl. s. al.; i. act. 12025° NH3 i. al., act. sl. s. al. s. al., act., NH3, SO2 i. al., NH4Cl s. aq. reg., h. conc. H2SO4 s . al ., HCl, HBr, H2C4H4O6 s . HCl, KOH, H2C4H4O6

v . sl . s .

sl . s .

0 .0001718°

d .

−2S, 135 629

i .

i .

5 .268 .7° d . i . 5 .60° cc

35 .7100° d . d . 2 .2350° cc

s . gly .; i . al .

s . HCl; alk ., NH4HS, K2S; i . ac . s . HCl, alk ., NH4HS

sulfide, pentatelluride, triAntimonyl potassium tartrate (tartar emetic) sulfate, normal sulfate, basic Argon

Sb2S5 Sb2Te3

403 .85 626 .32

golden gray

4 .120

(SbO)KC4H4O6⋅½H2O (SbO)2SO4 (SbO)2SO4⋅Sb2(OH)4 Ar

333 .94 371 .58 683 .20 39 .95

wh ., rhb . wh . pd . wh . pd . col . gas

2 .60 4 .89

−½H2O, 100 −189 .2

−185 .7

Arsenic (crystalline) (α) Arsenic (black) (β)

As4 As4

299 .69 299 .69

met ., hex . bk ., amor .

1 .65−288°; 1 .402−185 .7°; 1 .38 (A) 5 .72714° 4 .720°

81436atm .

subl . 615

i . i .

i . i .

s . HNO3 s . HNO3, aq . reg ., aq . Cl2, h . alk .

Arsenic (yellow) (γ) acid, orthoacid, metaacid, pyropentoxide sulfide, di- (realgar)

As4 H3AsO4⋅½H2O HAsO3 H4As2O7 As2O5 As2S2

299 .69 150 .95 123 .93 265 .87 229 .84 213 .97

yel ., cb . col ., hyg . wh ., hyg . col . wh ., amor . red, mn ., 2 .68

−H2O, 160

50 H3AsO4 H3AsO4 76 .7100° d .

s . alk .

d . 565

16 .7 d . to form d . to form 59 .50° i .

s . alk ., al . s . K2S, NaHCO3

sulfide, pentaArsenious chloride (butter of arsenic) hydride (arsine) oxide (arsenolite) oxide (claudetite) oxide

As2S5 AsCl3

310 .17 181 .28

d . 500 130

0 .0001360° d .

i . d .

s . HNO3, alk . s . HCl, HBr, PCl3

AsH3 As2O3 As2O3 As2O3

−55; d . 230

20 cc sl . s . sl . s . 1 .210°

sl . s . sl . s . sl . s . 2 .9340°

Auric chloride cyanide Aurous chloride cyanide Cf. also under Gold Barium acetate acetate bromide ∗Usually the solution . † See special tables . ‡ Usual commercial form .

sl . s . alk . i . al ., et . i . al ., et . s . HCl, alk ., Na2CO3; i . al ., et . s . HCl, al ., et .; sl . s . NH3 s . al . s . HCl, HBr; d . al . s . KCN; i . al ., et .

Ba Ba(C2H3O2)2 Ba(C2H3O2)2⋅H2O BaBr2

2 .020° 2 .0–2 .5

d . 358 35 .5 d . d . 206

4 .086 (α)3 .50619°; (β)3 .25419°

(α)tr . 267; (β)307

yel . oily lq .

lq . 2 .163

−18

77 .95 197 .84 197 .84 197 .84

col . gas col ., cb ., fibrous, 1 .755 col ., mn ., 1 .92 amor . or vitreous

2 .695 (A) 3 .865 254° 3 .85 3 .738

−113 .5 subl . subl . 315

AuCl3⋅2H2O

339 .36

or . cr .

d .

v . s .

v . s .

Au(CN)3⋅6H2O AuCl AuCN

383 .11 232 .42 222 .98

yel . cr . yel . cr .

7 .4

d . 50 AuCl3, 170 d .

d . 290

v . s . d . i .

v . s . d . i .

137 .33 255 .42 273 .43 297 .14

silv . met . col . wh ., tri . pr ., 1 .517 col .

3 .5 2 .468 2 .19 4 .781 244°

850

1140

−H2O, 41 847

d .

d . 58 .80° 7530°(anh .) 980°

d . 75 .0100° 7940°(anh .) 149100°

5 .1515° gly . 2425° cc al .

s . a .; d . al . i . al . v . s . m . al .; v . sl . s . act . (Continued )

2-7

2-8 TABLE 2-1

Physical Properties of the Elements and Inorganic Compounds (Continued )

Name Barium (Cont.) bromide carbonate (witherite) carbonate (α) carbonate (β) Barium chlorate chlorate chloride chloride chloride hydroxide hydroxide nitrate (nitrobarite) oxalate oxide peroxide peroxide phosphate, monobasic phosphate, dibasic phosphate, tribasic phosphate, pyrosilicofluoride sulfate (barite, barytes) sulfide, monosulfide, trisulfide, tetraBeryllium (glucinum) Bismuth carbonate, subchloride, dichloride, trinitrate nitrate, suboxide, trioxide, trioxide, trioxychloride

Formula

Formula weight

Color, crystalline form, and refractive index

333.17 197.34 197.34 197.34 304.23 322.24 208.23 208.23 244.26 171.34 315.46 261.34 225.35 153.33

col., mn., 1.7266 wh., rhb., 1.676 wh., hex. wh. col. col., mn., 1.577 col., mn., 1.7361 col., cb. col., mn., 1.646 col., mn. col., mn., 1.5017 col., cb., 1.572 wh. cr. col., cb., 1.98

BaO2∗ BaO2⋅8H2O BaH4(PO4)2 BaHPO4 Ba3(PO4)2 Ba2P2O7 BaSiF6 BaSO4

169.33 313.45 331.30 233.31 601.92 448.60 279.40 233.39

gray or wh. pd. pearly sc. tri. wh., rhb. nd., 1.635 wh., cb. wh., rhb. pr. col., rhb., 1.636

BaS BaS3 BaS4⋅2H2O Be(Gl) Bi

169.39 233.52 301.62 9.01 208.98

Bi2O3⋅CO2⋅H2O BiCl2 BiCl3∗ Bi(NO3)3⋅5H2O BiONO3⋅H2O Bi2O3 Bi2O3 Bi2O3 BiOCl

527.98 279.89 315.34 485.07 305.00 465.96 465.96 465.96 260.43

col., cb., 2.155 yel.-gn. red, rhb. gray, met., hex. silv. wh. or reddish, hex. wh. pd. bk. nd. wh. cr. col., tri. hex. pl. yel., rhb. yel., tet. yel., cb. wh., amor.

6.86 4.86 4.75 2.82 4.92815° 8.9 8.55 8.20 7.7215°

d. 163 230 d. 30 d. 260 820 860 tr. 704

wh., tri.

1.43515°

185 d.

2.32 2.54 1.85 1.49

2300 2450 577 d. d. 100 −7.2

61.83

H3BO3

Boron carbide oxide oxide (sassolite) Bromic acid Bromine

B B4C B2O3 B2O3⋅3H2O HBrO3 Br2

10.81 55.25 69.62 123.67 128.91 159.81

gray or bk., amor. or mn. bk. cr. col. glass, 1.459 tri., 1.456 col.; in soln. only rhb., or red lq.

Br2⋅10H2O Cd Cd(C2H3O2)2 Cd(C2H3O2)2⋅2H2O∗ CdCO3

339.96 112.41 230.50 266.53 172.42

red, oct. silv. met., hex. col. col., mn. wh., trig.

chloride

Melting point, °C

BaBr2⋅2H2O BaCO3 BaCO3 BaCO3 Ba(ClO3)2 Ba(ClO3)2⋅H2O∗ BaCl2 BaCl2 BaCl2⋅2H2O† Ba(OH)2 Ba(OH)2⋅8H2O Ba(NO3)2 BaC2O4 BaO

Boric acid

hydrate Cadmium acetate acetate carbonate

Specific gravity

CdCl2

183.32

wh., cb.

3.69 4.29

3.179 3.856 244° 3.097 244° 4.495 2.18816° 3.24428° 2.658 5.72 4.958 4°

2.9 4.16515° 4.116° 3.920° 4.27915° 4.49915° 4.2515° 2.98820° 1.816 9.8020°

3.11920°; 5.87 (A) 8.6520° 2.341 2.01 4.2584° 4.047

25 ° 4

Boiling point, °C

−2H2O, 100 tr. 811 to α tr. 982 to β 174090 atm. 414 d. 120 tr. 925 962 −2H2O, 100

d. d. 1450

77.9 592

−8H2O, 550 d.

1923

d. 400 d. 200 1284 271

d. 6.8 320.9 256 −H2O, 130 d. 3500 >1500 58.78 767 d.

960

s. i. v. s. v. s. i. 90

0°

34.2100° 0.002424° 90.880°

0.09100° 0.00028530°

i. i. 147100°

sl. s. al., act. sl. s. HCl, HNO3; i. al. sl. s. HCl, HNO3; i. al. v. sl. s. al.; i. et. sl. s. a.; i. al. s. a., NH4Cl; i. al. s. HCl, HNO3, abs. al.; i. NH3, act. s. dil. a.; i. act. s. dil. a.; i. al., et., act. s. a. s. a., NH4 salts s. a. s. a., NH4 salts sl. s. HCl, NH4Cl; i. al. s. conc. H2SO4; 0.006, 3% HCl d. HCl; i. al. i. al., CS2 s. dil. a., alk. s. aq. reg., conc. H2SO4, HNO3 s. a. s. al. 4219° act.; s. a.; i. al. s. a. s. a. s. a. s. a. s. a.; i. act., NH3, H2C4H4O6 22.220° gly., 0.2425° et.; s. al. s. HNO3; i. al. i. a. s. a., al., gly. s. al., et., alk., CS2 s. a., NH4NO3 s. m. al. s. al. s. a., KCN, NH4 salts; i. NH3 1.5215° al.; i. et., act.

CdCl2 ⋅2½H2O Cd(CN)2 Cd(OH)2 Cd(NO3)2 Cd(NO3)2⋅4H2O∗ CdO CdO Cd2O CdSO4 CdSO4⋅H2O 3CdSO4⋅8H2O∗ CdSO4⋅4H2O CdSO4⋅7H2O CdS Ca Ca(C2H2O2)2⋅H2O Ca(AlO2)2 CaO⋅Al2O3⋅2SiO2 Ca3(AsO4)2 CaBr2 CaCO3 CaCO3 CaCl2∗ CaCl2⋅H2O CaCl2⋅6H2O Ca3(C6H5O7)2⋅4H2O CaCN2 Ca2Fe(CN)6⋅12H2O CaF2 Ca(HCO2)2 CaH2 Ca(OH)2 Ca(ClO)2⋅4H2O Ca2P2O6⋅2H2O Ca(C3H5O3)2⋅5H2O

228 .36 164 .45 146 .43 236 .42 308 .48 128 .41 128 .41 240 .82 208 .47 226 .49 769 .54 280 .53 334 .58 144 .48 40 .08 176 .18 158 .04 278 .21 398 .07 199 .89 100 .09 100 .09 110 .98 129 .00 219 .08 570 .49 80 .10 508 .29 78 .07 130 .11 42 .09 74 .09 215 .04 274 .13 308 .29

col., mn., 1.6513

3.327

wh., trig. col. col. nd. brn., cb. brn., amor, 2.49 gn., amor. rhb. mn. col., mn., 1.565 col. mn. yel.-or., hex., 2.506 silv. met., cb. wh. nd. col., rhb. or mn. tri., 1.5832 wh. pd. delq. nd. col., rhb., 1.6809 col., hex., 1.550 wh., delq., cb, 1.52 col., delq. col., trig., 1.417 col. nd. col., rhombohedral yel., tri., 1.5818 wh., cb., 1.4339 col., rhb. wh. cr. or pd. col., hex., 1.574 wh., feathery cr. granular col., eff.

4.79 154°

CaO⋅MgO⋅2CO2 CaO⋅MgO⋅2SiO2 Ca(NO3)2 Ca(NO3)2⋅4H2O∗ Ca3N2 Ca(NO2)2⋅H2O CaC2O4 CaC2O4⋅H2O CaO

184 .40 216 .55 164 .09 236 .15 148 .25 150 .10 128 .10 146 .11 56 .08

trig ., 1 .68174 wh ., mn . col ., cb . col ., mn ., 1 .498 brn . cr . delq ., hex . col ., cb . col . col ., cb ., 1 .837

peroxide phosphate, monobasic phosphate, dibasic phosphate, tribasic phosphate, metaphosphate, pyrophosphate, pyro- (brushite) phosphide silicate (α) (pseudowollastonite)

CaO2⋅8H2O CaH4(PO4)2⋅H2O CaHPO4⋅2H2O Ca3(PO4)2 Ca(PO3)2 Ca2P2O7 Ca2P2O7⋅5H2O Ca3P2 CaSiO3

216 .20 252 .07 172 .09 310 .18 198 .02 254 .10 344 .18 182 .18 116 .16

silicate (β) (wollastonite) sulfate (anhydrite)

CaSiO3 CaSO4

116 .16 136 .14

pearly, tet . wh ., tri . wh ., mn . pl . wh ., amor . wh ., tet ., 1 .588 col ., biaxial, 1 .60 wh ., mn . red cr . col ., pseudo hex ., 1 .6150 or mn . col ., mn ., 1 .610 col ., rhb ., 1 .576, or mn ., 1 .50

chloride cyanide hydroxide nitrate nitrate oxide oxide oxide, subCadmium sulfate sulfate sulfate sulfate sulfate sulfide (greenockite) Calcium acetate aluminate aluminum silicate (anorthite) arsenate bromide carbonate (aragonite) carbonate (calcite) chloride (hydrophilite) chloride chloride citrate cyanamide ferrocyanide fluoride ( fluorite) formate hydride hydroxide hypochlorite hypophosphate lactate magnesium carbonate (dolomite) magnesium silicate (diopside) nitrate (nitrocalcite) nitrate nitride nitrite oxalate oxalate oxide

∗Usual commercial form . † The solubility of CaCO3 in H2O is greatly increased by increasing the amount of CO2 in the H2O .

2.455 174° 8.15 6.95 8.192 184° 4.691 244° 3.78620° 3.09 3.05 2.48 204° 4.58 1.5520°

tr. 34 d. >200 d. 300 350 59.4

132

d. 900–1000 d. 1000 tr. 108 tr. 41.5

3.6720° 2.765

tr. 4 1750100atm. 810 d. 1600 1551

3.353 254° 2.93 2.711 254° 2.152 154°

760 d. 825 1339103atm. 772

>1600

29.92 −2H2O, 130

−6H2O, 200 −4H2O, 185

17°

1.68

1.7 3.18020° 2.015 1.7 2.2

2 .872 3 .3 2 .36 1 .82 2 .6317° 2 .2334° 2 .24° 2 .2 3 .32 2 .220 164° 2 .306 164° 3 .14 2 .82 3 .09 2 .25 2 .5115° 2 .905 2 .915 2 .96

subl. in N2, 980 1200 ± 30

1810

1330 d. d. 675 −H2O, 580 d. −2H2O, 200 −3H2O, 100 d . 730–760 1391 561 42 .7 900 d . −H2O, 200 2570 −8H2O, 100 −H2O, 100 d . 1670 975 1230

2850 expl . 275 d . 200

32659.5° i. i. 60.8100° s. 127.660° s.

0.01325° 1250° 0.001220°† 0.001425° 59.50° s. v. s. 0.08518° s. d. s. 0.001618° 16.10° d. 0.1850° delq.; d. i. 10.5

i. 312105° 0.002100° 0.002100° 347260° s. v. s. 0.09626° d. 15090° 0.001726° 18.4100

0 .03218° i . 1020° 2660° d . 770° 0 .0006713° i . Forms Ca(OH)2 sl . s . 0 .02 0 .0025 i . i . sl . s . d . 0 .009517°

tr . 1193 to rhb .

180100°

76.50° s. 114.20° s. 350−5° 0.000001 d. 520° d.

24 .5°

>1600 1540 tr . 1190 to α 1450(mn .)

16820° 0.024718° 0.0002625° 109.70° 2150° i. i.

0 .29820°

Colloidal d. 45.580°

0.077100° d. ∞ i . 376151° v . s . d . 41790° 0 .001495° i . d . d . 0 .075100° d . i .

0 .1619100°

2.0515° m. al. s. a.; NH4OH, KCN s. a., NH4 salts; i. alk. v. s. a. s. al., NH3; i. HNO3 s. a., NH4 salts; i. alk. s. a., NH4 salts; i. alk. d. a., alk. i.act., NH3 i. al. i. al. i. al. s. a.; v. s. NH4OH s, a.; sl. s. al. sl. s. al. s. HCl s. dil. a. s. al., act.; sl. s. NH3 s. a., NH4Cl s. a., NH4Cl s. al. s. al. s. al. 0.006518° al. i. al. sl. s. a. i. al., et. d. a.; i. bz. s. NH4Cl d. a. s. HCl, H4P2O6 ∞h . al .; i . et .

1415° al .; s . amyl al ., NH3 s . dil . a .; i . abs . al . s . 90% al . s . a .; i . ac . s . a .; i . ac s . a .; i . al . s . a . d .; i . al ., et . s . a .; i . al ., ac . i . a . s . a . s . a .; i . NH4Cl s . dil . a .; i . al ., et . s . HCl s . a ., Na2S2O3, NH4 salts (Continued )

2-9

2-10

TABLE 2-1

Physical Properties of the Elements and Inorganic Compounds (Continued )

Name Calcium (Cont.) sulfate (gypsum)

Formula

Formula weight

Color, crystalline form, and refractive index

CaSO4⋅2H2O

172.17

col., mn., 1.5226

Ca(SH)2⋅6H2O CaS CaSO3⋅2H2O CaC4H4O6⋅4H2O Ca(CNS)2⋅3H2O CaS2O3⋅6H2O CaWO4

214.32 72.14 156.17 260.21 210.29 260.30 287.92

col. pr. col., cb. wh., cr., 1.595 col., rhb. wh., delq. cr. col., tri., 1.56 wh., tet., 1.9200

C C C CO2

12.01 12.01 12.01 44.01

bk., amor. col., cb., 2.4195 bk., hex. col. gas

disulfide

CS2

76.14

col. lq.

monoxide

CO

28.01

col., poisonous, odorless gas poisonous gas gas

sulfhydrate sulfide (oldhamite) sulfite tartrate thiocyanate thiosulfate tungstate (scheelite) Carbon, cf. table of organic compounds Carbon, amorphous Carbon, diamond Carbon, graphite dioxide

oxychloride (phosgene) oxysulfide suboxide thionyl chloride Ceric hydroxide hydroxynitrate oxide sulfate Cerium

COCl2 COS C3O2 CSCl2 2CeO2⋅3H2O Ce(OH)(NO3)3⋅3H2O CeO2 Ce(SO4)2⋅4H2O Ce

98.92 60.08 68.03 114.98 398.28 397.18 172.11 404.30 140.12

Cerous sulfate sulfate Cesium Chloric acid Chlorine

Ce2(SO4)3 Ce2(SO4)3⋅8H2O Cs HClO3⋅7H2O Cl2

568.42 712.54 132.91 210.57 70.91

hydrate Chloroplatinic acid Chlorostannic acid Chlorosulfonic acid Chromic acetate chloride chloride fluoride hydroxide

Cl2⋅8H2O H2PtCl6⋅6H2O H2SnCl6⋅6H2O HO⋅SO2⋅Cl Cr2(C2H3O2)6⋅2H2O CrCl3 CrCl3⋅6H2O∗ CrF3 Cr(OH)3

215.03 517.90 441.54 116.52 494.29 158.36 266.45 108.99 103.02

Cr(OH)3⋅2H2O Cr(NO3)3⋅9H2O∗ Cr(NO3)3⋅7½H2O Cr2O3 Cr2(SO4)3 Cr2(SO4)3⋅5H2O Cr2(SO4)3⋅15H2O Cr2(SO4)3⋅18H2O Cr2S3

139.05 400.15 373.13 151.99 392.18 482.26 662.41 716.46 200.19

hydroxide nitrate nitrate oxide sulfate sulfate sulfate sulfate sulfide

gas yel.-red lq. yel., gelatinous red, mn. wh. or pa. yel., cb. yel., rhb. steel gray, cb. or hex. wh., mn. or rhb. tri. silv. met., hex. lq. rhb., or gn.-yel. gas rhb. red-brn., delq. delq. col. lq. gn. pink, trig. vl. or gn., hex. pl. gn., rhb. gn. or blue, gelatinous gn. purple pr. purple, mn. dark gn., hex. rose pd. gn. vl. vl., cb., 1.564 brn.-bk. pd.

Specific gravity 2.32 2.815°

Melting point, °C −1½H2O, 128

Boiling point, °C −2H2O, 163

d. 15 −2H2O, 100 d.

d. 650

Solubility in 100 parts Cold water

Hot water

0.2230°

0.25750°

v. s. d. 0.004318° 0.0370° s. 71.29° 0.2

v. s. d. 0.002790° 0.2285° v. s. d.

Other reagents s. a., gly., Na2S2O3, NH4 salts s. al. s. a. s. H2SO3 sl. s. al. v. s. al. i. al. s. NH4Cl; i. a.

1.87316° 6.06

d.

1.8–2.1 3.5120° 2.2620° lq. 1.101−87°; 1.53 (A); solid 1.56−79° lq. 1.261 2220° ; 2.63 (A) ° lq. 0.814 −195 4 ; 0.968 (A) 1.392 194° lq. 1.24−87°; 2.10 (A) lq. 1.1140° 1.50915°

>3500 >3500 >3500 −56.65.2atm.

4200 4200 4200 subl. −78.5

i. i. i. 179.70° cc

i. i. i. 90.120° cc

i. a., alk. i. a., alk. i. a., alk. s. a., alk.

−108.6

46.3

0.20°

0.01450°

s. al.; et.

−207

−192

0.00440°; 3.50° cc v. s. sl. d. 1330° cc

0.001850° 2.3220° cc d. 40.330° cc

s. al., Cu2Cl2

7.3 3.91 6.920° cb.; 6.7 hex. 3.91 2.88617° 1.9020° 1.28214.2° lq. 1.56−33.6°; 2.490° (A) 1.23 2.431 1.97128° 1.78725° 2.75715° 1.835 254° 3.8

5.21 3.012 1.86717° 1.722° 3.7719°

756mm

−104 −138.2

8.2 −50.2760mm

−107

7761mm 73.5

1950 645

1400

d.

s. et. s. a.; sl. s. alk. carb.; i. alk

d. i. s. d. i.

i.

0°

−8H2O, 630 28.5 1000 −2H2O, 100 36.5 100 1900 100 −S, 1350

670 d. 40 −34.6

151.5765mm 1200–1500 d. d.

d. 100 d.

−10H2O, 100 −12H2O, 100

s. ac., CCl4, bs.; d.a. v. s. alk., al.

18.98 250° d. v. s. 1.460°; 31010° cc s. v. s. s. d. s. i.§ v. s. d. i. i. i. s. s. i. i.† s. s. 12020° i.

Slowly oxidized 0.4100° 7.640° 30°

0.57 ; 17730° cc v. s.

sl. s.

i. s. s. i. d. 67° d. d.

s. H2SO4, HCl s. dil. H2SO4 s. dil. a.; i. al.

s. a., al., NH3 s. alk. s. alk. s. al., et. d. al.; i. CS2 4.7615° m. al. i. a., act., CS2 s. al.; i. et. sl. s. a.; i. al., NH3 s. a., alk.; sl. s. NH3 s. a., alk. s. a., alk., al., act. sl. s. a. i. a. s. al., H2SO4 sl. s. al. s. al. s. h. HNO3

Chromium trioxide (chromic acid) Chromous chloride hydroxide oxide sulfate sulfide (daubrelite) Chromyl chloride Cobalt carbonyl sulfide, diCobaltic chloride chloride, dichro chloride, luteo chloride, praseo Cobaltic chloride, purpureo chloride, roseo hydroxide oxide sulfate sulfide Cobalto-cobaltic oxide Cobaltous acetate chloride chloride nitrate oxide sulfate sulfate sulfate (biebeorite) sulfide (syeporite) Copper Cupric acetate aceto-arsenite (Paris green) ammonium chloride

Cr

52 .00

CrO3 CrCl2 Cr(OH)2 CrO CrSO4⋅7H2O CrS CrO2Cl2 Co Co(CO)4 CoS2 CoCl3 Co(NH3)3Cl3⋅H2O Co(NH3)6Cl3 Co(NH3)4Cl3⋅H2O Co(NH3)5Cl3 Co(NH3)5Cl3⋅H2O Co(OH)3 Co2O3 Co2(SO4)3 Co2S3 Co3O4 Co(C2H3O2)2⋅4H2O CoCl2 CoCl2⋅6H2O∗ Co(NO3)2⋅6H2O

99 .99 122 .90 86 .01 68 .00 274 .17 84 .06 154 .90 58 .93 170 .97 123 .06 165 .29 234 .40 267 .48 251 .43 250 .44 268 .46 109 .96 165 .86 406 .05 214 .06 240 .80 249 .08 129 .84 237 .93 291 .03

CoO CoSO4 CoSO4⋅H2O

74 .93 155 .00 173 .01

CoSO4⋅7H2O∗ CoS Cu Cu(C2H3O2)2 Cu(C2H3O2)2⋅H2O (CuOAs2O3)3⋅ Cu(C2H3O2)2∗ CuCl2⋅2NH4Cl⋅2H2O

281 .10 91 .00 63 .55 181 .63 199 .65 1013 .79

gray, met., cb. red, rhb. wh., delq. yel.-brn. bk. pd. blue bk. pd. dark red lq. silv. met., cb. or. cr. bk., cb. red cr.

7.1

1615

2.70 2.75

197 d.

3.97 1.92 8.920° 1.7318° 4.269 2.94

1550 −96.5 1480 51 subl.

brn., cb. red pd. red pd., mn.(?), 1.639 red, mn., 1.483 brn. nd. yel.-red met., cb.

5.18

d. 100 −1½H2O, 100 d. 900

4.8 6.07 1.705318.7° 3.356 1.924 2525° 1.883 2525°

−4H2O, 140 subl. 86 1100 1083

−7H2O, 420

115

240 d.

1.98

d. 110

1.81 3.88

d. 150 d. 220

ammonium sulfate carbonate, basic (azurite)

CuSO4⋅4NH3⋅H2O 2CuCO3⋅Cu(OH)2

245 .75 344 .67

blue, tet., 1.670, 1.744 blue, rhb. blue, mn., 1.758

carbonate, basic (malachite) chloride (eriochalcite)

CuCO3⋅Cu(OH)2 CuCl2

221 .12 134 .45

dark gn., mn., 1.875 brn.-yel. pd.

3.9 3.054

d. 498

chloride chromate, basic cyanide dichromate ferricyanide ferrocyanide formate hydroxide lactate nitrate nitrate ∗Usual commercial form . † Also a soluble modification .

CuCl2⋅2H2O CuCrO4⋅2CuO⋅2H2O Cu(CN)2 CuCr2O7⋅2H2O Cu3[Fe(CN)6]2 Cu2Fe(CN)6⋅7H2O Cu(HCO2)2 Cu(OH)2 Cu(C3H5O3)2⋅2H2O Cu(NO3)2⋅3H2O∗ Cu(NO3)2⋅6H2O

170 .48 374 .66 115 .58 315 .56 614 .54 465 .15 153 .58 97 .56 277 .72 241 .60 295 .65

gn., rhb., 1.684 yel.-brn. yel.-gn. bk., tri. yel.-gn. red-brn. blue, mn. blue, gelatinous dark blue, mn. blue, delq. blue, rhb.

2.3922.4°

−2H2O, 110 −2H2O, 260 d. −2H2O, 100

277 .47

117.6 2900 d. 52

20°

1.7016 1.847 1.819 2525°

2.28618° 1.831 3.368 2.047 2.074

1049 −6H2O, 110 d.

114.5 −3H2O, 26.4

i.

164.9 v. s. d. i. 12.350° i. d. i. i. i. s. s. 4.260° v. s. 0.2320° 16.120° i. i. d. i. i. s. 457° 116.50° 84.030°(anh.) i. 25.60° s.

2300

3380° 0.0003818° i. s. 7.2 i. 33.80° 18.05 i.

Forms Cu2Cl2 993 d.

−H2O 3.9°

i. 0°

d.

or., mn. gn., rhb. rhb. brick red bk. bk. blue cr. bk. cr. bk., cb. red-vl., mn., 1.542 blue cr. red, mn. red, mn., 1.4

dark gn., mn. gn.

2200

−HNO3, 170

21.5°

206.7 v. s.

100°

i.

i. d. s. 12.7446.5° 1.03146.5° 24.8716° i. i. i. s. 10596° 17780° 334.990° (anh.) i. 83100° s. s. i.

s. HCl, dil. H2SO4; i. HNO3 s. H2SO4, al., et. sl. s. al.; i. et. s. conc. a. i. dil. HNO3 sl. s. al. v. s. a. s. et. s. a. s. al., et., CS2 s. HNO3, aq. reg. s. a.; al. i. al., NH4OH s. a.; i. al. i. al. sl. s. HCl s. a.; i. al. s. a. s. H2SO4 d. a. s. H2SO4; i. HCl, HNO3 s. a., al. 31 al.; 8.6 act. v. s. et., act. 10012.5° al.; s. act.; sl. s. NH3 s. a., NH4OH; i. al. 1.0418° m. al.; i. NH8 2.58° al. s. a., aq. reg. s. HNO3, h. H2SO4

20

7 al.; s. et.; gly. s. a., NH4OH

99.380°

s. a.

d. d.

i. al. s. NH4OH, h. aq. NaHCO3 s. KCN; 0.03 aq. CO 5315° al.; 6815° m. al.

i. 70.70°

d. 107.9100°

110.40° i. i. sl. s. i. i. 12.5 i. 16.7 38140° 243.70°

192.4100° d. i. d. d. 45100° 66680° ∞

s. al.; et., NH4Cl s. HNO3, NH4OH s. KCN, C5H5N s. a.; NH4OH s. NH4OH; i. HCl s. NH4OH; i. a., NH8 0.25 al. s. a., NH4OH, KCN, al. sl. s. al. 10012.5° al. s . al . (Continued )

2-11

2-12 TABLE 2-1

Physical Properties of the Elements and Inorganic Compounds (Continued )

Name

Formula

Formula weight

Color, crystalline form, and refractive index

Cupric (Cont.) oxide (paramelaconite) oxide (tenorite) oxychloride phosphide sulfate (hydrocyanite) sulfate (blue vitriol or chalcanthite) sulfide (covellite) tartate Cuprous ammonium iodide carbonate chloride (nantokite) cyanide

CuO CuO CuCl2⋅2CuO⋅4H2O Cu3P2 CuSO4

79 .55 79 .55 365 .60 252 .59 159 .61

CuSO4⋅5H2O∗ CuS CuC4H4O6⋅3H2O CuI⋅NH4I⋅H2O Cu2CO3 Cu2Cl2 Cu2(CN)2

249 .69 95 .61 265 .66 353 .41 187 .10 198 .00 179 .13

bk., cb. bk., tri., 2.63 blue-gn. bk. gn.-wh., rhb., 1.733 blue, tri., 1.5368 blue, hex. or mn., 1.45 1 gn. pd. rhb. pl. yel. wh., cb., 1.973 wh., mn.

ferricyanide ferrocyanide fluoride hydroxide oxide (cuprite) Cuprous phosphide sulfide (chalcocite) sulfide Cyanogen

Cu3Fe(CN)6 Cu4Fe(CN)6 Cu2F2 CuOH Cu2O Cu6P2 Cu2S Cu2S C 2 N2

402 .59 466 .13 165 .09 80 .55 143 .09 443 .22 159 .16 159 .16 52 .03

brn.-red brn.-red red cr. yel. red, cb., 2.705 gray-bk. bk., rhb. bk., cb. poisonous gas

Fe(OH)(C2H3O2)2

190 .94

brn., amor.

Cyanogen compounds, cf. table of organic compounds Ferric acetate, basic ammonium sulfate, cf. Alum chloride (molysite) chloride ferrocyanide (Prussian blue) hydroxide lactate nitrate oxide (hematite) sulfate sulfate (coquimbite) Ferroso-ferric chloride ferricyanide (Prussian green) oxide (magnetite; magnetic iron oxide) oxide, hydrated Ferrous ammonium sulfate

FeCl3 FeCl3⋅6H2O∗ Fe4[Fe(CN)6]3

162 .20 270 .30 859 .23

bk.-brn., hex. delq. red-yel., delq. dark blue

Fe(OH)3 Fe(C3H5O3)3 Fe(NO3)3⋅6H2O Fe2O3

106 .87 323 .06 349 .95 159 .69

red-brn . brn ., amor ., delq . rhb ., delq . red or bk ., trig ., 3 .042 rhb ., 1 .814 yel ., trig . yel ., delq . gn . bk ., cb ., 2 .42

Fe2(SO4)3 Fe2(SO4)3⋅9H2O FeCl2⋅2FeCl3⋅18H2O Fe4Fe3[Fe(CN)6]6 Fe3O4

399 .88 562 .02 775 .43 1662 .61 231 .53 303 .59 392 .14

chloride (lawrencite)

Fe3O4⋅4H2O FeSO4⋅(NH4)2SO4⋅ 6H2O FeCl2

chloroplatinate ferricyanide (Turnbull’s blue) ferrocyanide formate hydroxide nitrate oxide

FePtCl6⋅6H2O Fe3[Fe(CN)6]2 Fe2Fe(CN)6 Fe(HCO2)2⋅2H2O Fe(OH)2 Fe(NO3)2⋅6H2O FeO

571 .73 591 .43 323 .64 181 .91 89 .86 287 .95 71 .84

126 .75

bk . blue-gn ., mn ., 1 .4915 gn .-yel ., hex ., 1 .567 yel ., hex . dark blue blue-wh ., amor .

Specific gravity 6.40 6.45 6.35 3.60615°

Melting point, °C d. 1026 d. 1026 −3H2O, 140 d. d. >600

° 2.286 15.6 4 4.6

−4H2O, 110 tr. 103 d.

4.4 3.53 2.9

d. 422 474.5

3.4 6.0 6.4 to 6.8 5.6 5.80 lq. 0.866−17.2°; 1.806 (A)

908 −½H2O, 360 1235 1100 1130 −34.4

Forms CuO, 650 −5H2O, 250 d. 220

1366 d.

subl. 1100 −O, 1800

−20.5

Solubility in 100 parts Cold water i. i. i. i. 14.30° 24.30° 0.00003318° 0.0215° d. i. 1.5225° i. i. i. i. i. i. i. 0.000518° 0.000518° 45020° cc

Hot water i. i. 75.4100° 205100° 0.1485° i. i.

i. i.

i. 11°

2.804

282 37 d .

3 .4 to 3 .9

−1½H2O, 500

1 .68420° 5 .12

35 1560 d .

3 .09718° 2 .1

d . 480

315 280

d .

Other reagents s. a.; KCN, NH4Cl s. a., KCN, NH4Cl s. a. s. HNO3; i. HCl i. al. 1.18° al. s. HNO3, KCN s. a., KOH s. NH4I s. a., NH4OH s. HCl, NH4OH, al. s. KCN, HCl, NH4OH; sl. s. NH3 s. NH4OH; i. HCl s. NH4OH; i. NH4Cl s. HF, HCl, HNO3; i. al. s. a., NH4OH s. HCl, NH4Cl, NH4OH s. HNO3; i. HCl s. HNO3, NH4OH; i. act. s. HNO3, NH4OH; i. act. 230020° cc al.; 50018° cc et.

s. a.; al. 0°

100°

74.4 2460° i .

535.8 ∞ d .

v. s. al.; et. +HCl s . al ., act ., gly . s . HCl, conc . H2SO4; i . al ., et . s . a .; i . al ., et . i . et . s . al ., act . s . HCl

i . v . s . 1500° i .

i . v . s . ∞ d . d . s . i .

s . d . h . HCl i . al .

5 .2

d . 50 d . 180 1538 d .

sl . s . 440 s . i . i .

1 .864

d . d .

i . 180°

i . 10075°

s . a . i . al .

64 .410°

105 .7100°

100 al .; s . act .; i . et .

v . s . i . i . sl . s . 0 .00067 2000° i .

v . s .

2 .7

delq .

2 .714 d . d .

lt . gn . cr . bk .

Boiling point, °C

3 .4 5 .7

60 .5 1420

i . H2SO4, NH3 s . abs . al .

i . dil . a ., al .

30025° i .

s . a ., NH4Cl s . a .; i . alk .

phosphate (vivianite)

Fe3(PO4)2⋅8H2O

501 .60

silicate sulfate (siderotilate) sulfate (copperas) sulfide cf. also under iron Fluoboric acid Fluorine

FeSiO3 FeSO4⋅5H2O FeSO4⋅7H2O∗ FeS

131 .93 241 .98 278 .01 87 .91

HBF4 F2

87 .81 38 .00

Fluosilicic acid Gadolinium Gallium bromide Glucinum cf. Beryllium Gold Gold, colloidal Gold salts cf. under Auric and Aurous Hafnium Helium Hydrazine formate hydrate hydrochloride hydrochloride, dinitrate nitrate, disulfate sulfate Hydrazoic acid (azoimide) Hydriodic acid Hydriodic acid Hydriodic acid Hydriodic acid Hydriodic acid Hydrobromic acid Hydrobromic acid

H2SiF6 Gd GaBr3

144 .09 157 .25 309 .44

delq . cr .

Au Au

196 .97 196 .97

yel . met ., cb . blue to vl .

19 .320°

1063

2600

Hf He N2H4 N2H4⋅2HCO2H N2H4⋅H2O N2H4⋅HCl N2H4⋅2HCl N2H4⋅HNO3 N2H4⋅2HNO3 N2H4⋅½H2SO4 N2H4⋅H2SO4 HN3 HI HI⋅H2O HI⋅2H2O HI⋅3H2O HI⋅4H2O HBr HBr⋅H2O

178 .49 4 .00 32 .05 124 .10 50 .06 68 .51 104 .97 95 .06 158 .07 81 .08 130 .12 43 .03 127 .91 145 .93 163 .94 181 .96 199 .97 80 .91 98 .93

hex . col . gas col . lq . cb . col . yel . lq . wh ., cb . cr . nd . delq . pl . rhb . col . lq . col . gas col . lq . col . lq . col . lq . col . lq . col . gas; 1 .325 (lq .) col . lq .

12 .1 0 .1368 (A) 1 .011 154°

>1700 3200(?) −268 .9 113 .5

Hydrobromic acid Hydrobromic acid Hydrochloric acid Hydrochloric acid Hydrochloric acid Hydrochloric acid Hydrocyanic acid (prussic acid)

HBr (47 .8% in H2O) HBr⋅2H2O HCl† HCl (45 .2% in H2O) HCl⋅2H2O HCl⋅3H2O HCN

80 .91 118 .96 36 .46 36 .46 72 .49 90 .51 27 .03

Hydrofluoric acid Hydrofluoric acid Hydrogen

HF HF (35 .35% in H2O) H2

20 .01 20 .01 2 .02

col . lq . wh . cr . col . gas; 1 .256 (lq .) col . lq . col . lq . col . lq . poisonous gas or col . lq ., 1 .254 gas or col . lq . col . lq . col . gas or cb .

peroxide selenide sulfide Hydroxylamine hydrochloride nitrate sulfate

‡

H2O2 H2Se H2S NH2OH NH2OH⋅HCl NH2OH⋅HNO3 NH2OH⋅½H2SO4

∗Usual commercial form . † Usual commercial form about 31 percent . ‡ Usual commercial forms 3 or 30 percent .

34 .01 80 .98 34 .08 33 .03 69 .49 96 .04 82 .07

blue, mn., 1.592, 1.603 mn. gn., tri., 1.536 blue-gn., mn. bk., hex. col. lq. gn .-yel . gas

col . lq ., 1 .333 col . gas col . gas rhb ., delq . col ., mn . col . cr . col ., mn .

2.58 3.5 2.2 1.89914.8° 4.84 lq . 1 .51−187°; 1 .3115° (A)

1 .0321° 1 .42

1 .378 4 .40° (A) 1 .715°

2 .710° (A) 1 .78 1 .486 2 .11−15° 1 .2680° (A) 1 .48 ° 1 .46 −18.3 4 0 .69718° 0 .98813 .6° 1 .15 lq . 0 .0709−252 .7° 0 .06948 (A) 1 .438 204° 2 .12−42° 1 .1895 (A) 1 .3518° 1 .6717°

1550

i.

i.

s. a.; i. ac.

64 1193

−5H2O, 300 −7H2O, 300 d.

s. 32.80° 0.00061618°

s. 14950°

i. al. i. al. s. a.; i. NH3

130 d. −187

∞ d .

∞

s . al .

−223

s .

s .

s .

s .

i . s .

i .

s . aq . reg ., KCN; i . a . s . aq . reg ., KCN; i . a .

0 .970° cc ∞ s . ∞ v . s . s . 174 .910° v . s . v . s . 3 .05522° ∞ 42,50010° cc ∞ ∞ ∞ ∞ 2210°

1 .0850° cc ∞

Absorbed by Pt s . al .

∞ v . s . v . s . v . s .

∞ al .; i . et . sl . s . al . s . al .

198 70 .7 104 85 254 −80 −50 .8 −43 −48 −36 .5 −86

118 .5739 .5mm subl . 140 d . 37 −35 .5 127774mm

−67

126 −11 −111 −15 .35 0 −24 .4 −14 −83 −35 −259 .1 −0 .89 −64 −82 .9 34 151 48 170 d .

27 .6560° ∞ v . s .

130100°

i . al . v . sl . s . abs . al . ∞ al . s . al . ∞ al . s . al . s . al . s . al . s . al . Stable at −15 .5° and 1 atm ., and at −11 .3° and 2 .5 atm . s . al .

d . d . 26

∞ s . 82 .30° ∞ ∞ ∞ ∞

19 .4 120 −252 .7

∞ 0° to 19 .4° v . s . 2 .10° cc

0 .8580° cc

sl . s . Fe, Pd, Pt

∞ 3774° cc 4370° cc s . 83 .317° v . s . 32 .90°

27022 .5° cc 18640° cc d . v . s . d . 68 .590°

s . a ., et .; i . petr . et s . CS2, COCl2 9 .5415° cc al .; s . CS2 s . a ., al . s . al .; i . et . v . s . abs . al . v . sl . s . al .; i . et ., abs . al .

−85

760mm

151 .4 −42 −59 .6 56 .522mm d . d . 560 tr. 450 1171 d. >700

d. d.

−151.8 1800 1620

>4800 3000

102.5760mm

i. i. i. i. i. i. i. i.

11.050° cc d. i.

3.5760° cc

280 −3H2O, 75 22

19.70° 45.6415° s. v. s. v. s.

22150° 200100° s.

5.55

18.2

d. 140 d. >200

d. i. d. i. i. 0.45540°

d. 0.05100° 4.75100°

0.0001120° i.

d. i.

d. 190 −H2O, 130 d. 470

0.6730° 0.00000720° i. 1.616° 0.014 38.80°

3.34100° i. i. 18100° d.

d. red heat 888

i. 0.006818°

i.

col. gas lead gray silv. met., cb.

2.818 (A) 6.1520° 11.337 2020°

−169 826 327.5

Pb(C2H3O2)2 Pb(C2H3O2)2⋅3H2O† Pb(C2H3O2)2⋅10H2O Pb2(C2H3O2)3OH Pb(C2H3O2)2⋅ Pb(OH)2⋅H2O Pb(C2H3O2)2⋅ 2Pb(OH)2 PbH4(AsO4)2 PbHAsO4 Pb(AsO3)2 Pb2As2O7 PbN6 PbBr2

325.29 379.33 505.44 608.54 584.52

wh. cr. wh., mn. wh., rhb. wh. wh. nd.

3.251 204° 2.55 1.689

807.72

wh. nd.

489.07 347.13 453.04 676.24 291.24 367.01

tri., 1.82 wh., mn., 1.9097 hex. rhb., 2.03 col. nd. col., rhb.

4.4615° 5.94 6.4215° 6.85 1515° 6.66

802 expl. 350 373

carbonate (cerussite) carbonate, basic (hydrocerussite; white lead) chloride (cotunnite) chromate (crocoite) chromate, basic formate hydroxide nitrate

PbCO3 2PbCO3⋅Pb(OH)2†

267.21 775.63

wh., rhb., 2.0763 wh., hex.

6.6 6.14

d. 315 d. 400

PbCl2 PbCrO4 PbCrO4⋅PbO Pb(HCO2)2 3PbO⋅H2O Pb(NO3)2

278.11 323.19 546.39 297.23 687.61 331.21

5.80 6.12

501 844

4.56 7.592 4.53

oxide, suboxide, mono- (litharge)

Pb2O PbO

430.40 223.20

wh., rhb., 2.2172 yel., mn., 2.42 or.-yel. nd. wh., rhb. cb. col., cb. or mn., 1.7815 bk., amor. yel., tet.

8.34 9.53

oxide, mono (massicotite)

PbO

223.20

yel., rhb., 2.61

8.0

arsenate, monobasic arsenate, dibasic (schultenite) arsenate, metaarsenate, pyroazide bromide

Hot water

s. i. 2860°

155 110 d.

83.80 138.91 207.20

acetate, basic

Solubility in 100 parts Cold water

4050mm 1450

7.320° 4.6290°

Kr La Pb

acetate acetate (sugar of lead) acetate acetate, basic acetate, basic

Boiling point, °C

−H2O, 280

918

954760mm d.

i.

sl. s.

138.8100°

Other reagents s. a. v. s. 87% al.; i. abs. al. et., chl. s. al., KI, et. i. abs. al., et., chl. sl. s. aq. reg., aq. Cl2 s. a.; i. alk. s. a.; i. alk. s. a.; i. alk. s. a.; i. alk. s. a.; i. alk. s. a. s. al., H2SO4, alk. s. HCl, H2SO4 i. aq. reg. i. dil. a. i. dil. a.

sl. s. al., bz. s. a. s. HNO3; i. c. HCl, H2SO4 s. gly.; v. sl. s. al. s. gly.; sl. s. al. sl. s. al. s. al. s. al. s. HNO3 s. HNO3, NaOH s. HNO3 s. HCl, HNO3; i. sc. v. s. ac.; i. NH4OH s. a., KBr.; sl. s. NH3; i. al. s. a., alk.; i. NH3, al. s. ac.; sl. s. aq. CO2 sl. s. dil. HCl, NH3, i. al. s. a., alk.; i. NH3, ac. s. a., alk. i. al. s. a., alk. 8.822° al. s. a., alk. s. alk., PbAc, NH4Cl, CaCl2

oxide, mono-

PbO

223 .20

amor.

9.2 to 9.5

oxide, red (minium) oxide, sesquioxide, di- (plattnerite) silicate sulfate (anglesite)

Pb3O4 Pb2O3 PbO2 PbSiO3 PbSO4

685 .60 462 .40 239 .20 283 .28 303 .26

9.1

Pb(HSO4)2 ⋅H2O PbSO4⋅PbO PbS Pb(CNS)2 Li LiC7H5O2 LiBr

419 .36 526 .46 239 .27 323 .36 6 .94 128 .05 86 .85

LiBr⋅2H2O Li2CO3 LiCl

122 .88 73 .89 42 .39

citrate fluoride formate hydride hydroxide hydroxide nitrate nitrate oxide phosphate, monobasic phosphate, tribasic phosphate, tribasic salicylate sulfate sulfate sulfate, acid Lutecium Magnesium acetate acetate aluminate (spinel)

Li3C6H5O7⋅4H2O LiF LiHCO2⋅H2O LiH LiOH LiOH⋅H2O LiNO3 LiNO3⋅3H2O Li2O LiH2PO4 Li3PO4 Li3PO4⋅12H2O LiC7H5O3 Li2SO4 Li2SO4⋅H2O† LiHSO4 Lu Mg Mg(C2H3O2)2 Mg(C2H3O2)2⋅4H2O† MgO⋅Al2O3

281 .98 25 .94 69 .97 7 .95 23 .95 41 .96 68 .95 122 .99 29 .88 103 .93 115 .79 331 .98 144 .05 109 .94 127 .96 104 .01 174 .97 24 .31 142 .39 214 .45 142 .26

red, amor. red-yel., amor. brn., tet., 2.229 col., mn., 1.961 wh., mn. or rhb., 1.8823 cr. col., mn. lead gray, cb., 3.912 col., mn. silv. met. cb. wh. leaflets wh., delq., cb., 1.784 wh. pr. col., mn., 1.567 wh., delq., cb., 1.662 wh. cr. wh., cb., 1.3915 col., rhb. wh., cb. wh. cr. col., mn. col., trig., 1.735 col. col ., 1 .644 col . wh ., rhb . wh ., trig . col . col ., mn ., 1 .465 col ., mn ., 1 .477 pr .

ammonium chloride ammonium phosphate (struvite) ammonium sulfate (boussingaultite) benzoate carbonate (magnesite) carbonate (nesquehonite) carbonate, basic (hydromagnesite) Magnesium chloride (chloromagnesite) chloride (bischofite) hydroxide (brucite) nitride oxide (magnesia; periclase) perchlorate

MgCl2⋅NH4Cl⋅6H2O MgNH4PO4⋅6H2O

256 .79 245 .41

sulfate, acid sulfate, basic (lanarkite) sulfide (galena) thiocyanate Lithium benzoate bromide bromide carbonate chloride

∗See also a table of alloys . † Usual commercial form .

MgSO4⋅(NH4)2SO4⋅ 6H2O Mg(C7H5O2)2⋅3H2O MgCO3 MgCO3⋅3H2O 3MgCO3⋅Mg(OH)2⋅3H2O MgCl2 †

MgCl2⋅6H2O Mg(OH)2 Mg3N2 MgO Mg(ClO4)2†

360 .60

i.

i.

9.375 6.49 6.2

d. 500 d. 360 d. 290 766 1170

i. i. i. i. 0.00280°

i. i. i.

6.92 7.5 3.82 0.5320°

d. 977 1120 d. 190 186

1336 ± 5

25 ° 4

547

1265

0.000118° 0.004418° 0.0000918° 0.0520° d. 3325° 1430° (2H2O)

2.110° 2.068 254°

44 618 614

d. 1360

24620° 1.540° 670°

3.464

2.29521.5° 1.46 0.820 2.54 1.83 2.38 2 .013 254° 2 .461 2 .53717 .5° 1 .645

d. 870 −H2O, 94 680 445 261 29.88

2 .22 2 .06 2 .12313°

silv . met ., hex . wh . wh ., mn . pr ., 1 .491 col . cb ., 1 .718–23

1 .7420° 1 .42 1 .454 3 .6

651 323 80 2135

wh ., rhb ., delq . col ., rhb ., 1 .496

1 .456 1 .715

−4H2O, 195 d . 100

1 .72

wh . pd . wh ., trig . 1 .700 col ., rhb ., 1 .501 wh ., rhb ., 1 .530

3 .037 1 .852 2 .16

−3H2O, 110 d . 350 −H2O, 100 d .

95 .21

col ., hex ., 1 .675

2 .32525°

712

wh ., delq ., mn ., 1 .507 wh ., trig ., 1 .5617 gn .-yel ., amor . col ., cb ., 1 .7364 wh ., delq .

1 .56 2 .4 3 .65 2 .6025°

1110

>120

320 .58 84 .31 138 .36 365 .31

203 .30 58 .32 100 .93 40 .30 223 .21

925± d. subl . 100 837 100 d . 860 −H2O, 130 170 .5

col ., mn .

1670

118 d . d . d . 2800 d .

3600

0.72100° 127.5100° 66.7100° 0.13535° 346.6104°

0 .03418° v . sl . s . 12826° 35 .340° 43 .60° d .

v . sl . s . v . sl . s .

i . v . s . v . s . i .

sl . s . d . v . s . v . s .

16 .7 0 .02310°

s . 0 .019580°

0°

25°

d .

i. s. d. 40100° 266100° (1H2O)

61.215° 0.2718° 49.20° d. 12.70° 22.310° 53.40° v. s. forms LiOH

16 .86

1412

0.005640°

17.5100° 26.880° 19470° ∞

29 .9100° 35100°

s. alk., PbAc, NH4Cl, CaCl2 s. ac., h. HCl s. a., alk. s. ac., h. alk.; i. al. s. a. s. conc. a., NH4 salts; i. al. sl. s. H2SO4 sl. s. H2SO4 s. a.; i. alk. s. KCNS, HNO3 s. a., NH3 7.725°, 1078° al. s. al., act. s. al. s. dil. a.; i. al., act., NH3 2.4815° al.; s. et. sl. s. al., et. s. HF; i. act. sl. s. al., et. i. et. sl. s. al. sl. s. al. s. al., NH3

s . a ., NH4Cl; i . act . v . s . al . i . act ., 80% al . i . 80% al . s . a ., NH4 salts 5 .2515° m . al . v . s . al . v . sl . s . dil . HCl; i . dil . HNO3 s . a .; i . al .

100°

130

4 .5 (anh .) 0 .0106 0 .151819° 0 .04

d . 0 .011

s . act . s . a ., aq . CO2; i . act ., NH3 s . a ., aq . CO2 s . a ., NH4 salts; i . al .

52 .80°

73100°

50 al .

0°

281 0 .000918° i . 0 .00062 99 .625°

s .

100°

918 d . v . s .

50 al . s . NH4 salts, dil . a . s . a .; i . al . s . a ., NH4 salts; i . al . 2425 al ., 51 .825° m . al .; 0 .29 et . (Continued )

2-15

2-16 TABLE 2-1

Physical Properties of the Elements and Inorganic Compounds (Continued )

Name Magnesium (Cont.) peroxide phosphate, pyrophosphate, pyropotassium chloride (carnallite) potassium sulfate (picromerite) silicofluoride sodium chloride sulfate sulfate (epsom salt; epsomite) Manganese acetate acetate carbonate (rhodocrosite)

Formula

Formula weight

Color, crystalline form, and refractive index

Specific gravity

Melting point, °C

2.59822° 2.56 ° 1.60 19.4 4 2.15 ° 1.788 17.5 4

expl. 275 1383 −3H2O, 100 265 d. 72 d.

MgO2 Mg2P2O7 Mg2P2O7⋅3H2O MgCl2⋅KCl⋅6H2O MgSO4⋅K2SO4⋅6H2O MgSiF6⋅6H2O MgCl2⋅NaCl⋅H2O MgSO4 MgSO4⋅7H2O∗ Mn Mn(C2H3O2)2 Mn(C2H3O2)2⋅4H2O∗ MnCO3

56 .30 222 .55 276 .60 277 .85 402 .72 274 .47 171 .67 120 .37 246 .47 54 .94 173 .03 245 .09 114 .95

wh. pd. col., mn., 1.604 wh., amor. delq., rhb., 1.475 mn., 1.4629 col., trig., 1.3439 col. col. col., rhb., 1.4554 gray-pink met.

chloride (scacchite) chloride

MnCl2 MnCl2⋅4H2O∗

125 .84 197 .91

chloride, perhydroxide (ous) (pyrochroite) hydroxide (ic) (manganite) nitrate oxide (ous) (manganosite) oxide (ic) oxide, di- (pyrolusite; polianite) sulfate (ous) sulfate (ous) (szmikite)

MnCl4 Mn(OH)2 Mn2O3⋅H2O Mn(NO3)2⋅6H2O MnO Mn2O3 MnO2∗

196 .75 88 .95 175 .89 287 .04 70 .94 157 .87 86 .94

rose, delq., cb. rose red, delq., mn. 1 .575 gn . wh ., trig . brn ., rhb ., 2 .24 rose red, mn . gray-gn ., cb ., 2 .16 brn .-bk ., cb . bk ., rhb .

MnSO4 MnSO4⋅H2O

151 .00 169 .02

red-wh . pa . pink, mn ., 1 .595

sulfate (ous)

MnSO4⋅2H2O

187 .03

2 .52615° 15°

sulfate (ous)

MnSO4⋅3H2O

205 .05

sulfate (ous)

MnSO4⋅4H2O∗

223 .06

pa. pink, mn. rose, trig., 1.817

2.66 1.68 7.220° 1.74 204° 1.589 3.125

1185 70 d. 1260

2.977 254° 2.01

650 58.0

3 .25818° 3 .258 1 .8221° 5 .18 4 .81 5 .026

d . d . 25 .8 1650 −0, 1080 −0, >230

3 .235 2 .87

700 Stable 57 to 117 Stable 40 to 57

2 .356 pink, rhb . or mn ., 1 .518 pink, tri ., 1 .508

2 .107 15°

sulfate (ous)

MnSO4⋅5H2O

241 .08

sulfate (ous)

MnSO4⋅6H2O

259 .09

sulfate (ous)

MnSO4⋅7H2O

277 .11

pink, mn . or rhb .

2 .092

Mn2(SO4)3 Hg(C2H3O2)2 HgBr2 HgCO3⋅2HgO HgCl2 Hg(CNO)2 Hg(OH)2 HgO HgCl2⋅3HgO HgSiF6⋅HgO⋅3H2O HgSO4 HgSO4⋅2HgO HgC2H3O2 HgBr Hg2CO3

398 .06 318 .68 360 .40 693 .78 271 .50 284 .62 234 .60 216 .59 921 .26 613 .30 296 .65 729 .83 259 .63 280 .49 461 .19

gn ., delq . cr . wh . pl . wh ., rhb . brn .-red wh ., rhb ., 1 .859 cb .

3 .24 3 .270 6 .053

yel . or red, rhb ., 2 .5 yel ., hex . yel . nd . wh ., rhb . yel ., tet . wh . sc . wh ., tet . yel . pd .

11 .14 7 .93

sulfate (ic) Mercuric acetate bromide carbonate, basic chloride (corrosive sublimate) fulminate hydroxide oxide (montroydite) oxychloride (kleinite) silicofluoride, basic sulfate sulfate, basic (turpeth) Mercurous acetate bromide carbonate

2 .103

5 .44 4 .42

6 .47 6 .44 7 .307

Boiling point, °C

Hot water i. i. sl. s. d. 81.775° s. s. 68.3100° 17840°

63.40° 1518°

123.8100° ∞

s. al., m. al. s. aq. CO2, dil. a.; l. NH3, al. s. al.; i. et., NH3 s . al .; i . et .

129 .5

s . 0 .00220° i . 4260° i . i . i .

s . i . i . ∞ i . i . i .

s . al ., et . s . a ., NH4 salts; i . alk . s . h . H2SO4 v . s . al . s . a ., NH4Cl s . a .; i . act . s . HCl; i . HNO3, act .

d . 850

530° 98 .4748°

7350° 79 .77100°

s . al .; i . et .

85 .2735°

106 .855°

1900

1190 −H2O, 106; −4H2O, 200

5°

Stable 30 to 40 −4H2O, 450

s. 64.550°

74 .22

99 .3157°

13616°

16950°

5°

142

200

Stable −5 to +8 Stable −10 to −5; 19 d . d . 160 d . 237

2040°

2479°

1760°

25114°

v . s . 2510° 0 .520° i . 3 .60° sl . s . i . 0 .005225° i . d . d . 0 .005 0 .7513° 7 × 10−9 i .

d . 100100° 25100°

d . d . subl . 345 d . 130

−7H2O, 280

322 304

s. a. s. a.; i. alk. s. a.; i. al. d. al. d. HF s. al. s. al. s. dil. a.

i . al .

35°

Stable 8 to 18

277 expl . −H2O, 175 d . 100 d . 260

Other reagents

i. i. i. 64.519° d. 19.260° 64.817.5° s. 26.90° 72.40° d. s. s. 0.006525°

d.

Stable 18 to 30

Solubility in 100 parts Cold water

61 .3100° i . 0 .041100° d . 0 .167100° d . i . d .

s . HCl, dil . H2SO4; l . s . al . sl . d . 25 .20° al .; v . sl . s . et . s . aq . CO2, NH4Cl 3325° 99% al .; 33 et . s . NH4OH, al . s . a . s . a .; i . al . s . HCl s . a . s . a .; i . al ., act ., NH8 s . a .; i . al . s . H2SO4, HNO3; i . al . s . a .; i . al ., act . s . NH4Cl

HgCl

236 .04

wh., tet., 1.9733

7.150

302

383.7

0.00140°

0.000743°

iodide nitrate Mercurous oxide

HgI HgNO3⋅H2O Hg2O

327 .49 280 .61 417 .18

yel., tet. wh. mn. bk.

7.70 4.7853.9° 9.8

290 d. 70 d. 100

subl. 140; 310d. expl.

2 × 10−8 v. s. i.

v. sl. s. d. 0.0007

sulfate Mercury† Molybdenum

Hg2SO4 Hg Mo

497 .24 200 .59 95 .94

wh., mn. silv. lq. or hex.(?) gray, cb.

7.56 13.54620° 10.2

d. −38.87 2620 ± 10

0.05516.5° i. i.

0.092100° i. i.

MoCl2

166 .85

yel., amor.

3.714 254°

d.

i.

i.

25 ° 4

d.

i.

d.

chloride (calomel)

MoCl3

202 .30

dark red pd.

chloride, tetra-

MoCl4

237 .75

brn., delq.

volt.

d.

s.

d.

chloride, penta-

MoCl5

273 .21

bk. cr.

2.928 254°

194

268

s.

d.

MoO3 MoS2 MoS3 MoS4 H2MoO4 H2MoO4⋅H2O Nd Ne

143 .94 160 .07 192 .14 224 .20 161 .95 161 .95 144 .24 20 .18

col., rhb. bk., hex., 4.7 red-brn. brn. pd. yel-wh., hex. yel., mn. yellowish col. gas

4.5019.5° 4.80114°

795 1185 d. d. d. 115 −H2O, 70 840 −248.67

subl.

0.10718° i. sl. s. i. v. sl. s. 0.13318° d. 2.60° cc

2.10679° i. s. i. sl. s. 2.1370°

s. aq. reg., Hg(NO3)2; sl. s. HNO3, HCl; i. al., etc. s. KI; i. al. s. HNO3; i. al., et. s. h. ac.; i. alk., dil. HCl, NH3 s. H2SO4, HNO3 s. HNO3; i. HCl s. h. conc. H2SO4; i. HCl, HF, NH3, dil. H2SO4, Hg s. HCl, H2SO4, NH4OH, al., et. s. HNO3, H2SO4; v. sl. s. al., et. s. HNO3, H2SO4; sl. s. al., et. s. HNO3, H2SO4; i. abs. al., et. s. a., NH4OH s. H2SO4, aq. reg. s. alk. sulfides s. alk. sulfides; i. NH3 s. NH4OH, H2SO4; i. NH s. a., NH4OH, NH4, salts

1.145° cc

s. lq. O2, al., act., bz.

i.

s. dil. HNO3; sl. s. H2SO4, HCl; i. NH3 i. al.

chloride, dichloride, tri-

oxide, tri- (molybdite) sulfide, di- (molybdenite) sulfide, trisulfide, tetraMolybdic acid Molybdic acid Neodymium Neon Neptunium Nickel acetate ammonium chloride ammonium sulfate

Np Ni

239

239 .05 58 .69

1.798 1.645 1.923

d.

2.575 4.64 284°

carbonyl chloride chloride

170 .73 129 .60 237 .69

chloride, ammonia cyanide dimethylglyoxime

NiCl2⋅6NH3 Ni(CN)2⋅4H2O NiC8H14O4N4

lq. yel., delq. gn., delq., mn., 1.57±

231 .78 182 .79 288 .91

gn. pl. scarlet red cr.

formate hydroxide (ic) hydroxide (ous) nitrate nitrate, ammonia oxide, mono- (bunsenite)

Ni(HCO2)2⋅2H2O Ni(OH)3 Ni(OH)2⋅¼H2O Ni(NO3)2⋅6H2O Ni(NO3)2⋅4NH3⋅2H2O NiO

184 .76 109 .72 97 .21 290 .79 286 .86 74 .69

2-17

potassium cyanide sulfate ∗Usual commercial form . † See also Tables 2-28 and 2-280 .

Ni(CN)2⋅2KCN⋅H2O NiSO4

258 .97 154 .76

1.3117° 3.544

gn. cr. bk. lt. gn. gn., mn.

4.36 2.05

gn .-bk ., cb ., 2 .37

7 .45

red yel ., mn . yel ., cb .

2.154

11°

1 .875 3 .68

−245.9

Produced by Neutron bombardment of U 1452 2900 i.

gn. pr. gn., delq., mn. blue-gn., mn., 1.5007 gn., cb. yel., delq. gn., delq. vl. pd. trig. lt. gn., rhb. lt. gn.

1.837 3.715

−2H2O, 200

238

8.9020

176 .78 291 .18 394 .99 422 .59 218 .50 272 .55 320 .68 841 .29 118 .70 587 .59

3.12415° 6.920° lq. 1.204−245.9° 0.674 (A)

silv. met., cb.

Ni(C2H3O2)2 NiCl2⋅NH4Cl⋅6H2O NiSO4⋅(NH4)2SO4⋅ 6H2O Ni(BrO3)2⋅6H2O NiBr2 NiBr2⋅3H2O NiBr2⋅6NH3 NiPtBr6⋅6H2O NiCO3 2NiCO3⋅3Ni(OH)2⋅ 4H2O Ni(CO)4 NiCl2 NiCl2⋅6H2O∗

bromate bromide bromide bromide, ammonia bromoplatinate carbonate carbonate, basic

3.578

356.9 3700

16.6 15025° 2.53.5°

v. s. 39.288°

d. d. −3H2O, 200

28 112.80° 1999° v. s.

156100° 316100° d.

s. NH4OH s. al., et., NH4OH s. al., et., NH4OH i. c. NH4OH

d. d.

0.009325° i.

i. d.

s. a. s. a., NH4 salts

0.0189.8° 53.80° 180

i. 87.6100° v. s.

s. aq. reg., HNO3, al., et. s. NH4OH, al.; i. NH3 v. s. al.

s. i. i.

d. i. i.

s. NH4OH; i. al. s. KCN; i. dil. KCl s. abs. al., a.; i. ac., NH4OH

i. v. sl. s. ∞56 .7°

−25 subl.

43751mm 973

−4H2O, 200 subl. 250

d.

d. d. d. 56.7 Forms Ni2O3 at 400 −H2O, 100 −SO3, 840

136.7

v. sl. s. (NH4)2SO4

s. i. v. sl. s. 243.00° v . s . i .

i .

s. a., NH4OH, NH4Cl s. a., NH4OH; i. alk. s . NH4OH; i . abs . al . i . al . s . a ., NH4OH

s . 27 .20°

76 .7100°

d . a . i . al ., et ., act . (Continued )

2-18

TABLE 2-1

Physical Properties of the Elements and Inorganic Compounds (Continued )

Name

Formula

Formula weight

Color, crystalline form, and refractive index

Nickel (Cont.) sulfate

NiSO4⋅6H2O∗

262 .85

sulfate (morenosite) Nitric acid Nitric acid Nitric acid Nitro acid sulfite Nitrogen

NiSO4⋅7H2O HNO3 HNO3⋅H2O HNO3⋅3H2O NO2HSO3 N2

280 .86 63 .01 81 .03 117 .06 127 .08 28 .01

Nitrogen oxide, mono- (ous)

N2O

44 .01

col . gas

oxide, di- (ic)

NO or (NO)2

col . gas

oxide, tri-

N2O3

30 .01 60 .01 76 .01

gn. mn. or blue, tet., 1.5109 gn., rhb., 1.4893 col. lq. col . lq . col . lq . col ., rhb . col . gas or cb . cr .

red-brn . gas or blue lq . or solid yel . lq ., col . solid, red-brn . gas wh ., rhb .

oxide, tetra- (per- or di-)

NO2 or (NO2)2

oxide, penta-

N2O5

46 .01 92 .01 108 .01

oxybromide oxychloride

NOBr NOCl

109 .91 65 .46

brn . lq . red-yel . lq . or gas

Nitroxyl chloride Osmium chloride, dichloride, trichloride, tetraOxygen

NO2Cl Os OsCl2 OsCl3 OsCl4 O2

81 .46 190 .23 261 .14 296 .59 332 .04 32 .00

yel .-brn . gas blue, hex . gn ., delq . brn ., cb . red-yel . nd . col . gas or hex . solid

Ozone

O3

48 .00

Palladium

Pd

106 .42

silv . met ., cb .

PdBr2 PdCl2 PdCl2⋅2H2O Pd(CN)2

266 .23 177 .33 213 .36 158 .45

brn . brn ., cb . brn . pr . yel .

Pd2H Pd(NH3)2Cl2 HClO4 HClO4⋅H2O HClO4⋅2H2O∗ 73 .6% anh . HIO4 HIO4⋅2H2O HMnO4 HMoO4⋅2H2O H2S2O8 PONH2⋅(OH)2 H7P(Mo2O7)6⋅28H2O PH3

213 .85 211 .39 100 .46 118 .47 136 .49

met . red or yel ., tet . unstable, col . lq fairly stable nd . stable lq ., col .

bromide (ous) chloride chloride cyanide hydride Palladous dichlorodiammine Perchloric acid Perchloric acid Perchloric acid Periodic acid Periodic acid Permanganic acid Permolybdic acid Persulfuric acid Phosphamic acid Phosphatomolybdic acid Phosphine Phosphonium chloride

PH4Cl

191 .91 227 .94 119 .94 196 .98 194 .14 97 .01 2365 .71 34 .00 70 .46

col . gas

wh . cr . delq ., mn . exists only in solution wh . cr . hyg . cr . cb . yel . cb . col . gas wh ., cb .

Specific gravity

Melting point, °C

Boiling point, °C

Solubility in 100 parts Cold water

Hot water

Other reagents

2.07

tr. 53.3

−6H2O, 280

13150°

280100°

v. s. NH4OH, al.

1.948 1.502

98–100 −42 −38 −18 .5 73 d . −209 .86

−6H2O, 103 86

117.830° ∞ ∞ ∞

−195 .8

63.50° ∞ ∞ 263−20° d . 2 .350° cc

s. al. expl . with al . d . al . d . al . s . H2SO4 sl . s . al .

−102 .3

−90 .7

130 .520° cc

−161

−151

7 .340° cc

60 .8224° cc 0 .0100°

−102

3 .5

s .

1 .026−252 .5° 0 .808−195 .8° 12 .50° (D) lq . 1 .226−89° 1 .530 (A) lq . 1 .269−150 .2° 1 .0367 (A) 1 .4472° 20°

1 .448

−9 .3

21 .3

d .

1 .6318°

30

47

s .

>1 .0 1 .417−12° 2 .31 (A) lq . 1 .3214° 22 .4820°

−55 .5 −64 .5

−2 −5 .5

d . d .

5300

26 .6 cc al .; 3 .5 cc H2SO4; s . aq . FeSO4 s . a ., et . s . HNO3, H2SO4, chl ., CS2

Forms HNO3 s . fuming H2SO4

−218 .4

−183

−251

−112

0 .4940° cc

060° cc

s . oil turp ., oil cinn .

1555

2200

i .

i .

i . s . s . i .

i . s . s . i .

s . aq . reg ., h . H2SO4; i . NH3 s . HBr s . HCl, act ., al . s . HCl, act ., al . s . HCN, KCN, NH4OH; i . dil . a .

500 d . d . 11 .06 2 .5 1 .768 224° 1 .88 1 .71 254°

s . H2SO4, al .

d i . s . d . sl . s . s . d . 4 .890° cc

d . 560–600 1 .14−188° 1 .426−252 .5° 1 .1053 (A) 1 .71−183° 3 .03−80° 1 .658 (A) 12 .020° 111550°

1 .5520° cc

i .

2 .630° cc 1 .7100° cc

sl . s . aq . reg ., HNO3; i . NH3 s . NaCl, al ., et . s . a ., alk ., al .; sl . s . et . s . HCl, al . sl . s . al ., s . fused Ag

d .

−90°

lq . 0 .746 1 .146 (A)

−112 50 −17 .8

1618mm d . 200

d . 138 d . 110

subl . 110

1950 2450 >1300 1200 58 26 50 220

Other reagents

s. KOH sl. s. al.; i. et. 0.130° al.; i. et. v. s. NH3; sl. s. al.

s. al., et. 0.10520° m. al.; i. et. s. H2SO4; d. al. i. al. i. al. sl. s. al. i. al. s. a. i. al. s. al., et. i. al. i. al. i. al., act., CS2 s. al., gly.; i. et. sl. s. al.; i. NH3 i. abs. al. sl. s. al. s. a., alk.; i. al., ac. 20.822° act.; s. al. i. al. d. a. s. al. i. HF, HCl; s. H2SO4; HNO3 sl. s. aq. reg., a. v. sl. s. alk.; i. aq. reg., a. s. HCl, al.; i. et. s. a., al.

i. i.

700

i. i. v. s. d. i. i.

i. i.

sl. s. aq. reg., a.

>2700 2400 260 205 688 688

130030° v . s . i . i .

∞60°

s . H2SO4; d . al .; i . NH3

i . i .

s . CS2, H2SO4, CH2I2 s . CS2, H2SO4

Selenium Selenous acid Silicic acid, metaSilicic acid, orthoSilicon, crystalline

Se8 H2SeO3 H2SiO3 H4SiO4 Si

Silicon, graphitic

Si

Silicon, amorphous carbide chloride, trichloride, tetra-

Si SiC Si2Cl6 SiCl4

28.09 40.10 268.89 169.90

SiF4 SiH4 SiO2⋅xH2O SiO2

104.08 32.12

SiO2 SiO2 SiO2 Ag AgBr

60.08 60.08 60.08 107.87 187.77

carbonate chloride (cerargyrite)

Ag2CO3 AgCl

cyanide nitrate (lunar caustic) Sodium

steel gray hex. amor., 1.41 amor. gray, cb., 3.736

4.825° 3.004 154° 2.1–2.3 1.57617° 2.420°

cr.

2.0–2.5

brn., amor. blue-bk., trig., 2.654 lf. or lq. col., fuming lq., 1.412 gas col. gas iridescent, amor. col., cb. or tet., 1.487

2 3.17 1.580° 1.50

2600

i. 900° i. sl. s. i.

i. 40090° i. sl. s. i.

2600

i.

i.

>2700 −1 −70

2600 subl. 2200 144760mm 57.6

i. i. d. d.

i. i.

3.57 (A) lq. 0.68−185° 2.2 2.32

−95.7 −185 1600–1750 1710

−651810mm −112760mm subl. 1750 2230

v. s. d. i. i. i.

hex., 1.5442 trig., rhb., 1.469 silv. met., cb. pa. yel., cb., 2.252

2.20 2.65020° 2.26 10.520° 6.473 254°

tr. 315 d. 741

d., −H2O

75

−10H2O, 200

17.5°

bromate bromide bromide

NaBrO3 NaBr NaBr⋅2H2O

150.89 102.89 138.92

col., cb. col., cb., 1.6412 col., mn.

3.339 3.20517.5° 2.176

381 755 50.7

carbonate (soda ash) carbonate

Na2CO3 Na2CO3⋅H2O

105.99 124.00

2.533 1.55

851 −H2O, 100

carbonate carbonate (sal soda) ∗Usual commercial form.

Na2CO3⋅7H2O Na2CO3⋅10H2O

232.10 286.14

wh. pd., 1.535 wh., rhb., 1.506– 1.509 rhb. or trig. wh., mn., 1.425

1.51 1.46

d. 35.1

−7H2O, 100 −12H2O, 100

0.00002220° 1220° d., forms NaOH 46.520° v. s. s. d. 16.7 0.03112.8° 26.717° s. 6115° 5.590.1° v. s. 62.525° 6.90° 3.720° 500° sl. s. 1.30° 2262° (anh.)

d.

i. 0.00037100°

952100° 170100° v. s. v. s. 100

s. HNO3, al., et. i. al., et.; d. KOH s. HF, h. alk., fused CaCl2 s. HF; i. alk. s. HF; i. alk. s. HF; i. alk. s. HF; i. alk. s. HNO3, h. H2SO4; i. alk. 0.5118° NH4OH; s. KCN, Na2S2O3 s. NH4OH, Na2S2O3; i. al. s. NH4OH, KCN; sl. s. HCl s. NH4OH, KCN, HNO3 s. gly.; v. sl. s. al. i. bz.; d. al. 2.118° al. 7.825° abs. al. i. al. d. al. i. al. sl. s. al., NH4 salts; i. ac. 1.67 al., 5015° gly.

v. s. 140.730°

sl. s. al. sl. s. al. 2.325°, 8.378° al. i. al.

7.10° s.

76.9100° 16.460° s. 100100° s. 8.7940° 52.3100° (anh.) 20.380° (anh.) 90.9100° 121100° 118.380° (anh.) 48.5104° s.

i. al., et. s. gly.; i. al., et.

s. 21.50°

s. 23830°

i. al.

1.30.5 (anh.) 0°

1390

i. i.

i. CS2; s. H2SO4 v. s. al.; i. NH3 s. alk.; i. NH4Cl s. alk.; i. NH4Cl s. HNO3 + HF, Ag; sl. s. Pb, Zn; i. HF s. HNO3 + HF, fused alk.; i. HF. s. HF, KOH s. fused alk.; i. a. d. alk. d. conc. H2SO4, al.

27.5 9020° 79.50° (anh.)

d. al.; i. NH3 i. al., act. i. al. s. gly.; i. abs. al. i. al. sl. s. al. sl. s. al.

(Continued )

2-21

2-22 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued )

Name Sodium (Cont.) carbonate, sesqui- (trona) chlorate

Formula Na3H(CO3)2⋅2H2O NaClO3

Formula weight

Color, crystalline form, and refractive index

chloride chromate chromate citrate cyanide dichromate

NaCl Na2CrO4 Na2CrO4⋅10H2O 2Na3C6H5O7⋅11H2O NaCN Na2Cr2O7⋅2H2O

58 .44 161 .97 342 .13 714 .31 49 .01 298 .00

wh., mn., 1.5073 wh., cb., or trig., 1.5151 col., cb., 1.5443 yel., rhb. yel., delq., mn. wh ., rhb . wh ., cb ., 1 .452 red, mn ., 1 .6994

ferricyanide ferrocyanide

Na3Fe(CN)6⋅H2O Na4Fe(CN)6⋅10H2O

298 .93 484 .06

red, delq . yel ., mn .

fluoride (villiaumite) formate hydride

NaF NaHCO2 NaH

hydrosulfide hydrosulfide hydrosulfite hydroxide hydroxide hypochlorite iodide iodide lactate nitrate (soda niter) nitrite

NaSH⋅2H2O NaSH⋅3H2O Na2S2O4⋅2H2O NaOH NaOH⋅3½H2O NaOCl NaI∗ NaI⋅2H2O NaC3H5O3 NaNO3 NaNO2

oxide

Na2O

perborate perchlorate perchlorate peroxide peroxide phosphate, monobasic phosphate, monobasic phosphate, dibasic phosphate, dibasic phosphate, tribasic phosphate, tribasic phosphate, metaphosphate, pyrophosphate, pyrophosphate (pyrodisodium) phosphate (pyrodisodium) potassium tartrate silicate, metaSodium silicate, metasilicate, orthosilicofluoride stannate sulfate (thenardite) sulfate

NaBO3⋅H2O NaClO4 NaClO4⋅H2O Na2O2∗ Na2O2⋅8H2O NaH2PO4⋅H2O∗ NaH2PO4⋅2H2O Na2HPO4⋅7H2O Na2HPO4⋅12H2O Na3PO4 Na3PO4⋅12H2O∗ Na4P4O12 Na4P2O7∗ Na4P2O7⋅10H2O Na2H2P2O7 Na2H2P2O7⋅6H2O NaKC4H4O6⋅4H2O Na2SiO3 Na2SiO3⋅9H2O Na4SiO4 Na2SiF6 Na2SnO3⋅3H2O Na2SO4 Na2SO4

226 .03 106 .44

41 .99 68 .01 24 .00 92 .09 110 .11 210 .14 40 .00 103 .05 74 .44 149 .89 185 .92 112 .06 84 .99 69 .00 61 .98 99 .81 122 .44 140 .46 77 .98 222 .10 137 .99 156 .01 268 .07 358 .14 163 .94 380 .12 407 .85 265 .90 446 .06 221 .94 330 .03 282 .22 122 .06 284 .20 184 .04 188 .06 266 .73 142 .04 142 .04

tet ., 1 .3258 wh ., mn . silv . nd ., 1 .470 col ., delq ., nd . rhb . col . cr . wh ., delq . mn . pa . yel ., in soln . only col ., cb ., 1 .7745 col ., mn . col ., amor . col ., trig ., 1 .5874 pa . yel ., rhb . wh ., delq . wh . pd . rhb ., 1 .4617 hex . yel .-wh . pd . wh ., hex . col ., rhb ., 1 .4852 col ., rhb ., 1 .4629 col ., mn ., 1 .4424 col ., mn ., 1 .4361 wh . wh ., trig ., 1 .4458 col . wh . mn ., 1 .4525 col ., mn ., 1 .510 col ., mn ., 1 .4645 rhb ., 1 .493 col ., rhb ., 1 .520 rhb . col ., hex ., 1 .530 wh ., hex ., 1 .312 hex . tablets col ., rhb ., 1 .477 col ., mn .

Specific gravity 2.112 2.49015° 2.163 2.723 1.483 ° 1 .857 23.5 4 2 .5218°

Melting point, °C d. 248 800.4 392 19.9 −11H2O, 150 563 .7 −2H2O, 84 .6; 356 (anh .)

Boiling point, °C

d. 1413 d . 1496 d . 400

1 .458 2 .79 1 .919 0 .92

992 253 d . 800

2 .130

d . 22 d . 318 .4 15 .5 d . 651

3 .6670° 2 .448 2 .257 2 .1680°

d . 308 271

2 .27

subl .

2 .02 2 .805 2 .040 1 .91 1 .679 1 .52 2 .53717 .5° 1 .62 2 .476 2 .45 1 .82 1 .862 1 .848 1 .790

2 .679 2 .698

d . 40 482 d . d . 130 d . d . 30 −H2O, 100 60 d . 34 .6 1340 73 .4 616 d . 988 d . d . 220 70 to 80 1088 47 1018 d . d . 140 tr . 100 to mn . tr . 500 to hex .

Solubility in 100 parts Cold water 130° 790°

42100° 230100° 0°

1390 1300 d . 380 d . 320

d . 200 −12H2O, 180 −11H2O, 100

−4H2O, 215 −6H2O, 100

100°

35.7 320° v. s. 9125° 4810° 2380°

39.8 126100° ∞ 250100° 8235° 50880°

18 .90° 17 .920° (anh .)

67100° 6398 .5° (anh .) 5100° 160100°

40° 440° d . d .

Hot water

s . s . 2220° 420° s . 260° 158 .70° v . s . v . s . 730° 72 .10°

s . s . d . 347100° v . s . 15856° 302100° v . s . v . s . 180100° 163 .2100°

Forms NaOH sl . s . 1700° 20915° s . d . s . d . 710° 91 .10° 18540° 4 .30° 4 .50° 28 .315° s . 2 .260° 5 .40° 4 .50° 6 .90° 260° s . v . s . s . 0 .440° 500° 50° 48 .840°

d . 320100° 28450° d . d . 39083° 30840° 2000100° 76 .730° 77100° ∞ s . 4596° 93100° 2140° 3640° 6626° s . d . v . s . s . 2 .45100° 6750° 42100° 42 .5100°

Other reagents

s. al. sl. s. al.; i. conc. HCl sl . s . al . i . al . s . NH3; sl . s . al . i . al . i . al . v . sl . s . al . sl . s . al .; i . et . i . bz ., CS2, CCl4, NH3; s . molten metal s . al .; d . a . s . al .; d . a . i . al . v . s . al ., et ., gly .; i . act . v . s . al ., act . v . s . NH3 s . al .; i . et . s . NH3; sl . s . gly ., al . 0 .320° et .; 0 .3 abs . al .; 4 .420° m . al .; v . s . NH3 d . al . s . gly ., alk . s . al .; 51 m . al .; 52 act .; i . et . s . al . s . dil . a . i . al . i . al . i . CS2 s . a ., alk . d . a . i . al ., NH3 sl . s . al . i . Na or K salts, al . 2918°, aN NaOH i . al . i . al ., act . i . al . d . HI; s . H2SO4

sulfate sulfate sulfate (Glauber’s salt) sulfide, monosulfide, tetrasulfide, pentasulfite sulfite tartrate thiocyanate thiosulfate thiosulfate (hypo) tungstate tungstate tungstate, parauranate vanadate vanadate, pyroStannic chloride

Na2SO4 Na2SO4⋅7H2O Na2SO4⋅10H2O Na2S Na2S4 Na2S5 Na2SO3 Na2SO3⋅7H2O Na2C4H4O6⋅2H2O NaCNS Na2S2O3 Na2S2O3⋅5H2O∗ Na2WO4 Na2WO4⋅2H2O∗ Na6W7O24⋅16H2O Na2UO4 Na3VO4⋅16H2O Na4V2O7 SnCl4

142 .04 268 .15 322 .19 78 .04 174 .24 206 .30 126 .04 252 .15 230 .08 81 .07 158 .11 248 .18 293 .82 329 .85 2097 .05 348 .01 472 .15 305 .84 260 .52

col., hex. tet. col., mn., 1.396 pink or wh., amor. yel., cb. yel. hex. pr., 1.565 mn. rhb. delq., rhb., 1.625± mn. mn. pr., 1.5079 wh., rhb. wh., rhb. wh., tri. yel. col. nd. hex. col., fuming lq.

oxide (cassiterite)

SnO2

150 .71

wh ., tet ., 1 .9968

sulfate

Sn(SO4)2⋅2H2O

346 .87

col ., delq ., hex .

Stannous bromide chloride chloride (tin salt) sulfate Strontium

884 1.464 1.856 2.633 154° 1.561 1.818

2.226

866 (anh.) 654 −30.2

7 .0

1127

17°

yel ., rhb . wh ., rhb . wh ., tri . wh . cr . silv . met .

2 .6

acetate carbonate (strontianite) chloride chloride hydroxide hydroxide

Sr(C2H3O2)2 SrCO3 SrCl2 SrCl2⋅6H2O∗ Sr(OH)2 Sr(OH)2⋅8H2O∗

205 .71 147 .63 158 .53 266 .62 121 .63 265 .76

wh . cr . wh ., rhb ., 1 .664 wh ., cb ., 1 .6499 wh ., rhb ., 1 .5364 wh ., delq . col ., tet ., 1 .499

2 .099 3 .70 3 .052 1 .93317° 3 .625 1 .90

nitrate nitrate oxide (strontia)

Sr(NO3)2∗ Sr(NO3)2⋅4H2O SrO

211 .63 283 .69 103 .62

col ., cb ., 1 .5878 wh ., mn . col ., cb ., 1 .870

2 .986 2 .2 4 .7

SrO2 SrO2⋅8H2O SrSO4 Sr(HSO4)2 NH2SO3H S S8 S8 S2Br2 S2Cl2 SCl2 SCl4 SO2

119 .62 263 .74 183 .68 281 .76 97 .09 32 .07 256 .52 256 .52 223 .94 135 .04 102 .97 173 .88 64 .06

wh . pd . wh . cr . col ., rhb ., 1 .6237 col ., granular wh ., rhb . pa . yel . pd ., 2 .0–2 .9 pa . yel ., mn . pa . yel ., rhb . red, fuming lq . red-yel . lq . dark red fuming lq . yel .-brn . lq . col . gas

oxide, tri-(β) Sulfuric acid Sulfuric acid ∗Usual commercial form .

SO3 (SO3)2 H2SO4∗ H2SO4⋅H2O

80 .06 160 .13 98 .08 116 .09

col . pr . col ., silky, nd . col ., viscous lq . pr . or lq .

d.

287 d. 48.0 692 −2H2O, 100 −16H2O, 300

278 .52 189 .62 225 .65 214 .77 87 .62

oxide, tri-(α)

−10H2O, 100

275 251.8 d. −7H2O, 150

1.667 1.685 4.179 3.245 3.98714°

SnBr2 SnCl2 SnCl2⋅2H2O∗ SnSO4 Sr

peroxide peroxide sulfate (celestite) sulfate, acid Sulfamic acid Sulfur, amorphous Sulfur, monoclinic Sulfur, rhombic Sulfur bromide, monochloride, monochloride, dichloride, tetraoxide, di-

32.4

5 .12

2 .7115 .5°

3 .96 2 .03 124° 2 .046 1 .96 2 .07 2 .635 1 .687 1 .621 1515° lq ., 1 .4340°; 2 .264 (A) lq ., 1 .923; 2 .75 (A) 1 .9720° 1 .834 184° 1 .842 154°

215 .5 246 .8 37 .7 −SO2, 360 800 149760atm . 873 −4H2O, 61 375 −7H2O in dry air 570

114.1

620 623 d . 1150 d . −CO2, 1350 −6H2O, 100

19.420° 44.90° 3615° 15.410° s. s. 13.90° 34.72° 296° 11010° 500° 74.70° 57.580° 880° 8 i. v. s. s. s.

45.360° 202.626° 41234° 57.390° s. s. 28.384° 67.818° 6643° 225100° 23180° 301.860° 97100° 123.5100° d. i. d.

i .

i .

v . s .

d .

s . 83 .90° 118 .70° 1919° d .

d . 269 .815° ∞ 18100° Forms Sr(OH)2 36 .497° 0 .065100° 100 .8100° 19840° 21 .83100° 47 .7100°

36 .90° 0 .001118° 43 .50° 1040° 0 .410° 0 .900°

444 .6 444 .6 444 .6 540 .18mm 138 59 d . > −20 −10 .0

400° 62 .20° Forms Sr(OH)2 0 .00820° 0 .01820° 0 .01130° d . 200° i . i . i . d . d . d . d . 22 .80°

16 .83

44 .6

d .

50 10 .49 8 .62

d . 340 290

Forms H2SO4 ∞ ∞

2430 d . −8H2O, 100 1580 d . d . 205 d . 120 119 .0 112 .8 −46 −80 −78 −30 −75 .5

d .

d.

i. al. sl. s. al.; i. et. s. al. s. al. i. al., NH i. al. i. al. v. s. al. s. NH3; v. sl. s. al. sl. s. NH3; i. a., al. s. alk. carb., dil. a. i. al. i. al. s. abs. al., act., NH3; s. ∞ CS2 s . conc . H2SO4; i . alk .; NH4OH, NH3 s . dil . H2SO4, HCl; d . abs . al . s . C6H5N s . alk ., abs . al ., et . s . tart . a ., alk ., al . s . H2SO4 s . al ., a . 0 .2615° m . al . s . a ., NH4 salts, aq . CO2 v . sl . s . act ., abs . al .; i . NH3 s . NH4Cl s . NH4Cl; i . act .

10089° 12420°

s . NH3; 0 .012 abs . al . i . HNO3 sl . s . al .; i . et .

d . d . 0 .011432°

s . al ., NH4Cl; i . act . s . al .; i . NH4OH sl . s . a .; i . dil . H2SO4, al . 1470° H2SO4 sl . s . al ., act .; i . et . sl . s . CS2 s . CS2, al . 240°, 18155° CS2

4070° i . i . i .

s . CS2, et ., bz . d . al . 4 .550°

s . H2SO4; al ., ac . s . H2SO4

∞ ∞

s . H2SO4 d . al . d . al . (Continued )

2-23

2-24

TABLE 2-1

Physical Properties of the Elements and Inorganic Compounds (Continued )

Name

Formula

Formula weight

Color, crystalline form, and refractive index

Specific gravity

Melting point, °C

Boiling point, °C

Solubility in 100 parts Cold water

Hot water

Sulfuric acid Sulfuric acid, pyroSulfuric oxychloride Sulfurous oxybromide oxychloride Tantalum

H2SO4⋅2H2O H2S2O7 SO2Cl2 SOBr2 SOCl2 Ta

134 .11 178 .14 134 .97 207 .87 118 .97 180 .95

col. lq. cr . col . lq . or .-yel . lq . yel . fuming lq . bk .-gray, cb .

1.650 04° 1 .920° 1 .667 204° 2 .6818° 1 .631 16 .6

−38.9 35 −54 .1 −50 −104 .5 2850

167 d . 69 .1760mm 6840mm 75 .6 >4100

∞ d . d . d . d . i .

∞

Tellurium

Te

127 .60

met ., hex .

(α) 6 .24; (β) 6 .00

452

1390

i .

i .

Terbium Thallium acetate chloride, monochloride, sesquichloride, trichloride, trisulfate (ic) sulfate (ous) sulfate, acid Thio, cf. sulfo or sulfur Thorium

Tb Tl TlC2H3O2 TlCl Tl2Cl3 TlCl3 TlCl3⋅4H2O Tl2(SO4)3⋅7H2O Tl2SO4 TlHSO4

158 .93 204 .38 263 .43 239 .84 515 .13 310 .74 382 .80 823 .06 504 .83 301 .45

blue-wh ., tet . silky nd . wh ., cb . yel ., hex . hex . pl . nd . lf . col ., rhb ., 1 .8671 trimorphous

11 .85 3 .68 7 .00 5 .9

303 .5 110 430 400–500 25 37 −6H2O, 200 632 115 d .

1650 806 d . d . −4H2O, 100 d . d .

i . v . s . 0 .210° 0 .2615° v . s . 86 .217° d . 2 .700°

Th

232 .04

cb .

11 .2

1845

>3000

i .

i .

oxide, di- (thorianite) sulfate sulfate Thulium Tin

ThO2 Th(SO4)2 Th(SO4)2⋅9H2O Tm Sn

264 .04 424 .16 586 .30 168 .93 118 .71

wh ., cb .

>2800

4400

mn . pr .

9 .69 4 .22517° 2 .77

silv . met ., tet .

7 .31

231 .85

2260

i . 0 .740° sl . s . i . i .

5 .2250° sl . s . i . i .

Tin

Sn

118 .71

gray, cb .

5 .750

Stable −163 to +18

2260

i .

i .

Tin salts, cf. stannic and stannous Titanic acid

H2TiO3

97 .88

wh . pd .

i .

i .

i . d .

d .

s . s . i .

s . d . i .

i .

i .

6 .77

17 .5°

i .

i . 1 .8100° 1 .9100° d . d . 18 .45100°

Other reagents d . al . d . al . s . ac .; d . al . s . bz ., CS2, CCl4; d . act . s . bz ., chl . s . fused alk ., HF; i . HCl, HNO3, H2SO4 s . H2SO4, HNO3, KCN, KOH, aq . reg .; i . CS2 s . HNO3, H2SO4; i . NH3 v . s . al . sl . s . HCl; i . al ., NH4OH s . al ., et . s . al ., et . s . dil . H2SO4 v . sl . s . dil . H2SO4

−9H2O, 400

>3000

s . HCl, H2SO; sl . s . HNO3; i . HF, alk . s . h . H2SO4; i . alk .

s . HCl, H2SO4, dil . HNO3 h . aq KOH s . a ., h . alk . solns . s . alk .; v . sl . s . dil . a .; i . al . s . a . i . CS2, et ., chl .

Ti TiCl2

47 .87 118 .77

dark gray, cb . bk ., delq .

chloride, trichloride, tetraoxide, di- (anatase)

TiCl3 TiCl4∗ TiO2

154 .23 189 .68 79 .87

oxide, di- (brookite)

TiO2

4 .26

1640 d .

2130 −½H2O, 100; 1473 −H2O, 250 to 300 1133 2400 2176

oxide, di- (rutile) Tungsten carbide carbide

TiO2

79 .87 79 .87

lq ., 1 .726 3 .84

136 .4

4 .17

3500

i .

s . dil . HCl sl . s . alk .

oxide (pitchblende) sulfate (ous) Uranyl acetate carbonate (rutherfordine) nitrate sulfate Vanadic acid, metaVanadic acid, pyroVanadium chloride, dichloride, trichloride, tetraoxide, dioxide, trioxide, tetraoxide, pentaoxychloride, monoVanadyl chloride chloride, dichloride, triWater†

U3O8 U(SO4)2⋅4H2O UO2(C2H3O2)2⋅2H2O UO2CO3 UO2(NO3)2⋅6H2O UO2SO4⋅3H2O HVO3 H4V2O7 V VCl2 VCl3 VCl4 V2O2 V2O3 V2O4 V2O5 VOCl (VO)2Cl VOCl2 VOCl3 H2O

842 .08 502 .22 424 .15 330 .04 502 .13 420 .14 99 .95 217 .91 50 .94 121 .85 157 .30 192 .75 133 .88 149 .88 165 .88 181 .88 86 .39 169 .33 137 .85 173 .30 18 .02

Water, heavy Xenon

D 2O Xe

20 .029 131 .29

olive gn. gn., rhb. yel., rhb. tet. yel., rhb., 1.4967 yel . cr . yel . scales pa . yel ., amor . lt . gray, cb . gn ., hex ., delq . pink, tabular, delq . red lq . lt . gray cr . bk . cr . blue cr . red-yel ., rhb . brn . pd . yel . cr . gn ., delq . yel . lq . col . lq ., 1 .3330020°; hex . solid, 1 .309 col . lq ., 1 .3284420° col . gas

Ytterbium Yttrium Zinc acetate acetate bromide carbonate

Yb Y Zn Zn(C2H3O2)2 Zn(C2H3O2)2⋅2H2O∗ ZnBr2 ZnCO3

173 .04 88 .91 65 .41 183 .50 219 .53 225 .22 125 .42

dark gray, hex . silv . met ., hex . mn . wh ., mn ., 1 .494 rhb . wh ., trig ., 1 .818

chloride

ZnCl2

136 .32

cyanide hydroxide iodide

Zn(CN)2 Zn(OH)2 ZnI2

117 .44 99 .42 319 .22

wh ., delq ., 1 .687, uniaxial col ., rhb . col ., rhb . cb .

nitrate oxide (zincite) oxide peroxide phosphide silicate

Zn(NO3)2⋅6H2O ZnO ZnO ZnO2 Zn3P2 ZnSiO3

297 .51 81 .41 81 .41 97 .41 258 .17 141 .49

sulfate (zincosite) sulfate sulfate sulfate (goslarite) sulfide (α) (wurzite) sulfide (β) (sphalerite)

ZnSO4 ZnSO4⋅H2O ZnSO4⋅6H2O ZnSO4⋅7H2O∗ ZnS ZnS

161 .47 179 .49 269 .56 287 .58 97 .47 97 .47

2-25

sulfide (blende) ZnS 97 .47 sulfite ZnSO3⋅2½H2O 190 .51 Zirconium Zr 91 .22 oxide, di- (baddeleyite) ZrO2 123 .22 123 .22 oxide, di- ( free from Hf) ZrO2 ∗Usual commercial form . † Cf. special tables on water and steam, Tables 2-3, 2-4, and 2-5 . note: °F = 9⁄ 5°C + 32 .

col ., tet . wh ., hex ., 2 .004 wh ., amor . yel . steel gray, cb . hex . or rhb .; glass, 1 .650 wh ., rhb ., 1 .669 col . mn . rhb ., 1 .4801 wh ., hex ., 2 .356 wh ., cb .; glass (?) 2 .18–2 .25 wh ., granular mn . cb ., pd . ign . easily yel . or brn ., mn ., 2 .19 wh ., mn .

7.31 2.8915° 5.6 2.807 3 .2816 .5° 5 .96 3 .2318° 3 .0018° 1 .81630° 3 .64 4 .87 184° 4 .399 3 .357 184° 2 .824 3 .64 2 .8813° 1 .829 1 .004° (lq .); 0 .9150° (ice) 1 .10720° lq ., 3 .06−109 .1 2 .7−140° 4 .53 (A)

d. −4H2O, 300 −2H2O, 110 60.2 d . 100

118

1710

3000

d . −109 ign . 1970 1967 800

148 .5755mm

d . 1750

d . in air

i. 2311° 9.217°

i. 963° d.

s. HNO3, H2SO4 s. dil. a. s. al., act.

170.30° 18 .913 .2° i . i . i . s . s . s . d . i . sl . s . i . 0 .820° i . i . d . s . d .

∞60° 23025°

v . s . ac ., al ., et .; i . dil ., alk . 4 al .; s . a . s . a ., alk .; i . NH3 s . a ., alk ., NH4OH s . HNO3, H2SO4; i . aq ., alk . s . al ., et . s . abs . al ., et . s . abs . al ., et ., chl ., ac . s . a . s . HNO3, HF, alk . s . a ., alk . s . a ., alk .; i . abs . al . v . s . HNO3 s . HNO3 s . abs . al ., dil . HNO3 s . al ., et ., ∞Br2 ∞ al .; sl . s . et .

i . d . d . i . s . i .

1800 >1800 expl . 212 >420 1437

v . s . dil . a ., h . KOH s . a ., ac ., alk . 2 .825°, 16679° al . v . s . al . v . s . NH4OH, al ., et . s . a ., alk ., NH4 salts; i . act ., NH3 10012 .5° al .; v . s . et .; i . NH3 s . KCN, NH3, alk .; i . al . s . a ., alk ., NH4OH s . a ., al ., NH3, aq . (NH4)2CO3 v . s . al . s . a ., alk ., NH4Cl; i . NH3

3 .74 154° 3 .28 154° 2 .072 154° 1 .96616 .5° 4 .087 4 .102 254°

d . 740 d . 238 −5H2O, 70 tr . 39 1850150atm . tr . 1020

−6H2O, 105

1100

−7H2O, 280 subl . 1185

4 .04 6 .4 5 .49 5 .73

−2½H2O, 100 1700 2700

d . 200 >2900 4300

510100°

324 .5 0 .0004218° 0 .0004218° 0 .0022 i . i .

∞36 .4°

420° s . s . 115 .20° 0 .0006918° i .

61100° 89 .5100° s . 653 .6100° i . i .

sl . s . al .; i . act .; NH3 sl . s . al .; i . act .; NH3 v . s . a .; i . ac . s . a .

i . 0 .16 i . i . i .

i . d . i . i . i .

v . s . a .; i . ac . s . H2SO3, NH4OH; i . al . s . HF, aq . reg .; sl . s . a . s . H2SO4, HF s . H2SO4, HF

i . NH4OH; d . a . s . dil . a . sl . s . al .; s . gly .

2-26

TABLE 2-2 Physical Properties of Organic Compounds* Abbreviations Used in the Table (A), density referred to air cr., crystalline i-, iso-, containing the group al., ethyl alcohol d., decomposes (CH3)2CHamor., amorphous d-, dextrorotatory i., insoluble aq., aqua, water dl-, dextro-laevorotatory ign., ignites brn., brown et., ethyl ether l-, laevorotatory bz., benzene expl., explodes lf., leaflets c., cubic gn., green lq., liquid cc., cubic centimeter h., hot m-, meta chl., chloroform hex., hexagonal mn., monoclinic col., colorless n-, normal This table of the physical properties includes the organic compounds of most general interest . For the properties of other organic compounds, reference must be made to larger tables in Lange’s Handbook of Chemistry (Handbook Publishers), Handbook of Chemistry and Physics (Chemical Rubber Publishing Co .), Van Nostrand’s Chemical Annual, International Critical Tables (McGraw-Hill), and similar works . The molecular weights are based on the atomic weight values in “Atomic weights of the Elements 2001,” PURE Appl. Chem., 75, 1107, 2003 . The densities are given for the temperature indicated and are usually

nd., needles s-, sec-, secondary v. s., very soluble v. sl. s., very slightly soluble o-, ortho silv., silvery wh., white or., orange sl., slightly yel., yellow p-, para subl., sublimes (+), right rotation pd., powder sym., symmetrical >, greater than pet., petroleum ether t-, tertiary C6H4 CH2:CH⋅CHO CH2:CH⋅CO2H CH2:CH⋅CN (CH2CH2CO2H)2 (CH2CH2CONH2)2 (CH2CH2CN)2 C6H3(OH)2(CHOHCH2NHCH3) CH3CH(NH2)CO2H CH3CH(OH)CH2COH C6H4(CO)2C6H2(OH)2 CH2:CH⋅CH2OH CH2:CH⋅CH2Br CH2:CH⋅CH2Cl CH2:CH⋅CH2NCS CH2:CH⋅CH2NHCSNH2 Al(OCH2CH3)3 C6H4(CO)2C6H3NH2 C6H4(CO)2C6H3NH2 C6H5⋅N:N⋅C6H4NH2 H2N⋅C6H4CO2H H2N⋅C6H4CO2H

302 .45 154 .21 118 .17 44 .05 132 .16 61 .08 59 .07 135 .16 179 .22 179 .22 149 .19 149 .19 60 .05 102 .09 41 .05 58 .08 128 .13 120 .15 78 .50 150 .18 26 .04 96 .94 96 .94 174 .11 179 .22 56 .06 72 .06 53 .06 146 .14 144 .17 108 .14 183 .20 89 .09 88 .11 240 .21 58 .08 120 .98 76 .52 99 .15 116 .18 162 .16 223 .23 223 .23 197 .24 137 .14 137 .14

lf . rhb ./al . lq . col . lq . col . cr . col . cr . col . cr . rhb ./al . lf ./al . lf ./al . rhb . rhb . or mn . col . lq . col . lq . col . lq . col . lq . tri ./al . lf . col . lq . nd ./aq . col . gas col . lq . col . lq . cr ./aq . rhb ./aq . al . col . lq . col . lq . col . lq . mn . pr . cr . pd . col . oil col . pd . nd ./aq . col . lq . red rhb . col . lq . lq . col . lq . col . oil col . pr . pd . red nd . red nd . yel . mn . nd ./aq . mn . pr .

ethanamide antifebrin o-ethoxyacetanilide acetyl-m-phenetidine N-tolylacetamide N-tolylacetamide ethanoic acid, vinegar acid acetyl oxide, acetic oxide methyl cyanide propanone, dimethyl ketone dimethyl hydantoin methyl-phenyl ketone ethanoyl chloride amino-acetanilide (p) ethyne; ethine 1,2-dichloroethene dioform equisetic acid; citridic acid acrylic aldehyde, propenal propenoic acid vinyl cyanide hexandioc acid, adipinic acid tetramethylene 1-suprarenine 2-hydroxybutyraldehyde Anthraquinoic acid propen-1-ol-3,propenyl alcohol 3-bromo-propene-1 3-chloro-propene-1 mustard oil thiosinamide

aminodracylic acid

Specific gravity 1 .06995/95 0 .82122/4 0 .78318/4 0 .99420/4 1 .159 1 .214 1 .16815 1 .21215 1 .04920/4 1 .08220/4 0 .78320/4 0 .79220/4 1 .03315/15 1 .10520/4 (A) 0 .906 1 .29115/4 1 .26515/4 0 .84120/4 1 .06216/4 0 .81120 1 .36025/4 0 .95119/19 1 .10320/4 0 .85420/4 1 .39820/4 0 .93820/4 1 .01320/4 1 .21920/20 1 .14220/0

1 .5114°

Melting point, °C 182 95 −123 .5 10 .5–12 97 81(69 .4) 113–4 79 96–7 110 153 16 .7 −73 −41 −94 .6 175 20 .5 −112 .0 162 −81 .5891 −80 .5 −50 192 d . 110–1 −87 .7 12–13 −82 151–3 226–7 1 d . 207–11 295 d . 289–90 −129 −119 .4 −136 .4 −80 77–8 150–60 256 302 126–7 173–4 187–8

Boiling point, °C 278–9 102 .2 20 .2 124 .4752 100–10 d . 222 305 >250 296 306–7 118 .1 139 .6 81 .6–2 .0 56 .5 subl . 202 .3749 51–2 −84760 60 .3 48 .4 346 52 .5 141–2 78–9 26510 295 subl . >200 8320 430 96 .6 70–1753 44 .6 152 200–510 subl . subl . 225120

Solubility in 100 parts Water

Alcohol

Ether

i . i . 625 ∞ 1213 v . s . s . 0 .56 i . sl . s . 0 .8619 0 .0922 ∞ 12 c . ∞ ∞ s . i . d . s . h . 100 cc .18 0 .3520 0 .6320 3315 sl . s . h . 40 ∞ s . 1 .415 0 .412 v . sl . s . 0 .0320 2217 ∞ 0 .03100 ∞ i . 175

pr . mn . pr . rhb ./et . col . lq .

1 .2315 1 .26615/4 1 .19915/4 1 .00125/6

95 121 .7 42 −12 .9

1 .02220/4

1 .385 4 1 .123 20/4 1 .09815/15 1 .096 20/4 1 .089 55/55 0 .990 22/4 1 .25 27/4

1 .18715/4 1 .438 20/4

1 .54315/4

1 .20320/4 1 .248 20/20 1 .035 20/20 1 .046 20/4 1 .341 1 .314 0 .879 20/4

−135 −139 −124 22 .5 143 −6 .2

Boiling point, °C

Solubility in 100 parts Water

Alcohol

Ether

30–1 20 .5 771 31–2758 36 .4 37–8 235 .3 185 184 .4

i. i . i . v . sl . s . i . v . sl . s . i . 3 .618

∞ ∞ ∞ ∞ s . s . sl . s . ∞

∞ ∞ ∞ ∞ ∞ ∞ s . ∞

245

s . s . sl . s . v . s . v . s . ∞ ∞ s . s . s . 1 .520

i . sl . s . i . v . s . v . s . ∞ ∞ s . s . s .

198 d . 190 d . 73–4 184 .2 2 .5 5 .2 100 d . 251 .5 400740 348 d . 249 .2 360 190 .7

460 16 .910 i . v . s . h . 3 .128 137 0 .1 c . i .

0 .59°

i .

s . h . v . s . h . i . c . s . s . 720

v . s . i .

i . i . i . i . s . h . i . 0 .3 1 .35 25 i . 0 .07 22

s . s . 4 .220 11 .415 sl . s . s . ∞ 1725 430 s .

s . s . ∞ sl . s . sl . s . ∞

v . s . h . v . s . 0 .4316 i . 1 h . 0 .09 25 v . sl . s . i . 0 .217 i . 1100

v . s . v . s . v . s . v . s . 1 h . i .

v . s . i . v . s . s . 2 i .

v . s . 4615 s . ∞

v . s . 6615 s . ∞

520 s . 2 .320 s . s .

2-29

Benzoin (dl-) Benzophenone Benzotrichloride Benzoyl-benzoic acid (o-) -chloride -peroxide Benzyl acetate alcohol amine aniline benzoate butyrate chloride ether formate propionate Berberonic acid (2-,4-,5-) Biuret Borneol (dl-) (d- or l-) (iso-) Bornyl acetate (d-) Bromo-aniline (p-) -benzene -camphor (3-)(d-) -diphenyl (p-) -naphthalene (α-) (β-) -phenol (o-) (m-) (p-) -styrene (ω)(1) (2) -toluene (o-) (m-) (p-) Bromoform Butadiene (1-,2-) (1-,3-) Butadienyl acetylene Butane (i-) Butyl acetate (n-) (s-) (i-) (tert-) alcohol (n-) (s-) (i-) (tert-) amine (n-) (s-) (i-) (t-) p-aminophenol (N)(n) (N)(i-) aniline (n-) (i-) arsonic acid (n-) benzoate (n-) (i-) bromide (n-) (s-) (i-) (t-) butyrate (n-)(n-) (n-)(i-) (i-)(i-) caproate carbamate (i-) cellosolve (n-)

diphenyl ketone phenyl chloroform

phenyl carbinol ω-amino toluene phenyl-benzylamine ω-chlorotoluene dibenzyl ether

allophanamide

phenyl bromide α-bromocamphor α-naphthyl bromide β-naphthyl bromide

o-tolyl bromide tribromo-methane methyl-allene erythrene diethyl trimethyl-methane

butanol-1 butanol-2 2-methyl-propanol-1 2-methyl-propanol-2

1-bromo-butane 2-bromo-butane 1-Br-2-Me-propane 2-Br-2-Me-propane

2-BuO-ethanol-1

C6H5CO⋅CHOHC6H5 C6H5COC6H5 C6H5CCl3 C6H5COC6H4CO2H⋅H2O C6H5COCl (C6H5CO)2O2 CH3CO2CH2C6H5 C6H5CH2OH C6H5CH2NH2 C6H5CH2NHC6H5 C6H5CO2CH2C6H5 C2H5CH2CO2CH2C6H5 C6H5CH2Cl (C6H5CH2)2O HCO2CH2C6H5 C2H5CO2CH2C6H5 C5H2N(CO2H)3⋅2H2O NH(CONH2)2 C10H17OH C10H17OH C10H17OH CH3CO2C10H17 BrC6H4NH2 C6H5Br BrC10H15O BrC6H4⋅C6H5 C10H7Br C10H7Br BrC6H4OH BrC6H4OH BrC6H4OH C6H5CH:CHBr C6H5CH:CHBr CH3⋅C6H4Br CH3⋅C6H4Br CH3⋅C6H4Br CHBr3 CH3CH:C:CH2 CH2:CHCH:CH2 CH2:(CH)2:CH⋅C⋮CH CH3CH2CH2CH3 (CH3)2CHCH3 CH3CO2(CH2)2C2H5 CH3CO2CH(CH3)C2H5 CH3CO2CH2CH(CH3)2 CH3CO2C(CH3)3 C2H5CH2CH2OH C2H5CH(OH)CH3 (CH3)2CHCH2OH (CH3)3COH C2H5CH2CH2NH2 C2H5CH(NH2)CH3 (CH3)2CHCH2NH2 (CH3)3CNH2 C4H9NH⋅C6H4⋅OH C4H9NH⋅C6H4⋅OH C4H9NHC6H5 C4H9NHC6H5 C4H9AsO(OH)2 C6H5CO2C4H9 C6H5CO2C4H9 C2H5CH2CH2Br C2H5CH(Br)CH3 (CH3)2CHCH2Br (CH3)3CBr C2H5CH2CO2CH2CH2C2H5 C2H5CH2CO2CH2CH(CH3)2 (CH3)2CHCO2CH2CH(CH3)2 CH3(CH2)4CO2C4H9 NH2CO2CH2CH(CH3)2 C4H9OCH2CH2OH

212 .24 182 .22 195 .47 244 .24 140 .57 242 .23 150 .17 108 .14 107 .15 183 .25 212 .24 178 .23 126 .58 198 .26 136 .15 164 .20 247 .16 103 .08 154 .25 154 .25 154 .25 196 .29 172 .02 157 .01 231 .13 233 .10 207 .07 207 .07 173 .01 173 .01 173 .01 183 .05 183 .05 171 .03 171 .03 171 .03 252 .73 54 .09 54 .09 78 .11 58 .12 58 .12 116 .16 116 .16 116 .16 116 .16 74 .12 74 .12 74 .12 74 .12 73 .14 73 .14 73 .14 73 .14 165 .23 165 .23 149 .23 149 .23 182 .05 178 .23 178 .23 137 .02 137 .02 137 .02 137 .02 144 .21 144 .21 144 .21 172 .26 117 .15 118 .17

mn. col. rhb. col. lq. tri./aq. col. lq. rhb ./et . col . lq . col . lq . lq . mn . pr . nd . col . lq . col . lq . lq . col . lq . lq . tri . nd ./al . col . cr . col . cr . col . cr . rhb ./pet . rhb . col . lq . cr . cr ./al . col . oil lf ./al . col . lq . cr . tet . cr . lq . lq . col . lq . col . lq . cr ./al . col . lq . lq . col . gas col . lq . col . gas col . gas col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . lq . col . lq . col . lq . col . lq . col . lq . lq . oil col . lf . col . oil col . oil lq . lq . lq . lq . col . lq . col . lq . col . lq . col . lq . col . lf . col . lq .

1.08354 1.38014 1.21220/4 1 .05717 1 .04320/4 0 .98220/4 1 .065 25/25 1 .1220/4 1 .01616/18 1 .100 20/20 1 .03616 1 .08123 1 .03616/17 20/4

1 .011 1 .01120/4 0 .99115 1 .820 1 .495 20/4 1 .449 20/4 1 .48220/4 1 .605 0 1 .55380 1 .588 80 1 .42220/4 1 .427 20/4 1 .42220/4 1 .410 20/4 1 .390 20/4 2 .890 20/4 0 .62120/4 0 .773 20/4 0 .600 0 .600 0 .882 20 0 .865 25/4 0 .87120/4 0 .866 20/4 0 .810 20/4 0 .808 20/4 0 .80517 .5 0 .779 26 0 .739 25/4 0 .724 20/4 0 .73220/20 0 .69818/4

133–7 48.5 −4.75 93(128) −0.5 108 d . −51 .5 −15 .3 37–8 21 238–40 −39 3 .6 243 192–3 d . 210 .5 208–9 212 29 63–4 −30 .6 77–8 90–1 5–6 59 5 .6 32–3 63 .5 7 −7 .5 −28 −39 .8 28 .5 8–9 −108 .9 −135 −145 −76 .3 −98 .9 −79 .9 −114 .7 −108 25 .5 −50 −104 −85 −67 .5 71 79

0 .940 20/4 1 .005 25/25 0 .997 25/25 1 .277 20/4 1 .25125/4 1 .258 25/4 1 .21120/4 0 .87220/20 0 .86318/4 0 .875 0/4 0 .8820/0 0 .95676/4 0 .90320/4

158–9 −22 −112 .4 −112 −118 .5 −16 .2 −80 .7 65

344768 305.4 220.7 197.2 expl . 213 .5 204 .7 184 .5 306750 323–4 i . 179 .4 295–8 202–3747 220–2 subl . 212–3 226–7 156 .2 274 310 281 .1 281–2 194–5 236–7 238 221 10826 181 .8 183 .7 184–5 150 .5 18–9 −4 .41 83–6 −0 .6 −10 125 740 112744 118 95–6760 117 99 .5 107–8 82 .9 77 .8 66772 68–9 45 .2 235720 231–2 249–50 241 .5 101 .6 91 .3 91 .5 73 .3 165 .7736 156 .9 148–9 204 .3 206–7 171 .2

v. sl. s. i. i. sl. s. d. i . i . 417 ∞ i . i . v . s . i . i . i . i . v . sl . s . 1 .30 v . sl . s . v . sl . s . i . i . i . c . i . i . i . i . i . s . 1 .415 i . i . i . i . i . 0 .1 c . i . i . i . i . i . 0 .7 i . 0 .625 i . 915 12 .520 1015 ∞ ∞ ∞ ∞ i . i . i . 0 .0115 s . i . i . 0 .0616 i . 0 .0618 i . i . i . i . i . i . ∞

s. h. 6.515 s.

sl. s. 1513 s.

d. h. s . h . ∞ ∞ ∞

∞ s . ∞ ∞ ∞ s . ∞

∞ v . s . ∞ s . h . s . sl . s . h . s .

∞ s . ∞ i .

v . s .

v . s .

s . v . s . s . 2026 s . s . 620 s . s . v . s . ∞ ∞ s . s . s . ∞ ∞ ∞

s . v . s . ∞ v . s . 34 25 ∞ v . s . ∞ s . v . s . ∞ ∞ ∞25 s . ∞25 ∞ ∞ ∞

s . s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞

s . s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞

v . s . v . s . s . s . ∞ ∞

v . s . v . s . i . s . ∞ ∞

∞ ∞ ∞ ∞ ∞

∞ ∞ ∞ ∞ ∞

s . ∞

s . ∞ (Continued )

2-30

TABLE 2-2

Physical Properties of Organic Compounds (Continued )

Name chloride (n-) (s-) (i-) (t-) dimethylbenzene (t-)(1-,3-,5-) formate (n-) (s-) (i-) furoate (n-) iodide (n-) (s-) (i-) (t-) lactate (n-) mercaptan (n-) (i-) (t-) methacrylate (n-) (i-) phenol (p-)(t-) propionate (n-) (s-) (i-) stearate (n-) (i-) iso-thiocyanate (n-) (i-) (s-)(d-) (t-) valerate (n-)(n-) (i-)(n-) (i-)(s-) (i-)(i-) Butylene (α-) (β-) Butyraldehyde (n-) (i-) Butyric acid (n-) (i-) amide (n-) (i-) anhydride (n-) (i-) anilide (n-) Caffeic acid (3-,4-) Caffeine Camphene (dl-) (d- or l-) Camphor (d-) Camphoric acid (d-) Cantharidine Capric acid Caproic acid (n-) (i-) Caprylic acid (n-) Carbazole Carbitol Carbon disulfide monoxide suboxide tetrabromide tetrachloride tetrafluoride Carbonyl sulfide Carminic acid Carvacrol (1-,2-,4-)

Synonym 1-chloro-butane 2-chloro-butane 1-Cl2-2-Me-propane 2-Cl2-2-Me-propane

1-iodo-butane 2-iodo-butane 1-iodo-2-Me-propane 2-iodo-2-Me-propane butanthiol-1 2-Me-propanthiol-1

butyl mustard oil iso-Bu mustard oil

butene-1 butene-2 2-Me-propanol butanoic acid 2-Me-propanoic acid n-butyramide iso-butyramide n-butyranilide

decanoic acid hexanoic acid 2-Me-pentanoic-5 acid octanoic acid diphenylenelimine, dibenzopyrrole diethylene glycol mono-Et ether

tetrabromomethane tetrachloromethane tetrafluoromethane

Formula C2H5CH2CH2Cl C2H5⋅CHCl⋅CH3 (CH3)2CHCH2Cl (CH3)3CCl (CH3)3C⋅C6H3:(CH3)2 HCO2CH2CH2C2H5 HCO2CH(CH3)C2H5 HCO2CH2CH(CH3)2 OC4H3CO2C4H9 C2H5CH2CH2I C2H5CHICH3 (CH3)2CHCH2I (CH3)3CI CH3CH(OH)CO2C4H9 C2H5CH2CH2SH (CH3)2CHCH2SH (CH3)3CSH CH2:C(CH3)CO2C4H9 CH2:C(CH3)CO2C4H9 (CH3)3C⋅C6H4⋅OH C2H5CO2C4H9 C2H5CO2C4H9 C2H5CO2C4H9 CH3(CH2)16CO2C4H9 CH3(CH2)16CO2C4H9 C2H5CH2CH2⋅N:CS (CH3)2CHCH2⋅N:CS C4H9⋅N:CS (CH3)3C⋅N:CS CH3(CH2)3CO2(CH2)3CH3 (CH3)2CHCH2CO2(CH2)3CH3 (CH3)2CHCH2CO2C4H9 C4H9CO2C4H9 C2H5CH:CH2 CH3CH:CHCH3 CH3CH2CH2CHO (CH3)2CHCHO C2H5CH2CO2H (CH3)2CHCO2H C2H5CH2CONH2 (CH3)2CHCONH2 (C2H5CH2CO)2O [(CH3)2CHCO]2O C3H7CONHC6H5 (HO)2C6H3C2H2CO2H C8H10O2N4⋅H2O C10H16 C10H16 C10H16O C8H14(CO2H)2 C10H12O4 CH3(CH2)8CO2H CH3(CH2)4CO2H (CH3)2CH(CH2)2⋅CO2H CH3(CH2)6CO2H (C6H4)2NH C2H5O(CH2)2O(CH2)2OH CS2 CO OC:C:CO CBr4 CCl4 CF4 COS C22H20O13 CH3C6H3(OH)CH(CH3)2

Formula weight 92 .57 92 .57 92 .57 92 .57 162 .27 102 .13 102 .13 102 .13 168 .19 184 .02 184 .02 184 .02 184 .02 146 .18 90 .19 90 .19 90 .19 142 .20 142 .20 150 .22 130 .18 130 .18 130 .18 340 .58 340 .58 115 .20 115 .20 115 .20 115 .20 158 .24 158 .24 158 .24 158 .24 56 .11 56 .11 72 .11 72 .11 88 .11 88 .11 87 .12 87 .12 158 .19 158 .19 163 .22 180 .16 212 .21 136 .23 136 .23 152 .23 200 .23 196 .20 172 .26 116 .16 116 .16 144 .21 167 .21 134 .17 76 .14 28 .01 68 .03 331 .63 153 .82 88 .00 60 .08 492 .39 150 .22

Form and color

Specific gravity

Melting point, °C

Boiling point, °C

col. lq. col . lq . col . lq . col . lq . col . lq . lq . lq . lq . col . lq . lq . lq . lq . lq . col . lq . col . lq . lq . lq . lq . lq . nd ./aq . col . lq . col . lq . col . lq . col . lq . wax lq . lq . lq . lq . lq . lq . col . lq . col . lq . col . gas col . gas col . lq . col . lq . col . lq . col . lq . rhb . mn . pl . col . lq . col . lq . mn . pr . yel ./aq . nd ./al . cr . cr . trig . mn . cr . col . nd . oily lq . col . oil col . lf . lf . col . lq . col . lq . col . gas gas col . mn . col . lq . gas col . gas red pd . col . lq .

0.887 20 0 .87120/4 0 .88415 0 .84715

−123.1 −131 −131 .2 −26 .5

77.9763 67 .8767 68 .9 51–2 200–2147 106 .9 97 98 .2 118–2025 129 .9 118–9 120 99 75–66 97–8 88 65–7 155 155 236–8 146 132 .5 136 .8 220–525

0 .9110 0 .88220/4 0 .885 20/4 1 .056 20/4 1 .617 20/4 1 .595 20 1 .606 20/4 1 .370 19/15 0 .968 0 .837 25/4 0 .836 20/4 0 .889 15 .6 0 .889 15 .6 0 .908 112/4 0 .88315 0 .866 20/4 0 .888 0/4 0 .855 25/25 0 .95611 0 .96414/4 0 .943 20/4 0 .91910 0 .87015/4 0 .862 25/4 0 .848 20/4 0 .8740/4 0 .69 20/4

0 .817 0 .79420/4 0 .96420/4 0 .949 20/4 1 .032 1 .013 0 .968 20/20 0 .950 25/4 1 .134 1 .2319 0 .82278 0 .845 50/4 0 .999 9/9 1 .186 0 .889 87 0 .922 20/4 0 .925 20/4 0 .910 20/4 0 .990 20/20 1 .263 20/4 0 .81−195/4 1 .1140 3 .42 1 .595 20/4 1 .24−87 0 .977

20/4

−95 .3 −103 .5 −104 −90 .7 −34 −116

CH2 < (CH2CH2)2 > CH2 CH2 < (CH2CH2)2 > CHOH CH2 < (CH2CH2)2 > CO (⋅CH2⋅CH2CH:)2 CH3CO2C6H11 CH2 < (CH2CH2)2 > CHNH2 CH2 < (CH2CH2)2 > CHBr CH2 < (CH2CH2)2 > CHCl CH2 < (CH:CH)2 > CH2 < (CH2CH2)2 > < (CH2CH2)2 > CO < CH2CH2CH2 > CH3⋅C6H4CH(CH3)2 CH3⋅C6H4CH(CH3)2 CH3⋅C6H4CH(CH3)2 [⋅SCH2CH(NH2)CO2H]2 C6H6(OH)6 C10H18 C10H18 CH3(CH2)8CH3 CH3(CH2)8CH2OH (C6H10O5)x (CH3)2C(OH)⋅CH2COCH3 H2NC6H4COC6H4NH2 H2NC6H4NHC6H4NH2 H2NC6H4CH2C6H4NH2 (H2NC6H4NH)2CO [(CH3)2CHCH2CH2]2NH (C2H5CH2CH2CH2)2O [(CH3)2CH(CH2)2]2O [(CH3)2CHCH2CH2]2CO C6H4(CO2C5H11)2 C6H4(CO2C5H11)2 (HOCH⋅CO2C5H11)2 [NH2(OCH3)C6H3⋅]2 C6H5N:N⋅NHC6H5 C7H7N:N⋅NHC7H7 CH2:N2

Formula weight 164 .16 164 .16 146 .14 118 .13 149 .15 113 .12 138 .16 137 .18 108 .14 108 .14 108 .14 212 .24 212 .24 212 .24 86 .09 86 .09 70 .09 120 .19 164 .20 135 .21 42 .04 43 .02 85 .06 52 .03 105 .92 61 .47 165 .10 56 .11 98 .19 84 .16 100 .16 98 .14 82 .14 142 .20 99 .17 163 .06 118 .60 66 .10 70 .13 84 .12 42 .08 134 .22 134 .22 134 .22 240 .30 180 .16 138 .25 138 .25 142 .28 158 .28 162 .14 116 .16 212 .25 199 .25 198 .26 242 .28 157 .30 158 .28 158 .28 170 .29 306 .40 306 .40 290 .35 244 .29 197 .24 225 .29 42 .04

Form and color nd./aq. cr./aq. rhb./et. oil mn./aq. mn. pr. nd ./pet . cr . lq . pr . lq . cr . cr . col . mn . nd . col . lq . col . lq . tri . lq . col . nd . gas col . lq . col . gas nd . gas mn ./aq . col . gas oil col . lq . col . nd . col . oil lq . oil col . lq . col . lq . col . lq . col . lq . col . oil col . oil col . gas col . lq . col . lq . col . lq . pl . mn ./aq . lq . lq . col . lq . col . oil amor . lq . yel . nd . lf ./aq . nd ./aq . cr . col . lq . col . lq . col . lq . yel . oil col . lq . col . lq . lq . col . lf . yel . lf . or . cr . gas

Specific gravity

0.93520/4 1.07815/15 1.09220/20 20/4

1 .048 1 .03420/4 1 .03520/4

79 .7

0 .964 1 .03115/4 0 .85320/20 0 .86220/4 1 .1624 0 .953 1 .07348/4 1 .1400 0 .86617 2 .01520/4 1 .2220 1 .7680/4 0 .7030/4 0 .81020/4 0 .77920/4 0 .96220/4 0 .94719/4 0 .81020/4 0 .9850/4 0 .86520/0 1 .32420/20 0 .97718/4 0 .80519/4 0 .74520/4 0 .94820 0 .720−79 0 .87520/4 0 .86220 0 .85720/4 1 .752 0 .89518/4 0 .87220/4 0 .7302 0 .83020/4 1 .038 0 .93125

0 .76721/4 0 .77420/4 0 .77720/4 0 .82125/4

Melting point, °C

Boiling point, °C

207–8 206–7 d. 70

Hg(CN)2 Hg(ONC)2⋅½H2O (CH3)2C:CHCOCH3 C6H3(CH3)3 H2NC6H4SO3H CH4

Formula weight 144 .21 102 .17 102 .17 102 .17 130 .18 194 .27 179 .17 155 .15 180 .16 90 .08 27 .03 110 .11 122 .12 213 .23 145 .16 145 .16 262 .26 264 .28 117 .15 133 .15 204 .01 220 .01 393 .73 192 .30 192 .30 206 .32 147 .13 68 .12 42 .04 427 .34 90 .08 162 .14 144 .13 360 .31 200 .32 338 .61 186 .33 323 .44 267 .34 143 .19 131 .17 116 .12 136 .23 154 .25 196 .29 280 .45 116 .07 98 .06 134 .09 134 .09 104 .06 360 .31 152 .15 182 .17 180 .16 270 .45 342 .17 156 .27 167 .25 119 .21 252 .62 293 .63 98 .14 120 .19 173 .19 16 .04

Form and color

Specific gravity

col. lq. col. lq. lq . lq . lq . col . nd . rhb . lf ./aq . cr ./aq . syrup lq . cr . nd ./aq . pr ./al . pr ./al . pr . cr . gray lf ./aq . yel . pr . col . lq . nd ./aq . yel . hex . col . oil col . oil col . oil yel . red col . lq . col . gas cr . hyg . yel . oil tri ./al . col . rhb . col . nd . pl . lf . col . lq . col . lq . lq . cr . lf . lq . col . oil col . lq . yel . oil mn . cr . col . cr . col . cr . col . tri . col . nd . rhb ./aq . col . rhb . rhb . col . pl . nd ./al . col . cr . nd . cr . cr . cr ./aq . lq . col . lq . col . nd . gas

0.890 0/0 0.820 20/20 0 .821 20/0 0 .809 20/4 0 .898 0 1 .371 20/4

0 .697 18 1 .332 15 1 .129 130

1 .35

1 .824 25/4 1 .857 112 4 .008 17 0 .930 20 0 .944 20 0 .939 20

Melting point, °C −51.6 −14 −107 68–70 187–8 d . 287 175–80 −12 170 .3 116–7 135 199–200 75–6 390–2 52 85 −28 .5 93–4 119

0 .681 20/4

200–1 −120 −151

1 .249 15/4

16 .8

10/4

0 .862 1 .525 20 0 .869 50/4 0 .809 69/4 0 .831 24/4 1 .659 18/4 1 .995 20/4 1 .086 20 1 .29318 1 .140 20/20 0 .842 20/4 0 .868 20 0 .895 20 0 .903 18/4 1 .609 1 .5 1 .601 20/4 1 .595 20/4 1 .631 15 1 .540 17 1 .300 20/4 1 .489 20/4 1 .539 20/4 0 .853 60 15/15

0 .890 1 .4220/4 1 .50 4 .003 22 4 .4 0 .858 20/4 0 .865 20/4

0 .415 −164

124 .5 202 48(44) 69–70 24 −136 −27 .5 9–10 295 33 .5 −96 .9 −9 .5 130 .5 57–60 128–9 99–100 130–5 d . d . 118 .1 166 132 60–1 286–8 42–3 179 106 d . 320 expl . −59 −45(−52) d . −182 .6

Boiling point, °C 169.2 157.2 120–1 123762 153 .6 1797 d . d . 25–6 285730 subl . d . subl . 266 .6752 subl . 253–4 110 188 .6 d . subl . 136 .117 14018 14416 subl . 34 −56 12214 d . 250 255757 d . 225100 255–9 152291 110760 261–3 subl . 245–6 177 198–200 220762 d . 229–3016 135 d . 202 150 d . 140 d . d . 290–53 227100 d . 212 d .

130750 164 .8 −161 .4

Solubility in 100 parts Water i. 0.620 v . sl . s . v . sl . s . 0 .05 0 .420 s . s . h . ∞ 615 1 .3831 v . sl . s . h . s . h . v . sl . s . c . i . i . s . h . s . 0 .03420 sl . s . 0 .0125 sl . s . sl . s . v . sl . s . s . h . i . d . 7 .220 ∞ v . sl . s . v . sl . s . 1710 i . i . i . i . i . sl . s . 2 .218 v . s . i . v . sl . s . v . sl . s . i . 7925 16 .380 14426 v . s . 13816 10825 1620 1314 24817 i . v . s . 0 .04 c . i . 1 .660 12 .515 0 .0712 320 i . 215 0 .420 cc .

Alcohol

Ether

v. s. ∞ ∞ ∞ ∞ v . s . s . h . v . sl . s . v . s .

v. s. ∞ ∞ ∞ ∞ s . 0 .2518 i . sl . s .

∞ v . s .

∞ v . s .

s . v . s . s . i . s . s . h . s . s . v . s . 1 .517 ∞ ∞ v . s . v . s . h . ∞ d .

s . v . s . sl . s . i . s . s . s . ∞ v . s . 13 .625 ∞ ∞ v . s . sl . s . ∞ s .

∞ s . v . sl . s . c . i . s . i . c . s . sl . s . ∞ ∞

∞ s .

v . s . ∞ s . ∞ ∞ 7030

v . s . ∞ ∞ ∞ ∞ 825

v . s . v . s . 4225 v . sl . s . c . s . 0 .0114 v . sl . s . 3228 v . s . v . s . s .

v . s . 8 .415 815 i . s . i . i . v . s .

s . ∞ s . v . sl . s . 4720 cc .

i . s . s . ∞ ∞ ∞

v . s . sl . s .

∞ ∞ v . sl . s . 10410 cc .

2-39

Methoxy-methoxyethanol Methyl acetate acrylic acid (α-) alcohol -amine -amine hydrochloride aniline anthracene (α-) (β-) anthranilate (o-) anthraquinone (2-) benzoate benzylaniline bromide butyrate (n-) (i-) caprate caproate (n-) caprylate cellosolve chloride chloroacetate chloroformate cinnamate cyclohexane ethyl carbonate ethyl ketone ethyl oxalate formate furoate glucamine glycolate heptoate hypochlorite iodide lactate laurate mercaptan methacrylate myristate naphthalene (α-) (β-) nitrate nitrite nonyl ketone (n-) oleate orange palmitate phosphine propionate propyl ketone (n-) salicylate (o-) stearate toluate (o-) (m-) (p-) Methyl toluidine (o-) (m-) (p-) valerate (n-) (i-) vinyl ketone Methylal Methylene-bis-(phenyl-4-isocyanate) bromide chloride dianiline iodide Michler’s hydrol (p-,p′-) ketone Morphine Mucic acid

CH3(OCH2)2CH2OH CH3CO2CH3 CH2:C(CH3)CO2H CH3OH CH3NH2 CH3NH2⋅HCl C6H5NHCH3 C6H4:(CH)2:C6H3CH3 C6H4:(CH)2:C6H3CH3 NH2C6H4CO2CH3 C6H4:(CO)2:C6H3CH3 C6H5CO2CH3 C6H5N(CH3)CH2C6H5 CH3Br CH3(CH2)2CO2CH3 (CH3)2CHCO2CH3 CH3(CH2)8CO2CH3 CH3(CH2)4CO2CH3 CH3(CH2)6CO2CH3 CH3OCH2CH2OH CH3Cl ClCH2CO2CH3 ClCO2CH3 C6H5CH:CHCO2CH3 CH2 < (CH2CH2)2 > CHCH3 CH3O⋅CO⋅OC2H5 CH3 .CO⋅C2H5 CH3OCO⋅CO2C2H5 HCO2CH3 C4H3O⋅CO2CH3 CH2OH(CHOH)4CH2NHCH3 HOCH2CO2CH3 CH3(CH2)5CO2CH3 ClOCH3 CH3I CH3CH(OH)CO2CH3 CH3(CH2)10CO2CH3 CH3SH CH2:C(CH3)CO2CH3 CH3(CH2)12CO2CH3 C10H7CH3 C10H7CH3 CH3ONO2 CH3ONO CH3(CH2)8COCH3 C17H33CO2CH3 (CH3)2NC6H4N2C6H4SO3Na CH3(CH2)14CO2CH3 CH3PH2 CH3CH2CO2CH3 CH3COCH2CH2CH3 HO⋅C6H4CO2CH3 CH3(CH2)16CO2CH3 CH3⋅C6H4CO2CH3 CH3⋅C6H4CO2CH3 CH3⋅C6H4CO2CH3 CH3⋅C6H4NHCH3 CH3⋅C6H4NHCH3 CH3⋅C6H4NHCH3 CH3(CH2)3CO2CH3 (CH3)2CHCH2CO2CH3 CH3COCH:CH2 HCH(OCH3)2 (OCN⋅C6H4)2CH2 CH2Br2 CH2Cl2 (C6H5NH)2CH2 CH2I2 [(CH3)2NC6H4]2CHOH [(CH3)2NC6H4]2CO C17H19O3N⋅H2O (⋅CHOHCHOHCO2H)2

106 .12 74 .08 86 .09 32 .04 31 .06 67 .52 107 .15 192 .26 192 .26 151 .16 222 .24 136 .15 197 .28 94 .94 102 .13 102 .13 186 .29 130 .18 158 .24 76 .09 50 .49 108 .52 94 .50 162 .19 98 .19 104 .10 72 .11 132 .11 60 .05 126 .11 195 .21 90 .08 144 .21 66 .49 141 .94 104 .10 214 .34 48 .11 100 .12 242 .40 142 .20 142 .20 77 .04 61 .04 170 .29 296 .49 327 .33 270 .45 48 .02 88 .11 86 .13 152 .15 298 .50 150 .17 150 .17 150 .17 121 .18 121 .18 121 .18 116 .16 116 .16 70 .09 76 .09 250 .25 173 .83 84 .93 198 .26 267 .84 270 .37 268 .35 303 .35 210 .14

lq. col . lq . pr . col . lq . col . gas pl ./al . lq . lf ./al . col . lf . col . lq . col . nd . col . lq . lq . gas col . lq . col . lq . lq . col . lq . col . lq . col . lq . gas col . lq . col . lq . cr . col . lq . lq . col . lq . lq . lq . col . lq . lq . lq . gas col . lq . lq . lq . gas lq . cr ./al . oil mn . lq . gas col . oil oil red pd . col . cr . gas col . lq . col . lq . col . lq . col . cr . col . lq . col . lq . cr . lq . lq . lq . lq . col . lq . lq . col . lq . lq . col . lq . col . lq . cr . col . lq . gn . lf ./al . pr ./al . pd .

1.038 25 0 .924 20/4 1 .015 20/4 0 .792 20/4 0 .699 −11 1 .23 0 .989 20/4 1 .047 99 .4 1 .181 0/4 1 .168 19/4 1 .087 25/25 1 .732 0/0 0 .898 20/4 0 .891 20/4 0 .904 0/0 0 .887 18 0 .965 20/4 0 .952 0 1 .236 20/4 1 .236 15 1 .042 36/0 0 .769 20/4 1 .002 27 0 .805 20/4 1 .156 0/0 0 .974 20/4 1 .179 21/4

250 125 46–9 69–70 50 111–2

250.5100 16715 217.9

300 >300 278–80 285–6

300.8 306.1 subl.

d.

1.18 1.009 20/4

1 .207 156 1 .211 156 15

1 .442 1 .43 1 .437 14 1 .254 20/4 1 .233 20

1 .205

18/4

1 .575 4/4 1 .494 4/4 1 .550 22/4

89/4

1 .240 1 .067 20/4 1 .179 20/4 1 .313 17 1 .44

NH C5H4N⋅CH3 C5H4N⋅CH3 C5H4N⋅CH3 HO⋅C6H2(NH2)(NO2)2 HO⋅C6H2(NO2)3 ClC6H2(NO2)3 [(CH3)2C⋅OH]2 CH3COC(CH3)3 C10H16 C10H17Cl C10H16O CH2 < (CH2CH2)2 > NH HO2C⋅CH < (CH2CH2)2 > NH (CH2)5CS2H⋅HN(CH2)5 CH3CH2CH3 CH3CH2CO2H CH3CH2CHO (CH3CH2CO)2O CH3CO2CH2CH2CH3 CH3CO2CH(CH3)2 CH3CH2CH2OH (CH3)2CHOH CH3CH2CH2NH2 (CH3)2CHNH2 C6H5NHCH2CH2CH3 C6H5CO2CH2CH2CH3 C6H5CO2CH(CH3)2 CH3CH2CH2Br (CH3)2CHBr C2H5CH2CO2CH2C2H5 (CH3)2CHCO2CH2C2H5 C2H5CH2CO2CH(CH3)2 (CH3)2CHCO2CH(CH3)2 CH3CH2CH2Cl (CH3)2CHCl HCO2CH2CH2CH3 HCO2CH(CH3)2 C4H3O⋅CO2C3H7 CH3CH(OH)CO2CH2C2H5 CH3CH(OH)CO2CH(CH3)2 CH3CH2CH2SH (CH3)2CHSH C2H5CO2CH2C2H5 C2H5CO2CH(CH3)2 (CH3)2CH⋅CNS CH3(CH2)3CO2CH2C2H5 (CH3)2CHCH2CO2C3H7 (CH3)2CHCH2CO2C3H7 CH3CH:CH2 CH3CHBrCH2Br CH3CHClCH2OH CH3CHClCH2Cl CH3CH(OH)CH2OH CH3(CHCH2)O (HO)2C6H3CO2H⋅H2O

Formula weight

Form and color

108 .14 108 .14 108 .14 162 .14 138 .21 98 .92 166 .13 166 .13 148 .12 128 .13 134 .13 147 .13 93 .13 93 .13 93 .13 199 .12 229 .10 247 .55 118 .17 100 .16 136 .23 172 .69 152 .23 85 .15 129 .16 232 .43 44 .10 74 .08 58 .08 130 .14 102 .13 102 .13 60 .10 60 .10 59 .11 59 .11 135 .21 164 .20 164 .20 122 .99 122 .99 130 .18 130 .18 130 .18 130 .18 78 .54 78 .54 88 .11 88 .11 154 .16 132 .16 132 .16 76 .16 76 .16 116 .16 116 .16 101 .17 144 .21 144 .21 144 .21 42 .08 201 .89 94 .54 112 .99 76 .09 58 .08 172 .14

lf./aq. rhb. mn. rhb. yel. pr. gas mn./aq. nd./aq. rhb. cr. nd./aq. cr./et. col. lq. col . lq . lq . red nd . yel . rhb . yel . mn . col . nd . col . lq . col . lq . lf . lq . lq . cr . cr . gas col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . lq . lq . col . lq . col . lq . lq . lq . col . lq . col . lq . gas col . lq . col . lq . col . lq . col . oil col . lq . nd ./aq .

Specific gravity 1.139 15/15 0.885 20/4 1.392 19/4 1.593 20/4 1.527

4

1.164

99/4

0.950 15/4 0 .961 15/4 0 .957 15/4 1 .763 20/4 1 .797 20 0 .967 15 0 .800 16 0 .878 20/4 0 .953 20/20 0 .860 20/4 1 .13 0 .585 −45/4 0 .992 20/4 0 .807 20/4 1 .012 20/4 0 .886 20/4 0 .874 20/20 0 .804 20/4 0 .78920/4 0 .718 20/20 0 .694 15/4 0 .949 18 1 .021 25/25 1 .010 25/25 1 .353 20/4 1 .310 20/4 0 .879 15 0 .884 0/4 0 .865 18 0 .869 0/4 0 .890 20/4 0 .859 20 0 .901 20/4 0 .873 20/4 1 .075 26/4 0 .836 25/4 0 .809 25/4 0 .883 20/4 0 .893 0 0 .963 20 0 .874 15 0 .863 20/4 0 .854 17 0 .609 −47/4 1 .933 20/4 1 .103 20 1 .159 20/20 1 .040 19 .4 0 .831 20/20 1 .542 4/4

Melting point, °C

Boiling point, °C

103–4 62.8 140 117 28 −104 208 330 130.8 141 73(65) 238 −70

256–8 284–7 267 subl. 197.2743 8.2756 d. subl. 284.5

169 121 .8 83 43(38) −52 .5 −55 131–2 −9 264 175 −187 .1 −22 −81 −45 −92 .5 −73 .4 −127 −85 .8 −83 −101 −51 .6 −109 .9 −89 −95 .2

−122 .8 −117 −92 .9

−112 −130 .7 −76 −70 .7 −185 −55 .5

CH < (CHCH)2 > N C6H4(OH)2 C6H3(OH)3 CO < (CHCH)2 > O < (CH:CH)2 > NH < (CH2⋅CH2)2 > NH < (CH⋅CH2)2 > NH CH3COCO2H C21H20O11⋅2H2O CH3⋅C9H6N C9H7N C9H7N —C6H4CH:C(OH)N:C(OH)— CO < (CHCH)2 > CO HOC10H5(SO3)2Ca HOC10H5(SO3K)2 HOC10H5(SO3Na)2 C18H32O16⋅5H2O C6H4(OH)2 C18H18 CH3(CHOH)4CHO⋅H2O C17H32(OH)CO2H C20H21ON3 C20H16O3 C6H4(CO)(SO2) > NH CH2:CHCH2⋅C6H3:O2CH2 CH3⋅CH:CH⋅C6H3:O2CH2 HO⋅C6H4⋅CO2H HO⋅C6H4⋅CHO HO⋅C6H4⋅CH2OH (HOC10H6SO3)2Ca⋅5H2O HOC10H6SO3K HOC10H6SO3Na NH2⋅CO⋅NH⋅NH2 NH2⋅CO⋅NH⋅NH3Cl CH3⋅C8H6N CH3ONa [CH2OH(CHOH)2]2 C6H12O6 (C6H10O5)x CH3(CH2)16CO2H CH3(CH2)16CONH2 C6H5CH:CH2 HO2C(CH2)6CO2H HO2C(CH2)2CO2H C12H22O11 H2N⋅C6H4⋅SO3H C10H16 (CHOHCO2H)2 (CHOHCO2H)2⋅H2O (CHOHCO2H)2 CH(OH)(CO2H)2⋅½H2O C6H4(CO2H)2 C10H20O2⋅H2O C10H18O C10H18O CH3CO2⋅C10H17 Br2CH⋅CHBr2 Br3C⋅CH2Br Cl2CH⋅CHCl2 Cl3C⋅CH2Cl Cl2C:CCl2 CH3(CH2)22CH3 CH3(CH2)12CH3 [(C2H5)2NCS]2S2

154 .25 152 .23 68 .08 70 .09 84 .08 202 .25 80 .09 79 .10 110 .11 126 .11 96 .08 67 .09 71 .12 69 .11 88 .06 484 .41 143 .19 129 .16 129 .16 161 .16 108 .09 342 .36 380 .48 348 .26 594 .51 110 .11 234 .34 182 .17 298 .46 319 .40 304 .34 183 .18 162 .19 162 .19 138 .12 122 .12 124 .14 576 .60 262 .32 246 .21 75 .07 111 .53 131 .17 54 .02 182 .17 180 .16 162 .14 284 .48 283 .49 104 .15 174 .19 118 .09 342 .30 173 .19 136 .23 150 .09 168 .10 150 .09 129 .07 166 .13 190 .28 154 .25 154 .25 196 .29 345 .65 345 .65 167 .85 167 .85 165 .83 338 .65 198 .39 296 .54

col. lq. col. lq. nd ./et . lq . nd . yel . pr . lq . col . lq . nd ./aq . nd . cr . lq . lq . lq . col . lq . yel . nd . lq . lq . pl . cr . yel . mn . cr . cr . cr . cr ./aq . col . rhb . lf ./al . col . mn . lq . col . nd . red lf . mn . col . mn . col . lq . mn . col . oil rhb ./aq . cr . cr . cr . pr ./al . pr . lf . pd . cr . rhb . amor . mn . col . cr . col . lq . nd ./aq . col . mn . col . mn . col . cr . lq . cr . tri . mn . pr ./aq . cr . rhb . col . cr . col . cr . lq . col . lq . col . lq . col . lq . lq . col . lq . cr . col . lq . cr .

0.911 20/4 0.932 20/20 70 1 .277 0/4 1 .107 20/4 0 .982 20/4 1 .344 4 1 .453 4 1 .190 40 .3 0 .948 20/4 0 .852 22 .5 0 .910 20/4 1 .267 20/4 1 .059 20/4 1 .095 20 1 .099 21/4 1 .318 20/4

1 .465 0 1 .272 15 1 .1316 1 .47120/4 0 .954 16

1 .100 20/4 1 .122 20/4 1 .443 20/4 1 .153 25/4 1 .161 25

1 .654 15 1 .5021 0 .847 69 .3 0 .903 20/4 1 .266 25/4 1 .572 25/4 1 .588 15 0 .863 20/4 1 .737 1 .697 20/4 1 .760 20/4 1 .510 0 .935 15 0 .935 20/20 0 .966 20/4 2 .964 20/4 2 .875 20/4 1 .600 20/4 1 .588 20/4 1 .624 15/4 0 .779 51/4 0 .765 20/4 1 .17

165 149–50 −8 −42 104–5 133–4 32 .5

13 .6 182–5 −1 −15 24 .6 237 115 .7

119 110 .7 98–9 126 4–5 186 d . 308–10 d . 225–8 11 .2 6–7 159 −7 86–7

96 173 d . 95 d . 300 110–2 165 d . 70–1 108–9 −31 140–4 189–90 170–86 d . d . > 280

86–9 10 224754 186–8 144 subl . d . >360 208 115–6 240–5 309 215–7 131 87–8 90–1 165 244–5750 237 .1747 240 .5763 subl .

d . 130 276 .5 390–4 226–810 subl . 233–4 252–3 21120 196 .5 subl .

265–6755

291110 25112 145–6 279100 235 d . 176–7

159–60 205–6 168–70 d . 155–8 subl . 117 38–40 35 < −50 −1 .0 0 −36 −19 51 .1 5 .5 70

d . subl . d . 219–21 218–9752 220 d . 15154 10413 146 .3 129–30 120 .8 324 252 .5

v. sl. s. i. s . ∞ s . i . ∞ ∞ 45 .120 40 13 v . sl . s . i . ∞ v . s . ∞ 0 .04 20 v . sl . s . 6 sl . s . v . sl . s . sl . s . h . 30 .6 25 29 .5 25 25 .2 25 14 .3 20 14712 i . 60 .8 21 i . v . sl . s . 0 .1225 0 .4 25 i . i . 0 .223 1 .7 86 6 .615 4 .7620 3 .4625 6 .2925 v . s . v . s . 0 .05 c . d . v . s . 5517 i . 0 .0325 i . v . sl . s . 0 .1416 6 .820 1790 0 .810 12015 20 .620 13920 v . s . 0 .001 c . 0 .415 i . i . i . i . 20

0 .29 i . 0 .0220 i . i .

∞ s . ∞ v . s . 3 h . s . ∞ v . s . s . s . s . ∞ ∞ ∞ s . ∞ s .

0 .120 v . s . 69 h .

∞ s . sl . s . v . sl . s . v . s . s . s . v . s . s . v . s . s . ∞ ∞ ∞ sl . s . s . ∞ s . s .

∞ sl . s . v . s . h . 3 .1 c . s . ∞ 4915 ∞ v . s .

v . s . v . s . h . i . ∞ i . sl . s . 1 .05 c . ∞ ∞ 5115 ∞ v . s .

v . s . sl . s . s .

i . i . s .

v . s . h . sl . s . i . 220 s . h . ∞ s . 9 .915 0 .9 v . sl . s .

i . 6g s . h: ∞ 0 .815 1 .215 i . v . sl . s .

20 2515 v . s . sl . s . h . 1015 v . s . v . s . 20 ∞ s . ∞ ∞ ∞ v . s .

0 .09 0 .415 i . i . 115 v . s . v . s . ∞ ∞ ∞ ∞ s . v . s . (Continued )

2-44

TABLE 2-2

Physical Properties of Organic Compounds (Continued ) Name

Tetrafluoro-ethylene Tetrahydro-furan -furfuryl alcohol -pyran Tetralin Tetramethyl-thiuram disulfide Tetryl (2-,4-,6-) Theobromine Thio-acetic acid -aniline (4-,4′-) -carbanilide -naphthol (β-) -phenol -salicylic acid (o-) -urea Thiophene Thymol (5-,2-,1-) Tolidine (0-)(3-,3′-,4-,4′-) Toluene sulfonic acid (o-) (p-) sulfonic amide (p-) sulfonic chloride (p-) Toluic acid (o-) (m-) (p-) Toluidine (o-) (m-) (p-) hydrochloride (o-) sulfonic acid (1-,2-,3-) Toluylenediamine (1-,2-,4-) Tolylene diisocyanate (1-,2-,4-) Trehalose Triamylamine (n-) (i-) Tributyl-amine (n-) phosphite Trichloro-acetic acid -benzene (s-)(1-,3-,5-) -ethane (1-,1-,1-) -ethylene -phenol Tricosane (n-) Tricresyl phosphate (o-) Tridecane (n-) Triethanol amine Triethyl-amine -benzene (1-,3-,5-) (1-,2-,4-) borate citrate Triethylene glycol Trifluoro-chloromethane -chloroethylene -trichloroethane Trimethoxybutane (1-,3-,3-) Trimethylamine Trimethylene bromide chloride glycol

Formula

Formula weight

F2C:CF2 —CH2(CH2)2CH2⋅O— C4H7O⋅CH2OH —CH2(CH2)3CH2⋅O— —C6H4CH2(CH2)2CH2— [(CH3)2NCS]2S2 (NO2)3C6H2⋅N(CH3)NO2 C7H8O2N4 CH3⋅CO⋅SH (NH2⋅C6H4)2S (C6H5⋅NH)2CS C10H7⋅SH C6H5⋅SH HS⋅C6H4⋅CO2H NH2⋅CS⋅NH2 < (CH:CH)2 > S (CH3)(C3H7)C6H3OH [CH3(NH2)C6H3]2 C6H5⋅CH3 CH3⋅C6H4SO3H⋅2H2O CH3⋅C6H4SO3H⋅H2O CH3⋅C6H4SO2NH2 CH3⋅C6H4⋅SO2Cl CH3⋅C6H4⋅CO2H CH3⋅C6H4⋅CO2H CH3⋅C6H4⋅CO2H CH3⋅C6H4⋅NH2 CH3⋅C6H4⋅NH2 CH3⋅C6H4⋅NH2 CH3⋅C6H4⋅NH3Cl CH3(NH2)C6H3SO3H CH3⋅C6H3(NH2)2 CH3⋅C6H3(NCO)2 C12H22O11⋅2H2O [CH3(CH2)3CH2]3N [(CH3)2CH(CH2)2]3N [CH3(CH2)2CH2]3N [CH3(CH2)3O]3P Cl3C⋅CO2H C6H3Cl3 Cl3C⋅CH3 Cl2C:CHCl Cl3C6H2OH CH3(CH2)21CH3 OP(OC6H4CH3)3 CH3(CH2)11CH3 (HOCH2CH2)3N (CH3CH2)3N (C2H5)3C6H3 (C2H5)3C6H3 B(OCH2CH3)3 HOC3H4(CO2C2H5)3 (⋅CH2OCH2CH2OH)2 CF3Cl F2C:CFCl Cl2CF⋅CClF2 CH2(OCH3)CH2C(OCH3)2CH3 (CH3)3N BrCH2CH2CH2Br ClCH2CH2CH2Cl HOCH2CH2CH2OH

100 .02 72 .11 102 .13 86 .13 132 .20 240 .43 287 .14 180 .16 76 .12 216 .30 228 .31 160 .24 110 .18 154 .19 76 .12 84 .14 150 .22 212 .29 92 .14 208 .23 190 .22 171 .22 190 .65 136 .15 136 .15 136 .15 107 .15 107 .15 107 .15 143 .61 187 .22 122 .17 174 .16 378 .33 227 .43 227 .43 185 .35 250 .31 163 .39 181 .45 133 .40 131 .39 197 .45 324 .63 368 .36 184 .36 149 .19 101 .19 162 .27 162 .27 145 .99 276 .28 150 .17 104 .46 116 .47 187 .38 148 .20 59 .11 201 .89 112 .99 76 .09

Form and color

Specific gravity

Melting point, °C

Boiling point, °C

gas col. lq. col. lq. lq . col . lq . cr . yel . mn . rhb . yel . lq . nd ./aq . rhb ./al . cr ./al . col . lq . yel . nd . rhb ./al . col . lq . cr . lf . col . lq . cr . mn . mn . tri . cr ./aq . pr ./aq . cr ./aq . col . lq . col . lq . cr . mn . pr . cr . rhb . lq . rhb ./al . lq . col . lq . col . lq . lq . cr . nd . lq . col . lq . nd . lf . lq . col . lq . col . lq . col . oil lq . lq . lq . oil col . lq . gas gas lq . lq . gas lq . lq . oil

1.58−78 0.88821/4 1.05020/4 0 .88120/4 0 .97318/4 1 .29 1 .5719

−142.5 −65

−76.3 65–6 177–8743 88 206764

1 .07410 24

1 .3

−31 155–6 130 .5 330 < −17 108 154 81

23/4

1 .074

1 .40520/4 1 .07015/4 0 .97225/25 20/4

0 .866

1 .062115/4 1 .054112/4 20/4

0 .999 0 .98920/4 1 .04620/4

164 180–2 −30 51 .5 128–9 −95 d . 104–5 137 69 104–5 110–1 179–80 −16 .3 −31 .5 44–5 218–20 99

1 .2328

expl . 93 d . 286–8 168–9 subl . d . 84 232752 110 .8 128 .80 146–70 134 .510 259751 263 274–5 199 .7 203 .3 200 .3 242 283–5 134 .520

97 20/4

0 .786 0 .77820/20 0 .92520/4 1 .61746/15 1 .32526/4 1 .46620/20 1 .49075/4 0 .77948/4 0 .75720/4 1 .12620/20 0 .72920/20 0 .86120/4 0 .88217/4 0 .86420/20 1 .13720/4 1 .12520/20 1 .726−130 1 .57620/4 0 .932 0 .662 −5 1 .987 15/4 1 .201 15 1 .060 20/4

58 63 .5 −73 68–9 47 .7 −6 .2 20–1 −114 .8

−5 −182 −157 .5 −35 −124 −34 .4

240–5 235 216 .5761 122–312 195 .5754 208 .5764 74 .1 87 .2 246 23415 234 277–9150 89 .4 215 217–8755 120 294 290 −80 −27 .9 47 .6 63–525 3 .5 167 .5 123–5 214

Solubility in 100 parts Water 0.0130 s. ∞ s . i . i . i . 0 .0615 s . sl . s . h . i . v . sl . s . v . sl . s . sl . s . h . 9 .213 i . 0 .0919 v . sl . s . 0 .0516 v . s . v . s . 0 .29 i . 2 .17100 1 .6100 1 .3100 1 .525 sl . s . 0 .7421 s . 0 .9711 s . h . d . s . h . i . i . i . i . 12025 i . i . 0 .125 0 .0925 i . i . i . ∞ ∞ > 190 i . i . d . i . ∞ d . i . d . 4119 0 .1730 0 .2725 ∞

Alcohol

Ether

s. ∞

s. ∞

s .

s .

s . h . 0 .06 c . ∞ s . v . s . v . s . v . s . s . s . s . v . s . s . s . s . s . 7 .45 s . v . s . v . s . v . s . ∞ ∞ v . s . sl . s .

s . 0 .03 h . ∞ s . v . s . v . s . ∞

s . d . sl . s . h .

sl . s . v . s . s . ∞

s . v . s . v . s . ∞ ∞ v . s . s . i .

s .

∞

s . sl . s . ∞ ∞ v . s .

s .

v . s . ∞ ∞ s . s .

v . s . sl . s . ∞ s . s .

∞ ∞

∞ v . sl . s .

∞

∞

s . s . s . ∞

s . s . s .

∞ ∞ v . s .

Trinitro-benzene (1-,3-,5-) -benzoic acid (2-,4-,6-) -tert-butylxylene -naphthalene (α-)(1-,3-,5-) (β-)(1-,3-,8-) (γ-)(1-,4-,5-) -phenol (2-,3-,6-) -toluene (β-)(2-,3-,4-) (γ-)(2-,4-,5-) (α-)(2-,4-,6-) Trional Triphenyl-arsine carbinol guanidine (α-) methane methyl phosphate Tripropylamine (n-) Undecane (n-) Urea nitrate Uric acid Valeric acid (n-) (i-) aldehyde (n-) (i-) amide (n-) (i-) Vanillic acid (3-,4-,1-) alcohol (3-,4-,1-) hyl-thiuram disulfide Vanillin (3-,4-,1-) Veratrole (o-) Vinyl acetate (poly-) acetic acid acetylene alcohol (poly-) chloride propionate Xylene (o-) (m-) (p-) sulfonic acid (1-,4-,2-) Xylidine (1:2)(3-) (1:2)(4-) (1:3)(2-) (1:3)(4-) (1:3)(5-) (1:4)(2-) Xylose (l-)(+) Xylylene dichloride (p-) Zinc diethyl dimethyl dimethyl-dithiocarbamate note: °F = 9⁄5°C + 32 .

C6H3(NO2)3 (NO2)3C6H2CO2H (NO2)3C6(CH3)2C4H9 C10H5(NO2)3 C10H5(NO2)3 C10H5(NO2)3 (NO2)3C6H2OH CH3C6H2(NO2)3 CH3C6H2(NO2)3 CH3C6H3(NO2)3 (C2H5SO2C2H4)2 (C6H5)3As (C6H5)3COH C6H5N:C(NHC6H5)2 (C6H5)3CH (C6H5)3C . . . OP(OC6H5)3 (CH3CH2CH2)3N CH3(CH2)9CH3 H2N⋅CO⋅NH2 CO(NH2)2⋅HNO3 C5H4O3N4 C2H5CH2CH2CO2H (CH3)2CHCH2CO2H C2H5CH2CH2CHO (CH3)2CHCH2CHO C2H5CH2CH2CONH2 (CH3)2CHCH2CONH2 CH3O(OH)C6H3CO2H CH3O(OH)C6H3CH2OH [(C2H5)2NCS]2S2 CH3O(OH)C6H3CHO C6H4(OCH3)2 CH3CO2CH:CH2 (CH3CO2CH:CH2)x CH2:CH⋅CH2CO2H CH2:CH⋅C:CH CH2:CHOH (CH2:CHOH)x CH2:CHCl C2H5CO2CH:CH2 C6H4(CH3)2 C6H4(CH3)2 C6H4(CH3)2 (CH3)2C6H3SO3H⋅2H2O (CH3)2C6H3NH2 (CH3)2C6H3NH2 (CH3)2C6H3NH2 (CH3)2C6H3NH2 (CH3)2C6H3NH2 (CH3)2C6H3NH2 CH2OH(CHOH)3CHO C6H4(CH2Cl)2 Zn(CH2CH3)2 Zn(CH3)2 Zn[S2CN(CH3)2]2

213 .10 257 .11 297 .26 263 .16 263 .16 263 .16 229 .10 227 .13 227 .13 227 .13 242 .36 306 .23 260 .33 287 .36 244 .33 243 .32 326 .28 143 .27 156 .31 60 .06 123 .07 168 .11 102 .13 102 .13 86 .13 86 .13 101 .15 101 .15 168 .15 154 .16 296 .54 152 .15 138 .16 86 .09 (86 .09) 86 .09 52 .07 44 .05 (44 .05) 62 .50 100 .12 106 .17 106 .17 106 .17 222 .26 121 .18 121 .18 121 .18 121 .18 121 .18 121 .18 150 .13 175 .06 123 .53 95 .48 305 .84

col. rhb. rhb./aq. nd./al. rhb. cr./al. yel. cr. nd. cr. yel. pl. cr./al. pl./al. pl. cr. rhb./al. cr. col. cr. pr./al. col. lq. col . lq . col . pr . col . mn . cr . col . lq . col . lq . lq . col . lq . mn . pl . mn . nd ./aq . mn ./aq . cr . mn . cr . col . lq . col . lq . gas gas lq . col . lq . col . lq . col . lq . col . lf . lq . pr . lq . lq . oil oil nd . mn . col . lq . col . lq .

1.688 20/4

1.620 20/4 1.620 20/4 1.654 1.199 85/4 1.306 1.188 20/4 1.13 1.014 99/4 1.206 58/4 0.757 20/4 0 .741 20/4 1 .335 20/4 1 .893 20 0 .939 20/4 0 .931 20/20 0 .819 11 0 .803 17 1 .023 0 .965 20/4 1 .17 1 .056 1 .091 15/15 0 .932 20/4 1 .1920 1 .013 15/15 0 .705 1 .5 1 .320 0 .908 25/25 20/4

0 .881 0 .867 17/4 0 .861 20/4 0 .991 15 1 .076 17 .5 0 .980 15 0 .978 20/4 0 .972 20/4 0 .979 21/4 1 .535 0 1 .417 0 1 .182 18 1 .386 11 2 .0040/4

121 210–20 d. 110 122–3 218–9 148–9 117–8 112 104 80.8 76 59–60 162.5 144–5 93.4 145–7 49–50 −93.5 −25 .6 132 .7 152 d . d . −34 .5 −37 .6 −92 −51 106 135–7 207 115 70 81–2 22 .5 < −60 100–25 −39 d . >200 −160 −25 −47 .4 13 .2 86 < −15 49–50

15 .5 153–4 100 .5 −28 −40 248–50

d.

expl. expl. expl. d. >360 >360 d. 359754 d. 24511 156.5 194 .5 d . 187 176 103 .4 92 .5 232 subl . d . 285 207 .1 72–3 163 5 .5 −12 93–5 144 139 .3 138 .5 1490 .1 223 224–6 216–7 213–4 221–2 215789 240–5 d . 118 46

0.0315 2.0524 i. i. 0.02100 i. s. h. i. i. 0.0120 0.315 i. i. i. i. i. i. v. sl. s. i . 10017 v . s . h . 0 .06 h . 3 .316 4 .220 v . sl . s . sl . s . v . s . s . 0 .1214 v . s . h . i . 114 v . sl . s . 220 i . s . 0 .670 .6 s . sl . s . v . sl . s . i . i . i . s . v . sl . s . v . sl . s . v . sl . s . v . sl . s . v . sl . s . v . sl . s . 11720 i . d . d . i .

1.918

1.518

sl. s. s. 0.0523 0.1119 v. s. sl. s. c. s. h. 1.522 50 s. v. s. 40 v. s. h. sl. s. h. 15525 ∞ ∞ 2020 s . i . ∞ ∞ s . s . v . s . s . v . s . v . s .

s.

i . ∞ ∞ s . s . v . s . s . v . s . v . s .

v . s . s . ∞

v . s . s . ∞

∞

∞

s .

v . s .

s . s . s .

∞ ∞ v . s .

s .

s .

v . sl . s . s . d . d .

i . v . sl . s .

0.1315 0.419 v. s. s. v. s. 533 6.615 v. s. v. s. v. s. v. s. ∞ ∞ sl . s .

2-45

2-46

PHYSICAL AnD CHEMICAL DATA

VAPOR PRESSURES VAPOR PRESSURES OF PURE SUBSTAnCES

TABLE 2-3 Vapor Pressure of Water Ice from 0 to -40çC Vapor pressure t, °C 0 −0 .5 −1 .0 −1 .5 −2 .0 −2 .5 −3 .0 −3 .5 −4 .0 −4 .5 −5 .0 −5 .5 −6 .0 −6 .5 −7 .0 −7 .5 −8 .0 −8 .5 −9 .0 −9 .5 −10 .0 −10 .5 −11 .0 −11 .5 −12 .0 −12 .5 −13 .0

Vapor pressure

Vapor pressure

mmHg

kPa

t, °C

mmHg

kPa

t, °C

mmHg

kPa

4 .584 4 .399 4 .220 4 .049 3 .883 3 .724 3 .571 3 .423 3 .281 3 .145 3 .013 2 .887 2 .766 2 .649 2 .537 2 .429 2 .325 2 .225 2 .130 2 .038 1 .949 1 .865 1 .783 1 .705 1 .630 1 .558 1 .489

0 .6112 0 .5865 0 .5627 0 .5398 0 .5177 0 .4965 0 .4761 0 .4564 0 .4375 0 .4193 0 .4018 0 .3849 0 .3687 0 .3532 0 .3382 0 .3238 0 .3100 0 .2967 0 .2839 0 .2717 0 .2599 0 .2486 0 .2377 0 .2273 0 .2173 0 .2077 0 .1985

−13 .5 −14 .0 −14 .5 −15 .0 −15 .5 −16 .0 −16 .5 −17 .0 −17 .5 −18 .0 −18 .5 −19 .0 −19 .5 −20 .0 −20 .5 −21 .0 −21 .5 −22 .0 −22 .5 −23 .0 −23 .5 −24 .0 −24 .5 −25 .0 −25 .5 −26 .0 −26 .5

1 .423 1 .359 1 .298 1 .240 1 .184 1 .130 1 .079 1 .029 0 .9822 0 .9370 0 .8937 0 .8522 0 .8125 0 .7745 0 .7381 0 .7034 0 .6701 0 .6383 0 .6078 0 .5787 0 .5509 0 .5243 0 .4989 0 .4747 0 .4515 0 .4294 0 .4083

0 .1897 0 .1812 0 .1731 0 .1653 0 .1578 0 .1507 0 .1438 0 .1372 0 .1310 0 .1249 0 .1191 0 .1136 0 .1083 0 .1033 0 .09841 0 .09377 0 .08934 0 .08510 0 .08104 0 .07716 0 .07345 0 .06991 0 .06652 0 .06329 0 .06020 0 .05725 0 .05443

−27 .0 −27 .5 −28 .0 −28 .5 −29 .0 −29 .5 −30 .0 −30 .5 −31 .0 −31 .5 −32 .0 −32 .5 −33 .0 −33 .5 −34 .0 −34 .5 −35 .0 −35 .5 −36 .0 −36 .5 −37 .0 −37 .5 −38 .0 −38 .5 −39 .0 −39 .5 −40 .0

0 .3881 0 .3688 0 .3505 0 .3330 0 .3162 0 .3003 0 .2851 0 .2706 0 .2568 0 .2437 0 .2311 0 .2192 0 .2078 0 .1970 0 .1867 0 .1769 0 .1676 0 .1587 0 .1503 0 .1423 0 .1347 0 .1274 0 .1206 0 .1140 0 .1078 0 .1019 0 .0963

0 .05174 0 .04918 0 .04673 0 .04439 0 .04216 0 .04004 0 .03801 0 .03608 0 .03424 0 .03249 0 .03082 0 .02923 0 .02771 0 .02627 0 .02490 0 .02359 0 .02235 0 .02116 0 .02004 0 .01897 0 .01796 0 .01699 0 .01607 0 .01520 0 .01437 0 .01359 0 .01284

source: Formulation of Wagner, Saul, and Pruss, J. Phys. Chem. Ref. Data, 23, 515 (1994), implemented in Harvey, Peskin, and Klein, NIST/ASME Steam Properties, NIST Standard Reference Database 10, Version 2 .2, National Institute of Standards and Technology, Gaithersburg, Md ., 2000 . This source provides data down to 190 K (−83 .15°C) . A formula extending to 110 K may be found in Murphy and Koop, Q. J. R. Meteorol. Soc., 131, 1539 (2005) . TABLE 2-4 Vapor Pressure of Supercooled Liquid Water from 0 to -40çC* Vapor pressure

Vapor pressure

Vapor pressure

t, °C

mmHg

kPa

t, °C

mmHg

kPa

t, °C

mmHg

kPa

0 −0.5 −1.0 −1.5 −2.0 −2.5 −3.0 −3.5 −4.0 −4.5 −5.0 −5.5 −6.0 −6.5 −7.0 −7.5 −8.0 −8.5 −9.0 −9.5 −10.0 −10.5 −11.0 −11.5 −12.0 −12.5 −13.0

4.584 4.421 4.262 4.108 3.959 3.816 3.676 3.542 3.411 3.285 3.163 3.046 2.932 2.822 2.715 2.612 2.513 2.417 2.324 2.235 2.149 2.065 1.985 1.907 1.832 1.760 1.690

0.6112 0.5894 0.5682 0.5477 0.5279 0.5087 0.4901 0.4722 0.4548 0.4380 0.4218 0.4061 0.3909 0.3762 0.3620 0.3483 0.3351 0.3223 0.3099 0.2980 0.2865 0.2753 0.2646 0.2542 0.2442 0.2346 0.2253

−13.5 −14.0 −14.5 −15.0 −15.5 −16.0 −16.5 −17.0 −17.5 −18.0 −18.5 −19.0 −19.5 −20.0 −20.5 −21.0 −21.5 −22.0 −22.5 −23.0 −23.5 −24.0 −24.5 −25.0 −25.5 −26.0 −26.5

1.623 1.558 1.495 1.435 1.377 1.321 1.267 1.215 1.165 1.117 1.070 1.026 0.9827 0.9414 0.9016 0.8633 0.8265 0.7911 0.7571 0.7244 0.6930 0.6628 0.6337 0.6059 0.5791 0.5534 0.5288

0.2163 0.2077 0.1993 0.1913 0.1836 0.1761 0.1689 0.1620 0.1553 0.1489 0.1427 0.1367 0.1310 0.1255 0.1202 0.1151 0.1102 0.1055 0.1009 0.0965 0.0923 0.08836 0.08449 0.08078 0.07721 0.07379 0.07050

−27.0 −27.5 −28.0 −28.5 −29.0 −29.5 −30.0 −30.5 −31.0 −31.5 −32.0 −32.5 −33.0 −33.5 −34.0 −34.5 −35.0 −35.5 −36.0 −36.5 −37.0 −37.5 −38.0 −38.5 −39.0 −39.5 −40.0

0.5051 0.4824 0.4606 0.4397 0.4197 0.4005 0.3820 0.3644 0.3475 0.3313 0.3158 0.3009 0.2867 0.2731 0.2600 0.2476 0.2356 0.2242 0.2133 0.2029 0.1929 0.1834 0.1743 0.1656 0.1573 0.1494 0.1419

0.06734 0.06431 0.06141 0.05862 0.05595 0.05339 0.05094 0.04858 0.04633 0.04417 0.04210 0.04012 0.03822 0.03640 0.03467 0.03300 0.03141 0.02989 0.02844 0.02705 0.02572 0.02445 0.02324 0.02208 0.02098 0.01992 0.01891

∗source: Murphy and Koop, Q. J. R. Meteorol. Soc., 131, 1552 (2005) . The formula in the reference extends down to 123 K (−150 .15°C), although in practice pure liquid water cannot be supercooled below about 235 K .

Unit Conversions For this subsection, the following unit conversions are applicable: °F = 9⁄5°C + 32 . To convert millimeters of mercury to pounds-force per square inch, multiply by 0 .01934 . To convert cubic feet to cubic meters, multiply by 0 .02832 . To convert bars to pounds-force per square inch, multiply by 14 .504 . To convert bars to kilopascals, multiply by 1 × 102 . Additional References Additional vapor-pressure data may be found in major thermodynamic property databases, such as those produced by the AIChE’s DIPPR program (aiche .org/dippr), NIST’s Thermodynamics Research Center (trc .nist .gov), the Dortmund Databank (ddbst .de), and the Physical Property Data Service (ppds .co .uk) . Additional sources include the NIST Chemistry Webbook (webbook .nist .gov/chemistry/); Boublik, T ., V . Fried, and E . Hala, The Vapor Pressures of Pure Substances, 2d ed ., Elsevier, Amsterdam, 1984; Bruce Poling, JohnPrausnitz, and John O’Connell, The Properties of Gases and Liquids, 5th ed ., McGraw-Hill, New York, 2001; Vapor Pressure of Chemicals (subvolumes A, B, and C), vol . IV/20 in Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology—New Series, Springer-Verlag, Berlin, 1999–2001 . The most recent work on water may be found at The International Association for the Properties of Water and Steam website http:// iapws .org . TABLE 2-5 Vapor Pressure (MPa) of Liquid Water from 0 to 100çC t, °C 0 .01 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Pvp, MPa

t, °C

Pvp, MPa

t, °C

Pvp, MPa

0 .00061165 0 .00065709 0 .00070599 0 .00075808 0 .00081355 0 .00087258 0 .00093536 0 .0010021 0 .0010730 0 .0011483 0 .0012282 0 .0013130 0 .0014028 0 .0014981 0 .0015990 0 .0017058 0 .0018188 0 .0019384 0 .0020647 0 .0021983 0 .0023393 0 .0024882 0 .0026453 0 .0028111 0 .0029858 0 .0031699 0 .0033639 0 .0035681 0 .0037831 0 .0040092 0 .0042470 0 .0044969 0 .0047596 0 .0050354

34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67

0 .0053251 0 .0056290 0 .0059479 0 .0062823 0 .0066328 0 .0070002 0 .0073849 0 .0077878 0 .0082096 0 .0086508 0 .0091124 0 .0095950 0 .010099 0 .010627 0 .011177 0 .011752 0 .012352 0 .012978 0 .013631 0 .014312 0 .015022 0 .015762 0 .016533 0 .017336 0 .018171 0 .019041 0 .019946 0 .020888 0 .021867 0 .022885 0 .023943 0 .025042 0 .026183 0 .027368

68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

0 .028599 0 .029876 0 .031201 0 .032575 0 .034000 0 .035478 0 .037009 0 .038595 0 .040239 0 .041941 0 .043703 0 .045527 0 .047414 0 .049367 0 .051387 0 .053476 0 .055635 0 .057867 0 .060173 0 .062556 0 .065017 0 .067558 0 .070182 0 .072890 0 .075684 0 .078568 0 .081541 0 .084608 0 .087771 0 .091030 0 .094390 0 .097852 0 .10142

From E . W . Lemmon, M . O . McLinden, and D . G . Friend, “ Thermophysical Properties of Fluid Systems” in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds . P . J . Linstrom and W . G . Mallard, June 2005, National Institute of Standards and Technology, Gaithersburg, Md . (http://webbook .nist .gov) and Wagner, W ., and A ., Pruss, “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2):387–535, 2002 . The website mentioned above allows users to generate their own tables of thermodynamic properties . The user can select the units as well as the temperatures and/or pressures for which properties are to be generated . The results can then be copied into spreadsheets or other files .

VAPOR PRESSURES TABLE 2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Sorted by Chemical Family Name

Cmpd. no.

Formula

Paraffins Methane Ethane Propane Butane Pentane Hexane Heptane Octane Nonane Decane Undecane Dodecane Tridecane Tetradecane Pentadecane Hexadecane Heptadecane Octadecane Nonadecane Eicosane 2-Methylpropane 2-Methylbutane 2,3-Dimethylbutane 2-Methylpentane 2,3-Dimethylpentane 2,2,3,3-Tetramethylbutane 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane Cyclopropane Cyclobutane Cyclopentane Cyclohexane Methylcyclopentane Ethylcyclopentane Methylcyclohexane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Ethylcyclohexane

193 125 295 31 279 171 160 265 256 74 336 123 327 319 277 169 158 263 254 124 236 202 107 234 114 323 332 333 71 64 69 65 217 134 213 108 109 110 133

CH4 C2H6 C 3H 8 C4H10 C5H12 C6H14 C7H16 C8H18 C9H20 C10H22 C11H24 C12H26 C13H28 C14H30 C15H32 C16H34 C17H36 C18H38 C19H40 C20H42 C4H10 C5H12 C6H14 C6H14 C7H16 C8H18 C8H18 C8H18 C 3H 6 C 4H 8 C5H10 C6H12 C6H12 C7H14 C7H14 C8H16 C8H16 C8H16 C8H16

135 305 36 37 38 70 285 68 177 166 271 260 77 238 205 206 218 219 298 294 29 30 201

C 2H 4 C 3H 6 C4H8 C4H8 C4H8 C5H8 C5H10 C6H10 C6H12 C7H14 C8H16 C9H18 C10H20 C4H8 C5H10 C5H10 C6H10 C6H10 C9H14 C3H4 C4H6 C4H6 C5H8

7 43 288 289 178 180 181 168

C2H2 C4H6 C5H8 C5H8 C6H10 C6H10 C6H10 C7H12

Olefins Ethylene Propylene 1-Butene cis-2-Butene trans-2-Butene Cyclopentene 1-Pentene Cyclohexene 1-Hexene 1-Heptene 1-Octene 1-Nonene 1-Decene 2-Methyl propene 2-Methyl-1-butene 2-Methyl-2-butene 1-Methylcyclopentene 3-Methylcyclopentene Propenylcyclohexene Propadiene 1,2-Butadiene 1,3-Butadiene 3-Methyl-1,2-butadiene Acetylenes Acetylene 1-Butyne 1-Pentyne 2-Pentyne 3-Hexyne 1-Hexyne 2-Hexyne 1-Heptyne

Name

Cmpd. no.

Formula

Acetylenes 1-Octyne 1-Nonyne 1-Decyne Methyl acetylene Vinyl acetylene Dimethyl acetylene 2-Methyl -1-butene-3-yne 3-Methyl-1-butyne

273 262 79 197 339 105 207 210

C8H14 C9H16 C10H18 C3H4 C4H4 C4H6 C5H6 C5H8

16 325 312 129 343 344 345 243 62 304 330 331 246 321 40 24 290 318

C6H6 C7H8 C8H8 C8H10 C8H10 C8H10 C8H10 C9H10 C9H12 C9H12 C9H12 C9H12 C10H8 C10H12 C10H14 C12H10 C14H10 C18H14

153 1 299 44 278 170 159 264 255 73

CH2O C2H4O C3H6O C4H8O C5H10O C6H12O C7H14O C8H16O C9H18O C10H20O

8 5 222 229 283 284 310 67 144 175 176 226 102 164 165 269 270 20

C3H4O C3H6O C4H8O C5H10O C5H10O C5H10O C6H4O2 C6H10O C6H12O C6H12O C6H12O C6H12O C7H14O C7H14O C7H14O C8H16O C8H16O C13H10O

156 324 320 322

C4H4O C4H4S C4H8O C4H8S

14 25 52 80 149

Ar Br2 Cl2 D2 F2

Aromatics Benzene Toluene Styrene Ethylbenzene m-Xylene o-Xylene p-Xylene alpha-Methyl styrene Cumene Propylbenzene 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene Naphthalene 1,2,3,4-Tetrahydronaphthalene Butylbenzene Biphenyl Phenanthrene o-Terphenyl Aldehydes Formaldehyde Acetaldehyde Propionaldehyde Butyraldehyde Pentanal Hexanal Heptanal Octanal Nonanal Decanal Ketones Acrolein Acetone Methylethyl ketone Methylisopropyl ketone 2-Pentanone 3-Pentanone Quinone Cyclohexanone Ethylisopropyl ketone 2-Hexanone 3-Hexanone Methylisobutyl ketone Diisopropyl ketone 3-Heptanone 2-Heptanone 2-Octanone 3-Octanone Benzophenone Heterocyclics Furan Thiophene Tetrahydrofuran Tetrahydrothiophene Elements Argon Bromine Chlorine Deuterium Fluorine

(Continued )

2-47

2-48

PHYSICAL AnD CHEMICAL DATA

TABLE 2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Sorted by Chemical Family (Continued ) Name

Cmpd. no.

Formula

Elements Hydrogen Helium-4 Nitrogen Neon Oxygen

183 157 249 247 275

H2 He N2 Ne O2

194 126 296 297 34 35 281 282 66 173 174 162 163 267 268 258 259 76 337 237 204 21 214 215 216 137 309 32 33

CH4O C2H6O C3H8O C3H8O C4H10O C4H10O C5H12O C5H12O C6H12O C6H14O C6H14O C7H16O C7H16O C8H18O C8H18O C9H20O C9H20O C10H22O C11H24O C4H10O C5H12O C7H8O C7H14O C7H14O C7H14O C2H6O2 C3H8O2 C4H10O2 C4H10O2

291 59 60 61

C6H6O C7H8O C7H8O C7H8O

112 245 221 120 95 240 228 103 208 225 244 147 143 104 101 235 13 84 142 22 121

C2H6O C3H6O C3H8O C4H8O2 C4H10O C4H10O C4H10O C4H10O2 C5H12O C5H12O C5H12O C5H12O C5H12O C5H12O2 C6H14O C6H14O C7H8O C8H18O C8H18O C9H12O C12H10O

155 274 3 9 191 300

CH2O2 C2H2O4 C2H4O2 C3H4O2 C3H4O4 C3H6O2

Alcohols Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol 1-Pentanol 2-Pentanol Cyclohexanol 1-Hexanol 2-Hexanol 1-Heptanol 2-Heptanol 1-Octanol 2-Octanol 1-Nonanol 2-Nonanol 1-Decanol 1-Undecanol 2-Methyl-2-propanol 3-Methyl-1-butanol Benzyl alcohol 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Ethylene glycol 1,2-Propylene glycol 1,2-Butanediol 1,3-Butanediol Phenols Phenol m-Cresol o-Cresol p-Cresol Ethers Dimethyl ether Methyl vinyl ether Methylethyl ether 1,4-Dioxane Diethyl ether Methylpropyl ether Methylisopropyl ether 1,1-Dimethoxyethane Methylbutyl ether Methylisobutyl ether Methyl tert-butyl ether Ethylpropyl ether Ethylisopropyl ether 1,2-Dimethoxypropane Di-isopropyl ether Methyl pentyl ether Anisole Dibutyl ether Ethylhexyl ether Benzyl ethyl ether Diphenyl ether Acids Formic acid Oxalic acid Acetic acid Acrylic acid Malonic acid Propionic acid

Name

Cmpd. no.

Formula

Methacrylic acid Acetic anhydride Succinic acid Butyric acid Isobutyric acid 2-Methylbutanoic acid Pentanoic acid 2-Ethyl butanoic acid Hexanoic acid Benzoic acid Heptanoic acid Phthalic anhydride Terephthalic acid 2-Ethyl hexanoic acid Octanoic acid 2-Methyloctanoic acid Nonanoic acid Decanoic acid

192 4 313 45 189 203 280 131 172 18 161 293 317 141 266 233 257 75

C4H6O2 C4H6O3 C4H6O4 C4H8O2 C4H8O2 C5H10O2 C5H10O2 C6H12O2 C6H12O2 C7H6O2 C7H14O2 C8H4O3 C8H6O4 C8H16O2 C8H16O2 C9H18O2 C9H18O2 C10H20O2

224 140 196 198 338 127 239 306 232 146 211 302 39 132 200 130 115 119

C2H4O2 C3H6O2 C3H6O2 C4H6O2 C4H6O2 C4H8O2 C4H8O2 C4H8O2 C5H8O2 C5H10O2 C5H10O2 C5H10O2 C6H12O2 C6H12O2 C8H8O2 C9H10O2 C10H10O4 C10H10O4

199 138 106 128 136 190 303 329 94 93 100 122 328

CH5N C2H5N C2H7N C2H7N C2H8N2 C3H9N C3H9N C3H9N C4H11N C4H11NO2 C6H15N C6H15N C6H15N

154 2 113 195 15

CH3NO C2H5NO C3H7NO C3H7NO C7H7NO

6 63 10 301 46 19

C2H3N C2N2 C3H3N C3H5N C4H7N C7H5N

251 248

CH3NO2 C2H5NO2

Acids

Esters Methyl formate Ethyl formate Methyl acetate Methyl acrylate Vinyl acetate Ethyl acetate Methyl propionate Propyl formate Methyl methacrylate Ethyl propionate Methyl butyrate Propyl acetate Butyl acetate Ethyl butyrate Methyl benzoate Ethyl benzoate Dimethyl phthalate Dimethyl terephthalate Amines Methyl amine Ethyleneimine Dimethyl amine Ethyl amine Ethylenediamine Isopropyl amine Propyl amine Trimethyl amine Diethyl amine Diethanol amine Di-isopropyl amine Dipropyl amine Triethyl amine Amides Formamide Acetamide N,N-Dimethyl formamide N-Methyl acetamide Benzamide Nitriles Acetonitrile Cyanogen Acrylonitrile Propionitrile Butyronitrile Benzonitrile Nitro Compounds Nitromethane Nitroethane

VAPOR PRESSURES

2-49

TABLE 2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Sorted by Chemical Family (Continued ) Name

Cmpd. no.

Formula

1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene

334 335

C6H3N3O6 C7H5N3O6

227 292

C2H3NO C7H5NO

231 145 308 307 41 42 287 286 17 72 179 23 167 272 261 78

CH4S C2H6S C3H8S C3H8S C4H10S C4H10S C5H12S C5H12S C6H6S C6H12S C6H14S C7H8S C7H16S C8H18S C9H20S C10H22S

117 111 223 96 230 241 209

C2H6S C2H6S2 C3H8S C4H10S C4H10S C4H10S C5H12S

50 51 55 83 90 99 28 56 152 340 326 81 82 88

CCl4 CF4 CHCl3 CH2Br2 CH2Cl2 CH2F2 CH3Br CH3Cl CH3F C2H3Cl C2H3Cl3 C2H4Br2 C2H4Br2 C2H4Cl2

Isocyanates Methyl isocyanate Phenyl isocyanate Mercaptans Methyl mercaptan Ethyl mercaptan Propyl mercaptan 2-Propyl mercaptan Butyl mercaptan sec-Butyl mercaptan Pentyl mercaptan 2-Pentyl mercaptan Benzenethiol Cyclohexyl mercaptan Hexyl mercaptan Benzyl mercaptan Heptyl mercaptan Octyl mercaptan Nonyl mercaptan Decyl mercaptan Sulfides Dimethyl sulfide Dimethyl disulfide Methylethyl sulfide Diethyl sulfide Methylisopropyl sulfide Methylpropyl sulfide Methylbutyl sulfide

Cmpd. no.

Formula

1,2-Dichloroethane 1,1-Difluoroethane 1,2-Difluoroethane Bromoethane Chloroethane Fluoroethane 1,1-Dichloropropane 1,2-Dichloropropane 1-Chloropropane 2-Chloropropane m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene Bromobenzene Chlorobenzene Fluorobenzene

89 97 98 27 54 151 91 92 57 58 85 86 87 26 53 150

C2H4Cl2 C2H4F2 C2H4F2 C2H5Br C2H5Cl C2H5F C3H6Cl2 C3H6Cl2 C3H7Cl C3H7Cl C6H4Cl2 C6H4Cl2 C6H4Cl2 C6H5Br C6H5Cl C6H5F

242 212 220 341 148 116 311

CH6Si CH5ClSi CH4Cl2Si C2H3Cl3Si C2H5Cl3Si C2H8Si F4Si

186 49 47 48 250 315 184 185 187 188 12 182 253 252 314 276 316

CHN CO CO2 CS2 F3N F6S HBr HCl HF H2S H3N H4N2 NO N2 O O2 S O3 O3 S

11 139 118 342

Mixture C2H4O C2H6OS H2O

Silanes Methylsilane Methylchlorosilane Methyldichlorosilane Vinyl trichlorosilane Ethyltrichlorosilane Dimethylsilane Silicon tetrafluoride Light Gases

Halogenated Hydrocarbons Carbon tetrachloride Carbon tetrafluoride Chloroform Dibromomethane Dichloromethane Difluoromethane Bromomethane Chloromethane Fluoromethane Vinyl chloride 1,1,2-Trichloroethane 1,1-Dibromoethane 1,2-Dibromoethane 1,1-Dichloroethane

Name Halogenated Hydrocarbons

Nitro Compounds

Hydrogen cyanide Carbon monoxide Carbon dioxide Carbon disulfide Nitrogen trifluoride Sulfur hexafluoride Hydrogen bromide Hydrogen chloride Hydrogen fluoride Hydrogen sulfide Ammonia Hydrazine Nitric oxide Nitrous oxide Sulfur dioxide Ozone Sulfur trioxide Others Air Ethylene oxide Dimethyl sulfoxide Water

2-50

PHYSICAL AnD CHEMICAL DATA TABLE 2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Formula

No.

Name

Ar Br2 CCl4 CF4 CHCl3 CHN CH2Br2 CH2Cl2 CH2F2 CH2O CH2O2 CH3Br CH3Cl CH3F CH3NO CH3NO2 CH4 CH4Cl2Si CH4O CH4S CH5ClSi CH5N CH6Si CO CO2 CS2 C2H2 C2H2O4 C2H3Cl C2H3Cl3 C2H3Cl3Si C2H3N C2H3NO C2H4 C2H4Br2 C2H4Br2 C2H4Cl2 C2H4Cl2 C2H4F2 C2H4F2 C2H4O C2H4O C2H4O2 C2H4O2 C2H5Br C2H5Cl C2H5Cl3Si C2H5F C2H5N C2H5NO C2H5NO2 C2H6 C2H6O C2H6O C2H6O2 C2H6OS C2H6S C2H6S C2H6S2 C2H7N C2H7N C2H8N2 C2H8Si C2N2 C3H3N C3H4 C3H4 C3H4O C3H4O2 C3H4O4 C3H5N C3H6 C3H6 C3H6Cl2

11 14 25 50 51 55 186 83 90 99 153 155 28 56 152 154 251 193 220 194 231 212 199 242 49 47 48 7 274 340 326 341 6 227 135 81 82 88 89 97 98 1 139 3 224 27 54 148 151 138 2 248 125 112 126 137 118 117 145 111 106 128 136 116 63 10 197 294 8 9 191 301 71 305 91

Air Argon Bromine Carbon tetrachloride Carbon tetrafluoride Chloroform Hydrogen cyanide Dibromomethane Dichloromethane Difluoromethane Formaldehyde Formic acid Bromomethane Chloromethane Fluoromethane Formamide Nitromethane Methane Methyldichlorosilane Methanol Methyl mercaptan Methylchlorosilane Methyl amine Methylsilane Carbon monoxide Carbon dioxide Carbon disulfide Acetylene Oxalic acid Vinyl chloride 1,1,2-Trichloroethane Vinyl trichlorosilane Acetonitrile Methyl Isocyanate Ethylene 1,1-Dibromoethane 1,2-Dibromoethane 1,1-Dichloroethane 1,2-Dichloroethane 1,1-Difluoroethane 1,2-Difluoroethane Acetaldehyde Ethylene oxide Acetic acid Methyl formate Bromoethane Chloroethane Ethyltrichlorosilane Fluoroethane Ethyleneimine Acetamide Nitroethane Ethane Dimethyl ether Ethanol Ethylene glycol Dimethyl sulfoxide Dimethyl sulfide Ethyl mercaptan Dimethyl disulfide Dimethyl amine Ethyl amine Ethylenediamine Dimethylsilane Cyanogen Acrylonitrile Methyl acetylene Propadiene Acrolein Acrylic acid Malonic acid Propionitrile Cyclopropane Propylene 1,1-Dichloropropane

Formula

No.

Name

C3H6Cl2 C3H6O C3H6O C3H6O C3H6O2 C3H6O2 C3H6O2 C3H7Cl C3H7Cl C3H7NO C3H7NO C3H8 C3H8O C3H8O C3H8O C3H8O2 C3H8S C3H8S C3H8S C3H9N C3H9N C3H9N C4H4 C4H4O C4H4S C4H6 C4H6 C4H6 C4H6 C4H6O2 C4H6O2 C4H6O2 C4H6O3 C4H6O4 C4H7N C4H8 C4H8 C4H8 C4H8 C4H8 C4H8O C4H8O C4H8O C4H8O2 C4H8O2 C4H8O2 C4H8O2 C4H8O2 C4H8O2 C4H8S C4H10 C4H10 C4H10O C4H10O C4H10O C4H10O C4H10O C4H10O C4H10O2 C4H10O2 C4H10O2 C4H10S C4H10S C4H10S C4H10S C4H10S C4H11N C4H11NO2 C5H6 C5H8 C5H8 C5H8 C5H8 C5H8 C5H8O2

92 5 245 299 140 196 300 57 58 113 195 295 221 296 297 309 223 308 307 190 303 329 339 156 324 29 30 43 105 192 198 338 4 313 46 36 37 38 64 238 44 222 320 45 120 127 189 239 306 322 31 236 34 35 95 237 240 228 32 33 103 41 42 96 230 241 94 93 207 70 201 210 288 289 232

1,2-Dichloropropane Acetone Methyl vinyl ether Propionaldehyde Ethyl formate Methyl acetate Propionic acid 1-Chloropropane 2-Chloropropane N,N-Dimethyl formamide N-Methyl acetamide Propane Methylethyl ether 1-Propanol 2-Propanol 1,2-Propylene glycol Methylethyl sulfide Propyl mercaptan 2-Propyl mercaptan Isopropyl amine Propyl amine Trimethyl amine Vinyl acetylene Furan Thiophene 1,2-Butadiene 1,3-Butadiene 1-Butyne Dimethyl acetylene Methacrylic acid Methyl acrylate Vinyl acetate Acetic anhydride Succinic acid Butyronitrile 1-Butene cis-2-Butene trans-2-Butene Cyclobutane 2-Methyl propene Butyraldehyde Methylethyl ketone Tetrahydrofuran Butyric acid 1,4-Dioxane Ethyl acetate Isobutyric acid Methyl propionate Propyl formate Tetrahydrothiophene Butane 2-Methylpropane 1-Butanol 2-Butanol Diethyl ether 2-Methyl-2-propanol Methylpropyl ether Methylisopropyl ether 1,2-Butanediol 1,3-Butanediol 1,1-Dimethoxyethane Butyl mercaptan sec-Butyl mercaptan Diethyl sulfide Methylisopropyl sulfide Methylpropyl sulfide Diethyl amine Diethanol amine 2-Methyl-1-butene-3-yne Cyclopentene 3-Methyl-1,2-butadiene 3-Methyl-1-butyne 1-Pentyne 2-Pentyne Methyl methacrylate

VAPOR PRESSURES

2-51

TABLE 2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 (Continued ) Formula

No.

Name

C5H10 C5H10 C5H10 C5H10 C5H10O C5H10O C5H10O C5H10O C5H10O2 C5H10O2 C5H10O2 C5H10O2 C5H10O2 C5H12 C5H12 C5H12O C5H12O C5H12O C5H12O C5H12O C5H12O C5H12O C5H12O C5H12O2 C5H12S C5H12S C5H12S C6H3N3O6 C6H4Cl2 C6H4Cl2 C6H4Cl2 C6H4O2 C6H5Br C6H5Cl C6H5F C6H6 C6H6O C6H6S C6H10 C6H10 C6H10 C6H10 C6H10 C6H10 C6H10O C6H12 C6H12 C6H12 C6H12O C6H12O C6H12O C6H12O C6H12O C6H12O C6H12O2 C6H12O2 C6H12O2 C6H12O2 C6H12S C6H14 C6H14 C6H14 C6H14O C6H14O C6H14O C6H14O C6H14S C6H15N C6H15N C6H15N C7H5N C7H5N3O6 C7H5NO C7H6O2 C7H7NO

69 205 206 285 229 278 283 284 146 203 211 280 302 202 279 143 147 204 208 225 244 281 282 104 209 286 287 334 85 86 87 310 26 53 150 16 291 17 218 68 178 180 181 219 67 65 177 217 66 144 170 175 176 226 39 131 132 172 72 107 171 234 101 173 174 235 179 100 122 328 19 335 292 18 15

Cyclopentane 2-Methyl-1-butene 2-Methyl-2-butene 1-Pentene Methylisopropyl ketone Pentanal 2-Pentanone 3-Pentanone Ethyl propionate 2-Methylbutanoic acid Methyl butyrate Pentanoic acid Propyl acetate 2-Methylbutane Pentane Ethylisopropyl ether Ethylpropyl ether 3-Methyl-1-butanol Methylbutyl ether Methylisobutyl ether Methyl tert-butyl ether 1-Pentanol 2-Pentanol 1,2-Dimethoxypropane Methylbutyl sulfide 2-Pentyl mercaptan Pentyl mercaptan 1,3,5-Trinitrobenzene m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene Quinone Bromobenzene Chlorobenzene Fluorobenzene Benzene Phenol Benzenethiol 1-Methylcyclopentene Cyclohexene 3-Hexyne 1-Hexyne 2-Hexyne 3-Methylcyclopentene Cyclohexanone Cyclohexane 1-Hexene Methylcyclopentane Cyclohexanol Ethylisopropyl ketone Hexanal 2-Hexanone 3-Hexanone Methylisobutyl ketone Butyl acetate 2-Ethyl butanoic acid Ethyl butyrate Hexanoic acid Cyclohexyl mercaptan 2,3-Dimethylbutane Hexane 2-Methylpentane Di-isopropyl ether 1-Hexanol 2-Hexanol Methyl pentyl ether Hexyl mercaptan Di-isopropyl amine Dipropyl amine Triethyl amine Benzonitrile 2,4,6-Trinitrotoluene Phenyl isocyanate Benzoic acid Benzamide

Formula C7H8 C7H8O C7H8O C7H8O C7H8O C7H8O C7H8S C7H12 C7H14 C7H14 C7H14 C7H14O C7H14O C7H14O C7H14O C7H14O C7H14O C7H14O C7H14O2 C7H16 C7H16 C7H16O C7H16O C7H16S C8H4O3 C8H6O4 C8H8 C8H8O2 C8H10 C8H10 C8H10 C8H10 C8H14 C8H16 C8H16 C8H16 C8H16 C8H16 C8H16O C8H16O C8H16O C8H16O2 C8H16O2 C8H18 C8H18 C8H18 C8H18 C8H18O C8H18O C8H18O C8H18O C8H18S C9H10 C9H10O2 C9H12 C9H12 C9H12 C9H12 C9H12O C9H14 C9H16 C9H18 C9H18O C9H18O2 C9H18O2 C9H20 C9H20O C9H20O C9H20S C10H8 C10H10O4 C10H10O4 C10H12 C10H14 C10H18

No.

Name

325 13 21 59 60 61 23 168 134 166 213 102 159 164 165 214 215 216 161 114 160 162 163 167 293 317 312 200 129 343 344 345 273 108 109 110 133 271 264 269 270 141 266 265 323 332 333 84 142 267 268 272 243 130 62 304 330 331 22 298 262 260 255 233 257 256 258 259 261 246 115 119 321 40 79

Toluene Anisole Benzyl alcohol m-Cresol o-Cresol p-Cresol Benzyl mercaptan 1-Heptyne Ethylcyclopentane 1-Heptene Methylcyclohexane Di-isopropyl ketone Heptanal 3-Heptanone 2-Heptanone 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Heptanoic acid 2,3-Dimethylpentane Heptane 1-Heptanol 2-Heptanol Heptyl mercaptan Phthalic anhydride Terephthalic acid Styrene Methyl benzoate Ethylbenzene m-Xylene o-Xylene p-Xylene 1-Octyne 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Ethylcyclohexane 1-Octene Octanal 2-Octanone 3-Octanone 2-Ethyl hexanoic acid Octanoic acid Octane 2,2,3,3-Tetramethylbutane 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane Dibutyl ether Ethylhexyl ether 1-Octanol 2-Octanol Octyl mercaptan alpha-Methyl styrene Ethyl benzoate Cumene Propylbenzene 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene Benzyl ethyl ether Propenylcyclohexene 1-Nonyne 1-Nonene Nonanal 2-Methyloctanoic acid Nonanoic acid Nonane 1-Nonanol 2-Nonanol Nonyl mercaptan Naphthalene Dimethyl phthalate Dimethyl terephthalate 1,2,3,4-Tetrahydronaphthalene Butylbenzene 1-Decyne (Continued )

2-52

PHYSICAL AnD CHEMICAL DATA TABLE 2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 (Continued ) Formula

No.

Name

Formula

No.

Name

C10H20 C10H20O C10H20O2 C10H22 C10H22O C10H22S C11H24 C11H24O C12H10 C12H10O C12H26 C13H10O C13H28 C14H10 C14H30 C15H32 C16H34 C17H36 C18H14 C18H38 C19H40 C20H42 Cl2

77 73 75 74 76 78 336 337 24 121 123 20 327 290 319 277 169 158 318 263 254 124 52

1-Decene Decanal Decanoic acid Decane 1-Decanol Decyl mercaptan Undecane 1-Undecanol Biphenyl Diphenyl ether Dodecane Benzophenone Tridecane Phenanthrene Tetradecane Pentadecane Hexadecane Heptadecane o-Terphenyl Octadecane Nonadecane Eicosane Chlorine

D2 F2 F3N F4Si F6S HBr HCl HF H2 H2O H2S H3N H4N2 He NO N2 N2O Ne O2 O2S O3 O3S

80 149 250 311 315 184 185 187 183 342 188 12 182 157 253 249 252 247 275 314 276 316

Deuterium Fluorine Nitrogen trifluoride Silicon tetrafluoride Sulfur hexafluoride Hydrogen bromide Hydrogen chloride Hydrogen fluoride Hydrogen Water Hydrogen sulfide Ammonia Hydrazine Helium-4 Nitric oxide Nitrogen Nitrous oxide Neon Oxygen Sulfur dioxide Ozone Sulfur trioxide

TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K Cmpd. no.∗ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol

Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O

CAS

C1

75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7

52.9107 125.8 1 53.27 67.1818 69.006 46.735 39.63 138.4 46.745 57.3157 21.662 90.483 128.06 42.127 85.474 83.107 77.765 88.513 55.0403 88.404 100.68 68.541 118.02 77.314 108.26 63.749 57.3242 44.7643 39.714 75.572 66.343 103.28 123.22 106.29483 122.552 51.836 72.541 71.704 122.82 101.22 65.382 60.649 77.004 51.648 78.1171 60.6576 47.0169 67.114 45.698 78.441 61.89 71.334 54.144 44.677 146.43 44.555 58.3592 46.854 95.403 210.88

C2 −4643.14 −12,376 −6304.5 −7463.47 −5599.6 −5126.18 −2552.2 −7122.7 −6587.1 −5662.2 −692.39 −4669.7 −9307.7 −1093.1 −11,932 −6486.2 −8455.1 −11,829 −7363.83 −11,769 −11,059 −7886.2 −10,527 −9910.4 −6592 −7130.2 −4931.2 −3907.8 −3769.9 −4621.9 −4363.2 −11,548 −12,620 −9866.35511 −10,236.2 −4019.2 −4691.2 −4563.1 −9253.2 −9255.4 −6262.4 −5785.9 −5054.5 −5301.36 −8924.37 −6404.32 −2839 −4820.4 −1076.6 −6128.1 −2296.3 −3855 −6244.4 −4026 −7792.3 −3521.3 −5111.33 −4445.5 −10,581 −13,928

C3 −4.50683 −14.589 −4.2985 −6.24388 −7.0985 −3.54064 −2.78 −19.638 −3.2208 −5.06221 −0.39208 −11.607 −16.693 −4.1425 −8.3348 −9.2194 −7.7404 −8.6826 −4.50612 −8.9014 −10.709 −6.5804 −13.91 −7.5079 −14.16 −5.879 −5.2244 −3.4016 −2.6407 −8.5323 −7.046 −10.925 −13.986 −11.6553 −14.125 −4.5229 −7.9776 −7.9053 −14.99 −11.538 −6.2585 −5.6113 −8.5665 −4.2559 −7.59929 −5.49286 −3.86388 −7.5303 −4.8814 −8.5766 −7.086 −8.5171 −4.5343 −3.371 −20.614 −3.4258 −5.35261 −3.6533 −10.004 −29.483

C4 2.70E-17 5.0824E-06 8.89E-18 6.86E-18 6.2237E-06 1.40E-17 2.39E-16 0.026447 5.2253E-07 1.51E-17 0.0047574 0.017194 0.014919 0.000057254 1.29E-18 6.9844E-06 4.31E-18 2.32E-19 1.95E-18 1.93E-18 3.06E-18 2.4285E-06 6.4794E-06 2.24E-18 0.016043 5.21E-18 3.08E-17 2.95E-17 6.94E-18 0.000012269 9.4509E-06 4.26E-18 0.000003926 1.08E-17 2.36E-17 4.88E-17 0.000010368 0.000011319 0.00001047 5.9208E-06 1.49E-17 1.59E-17 0.000010161 1.14E-17 7.39E-18 1.13E-17 2.81E-16 0.0091695 0.000075673 6.8465E-06 0.000034687 0.012378 4.70E-18 2.27E-17 0.024578 5.63E-17 2.47E-17 1.33E-17 4.30E-18 0.025182

C5

Tmin, K

P at Tmin

6 2 6 6 2 6 6 1 2 6 1 1 1 2 6 2 6 6 6 6 6 2 2 6 1 6 6 6 6 2 2 6 2 6 6 6 2 2 2 2 6 6 2 6 6 6 6 1 2 2 2 1 6 6 1 6 6 6 6 1

149.78 353.33 289.81 200.15 178.45 229.32 192.4 185.45 286.15 189.63 59.15 195.41 235.65 83.78 403 278.68 258.27 395.45 260.28 321.35 257.85 275.65 243.95 342.2 265.85 242.43 154.25 179.44 136.95 164.25 134.86 220 196.15 183.85 158.45 87.8 134.26 167.62 199.65 185.3 157.46 133.02 147.43 176.8 267.95 161.3 216.58 161.11 68.15 250.33 89.56 172.12 227.95 136.75 207.15 175.45 150.35 155.97 285.39 304.19

5.15E-01 3.36E+02 1.28E+03 4.10E-02 2.79E+00 1.71E+02 1.27E+05 1.03E+01 2.57E+02 2.47E+00 5.64E+03 6.11E+03 2.45E+00 6.87E+04 3.55E+02 4.76E+03 7.68E+00 7.96E+02 5.40E+00 1.49E+00 1.88E-01 2.31E+01 2.98E-01 9.42E+01 5.85E+03 7.84E+00 3.80E-01 2.07E+02 4.47E-01 6.92E+01 6.74E-01 2.93E-04 3.74E-07 2.91E-04 1.24E-06 6.94E-07 2.72E-01 7.45E+01 8.17E-02 1.54E-04 2.35E-03 3.40E-05 1.18E+00 6.97E-01 1.03E+01 9.41E-04 5.18E+05 1.49E+00 1.54E+04 1.12E+03 1.08E+02 1.37E+03 8.45E+00 2.61E-01 5.25E+01 8.84E+02 8.47E-02 9.08E-01 5.86E+00 6.53E+01

Tmax, K 466 761 591.95 606 508.2 545.5 308.3 506 615 540 132.45 405.65 645.6 150.86 824 562.05 689 751 702.3 830 720.15 662 718 773 584.15 670.15 503.8 464 452 425 425.12 680 676 563.1 535.9 419.5 435.5 428.6 575.4 660.5 570.1 554 440 537.2 615.7 585.4 304.21 552 132.92 556.35 227.51 417.15 632.35 460.35 536.4 416.25 503.15 489 705.85 697.55

P at Tmax 5.570E+06 6.569E+06 5.739E+06 4.000E+06 4.709E+06 4.850E+06 6.106E+06 5.020E+06 5.661E+06 4.660E+06 3.793E+06 1.130E+07 4.273E+06 4.896E+06 5.047E+06 4.875E+06 4.728E+06 4.469E+06 4.215E+06 3.357E+06 4.372E+06 3.113E+06 4.074E+06 3.407E+06 1.028E+07 4.520E+06 5.565E+06 6.929E+06 4.361E+06 4.303E+06 3.770E+06 5.202E+06 4.033E+06 4.414E+06 4.190E+06 4.021E+06 4.238E+06 4.100E+06 3.087E+06 2.882E+06 3.973E+06 4.060E+06 4.599E+06 4.410E+06 4.060E+06 3.880E+06 7.384E+06 8.041E+06 3.494E+06 4.544E+06 3.742E+06 7.793E+06 4.529E+06 5.267E+06 5.554E+06 6.759E+06 4.425E+06 4.510E+06 4.522E+06 5.058E+06

2-53

(Continued )

2-54 TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K (Continued ) Cmpd. no.∗

Name

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Di-sopropyl amine Di-sopropyl ether Di-sopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane

Formula C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2

CAS 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1

C1

C2

C3

118.53 102.81 39.0596 85.899 51.087 189.19 85.424 88.184 66.341 67.952 40.608 85.146 93.5742 112.73 126.405 156.23933 68.401 91.91 142.94 18.947 62.711 43.751 86.295 72.227 53.187 77.105 88.31 66.611 92.355 101.6 83.495 65.955 106.38 49.314 136.9 46.705 73.491 84.625 69.132 462.84 41.631 50.868 53.637 62.097 66.592 71.738 77.161 81.184 78.952 78.429 81.045 44.704 82.762 78.335 72.517 63.08 84.39 56.273 66.1795 44.494

−11,957 −8674.6 −3473.98 −4884.4 −5226.4 −14,337 −7944.4 −6624.9 −5198.5 −5187.5 −3179.6 −7843.7 −10,403.8 −9749.6 −14,864.6 −15,212.33492 −7776.9 −10,565 −11,119 −154.47 −6503.5 −5587.7 −7010.3 −7537.6 −6827.5 −8111.1 −8463.4 −5493.1 −6920.4 −6541.6 −6661.4 −6015.6 −13,714 −4949 −6954.3 −5177.4 −4385.9 −5217.4 −3847.7 −18,227 −4668.7 −6036.5 −5251.2 −6174.9 −4999.8 −5302 −5691.1 −6927 −7075.4 −6882.1 −6941.3 −3525.6 −7955.5 −6348.7 −10,415 −4062.3 −5740.6 −7620.6 −9870.41 −5406.7

−13.293 −11.922 −2.48683 −10.883 −4.2278 −24.148 −9.2862 −10.059 −6.8103 −7.0785 −2.8937 −9.2982 −9.79483 −13.245 −13.9067 −18.42393 −6.4637 −9.5957 −17.818 −0.57226 −5.7669 −3.0891 −9.5972 −7.0596 −4.3233 −7.8886 −9.6308 −6.7301 −10.651 −12.247 −9.2386 −6.5509 −11.06 −3.9256 −19.254 −3.5985 −8.1851 −9.871 −7.5868 −73.734 −2.8551 −4.066 −4.5649 −5.715 −6.8387 −7.3324 −8.501 −8.8498 −8.4344 −8.4129 −8.777 −3.4444 −8.8038 −8.5105 −6.755 −6.425 −9.6454 −4.6279 −5.85599 −3.1287

C4 8.70E-18 7.0048E-06 2.86E-17 0.014934 9.76E-18 0.00001074 4.9957E-06 8.2566E-06 0.000006193 6.8165E-06 5.61E-17 5.1788E-06 4.57E-18 7.1266E-06 2.51E-18 8.50E-18 6.38E-18 5.70E-18 0.00001102 0.038899 1.0427E-06 8.2664E-07 6.7794E-06 9.14E-18 2.31E-18 2.7267E-06 4.5833E-06 5.3579E-06 9.1426E-06 0.000012311 6.7652E-06 4.3172E-06 3.26E-18 9.20E-18 0.024508 1.7147E-06 0.000012978 0.00001305 0.000015065 0.092794 0.00063693 1.1326E-06 1.68E-17 1.23E-17 6.6793E-06 6.42E-17 8.0325E-06 0.000005458 4.5035E-06 4.9831E-06 5.5501E-06 5.46E-17 4.2431E-06 6.4311E-06 1.3269E-06 1.51E-16 0.000010073 4.3819E-07 1.47E-18 2.89E-18

C5

Tmin, K

P at Tmin

6 2 6 1 6 2 2 2 2 2 6 2 6 2 6 6 6 6 2 1 2 2 2 6 6 2 2 2 2 2 2 2 6 6 1 2 2 2 2 1 1 2 6 6 2 6 2 2 2 2 2 6 2 2 2 6 2 2 6 6

307.93 177.14 245.25 182.48 279.69 296.6 242 169.67 179.28 138.13 145.59 189.64 285 243.51 304.55 280.05 206.89 247.56 229.15 18.73 210.15 282.85 220.6 175.3 248.39 256.15 326.14 176.19 237.49 178.01 192.5 172.71 301.15 223.35 156.85 169.2 154.56 179.6 136.95 176.85 187.65 204.81 159.95 226.1 240.91 180.96 145.19 239.66 223.16 184.99 188.44 131.65 212.72 160 274.18 122.93 174.88 291.67 413.79 284.95

3.45E+01 4.71E-04 7.44E+04 1.80E+02 5.36E+03 7.65E+01 6.80E+00 1.04E-01 9.07E+00 1.28E-02 7.80E+01 8.24E-03 5.51E+00 1.39E+00 1.45E-01 1.50E-01 2.59E-02 2.59E-02 1.60E-01 1.72E+04 2.64E+00 7.53E+02 2.13E+01 7.14E-04 6.41E+00 6.49E+00 1.23E+03 2.21E+00 2.37E+02 5.93E+00 1.72E+00 8.25E-02 1.02E-01 3.74E+02 3.95E-01 9.93E-02 6.45E+01 1.17E+02 5.43E+01 4.47E-03 6.86E+00 8.21E-01 9.45E-02 4.50E+01 6.12E+03 7.56E+01 1.52E-02 6.06E+01 6.41E+00 8.04E-02 2.07E-01 3.05E+00 1.95E-01 1.26E-02 3.72E-02 4.15E-01 7.86E+00 5.02E+01 1.15E+03 2.53E+03

Tmax, K 704.65 631 400.15 459.93 553.8 650.1 653 560.4 511.7 507 398 664 674 617.7 722.1 688 616.6 696 619.85 38.35 628 650.15 611 584.1 683.95 705 684.75 523 561.6 510 560 572 736.6 496.6 466.7 557.15 386.44 445 351.26 523.1 500.05 576 507.8 543 473.2 437.2 500 591.15 606.15 596.15 615 400.1 649.6 537.3 766 402 503.04 729 777.4 587

P at Tmax 5.151E+06 3.226E+06 5.924E+06 4.991E+06 4.093E+06 4.265E+06 3.989E+06 4.392E+06 4.513E+06 4.799E+06 5.494E+06 3.970E+06 2.600E+06 2.091E+06 2.280E+06 2.308E+06 2.223E+06 2.130E+06 2.363E+06 1.663E+06 6.034E+06 5.375E+06 7.170E+06 2.459E+06 4.070E+06 4.074E+06 4.070E+06 5.106E+06 5.318E+06 6.093E+06 4.239E+06 4.232E+06 4.260E+06 3.674E+06 3.641E+06 3.961E+06 4.507E+06 4.372E+06 5.761E+06 3.199E+06 2.869E+06 3.017E+06 3.773E+06 3.447E+06 4.870E+06 5.258E+06 3.130E+06 2.939E+06 2.939E+06 2.938E+06 5.363E+06 5.274E+06 4.365E+06 2.882E+06 2.779E+06 3.561E+06 5.533E+06 5.648E+06 2.759E+06 5.158E+06

121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183

Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen

C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2

101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0

59.969 54 137.47 203.66 51.857 73.304 66.824 81.56 89.063 52.923 90.464 57.661 80.208 88.671 53.963 73.51 84.09 66.51 91.944 73.833 122.364 77.523 57.723 57.459 65.551 105.64 86.898 61.6271 42.393 51.915 38.593 41.2744 49.3632 100.3 43.8066 74.738 11.533 156.95 55.3058 87.829 112.372 147.41 153.088 78.463 75.494 65.922 79.858 59.083 156.06 58.7734 104.65 98.3767 135.42149 122.695 107.44 73.155 51.9766 47.091 68.467 133.2 123.71 76.858 12.69

−8585.5 −6018.5 −11,976 −19,441 −2598.7 −7122.3 −6227.6 −5596.9 −7733.7 −7531.7 −10,243 −6346.5 −7203.2 −7012.7 −2443 −7572.7 −10,411 −6019.2 −5293.4 −5817 −13,308.8 −7978.8 −5236.9 −6356.8 −5027.4 −8007 −6646.4 −6095.88 −1103.3 −5439 −3123.34 −2676.65 −3847.87 −10,763 −5131.03 −5417 −8.99 −15,557 −6694.68 −6996.4 −12,660.1 −13,466 −12,618.7 −8077.2 −7896.5 −6189 −8501.8 −6031.8 −15,015 −6529.3 −6995.5 −11,394 −12,288.40621 −10,870 −8528.6 −7242.9 −5104.66 −5104 −7390.5 −7492.9 −7639 −7245.2 −94.896

−5.1538 −4.4981 −16.698 −25.525 −5.1283 −7.1424 −6.41 −9.0779 −9.917 −4.2347 −9.2836 −5.032 −8.6023 −10.045 −5.5643 −7.1435 −8.1976 −6.3332 −11.682 −7.809 −13.5709 −7.7757 −5.2136 −4.9545 −6.6853 −12.477 −9.5758 −5.69714 −4.1203 −4.2896 −2.53014 −3.03914 −4.09834 −10.946 −3.18777 −8.0636 0.6724 −18.966 −4.64122 −9.8802 −12.147 −17.353 −18.7479 −7.9062 −7.5047 −6.3629 −8.1043 −5.3072 −18.941 −5.17151 −12.702 −10.2239 −15.73191 −14.192 −12.679 −7.2569 −4.34844 −3.6371 −6.5456 −18.405 −16.451 −8.22 1.1125

2.00E-18 9.97E-18 8.0906E-06 8.8382E-06 0.000014913 2.8853E-06 1.79E-17 0.000008792 0.000005986 1.1835E-06 5.26E-18 8.25E-18 4.5901E-06 7.4578E-06 0.000019079 1.21E-17 1.65E-18 1.04E-17 0.014902 0.00000632 6.42E-18 1.01E-17 2.30E-17 5.20E-18 6.3208E-06 0.000009 5.96E-17 1.06E-17 0.000057815 8.75E-18 5.30E-17 2.45E-16 4.64E-17 3.8503E-06 2.37819E-06 0.00000747 0.2743 6.4559E-06 5.28E-18 7.2099E-06 4.39E-18 1.13E-17 7.45073E-06 8.05E-18 8.91E-18 2.01E-17 8.15E-18 1.44E-17 6.8172E-06 6.95E-18 0.000012381 3.29E-18 1.27E-17 0.000003871 8.4606E-06 1.27E-17 1.17E-17 0.00051621 7.76E-18 0.022062 0.016495 0.0061557 0.00032915

6 6 2 2 2 2 6 2 2 2 6 6 2 2 2 6 6 6 1 2 6 6 6 6 2 2 6 6 2 6 6 6 6 2 2 2 1 2 6 2 6 6 2 6 6 6 6 6 2 6 2 6 6 2 2 6 6 1 6 1 1 1 2

300.03 210.15 263.57 309.58 90.35 159.05 189.6 192.15 178.2 238.45 258.15 175.15 161.84 134.71 104 284.29 260.15 195.2 160.65 193.55 155.15 180 140 204.15 125.26 199.25 145.65 167.55 53.48 230.94 129.95 131.35 155.15 275.6 281.45 187.55 1.76 295.13 229.8 182.57 265.83 239.15 220 234.15 238.15 154.12 229.92 192.22 291.31 214.93 177.83 269.25 228.55 223 217.35 217.5 133.39 170.05 192.62 141.25 183.65 274.69 13.95

7.09E+00 3.69E+00 6.15E-01 9.26E-03 1.13E+00 4.96E-04 1.43E+00 1.52E+02 3.91E-03 1.69E-01 4.63E-01 1.04E-02 3.57E-04 3.71E-06 1.26E+02 6.78E+02 2.19E-01 9.71E+00 7.79E+00 1.81E+01 1.44E-14 7.60E-04 4.31E-03 9.70E-01 1.14E-03 7.80E-01 1.61E-03 1.96E-02 2.53E+02 1.51E+02 9.43E+00 4.34E+02 4.89E+01 1.04E+00 2.41E+03 5.00E+01 1.46E+03 4.65E-02 2.56E+00 1.83E-01 4.66E-02 1.95E-02 6.55E-03 2.30E+00 3.54E+00 1.86E-03 3.05E-01 8.15E-01 9.23E-02 1.86E+00 9.02E-01 3.17E-01 2.25E-02 7.46E-02 1.45E+00 2.22E+00 5.16E-04 2.20E-01 1.31E-02 3.92E-04 5.40E-01 4.08E+02 7.21E+03

766.8 550 658 768 305.32 514 523.3 456.15 617.15 698 655 571 609.15 569.5 282.34 593 720 537 469.15 508.4 674.6 583 489 567 499.15 546 500.23 559.95 144.12 560.09 375.31 317.42 420 771 588 490.15 5.2 736 620 540.2 677.3 632.3 608.3 606.6 611.4 537.4 645 547 723 594 507.6 660.2 611.3 585.3 587.61 582.82 504 544 623 516.2 549 653.15 33.19

3.097E+06 3.111E+06 1.822E+06 1.175E+06 4.852E+06 6.109E+06 3.850E+06 5.594E+06 3.590E+06 3.203E+06 3.403E+06 2.935E+06 3.041E+06 3.412E+06 5.032E+06 6.290E+06 8.257E+06 6.850E+06 7.255E+06 4.708E+06 2.780E+06 2.460E+06 3.414E+06 3.293E+06 5.492E+06 3.336E+06 3.372E+06 3.321E+06 5.167E+06 4.544E+06 4.980E+06 5.875E+06 6.590E+06 7.751E+06 5.810E+06 5.550E+06 2.284E+05 1.344E+06 3.160E+06 2.719E+06 3.042E+06 3.013E+06 3.000E+06 2.919E+06 2.946E+06 2.921E+06 2.772E+06 3.209E+06 1.411E+06 3.460E+06 3.045E+06 3.309E+06 3.446E+06 3.323E+06 3.286E+06 3.322E+06 3.210E+06 3.540E+06 3.079E+06 3.635E+06 3.530E+06 1.473E+07 1.315E+06

2-55

(Continued )

2-56 TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K (Continued ) Cmpd. no.∗ 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242

Name Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl-1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane

Formula BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si

CAS 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9

C1 29.315 104.27 36.75 59.544 85.584 110.38 136.66 119.172 109.53 39.205 82.718 79.128 61.267 50.242 107.69 75.206 84.828 66.575 71.308 85.383 117.074 93.131 83.927 95.453 60.164 96.344 69.459 71.87 95.984 92.684 134.63 125.1 54.179 55.368 52.732 52.601 79.788 78.586 72.698 79.07 77.184 57.984 80.503 57.612 53.867 45.242 52.82 54.15 107.36 105.7 53.579 61.907 108.43 172.27 78.01 70.717 67.942 83.711 37.205

C2 −2424.5 −3731.2 −3927.1 −4143.8 −3839.9 −10,540 −7201.5 −15,688.8 −10,410 −1324.4 −6904.5 −9523.9 −5618.6 −3811.9 −7027.2 −5082.8 −9334.7 −5213.4 −4976 −9575.4 −10,743.2 −5525.4 −5640.5 −5448.8 −5621.7 −7856.3 −5250 −6885.7 −5401.7 −7080.8 −10,682 −10,288 −7477.2 −5149.8 −5286.9 −5120.3 −5420 −5176.3 −6143.6 −6114.1 −5606.1 −5339.6 −7421.8 −5197.9 −4701 −5324.4 −5437.7 −4337.7 −8085.3 −12,458 −5041.2 −6188.9 −5039.9 −11,589 −4634.1 −6439.7 −5419.1 −6786.9 −2590.3

C3 −1.1354 −15.047 −2.1245 −6.1764 −11.199 −12.262 −18.934 −12.6757 −12.289 −3.4366 −8.8622 −7.7355 −5.6473 −4.2526 −13.916 −8.0919 −8.7063 −6.7693 −7.7169 −8.6164 −13.1654 −11.852 −9.6453 −12.384 −5.53 −11.058 −7.1125 −7.0944 −11.829 −10.695 −16.511 −15.157 −4.22 −5.0136 −4.4509 −4.4554 −9.0702 −8.7501 −7.5779 −8.631 −8.392 −5.2362 −8.379 −5.1269 −4.7052 −3.2551 −4.442 −4.8127 −12.72 −11.234 −4.6404 −5.706 −15.012 −22.113 −8.9575 −6.9845 −6.8067 −9.2526 −2.5993

C4 2.38E-18 0.03134 3.89E-17 0.000014161 0.018848 1.43E-17 0.022255 1.55E-18 0.000003199 0.000031019 7.4664E-06 3.16E-18 2.11E-17 6.53E-17 0.015185 0.000008113 6.17E-18 4.8106E-06 8.7271E-06 5.61E-18 1.17E-17 0.014205 0.000011121 0.015643 1.86E-17 0.000007308 7.93E-17 1.49E-17 0.000018092 8.1366E-06 8.4427E-06 0.000010918 3.52E-18 0.000003222 1.09E-17 1.33E-17 0.000011489 9.1727E-06 5.6476E-06 6.5333E-06 7.8468E-06 2.08E-17 1.81E-17 2.17E-17 2.88E-17 3.04E-18 9.51E-18 4.50E-17 8.3307E-06 4.46E-18 1.94E-17 1.18E-17 0.022725 0.000013703 0.000013413 2.01E-17 4.78E-17 6.6666E-06 6.0508E-06

C5

Tmin, K

P at Tmin

6 1 6 2 1 6 1 6 2 2 2 6 6 6 1 2 6 2 2 6 6 1 2 1 6 2 6 6 2 2 2 2 6 2 6 6 2 2 2 2 2 6 6 6 6 6 6 6 2 6 6 6 1 2 2 6 6 2 2

185.15 158.97 259.83 189.79 187.68 227.15 177.95 409.15 288.15 90.69 175.47 301.15 175.15 170.45 196.32 179.69 260.75 159.53 113.25 193 155.95 135.58 139.39 160.15 157.48 175.3 183.45 187.35 139.05 146.58 299.15 280.15 269.15 130.73 146.62 168.54 182.55 160 186.48 167.23 174.15 188 189.15 256.15 127.93 180.15 171.64 150.18 224.95 240 119.55 176 113.54 298.97 132.81 185.65 133.97 160.17 116.34

2.95E+04 1.35E+04 1.87E+04 3.37E+02 2.29E+04 7.82E-02 7.73E+00 9.97E+01 5.86E+01 1.17E+04 1.11E-01 2.86E+01 1.02E+00 4.15E+02 4.07E+00 1.77E+02 1.81E+00 7.28E-01 1.21E-04 6.94E-05 1.14E-08 2.05E-02 1.94E-02 2.92E+00 2.99E-02 4.61E-03 4.36E+01 1.34E-01 4.12E-01 1.52E-04 2.57E+02 4.56E+01 1.62E+01 2.25E-04 3.98E-03 5.37E-01 2.58E+01 7.85E+00 1.39E+00 2.25E-01 6.88E+00 8.70E+00 6.99E-02 7.28E+03 3.32E-03 2.95E-01 1.80E-01 3.15E+00 1.91E+01 4.19E-04 2.07E-05 6.33E-02 1.21E-02 5.88E+03 6.45E-01 6.34E-01 2.90E-03 4.26E-03 1.43E+01

Tmax, K 363.15 324.65 456.65 461.15 373.53 605 471.85 834 662 190.56 512.5 718 506.55 402.4 536 430.05 693 490 460.4 643 577.2 465 470 492 512.74 593 463.2 554.5 442 572.1 686 614 617 532.7 542 526 483 437.8 535.5 533 487.2 497 574.6 488 464.48 553.4 553.1 469.95 566 694 497.7 546.49 407.8 506.2 417.9 530.6 476.25 565 352.5

P at Tmax 8.463E+06 8.356E+06 5.353E+06 6.487E+06 8.999E+06 3.683E+06 4.540E+06 6.097E+06 4.812E+06 4.590E+06 8.145E+06 4.997E+06 4.695E+06 5.619E+06 4.277E+06 7.414E+06 3.589E+06 3.831E+06 3.366E+06 3.886E+06 3.933E+06 3.465E+06 3.394E+06 4.469E+06 3.377E+06 3.464E+06 4.199E+06 3.480E+06 4.170E+06 3.486E+06 3.994E+06 3.807E+06 3.767E+06 3.759E+06 4.130E+06 4.129E+06 3.964E+06 4.433E+06 4.120E+06 4.261E+06 5.983E+06 3.416E+06 3.272E+06 5.480E+06 3.764E+06 3.792E+06 4.022E+06 7.231E+06 3.674E+06 2.545E+06 3.044E+06 3.041E+06 3.630E+06 3.957E+06 4.004E+06 4.028E+06 3.802E+06 3.972E+06 4.702E+06

243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305

alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene

C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N CH3NO2 N2 O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6

98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1

56.485 57.1299 51.085 62.964 29.755 75.632 58.282 68.149 57.278 96.512 72.974 182.54 80.3832 109.35 123.374 162.854 213.069 63.313 106.2 114.77 157.68 74.0298 96.084 116.477 144.11083 185.828 63.775 72.382 74.936 78.368 64.612 107.476 51.245 40.067 135.57 28.3041 78.741 93.2079 114.74801 116.828 84.635 44.286 46.994 58.985 67.309 82.805 137.29 72.958 95.444 86.779 126.5 57.069 59.078 84.66416 110.717 64.268 50.8769 54.552 59.9958 115.16 58.398 91.379 43.905

−6954.2 −5200.7 −4271 −8137.5 −271.06 −7202.3 −1084.1 −2257.9 −6089 −4045 −2650 −17,897 −9096.15 −9030.4 −14,215.3 −15,204.55331 −16,246 −7040.4 −10,982 −9430.8 −16,093 −8302.12 −7900.2 −13,300.4 −13,667.15667 −14,520.2 −7711.3 −8054.8 −7155.9 −8855.4 −6802.5 −12,833.4 −1200.2 −2204.8 −13,478 −4657.56 −5420.3 −10,470.5 −10,643.3 −10,453 −7078.4 −5415.1 −4289.5 −6193.1 −6880.8 −5683.8 −7447.1 −10,943 −10,113 −8101.8 −12,551 −3682.7 −3492.6 −8307.24422 −9040 −7298.9 −4931 −7149.4 −6006.16 −8433.9 −5312.7 −8276.8 −3097.8

−4.7889 −5.13976 −4.307 −5.6317 −2.6081 −7.6464 −8.3144 −8.9118 −4.9821 −12.277 −8.261 −22.498 −8.03581 −12.882 −13.5607 −19.42436 −27.6195 −5.8055 −11.696 −13.631 −18.954 −7.19776 −11.003 −12.6746 −16.82611 −23.6236 −5.7359 −7.0002 −7.5843 −7.8202 −6.0261 −11.3837 −6.4361 −2.9351 −16.022 −0.732149 −8.8253 −9.61345 −12.85754 −13.1768 −9.3 −3.0913 −3.7345 −5.2746 −6.4449 −9.4301 −19.01 −6.7902 −10.09 −9.5303 −15.002 −5.5662 −6.0669 −8.57673 −12.676 −5.9109 −4.16673 −4.2769 −5.46004 −13.934 −5.2876 −10.176 −3.4425

2.78E-18 1.65E-17 3.05E-17 2.27E-18 0.000527 1.83E-17 0.044127 0.023233 1.22E-17 0.00002886 9.70E-15 7.4008E-06 4.71E-18 7.8544E-06 3.17E-18 1.07E-17 1.31827E-05 7.58E-18 8.90E-18 8.1918E-06 5.9272E-06 5.31E-18 7.1802E-06 3.98E-18 9.37E-18 1.08854E-05 3.09E-18 5.83E-18 1.71E-17 5.66E-18 1.10E-17 1.34E-18 0.028405 7.75E-16 5.6136E-06 –8.31E-18 9.6171E-06 5.62E-18 1.25E-17 1.07E-17 6.2702E-06 1.86E-18 2.54E-17 7.40E-18 1.01E-17 0.000010767 0.021415 1.09E-18 6.76E-18 6.1367E-06 7.7521E-06 6.5133E-06 0.000010919 7.51E-18 0.000005538 4.85E-18 1.67E-17 1.18E-18 1.70E-17 0.000010346 1.9913E-06 0.000005624 1.00E-16

6 6 6 6 2 6 1 1 6 2 6 2 6 2 6 6 2 6 6 2 2 6 2 6 6 2 6 6 6 6 6 6 1 6 2 6 2 6 6 6 2 6 6 6 6 2 1 6 6 2 2 2 2 6 2 6 6 6 6 2 2 2 6

249.95 164.55 151.15 353.43 24.56 183.63 63.15 66.46 244.6 182.3 109.5 305.04 267.3 219.66 285.55 268.15 238.15 191.91 253.05 223.15 301.31 251.65 216.38 289.65 257.65 241.55 252.85 255.55 171.45 223.95 193.55 462.65 54.36 80.15 283.07 191.59 143.42 239.15 195.56 200 196.29 234.18 108.02 160.75 197.45 167.45 163.83 372.38 314.06 243.15 404.15 136.87 85.47 146.95 185.26 199 165 252.45 180.37 178.15 188.36 173.55 87.89

9.23E+00 4.94E-01 3.37E+00 9.91E+02 4.38E+04 3.18E-02 1.25E+04 1.86E-01 1.47E+02 8.69E+04 2.20E+04 1.59E-02 4.25E+00 4.31E-01 4.58E-02 8.58E-02 3.85E-03 2.04E-02 1.47E-01 4.50E-01 3.39E-02 3.49E+00 2.11E+00 2.76E-01 9.60E-02 3.79E-02 4.68E+00 7.84E+00 2.98E-03 3.05E-02 1.04E-01 1.97E+04 1.48E+02 7.35E-01 1.29E-01 1.16E+00 6.86E-02 3.97E-02 5.47E-04 5.24E-03 7.52E-01 7.34E+01 3.71E-05 1.77E-03 2.01E-01 2.40E+00 2.05E-01 2.93E+01 1.88E+02 4.33E+00 7.90E+02 1.82E+01 1.68E-04 4.27E-07 1.69E-02 2.48E-02 7.54E-01 1.31E+01 1.89E-01 1.71E-02 1.30E+01 1.81E-04 1.17E-03

654 497.1 437 748.4 44.4 593 126.2 234 588.15 309.57 180.15 758 658.5 594.6 710.7 670.9 649.5 593.1 681 598.05 747 638.9 568.7 694.26 652.3 629.8 632.7 627.7 566.9 667.3 574 828 154.58 261 708 566.1 469.7 639.16 588.1 561 561.08 560.95 464.8 584.3 598 481.2 519 869 694.25 653 791 394 369.83 536.8 508.3 636 503.6 600.81 561.3 549.73 496.95 638.35 364.85

3.341E+06 3.286E+06 4.583E+06 4.069E+06 2.665E+06 5.159E+06 3.391E+06 4.500E+06 6.309E+06 7.278E+06 6.516E+06 1.208E+06 2.680E+06 2.305E+06 2.513E+06 2.528E+06 2.540E+06 2.427E+06 2.330E+06 2.619E+06 1.255E+06 2.960E+06 2.467E+06 2.779E+06 2.781E+06 2.749E+06 2.647E+06 2.705E+06 2.663E+06 2.523E+06 2.880E+06 8.203E+06 5.021E+06 5.566E+06 1.474E+06 3.845E+06 3.364E+06 3.630E+06 3.897E+06 3.699E+06 3.706E+06 3.699E+06 3.562E+06 3.537E+06 3.473E+06 4.170E+06 4.020E+06 2.902E+06 6.058E+06 4.063E+06 4.734E+06 5.218E+06 4.213E+06 5.169E+06 4.771E+06 3.130E+06 5.040E+06 4.608E+06 4.260E+06 3.366E+06 4.738E+06 3.202E+06 4.599E+06

2-57

(Continued )

2-58 TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K (Continued ) Cmpd. no.∗

Name

306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345

Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene

Formula C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O 2S F6S O 3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10

CAS 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3

C1

C2

104.08 60.43 62.165 212.8 48.651 272.85 105.93 165.977 47.365 29.16 180.99 124.004 110.52 140.47 54.898 137.23 75.881 57.963 93.193 76.945 54.153 137.45 56.55 134.68 78.341 85.301 84.912 83.105 506.33 302 131 182.57122 57.406 55.682 91.432 54.571 73.649 85.099 90.405 88.72

−7535.9 −5276.9 −5624 −15,420 −7289.5 −9548.9 −8685.9 −19,914.4 −4084.5 −2383.6 −12,060 −17,894.4 −14,045 −13,231 −5305.4 −10,620 −6910.6 −5901.5 −7001.5 −6729.8 −6041.8 −12,549 −5681.9 −6055.8 −8019.8 −8215.9 −6722.2 −6903.7 −37,483 −24,324 −11,143 −17,112.47062 −5702.8 −4439.3 −5141.7 −5561.5 −7258.2 −7615.9 −7955.2 −7741.2

C3 −12.348 −5.6572 −5.8595 −28.109 −3.4453 −40.089 −12.42 −18.9344 −3.6469 −1.1342 −22.839 −13.156 −11.861 −16.859 −4.7627 −17.908 −7.9499 −5.2048 −10.738 −8.179 −4.5383 −16.543 −4.9815 −19.415 −8.1458 −9.2166 −9.5157 −9.1858 −69.22 −40.13 −15.855 −22.1251 −5.0307 −5.0136 −10.981 −4.712 −7.3037 −9.3072 −10.086 −9.8693

C5

Tmin, K

P at Tmin

0.000009602 2.60E-17 2.06E-17 0.000021564 1.01E-18 6.37E-15 7.5583E-06 1.91E-18 1.80E-17

2 6 6 2 6 6 2 6 6

7.24E-17 1.18E-18 2.21E-18 6.5877E-06 1.43E-17 0.014506 4.4315E-06 9.13E-18 8.2308E-06 5.3017E-06 4.98E-18 7.1275E-06 1.24E-17 0.028619 3.8971E-06 4.7979E-06 7.2244E-06 6.4703E-06 0.000027381 0.000017403 8.1871E-06 1.13E-17 1.10E-17 1.97E-17 0.000014318 1.07E-17 4.1653E-06 5.5643E-06 5.9594E-06 0.000006077

6 6 6 2 6 1 2 6 2 2 6 2 6 1 2 2 2 2 2 2 2 6 6 6 2 6 2 2 2 2

180.25 142.61 159.95 213.15 388.85 186.35 242.54 460.85 197.67 223.15 289.95 700.15 329.35 279.01 164.65 237.38 176.99 373.96 234.94 178.18 236.5 267.76 158.45 156.08 247.79 229.33 165.78 172.22 398.4 354 247.57 288.45 180.35 173.15 119.36 178.35 273.16 225.3 247.98 286.41

2.11E-01 9.73E-03 6.51E-02 9.29E-05 1.17E+04 2.21E+05 1.06E+01 7.78E+02 1.67E+03 2.30E+05 2.09E+04 2.42E+05 4.14E-01 2.53E-01 1.96E-01 1.33E-01 1.54E-02 8.69E+04 1.86E+02 4.75E-02 4.47E+01 2.51E-01 1.06E-02 9.92E+00 3.71E+00 6.93E-01 1.71E-02 1.68E-02 8.50E+00 9.36E-01 4.08E-01 1.25E-01 7.06E-01 6.69E+01 1.92E-02 3.54E-01 6.11E+02 3.18E+00 2.18E+01 5.76E+02

C4

Tmax, K 538 517 536.6 626 683 259 636 838 430.75 318.69 490.85 883.6 857 693 540.15 720 631.95 568 579.35 591.75 602 675 535.15 433.25 664.5 649.1 543.8 573.5 846 828 639 703.9 519.13 454 432 543.15 647.1 617 630.3 616.2

P at Tmax 4.031E+06 4.752E+06 4.627E+06 6.041E+06 5.925E+06 3.748E+06 3.823E+06 5.001E+06 7.860E+06 3.771E+06 8.192E+06 3.487E+06 2.974E+06 1.569E+06 5.203E+06 3.624E+06 5.117E+06 2.871E+06 5.702E+06 4.080E+06 4.447E+06 1.679E+06 3.037E+06 4.102E+06 3.447E+06 3.211E+06 2.550E+06 2.812E+06 3.410E+06 3.019E+06 1.949E+06 2.119E+06 3.930E+06 4.887E+06 5.749E+06 3.058E+06 2.193E+07 3.528E+06 3.741E+06 3.501E+06

Vapor pressure Ps is calculated by Ps = exp(C1 + C2/T + C3 ln(T) + C4T C5) where Ps is in Pa and T is in K. ∗All substances and their numbers are listed by chemical family in Table 2-6 and by formula in Table 2-7. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.

VAPOR PRESSURES TABLE 2-9

2-59

Vapor Pressures of Inorganic Compounds, up to 1 atm* Compound

Pressure, mmHg 1

Name Aluminum borohydride bromide chloride fluoride iodide oxide Ammonia heavy Ammonium bromide carbamate chloride cyanide hydrogen sulfide iodide Antimony tribromide trichloride pentachloride triiodide trioxide Argon Arsenic Arsenic tribromide trichloride trifluoride pentafluoride trioxide Arsine Barium Beryllium borohydride bromide chloride iodide Bismuth tribromide trichloride Diborane hydrobromide Borine carbonyl triamine Boron hydrides dihydrodecaborane dihydrodiborane dihydropentaborane tetrahydropentaborane tetrahydrotetraborane Boron tribromide trichloride trifluoride Bromine pentafluoride Cadmium chloride fluoride iodide oxide Calcium Carbon (graphite) dioxide disulfide monoxide oxyselenide oxysulfide selenosulfide subsulfide tetrabromide tetrachloride tetrafluoride Cesium bromide chloride fluoride iodide

5

10

20

Formula Al Al(BH4)3 AlBr3 Al2Cl6 AlF3 AlI3 Al2O3 NH3 ND3 NH4Br N2H6CO2 NH4Cl NH4CN NH4HS NH4I Sb SbBr3 SbCl3 SbCl5 SbI3 Sb4O6 A As AsBr3 AsCl3 AsF3 AsF5 As2O3 AsH3 Ba Be(BH4)2 BeBr2 BeCl2 BeI2 Bi BiBr3 BiCl3 B2H5Br BH3CO B3N3H6 B10H14 B2H6 B5H9 B5H11 B4H10 BBr3 BCl3 BF3 Br2 BrF5 Cd CdCl2 CdF2 CdI2 CdO Ca C CO2 CS2 CO COSe COS CSeS C3S2 CBr4 CCl4 CF4 Cs CsBr CsCl CsF CsI

40

60

100

200

400

760

Melting point, °C

1749 −3.9 176.1 152.0 1422 294.5 2665 −68.4 −67.4 320.0 26.7 271.5 −0.5 0.0 331.8 1223 203.5 143.3 114.1 303.5 957 −200.5 518 145.2 70.9 13.2 −84.3 332.5 −98.0 1301 58.6 405 411 411 1271 360 343 −29.0 −95.3 +4.0

1844 +11.2 199.8 161.8 1457 322.0 2766 −57.0 −57.0 345.3 37.2 293.2 +9.6 +10.5 355.8 1288 225.7 165.9

1947 28.1 227.0 171.6 1496 354.0 2874 −45.4 −45.4 370.8 48.0 316.5 20.5 21.8 381.0 1364 250.2 192.2

2056 45.9 256.3 180.2 1537 385.5 2977 −33.6 −33.4 396.0 58.3 337.8 31.7 33.3 404.9 1440 275.0 219.0

660 −64. 97. 192.4 1040

333.8 1085 −195.6 548 167.7 89.2 26.7 −75.5 370.0 −87.2 1403 69.0 427 435 435 1319 392 372 −15.4 −85.5 18.5

368.5 1242 −190.6 579 193.6 109.7 41.4 −64.0 412.2 −75.2 1518 79.7 451 461 461 1370 425 405 0.0 −74.8 34.3

401.0 1425 −185.6 610 220.0 130.4 56.3 −52.8 457.2 −62.1 1638 90.0 474 487 487 1420 461 441 +16.3 −64.0 50.6

142.3 −120.9 +9.6 20.1 −28.1 33.5 −32.4 −123.0 +9.3 −4.5 611 797 1486 640 1341 1207 4373 −100.2 −5.1 −205.7 −61.7 −85.9 28.3 109.9 119.7 23.0 −150.7 509 1072 1069 1025 1055

163.8 −111.2 24.6 34.8 −14.0 50.3 −18.9 −115.9 24.3 +9.9 658 847 1561 688 1409 1288 4516 −93.0 +10.4 −201.3 −49.8 −75.0 45.7 130.8 139.7 38.3 −143.6 561 1140 1139 1092 1124

−99.6 40.8 51.2 +0.8 70.0 −3.6 −108.3 41.0 25.7 711 908 1651 742 1484 1388 4660 −85.7 28.0 −196.3 −35.6 −62.7 65.2

−86.5 58.1 67.0 16.1 91.7 +12.7 −100.7 58.2 40.4 765 967 1751 796 1559 1487 4827 −78.2 46.5 −191.3 −21.9 −49.9 85.6

163.5 57.8 −135.5 624 1221 1217 1170 1200

189.5 76.7 −127.7 690 1300 1300 1251 1280

Temperature, °C 1284 81.3 100.0 1238 178.0 2148 −109.1

1421 −52.2 103.8 116.4 1298 207.7 2306 −97.5

1487 −42.9 118.0 123.8 1324 225.8 2385 −91.9

1555 −32.5 134.0 131.8 1350 244.2 2465 −85.8

1635 −20.9 150.6 139.9 1378 265.0 2549 −79.2

198.3 −26.1 160.4 −50.6 −51.1 210.9 886 93.9 49.2 22.7 163.6 574 −218.2 372 41.8 −11.4

234.5 −10.4 193.8 −35.7 −36.0 247.0 984 126.0 71.4 48.6 203.8 626 −213.9 416 70.6 +11.7

252.0 −2.9 209.8 −28.6 −28.7 263.5 1033 142.7 85.2 61.8 223.5 666 −210.9 437 85.2 +23.5

270.6 +5.3 226.1 −20.9 −20.8 282.8 1084 158.3 100.6 75.8 244.8 729 −207.9 459 101.3 36.0

−117.9 212.5 −142.6

−108.0 242.6 −130.8 984 19.8 325 328 322 1099 261 242 −75.3 −127.3 −45.0

−103.1 259.7 −124.7 1049 28.1 342 346 341 1136 282 264 −66.3 −121.1 −35.3

−98.0 279.2 −117.7 1120 36.8 361 365 361 1177 305 287 −56.4 −114.1 −25.0

290.0 14.0 245.0 −12.6 −12.3 302.8 1141 177.4 117.8 91.0 267.8 812 −204.9 483 118.7 50.0 −2.5 −92.4 299.2 −110.2 1195 46.2 379 384 382 1217 327 311 −45.4 −106.6 −13.2

1684 −13.4 161.7 145.4 1398 277.8 2599 −74.3 −74.0 303.8 19.6 256.2 −7.4 −7.0 316.0 1176 188.1 128.3 101.0 282.5 873 −202.9 498 130.0 58.7 +4.2 −88.5 310.3 −104.8 1240 51.7 390 395 394 1240 340 324 −38.2 −101.9 −5.8

3586 −134.3 −73.8 −222.0 −117.1 −132.4 −47.3 14.0

80.8 −149.5 −40.4 −29.9 −73.1 −20.4 −75.2 −145.4 −32.8 −51.0 455 618 1231 481 1100 926 3828 −124.4 −54.3 −217.2 −102.3 −119.8 −26.5 41.2

90.2 −144.3 −30.7 −19.9 −64.3 −10.1 −66.9 −141.3 −25.0 −41.9 484 656 1286 512 1149 983 3946 −119.5 −44.7 −215.0 −95.0 −113.3 −16.0 54.9

100.0 −138.5 −20.0 −9.2 −54.8 +1.5 −57.9 −136.4 −16.8 −32.0 516 695 1344 546 1200 1046 4069 −114.4 −34.3 −212.8 −86.3 −106.0 −4.4 69.3

−50.0 −184.6 279 748 744 712 738

−30.0 −174.1 341 838 837 798 828

−19.6 −169.3 375 887 884 844 873

−8.2 −164.3 409 938 934 893 923

117.4 −131.6 −8.0 +2.7 −44.3 14.0 −47.8 −131.0 −8.0 −21.0 553 736 1400 584 1257 1111 4196 −108.6 −22.5 −210.0 −76.4 −98.3 +8.6 85.6 96.3 +4.3 −158.8 449 993 989 947 976

127.8 −127.2 −0.4 10.2 −37.4 22.1 −41.2 −127.6 −0.6 −14.0 578 762 1436 608 1295 1152 4273 −104.8 −15.3 −208.1 −70.2 −93.0 17.0 96.0 106.3 12.3 −155.4 474 1026 1023 980 1009

+1.0 289 291 283 1021 −93.3 −139.2 −63.0 60.0 −159.7 −50.2 −90.9 −41.4 −91.5 −154.6 −48.7 −69.3 394 1112 416 1000

∗Compiled from the extended tables published by D. R. Stull in Ind. Eng. Chem., 39, 517 (1947).

2050 −77.7 −74.0 520 36 630.5 96.6 73.4 2.8 167 656 −189.2 814 −18 −5.9 −79.8 312.8 −116.3 850 123 490 405 488 271 218 230 −104.2 −137.0 −58.2 99.6 −169 −47.0 −119.9 −45 −107 −126.8 −7.3 −61.4 320.9 568 520 385 851 −57.5 −110.8 −205.0 −138.8 −75.2 +0.4 90.1 −22.6 −183.7 28.5 636 646 683 621

(Continued )

2-60

PHYSICAL AnD CHEMICAL DATA

TABLE 2-9 Vapor Pressures of Inorganic Compounds, up to 1 atm (Continued ) Compound

Pressure, mmHg 1

Name Chlorine fluoride trifluoride monoxide dioxide heptoxide Chlorosulfonic acid Chromium carbonyl oxychloride Cobalt chloride nitrosyl tricarbonyl Columbium fluoride Copper Cuprous bromide chloride iodide Cyanogen bromide chloride fluoride Deuterium cyanide Fluorine oxide Germanium bromide chloride hydride Trichlorogermane Tetramethylgermane Digermane Trigermane Gold Helium para-Hydrogen Hydrogen bromide chloride cyanide fluoride iodide oxide (water) sulfide disulfide selenide telluride Iodine heptafluoride Iron pentacarbonyl Ferric chloride Ferrous chloride Krypton Lead bromide chloride fluoride iodide oxide sulfide Lithium bromide chloride fluoride iodide Magnesium chloride Manganese chloride Mercury Mercuric bromide chloride iodide Molybdenum hexafluoride oxide

5

10

20

Formula Cl2 ClF ClF3 Cl2O ClO2 Cl2O7 HSO3Cl Cr Cr(CO)6 CrO2Cl2 CoCl2 Co(CO)3NO CbF5 Cu Cu2Br2 Cu2Cl2 Cu2I2 C2N2 CNBr CNCl CNF DCN F2 F2O GeBr4 GeCl4 GeH4 GeHCl3 Ge(CH3)4 Ge2H6 Ge3H8 Au He H2 HBr HCl HCN H2F2 HI H2O H2S HSSH H2Se H2Te I2 IF7 Fe Fe(CO)5 Fe2Cl6 FeCl2 Kr Pb PbBr2 PbCl2 PbF2 PbI2 PbO PbS Li LiBr LiCl LiF LiI Mg MgCl2 Mn MnCl2 Hg HgBr2 HgCl2 HgI2 Mo MoF6 MoO3

40

60

100

200

400

760

Melting point, °C

−71.7 −120.8 −34.7 −39.4 −29.4 29.1 105.3 2139 108.0 58.0 843 29.0 148.5 2207 951 960 907 −51.8 22.6 −24.9 −97.0 −17.5 −202.7 −165.8 113.2 27.5 −120.3 26.5 −6.3 −20.3 47.9 2521 −270.3 −257.9 −97.7 −114.0 −17.8 −28.2 −72.1 51.6 −91.6 22.0 −74.2 −45.7 116.5 −31.9 2360 50.3 272.5 842 −171.8 1421 745 784 1080 701 1265 1108 1097 1076 1129 1425 993 909 1142 1792 960 261.7 237.8 237.0 261.8 4109 −8.0 955

−60.2 −114.4 −20.7 −26.5 −17.8 44.6 120.0 2243 121.8 75.2 904 44.4 172.2 2325 1052 1077 1018 −42.6 33.8 −14.1 −89.2 −5.4 −198.3 −159.0 135.4 44.4 −111.2 41.6 +8.8 −4.7 67.0 2657 −269.8 −256.3 −88.1 −105.2 −5.3 −13.2 −60.3 66.5 −82.3 35.3 −65.2 −32.4 137.3 −20.7 2475 68.0 285.0 897 −165.9 1519 796 833 1144 750 1330 1160 1178 1147 1203 1503 1049 967 1223 1900 1028 290.7 262.7 256.5 291.0 4322 +4.1 1014

−47.3 −107.0 −4.9 −12.5 −4.0 62.2 136.1 2361 137.2 95.2 974 62.0 198.0 2465 1189 1249 1158 −33.0 46.0 −2.3 −80.5 +10.0 −193.2 −151.9 161.6 63.8 −100.2 58.3 26.0 +13.3 88.6 2807 −269.3 −254.5 −78.0 −95.3 +10.2 +2.5 −48.3 83.0 −71.8 49.6 −53.6 −17.2 159.8 −8.3 2605 86.1 298.0 961 −159.0 1630 856 893 1219 807 1402 1221 1273 1226 1290 1591 1110 1034 1316 2029 1108 323.0 290.0 275.5 324.2 4553 17.2 1082

−33.8 −100.5 +11.5 +2.2 +11.1 78.8 151.0 2482 151.0 117.1 1050 80.0 225.0 2595 1355 1490 1336 −21.0 61.5 +13.1 −72.6 26.2 −187.9 −144.6 189.0 84.0 −88.9 75.0 44.0 31.5 110.8 2966 −268.6 −252.5 −66.5 −84.8 25.9 19.7 −35.1 100.0 −60.4 64.0 −41.1 −2.0 183.0 +4.0 2735 105.0 319.0 1026 −152.0 1744 914 954 1293 872 1472 1281 1372 1310 1382 1681 1171 1107 1418 2151 1190 357.0 319.0 304.0 354.0 4804 36.0 1151

−100.7 −145 −83 −116 −59 −91 −80 1615

Temperature, °C −118.0 −98.5

−106.7 −143.4 −80.4 −81.6

−45.3 32.0 1616 36.0 −18.4

−23.8 53.5 1768 58.0 +3.2

1628 572 546 −95.8 −35.7 −76.7 −134.4 −68.9 −223.0 −196.1 −45.0 −163.0 −41.3 −73.2 −88.7 −36.9 1869 −271.7 −263.3 −138.8 −150.8 −71.0 −123.3 −17.3 −134.3 −43.2 −115.3 −96.4 38.7 −87.0 1787 194.0 −199.3 973 513 547 479 943 852 723 748 783 1047 723 621 778 1292 126.2 136.5 136.2 157.5 3102 −65.5 734

1795 666 645 610 −83.2 −18.3 −61.4 −123.8 −54.0 −216.9 −186.6 43.3 −24.9 −151.0 −22.3 −54.6 −69.8 −12.8 2059 −271.5 −261.9 −127.4 −140.7 −55.3 −74.7 −109.6 +1.2 −122.4 −24.4 −103.4 −82.4 62.2 −70.7 1957 −6.5 221.8 −191.3 1099 578 615 861 540 1039 928 838 840 880 1156 802 702 877 1434 736 164.8 165.3 166.0 189.2 3393 −49.0 785

−101.6 −139.0 −71.8 −73.1 −59.0 −13.2 64.0 1845 68.3 13.8

−93.3 −134.3 −62.3 −64.3 −51.2 −2.1 75.3 1928 79.5 25.7

86.3 1879 718 702 656 −76.8 −10.0 −53.8 −118.5 −46.7 −214.1 −182.3 56.8 −15.0 −145.3 −13.0 −45.2 −60.1 −0.9 2154 −271.3 −261.3 −121.8 −135.6 −47.7 −65.8 −102.3 11.2 −116.3 −15.2 −97.9 −75.4 73.2 −63.0 2039 +4.6 235.5 700 −187.2 1162 610 648 904 571 1085 975 881 888 932 1211 841 743 930 1505 778 184.0 179.8 180.2 204.5 3535 −40.8 814

−1.3 103.0 1970 777 766 716 −70.1 −1.0 −46.1 −112.8 −38.8 −211.0 −177.8 71.8 −4.1 −139.2 −3.0 −35.0 −49.9 +11.8 2256 −271.1 −260.4 −115.4 −130.0 −39.7 −56.0 −94.5 22.1 −109.7 −5.1 −91.8 −67.8 84.7 −54.5 2128 16.7 246.0 737 −182.9 1234 646 684 950 605 1134 1005 940 939 987 1270 883 789 988 1583 825 204.6 194.3 195.8 220.0 3690 −32.0 851

−84.5 −128.8 −51.3 −54.3 −42.8 +10.3 87.6 2013 91.2 38.5 770 +11.0 121.5 2067 844 838 786 −62.7 +8.6 −37.5 −106.4 −30.1 −207.7 −173.0 88.1 +8.0 −131.6 +8.8 −23.4 −38.2 26.3 2363 −270.7 −259.6 −108.3 −123.8 −30.9 −45.0 −85.6 34.0 −102.3 +6.0 −84.7 −59.1 97.5 −45.3 2224 30.3 256.8 779 −178.4 1309 686 725 1003 644 1189 1048 1003 994 1045 1333 927 838 1050 1666 879 228.8 211.5 212.5 238.2 3859 −22.1 892

−79.0 −125.3 −44.1 −48.0 −37.2 +18.2 95.2 2067 98.3 46.7 801 18.5 133.2 2127 887 886 836 −57.9 14.7 −32.1 −102.3 −24.7 −205.6 −170.0 98.8 16.2 −126.7 16.2 −16.2 −30.7 35.5 2431 −270.6 −258.9 −103.8 −119.6 −25.1 −37.9 −79.8 41.5 −97.9 12.8 −80.2 −53.7 105.4 −39.4 2283 39.1 263.7 805 −175.7 1358 711 750 1036 668 1222 1074 1042 1028 1081 1372 955 868 1088 1720 913 242.0 221.0 222.2 249.0 3964 −16.2 917

735 −11 75.5 1083 504 422 605 −34.4 58 −6.5 −12 −223 −223.9 26.1 −49.5 −165 −71.1 −88 −109 −105.6 1063 −259.1 −87.0 −114.3 −13.2 −83.7 −50.9 0.0 −85.5 −89.7 −64 −49.0 112.9 5.5 1535 −21 304 −156.7 327.5 373 501 855 402 890 1114 186 547 614 870 446 651 712 1260 650 −38.9 237 277 259 2622 17 795

VAPOR PRESSURES TABLE 2-9

2-61

Vapor Pressures of Inorganic Compounds, up to 1 atm (Continued ) Compound

Pressure, mmHg 1

Name Neon Nickel carbonyl chloride Nitrogen Nitric oxide Nitrogen dioxide Nitrogen pentoxide Nitrous oxide Nitrosyl chloride fluoride Osmium tetroxide (yellow) (white) Oxygen Ozone Phosgene Phosphorus (yellow) (violet) tribromide trichloride pentachloride Phosphine Phosphonium bromide chloride iodide Phosphorus trioxide pentoxide oxychloride thiobromide thiochloride Platinum Potassium bromide chloride fluoride hydroxide iodide Radon Rhenium heptoxide Rubidium bromide chloride fluoride iodide Selenium dioxide hexafluoride oxychloride tetrachloride Silicon dioxide tetrachloride tetrafluoride Trichlorofluorosilane Iodosilane Diiodosilane Disiloxan Trisilane Trisilazane Tetrasilane Octachlorotrisilane Hexachlorodisiloxane Hexachlorodisilane Tribromosilane Trichlorosilane Trifluorosilane Dibromosilane Difluorosilane Monobromosilane Monochlorosilane Monofluorosilane Tribromofluorosilane Dichlorodifluorosilane Trifluorobromosilane

5

10

20

Formula Ne Ni Ni(CO)4 NiCl2 N2 NO NO2 N2O5 N2O NOCl NOF OsO4 OsO4 O2 O3 COCl2 P P PBr3 PCl3 PCl5 PH3 PH4Br PH4Cl PH4I P4O6 P4O10 POCl3 PSBr3 PSCl3 Pt K KBr KCl KF KOH KI Rn Re2O7 Rb RbBr RbCl RbF RbI Se SeO2 SeF6 SeOCl2 SeCl4 Si SiO2 SiCl4 SiF4 SiFCl3 SiH3I SiH2I2 (SiH3)2O Si3H8 (SiH3)3N Si4H10 Si3Cl3 (SiCl3)2O Si2Cl6 SiHBr3 SiHCl3 SiHF3 SiH2Br2 SiH2F2 SiH3Br SiH3Cl SiH3F SiFBr3 SiF2Cl2 SiF3Br

40

60

100

200

400

760

Melting point, °C

−251.0 2364 −6.0 866 −209.7 −166.0 −14.7 7.4 −110.3 −46.3 −88.8 71.5 71.5 −198.8 −141.0 −35.6 197.3 349 103.6 21.0 117.0 −118.8 7.4 −52.0 29.3 108.3 510 47.4 126.3 63.8 3714 586 1137 1164 1245 1064 1080 −99.0 289.0 514 1114 1133 1168 1072 554 258.0 −73.9 118.0 147.5 2083 1969 +5.4 −113.3 −33.2 −4.4 79.4 −55.9 +1.6 −1.1 47.4 146.0 75.4 85.4 51.6 −16.4 −118.7 14.1 −107.3 −42.3 −68.5 −122.4 28.6 −70.3

−249.7 2473 +8.8 904 −205.6 −162.3 −5.0 15.6 −103.6 −34.0 −79.2 89.5 89.5 −194.0 −132.6 −22.3 222.7 370 125.2 37.6 131.3 −109.4 17.6 −44.0 39.9 129.0 532 65.0 141.8 82.0 3923 643 1212 1239 1323 1142 1152 −87.7 307.0 563 1186 1207 1239 1141 594 277.0 −64.8 134.6 161.0 2151 2053 21.0 −170.2 −19.3 +10.7 101.8 −43.5 17.8 +14.0 63.6 166.2 92.5 102.2 70.2 −1.8 −111.3 31.6 −98.3 −28.6 −57.0 −115.2 45.7 −58.0 −69.8

−248.1 2603 25.8 945 −200.9 −156.8 +8.0 24.4 −96.2 −20.3 −68.2 109.3 109.3 −188.8 −122.5 −7.6 251.0 391 149.7 56.9 147.2 −98.3 28.0 −35.4 51.6 150.3 556 84.3 157.8 102.3 4169 708 1297 1322 1411 1233 1238 −75.0 336.0 620 1267 1294 1322 1223 637 297.7 −55.2 151.7 176.4 2220 2141 38.4 −100.7 −4.0 27.9 125.5 −29.3 35.5 31.0 81.7 189.5 113.6 120.6 90.2 +14.5 −102.8 50.7 −87.6 −13.3 −44.5 −106.8 64.6 −45.0 −55.9

−246.0 2732 42.5 987 −195.8 −151.7 21.0 32.4 −85.5 −6.4 −56.0 130.0 130.0 −183.1 −111.1 +8.3 280.0 417 175.3 74.2 162.0 −87.5 38.3 −27.0 62.3 173.1 591 105.1 175.0 124.0 4407 774 1383 1407 1502 1327 1324 −61.8 362.4 679 1352 1381 1408 1304 680 317.0 −45.8 168.0 191.5 2287 2227 56.8 −94.8 +12.2 45.4 149.5 −15.4 53.1 48.7 100.0 211.4 135.6 139.0 111.8 31.8 −95.0 70.5 −77.8 +2.4 −30.4 −98.0 83.8 −31.8 −41.7

−248.7 1452 −25 1001 −210.0 −161 −9.3 30 −90.9 −64.5 −134 56 42 −218.7 −251 −104 44.1 590 −40 −111.8

Temperature, °C −257.3 1810

−255.5 1979

−254.6 2057

−253.7 2143

671 −226.1 −184.5 −55.6 −36.8 −143.4

731 −221.3 −180.6 −42.7 −23.0 −133.4

759 −219.1 −178.2 −36.7 −16.7 −128.7

789 −216.8 −175.3 −30.4 −10.0 −124.0

−132.0 3.2 −5.6 −219.1 −180.4 −92.9 76.6 237 7.8 −51.6 55.5

−120.3 22.0 +15.6 −213.4 −168.6 −77.0 111.2 271 34.4 −31.5 74.0

−114.3 31.3 26.0 −210.6 −163.2 −69.3 128.0 287 47.8 −21.3 83.2

−107.8 41.0 37.4 −207.5 −157.2 −60.3 146.2 306 62.4 −10.2 92.5

−43.7 −91.0 −25.2 384

−28.5 −79.6 −9.0 39.7 424

50.0 −18.3 2730 341 795 821 885 719 745 −144.2 212.5 297 781 792 921 748 356 157.0 −118.6 34.8 74.0 1724

72.4 +4.6 3007 408 892 919 988 814 840 −132.4 237.5 358 876 887 982 839 413 187.7 −105.2 59.8 96.3 1835

−63.4 −144.0 −92.6

−44.1 −134.8 −76.4 −53.0 3.8 −95.8 −49.7 −49.9 −6.2 74.7 17.8 27.4 −8.0 −62.6 −142.7 −40.0 −136.0 −85.7 −104.3 −145.5 −25.4 −110.5

−21.2 −74.0 −1.1 53.0 442 2.0 83.6 16.1 3146 443 940 968 1039 863 887 −126.3 248.0 389 923 937 1016 884 442 202.5 −98.9 71.9 107.4 1888 1732 −34.4 −130.4 −68.3 −47.7 18.0 −88.2 −40.0 −40.4 +4.3 89.3 29.4 38.8 +3.4 −53.4 −138.2 −29.4 −130.4 −77.3 −97.7 −141.2 −15.1 −102.9

−13.3 −68.0 +7.3 67.8 462 13.6 95.5 29.0 3302 483 994 1020 1096 918 938 −119.2 261.0 422 975 990 1052 935 473 217.5 −92.3 84.2 118.1 1942 1798 −24.0 −125.9 −59.0 −33.4 34.1 −79.8 −29.0 −30.0 15.8 104.2 41.5 51.5 16.0 −43.8 −132.9 −18.0 −124.3 −68.3 −90.1 −136.3 −3.7 −94.5

−112.5 −68.9 −68.7 −27.7 46.3 −5.0 +4.0 −30.5 −80.7 −152.0 −60.9 −146.7 −117.8 −153.0 −46.1 −124.7

−252.6 2234 −23.0 821 −214.0 −171.7 −23.9 −2.9 −118.3 −60.2 −100.3 51.7 50.5 −204.1 −150.7 −50.3 166.7 323 79.0 +2.3 102.5 −129.4 −5.0 −61.5 16.1 84.0 481 27.3 108.0 42.7 3469 524 1050 1078 1156 976 995 −111.3 272.0 459 1031 1047 1096 991 506 234.1 −84.7 98.0 130.1 2000 1867 −12.1 −120.8 −48.8 −21.8 52.6 −70.4 −16.9 −18.5 28.4 121.5 55.2 65.3 30.0 −32.9 −127.3 −5.2 −117.6 −57.8 −81.8 −130.8 +9.2 −85.0

−251.9 2289 −15.9 840 −212.3 −168.9 −19.9 +1.8 −114.9 −54.2 −95.7 59.4 59.4 −201.9 −146.7 −44.0 179.8 334 89.8 10.2 108.3 −125.0 +0.3 −57.3 21.9 94.2 493 35.8 116.0 51.8 3574 550 1087 1115 1193 1013 1030 −106.2 280.0 482 1066 1084 1123 1026 527 244.6 −80.0 106.5 137.8 2036 1911 −4.8 −117.5 −42.2 −14.3 64.0 −64.2 −9.0 −11.0 36.6 132.0 63.8 73.9 39.2 −25.8 −123.7 +3.2 −113.3 −51.1 −76.0 −127.2 17.4 −78.6

−132.5 −28.5 22.5 569 2 38 −36.2 1755 62.3 730 790 880 380 723 −71 296 38.5 682 715 760 642 217 340 −34.7 8.5 1420 1710 −68.8 −90 −120.8 −57.0 −1.0 −144.2 −117.2 −105.7 −93.6 −33.2 −1.2 −73.5 −126.6 −131.4 −70.2 −93.9 −82.5 −139.7 −70.5

(Continued )

2-62

PHYSICAL AnD CHEMICAL DATA

TABLE 2-9 Vapor Pressures of Inorganic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Trifluorochlorosilane Hexafluorodisilane Dichlorofluorobromosilane Dibromochlorofluorosilane Silane Disilane Silver chloride iodide Sodium bromide chloride cyanide fluoride hydroxide iodide Strontium Strontium oxide Sulfur monochloride hexafluoride Sulfuryl chloride Sulfur dioxide trioxide (α) trioxide (β) trioxide (γ) Tellurium chloride fluoride Thallium Thallous bromide chloride iodide Thionyl bromide Thionyl chloride Tin Stannic bromide Stannous chloride Stannic chloride iodide hydride Tin tetramethyl trimethyl-ethyl trimethyl-propyl Titanium chloride Tungsten Tungsten hexafluoride Uranium hexafluoride Vanadyl trichloride Xenon Zinc chloride fluoride diethyl Zirconium bromide chloride iodide

1

5

10

20

Formula SiF3Cl Si2F6 SiFCl2Br SiFClBr2 SiH4 Si2H6 Ag AgCl AgI Na NaBr NaCl NaCN NaF NaOH NaI Sr SrO S S2Cl2 SF6 SO2Cl2 SO2 SO3 SO3 SO3 Te TeCl4 TeF6 Tl TlBr TlCl TlI SOBr2 SOCl2 Sn SnBr4 SnCl2 SnCl4 SnI4 SnH4 Sn(CH3)4 Sn(CH3)3⋅C2H5 Sn(CH3)3⋅C3H7 TiCl4 W WF6 UF6 VOCl3 Xe Zn ZnCl2 ZnF2 Zn(C2H5)2 ZrBr4 ZrCl4 ZrI4

40

100

200

400

760

Melting point, °C

−108.2 −46.7 −29.0 −4.7 −146.3 −66.4 1795 1242 1152 662 1099 1169 1156 1403 1057 1039 1057

−101.7 −41.7 −19.5 +6.3 −140.5 −57.5 1865 1297 1210 701 1148 1220 1214 1455 1111 1083 1111

−91.7 −34.2 −3.2 23.0 −131.6 −44.6 1971 1379 1297 758 1220 1296 1302 1531 1192 1150 1192

−81.0 −26.4 +15.4 43.0 −122.0 −29.0 2090 1467 1400 823 1304 1379 1401 1617 1286 1225 1285

−70.0 −18.9 35.4 59.5 −111.5 −14.3 2212 1564 1506 892 1392 1465 1497 1704 1378 1304 1384

305.5 63.2 −96.8 +7.2 −54.6 +4.0 8.0 21.4 789 287 −73.8 1143 621 612 631 68.3 10.4 1903 116.2 467 43.5 234.2 −96.6 11.7 38.4 57.5 58.0 5007 −27.5 10.4 49.8 −137.7 700 584 1207 47.2 289 268 355

327.2 75.3 −90.9 17.8 −46.9 10.5 14.3 28.0 838 304 −67.9 1196 653 645 663 80.6 21.4 1968 131.0 493 54.7 254.2 −89.2 22.8 50.0 69.8 71.0 5168 −20.3 18.2 62.5 −132.8 736 610 1254 59.1 301 279 369

359.7 93.5 −82.3 33.7 −35.4 20.5 23.7 35.8 910 330 −57.3 1274 703 694 712 99.0 37.9 2063 152.8 533 72.0 283.5 −78.0 39.8 67.3 88.0 90.5 5403 −10.0 30.0 82.0 −125.4 788 648 1329 77.0 318 295 389

399.6 115.4 −72.6 51.3 −23.0 32.6 32.6 44.0 997 360 −48.2 1364 759 748 763 119.2 56.5 2169 177.7 577 92.1 315.5 −65.2 58.5 87.6 109.6 112.7 5666 +1.2 42.7 103.5 −117.1 844 689 1417 97.3 337 312 409

444.6 138.0 −63.5 69.2 −10.0 44.8 44.8 51.6 1087 392 −38.6 1457 819 807 823 139.5 75.4 2270 204.7 623 113.0 348.0 −52.3 78.0 108.8 131.7 136.0 5927 17.3 55.7 127.2 −108.0 907 732 1497 118.0 357 331 431

−142 −18.6 −112.3 −99.3 −185 −132.6 960.5 455 552 97.5 755 800 564 992 318 651 800 2430 112.8 −80 −50.2 −54.1 −73.2 16.8 32.3 62.1 452 224 −37.8 3035 460 430 440 −52.2 −104.5 231.9 31.0 246.8 −30.2 144.5 −149.9

60

Temperature, °C −144.0 −81.0 −86.5 −65.2 −179.3 −114.8 1357 912 820 439 806 865 817 1077 739 767 2068 183.8 −7.4 −132.7 −95.5 −39.0 −34.0 −15.3 520 −111.3 825 440 −6.7 −52.9 1492 316 −22.7 −140.0 −51.3 −30.0 −12.0 −13.9 3990 −71.4 −38.8 −23.2 −168.5 487 428 970 −22.4 207 190 264

−133.0 −68.8 −68.4 −45.5 −168.6 −99.3 1500 1019 927 511 903 967 928 1186 843 857 847 2198 223.0 +15.7 −120.6 −35.1 −83.0 −23.7 −19.2 −2.0 605 −98.8 931 490 487 502 +18.4 −32.4 1634 58.3 366 −1.0 156.0 −125.8 −31.0 −7.6 +10.7 +9.4 4337 −56.5 −22.0 +0.2 −158.2 558 481 1055 0.0 237 217 297

−127.0 −63.1 −59.0 −35.6 −163.0 −91.4 1575 1074 983 549 952 1017 983 1240 897 903 898 2262 243.8 27.5 −114.7 −24.8 −76.8 −16.5 −12.3 +4.3 650 233 −92.4 983 522 517 531 31.0 −21.9 1703 72.7 391 +10.0 175.8 −118.5 −20.6 +3.8 21.8 21.3 4507 −49.2 −13.8 12.2 −152.8 593 508 1086 +11.7 250 230 311

−120.5 −57.0 −48.8 −24.5 −156.9 −82.7 1658 1134 1045 589 1005 1072 1046 1300 953 952 953 2333 264.7 40.0 −108.4 −13.4 −69.7 −9.1 −4.9 11.1 697 253 −86.0 1040 559 550 567 44.1 −10.5 1777 88.1 420 22.0 196.2 −111.2 −9.3 16.1 34.0 34.2 4690 −41.5 −5.2 26.6 −147.1 632 536 1129 24.2 266 243 329

−112.8 −50.6 −37.0 −12.0 −150.3 −72.8 1743 1200 1111 633 1063 1131 1115 1363 1017 1005 1018 2410 288.3 54.1 −101.5 −1.0 −60.5 −1.0 +3.2 17.9 753 273 −78.4 1103 598 589 607 58.8 +2.2 1855 105.5 450 35.2 218.8 −102.3 +3.5 30.0 48.5 48.4 4886 −33.0 +4.4 40.0 −141.2 673 566 1175 38.0 281 259 344

−30 3370 −0.5 69.2 −111.6 419.4 365 872 −28 450 437 499

VAPOR PRESSURES

2-63

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm* Pressure, mmHg Compound

1

Name

Formula

Acenaphthalene Acetal Acetaldehyde Acetamide Acetanilide Acetic acid anhydride Acetone Acetonitrile Acetophenone Acetyl chloride Acetylene Acridine Acrolein (2-propenal) Acrylic acid Adipic acid Allene (propadiene) Allyl alcohol (propen-1-ol-3) chloride (3-chloropropene) isopropyl ether isothiocyanate n-propyl ether 4-Allylveratrole iso-Amyl acetate n-Amyl alcohol iso-Amyl alcohol sec-Amyl alcohol (2-pentanol) tert-Amyl alcohol sec-Amylbenzene iso-Amyl benzoate bromide (1-bromo-3-methylbutane) n-butyrate formate iodide (1-iodo-3-methylbutane) isobutyrate Amyl isopropionate iso-Amyl isovalerate n-Amyl levulinate iso-Amyl levulinate nitrate 4-tert-Amylphenol Anethole Angelonitrile Aniline 2-Anilinoethanol Anisaldehyde o-Anisidine (2-methoxyaniline) Anthracene Anthraquinone Azelaic acid Azelaldehyde Azobenzene Benzal chloride (α,α-Dichlorotoluene) Benzaldehyde Benzanthrone Benzene Benzenesulfonylchloride Benzil Benzoic acid anhydride Benzoin Benzonitrile Benzophenone Benzotrichloride (α,α,α-Trichlorotoluene) Benzotrifluoride (α,α,α-Trifluorotoluene) Benzoyl bromide chloride nitrile Benzyl acetate alcohol

C12H10 C6H14O2 C2H4O C2H5NO C8H9NO C2H4O2 C4H6O3 C3H6O C2H3N C8H8O C2H3OCl C2H2 C13H9N C3H4O C3H4O2 C6H10O4 C3H4 C3H6O C3H5Cl C6H12O C4H5NS C6H12O C11H14O2 C7H14O2 C5H12O C5H12O C5H12O C5H12O C11H16 C12H16O2 C5H11Br C9H18O2 C6H12O2 C5H11I C9H18O2 C8H16O2 C10H20O2 C10H18O3 C10H18O3 C5H11NO3 C11H16O C10H12O C5H7N C6H7N C8H11NO C8H8O2 C7H9NO C14H10 C14H8O2 C9H16O4 C9H18O C12H10N2 C7H6Cl2 C7H6O C17H10O C6H6 C6H5ClO2S C14H10O2 C7H6O2 C14H10O3 C14H12O2 C7H5N C13H10O C7H5Cl3 C7H5F3 C7H5BrO C7H5ClO C8H5NO C9H10O2 C7H8O

5

10

20

114.8 −2.3 −65.1 92.0 146.6 +6.3 24.8 −40.5 −26.6 64.0 −35.0 −133.0 165.8 −46.0 27.3 191.0 −108.0 +0.2 −52.0 −23.1 +25.3 −18.2 113.9 +23.7 34.7 30.9 22.1 +7.2 55.8 104.5 +2.1 47.1 +5.4 +21.9 40.1 33.7 54.4 110.0 104.0 28.8 109.8 91.6 +15.0 57.9 134.3 102.6 88.0 173.5 219.4 210.4 58.4 135.7 64.0 50.1 274.5 −19.6 96.5 165.2 119.5 180.0 170.2 55.3 141.7 73.7 −10.3 75.4 59.1 71.7 73.4 80.8

131.2 +8.0 −56.8 105.0 162.0 17.5 36.0 −31.1 −16.3 78.0 −27.6 −128.2 184.0 −36.7 39.0 205.5 −101.0 10.5 −42.9 −12.9 38.3 −7.9 127.0 35.2 44.9 40.8 32.2 17.2 69.2 121.6 13.6 59.9 17.1 34.1 52.8 46.3 68.6 124.0 118.8 40.3 125.5 106.0 28.0 69.4 149.6 117.8 101.7 187.2 234.2 225.5 71.6 151.5 78.7 62.0 297.2 −11.5 112.0 183.0 132.1 198.0 188.1 69.2 157.6 87.6 −0.4 89.8 73.0 85.5 87.6 92.6

148.7 19.6 −47.8 120.0 180.0 29.9 48.3 −20.8 −5.0 92.4 −19.6 −122.8 203.5 −26.3 52.0 222.0 −93.4 21.7 −32.8 −1.8 52.1 +3.7 142.8 47.8 55.8 51.7 42.6 27.9 83.8 139.7 26.1 74.0 30.0 47.6 66.6 60.0 83.8 139.7 134.4 53.5 142.3 121.8 41.0 82.0 165.7 133.5 116.1 201.9 248.3 242.4 85.0 168.3 94.3 75.0 322.5 −2.6 129.0 202.8 146.7 218.0 207.0 83.4 175.8 102.7 12.2 105.4 87.6 100.2 102.3 105.8

40

60

100

200

400

760

197.5 50.1 −22.6 158.0 227.2 63.0 82.2 +7.7 27.0 133.6 +3.2 −107.9 256.0 +2.5 86.1 265.0 −72.5 50.0 −4.5 29.0 89.5 35.8 183.7 83.2 85.8 80.7 70.7 55.3 124.1 186.8 60.4 113.1 65.4 84.4 104.4 97.6 125.1 180.5 177.0 88.6 189.0 164.2 77.5 119.9 209.5 176.7 155.2 250.0 285.0 286.5 123.0 216.0 138.3 112.5 390.0 26.1 174.5 255.8 186.2 270.4 258.0 123.5 224.4 144.3 45.3 147.7 128.0 141.0 144.0 141.7

222.1 66.3 −10.0 178.3 250.5 80.0 100.0 22.7 43.7 154.2 16.1 −100.3 284.0 17.5 103.3 287.8 −61.3 64.5 10.4 44.3 108.0 52.6 204.0 101.3 102.0 95.8 85.7 69.7 145.2 210.2 78.7 133.2 83.2 103.8 124.2 117.3 146.1 203.1 198.1 106.7 213.0 186.1 96.3 140.1 230.6 199.0 175.3 279.0 314.6 309.6 142.1 240.0 160.7 131.7 426.5 42.2 198.0 283.5 205.8 299.1 284.4 144.1 249.8 165.6 62.5 169.2 149.5 161.3 165.5 160.0

250.0 84.0 +4.9 200.0 277.0 99.0 119.8 39.5 62.5 178.0 32.0 −92.0 314.3 34.5 122.0 312.5 −48.5 80.2 27.5 61.7 129.8 71.4 226.2 121.5 119.8 113.7 102.3 85.7 168.0 235.8 99.4 155.3 102.7 125.8 146.0 138.4 169.5 227.4 222.7 126.5 239.5 210.5 117.7 161.9 254.5 223.0 197.3 310.2 346.2 332.8 163.4 266.1 187.0 154.1

277.5 102.2 20.2 222.0 303.8 118.1 139.6 56.5 81.8 202.4 50.8 −84.0 346.0 52.5 141.0 337.5 −35.0 96.6 44.6 79.5 150.7 90.5 248.0 142.0 137.8 130.6 119.7 101.7 193.0 262.0 120.4 178.6 123.3 148.2 168.8 160.2 194.0 253.2 247.9 147.5 266.0 235.3 140.0 184.4 279.6 248.0 218.5 342.0 379.9 356.5 185.0 293.0 214.0 179.0

60.6 224.0 314.3 227.0 328.8 313.5 166.7 276.8 189.2 82.0 193.7 172.8 185.0 189.0 183.0

80.1 251.5 347.0 249.2 360.0 343.0 190.6 305.4 213.5 102.2 218.5 197.2 208.0 213.5 204.7

Temperature, °C −23.0 −81.5 65.0 114.0 −17.2 1.7 −59.4 −47.0 37.1 −50.0 −142.9 129.4 −64.5 +3.5 159.5 −120.6 −20.0 −70.0 −43.7 −2.0 −39.0 85.0 0.0 +13.6 +10.0 +1.5 −12.9 29.0 72.0 −20.4 21.2 −17.5 −2.5 14.8 +8.5 27.0 81.3 75.6 +5.2 62.6 −8.0 34.8 104.0 73.2 61.0 145.0 190.0 178.3 33.3 103.5 35.4 26.2 225.0 −36.7 65.9 128.4 96.0 143.8 135.6 28.2 108.2 45.8 −32.0 47.0 32.1 44.5 45.0 58.0

168.2 31.9 −37.8 135.8 199.6 43.0 62.1 −9.4 +7.7 109.4 −10.4 −116.7 224.2 −15.0 66.2 240.5 −85.2 33.4 −21.2 +10.9 67.4 16.4 158.3 62.1 68.0 63.4 54.1 38.8 100.0 158.3 39.8 90.0 44.0 62.3 81.8 75.5 100.6 155.8 151.7 67.6 160.3 139.3 55.8 96.7 183.7 150.5 132.0 217.5 264.3 260.0 100.2 187.9 112.1 90.1 350.0 +7.6 147.7 224.5 162.6 239.8 227.6 99.6 195.7 119.8 25.7 122.6 103.8 116.6 119.6 119.8

181.2 39.8 −31.4 145.8 211.8 51.7 70.8 −2.0 15.9 119.8 −4.5 −112.8 238.7 −7.5 75.0 251.0 −78.8 40.3 −14.1 18.7 76.2 25.0 169.6 71.0 75.5 71.0 61.5 46.0 110.4 171.4 48.7 99.8 53.3 71.9 91.7 85.2 110.3 165.2 162.6 76.3 172.6 149.8 65.2 106.0 194.0 161.7 142.1 231.8 273.3 271.8 110.0 199.8 123.4 99.6 368.8 15.4 158.2 238.2 172.8 252.7 241.7 109.8 208.2 130.0 34.0 133.4 114.7 127.0 129.8 129.3

Melting point, °C 95 −123.5 81 113.5 16.7 −73 −94.6 −41 20.5 −112.0 −81.5 110.5 −87.7 14 152 −136 −129 −136.4 −80

−117.2 −11.9

93 22.5 −6.2 2.5 5.2 217.5 286 106.5 68 −16.1 −26 174 +5.5 14.5 95 121.7 42 132 −12.9 48.5 −21.2 −29.3 0 −0.5 33.5 −51.5 −15.3

∗Compiled from the extended tables published by D. R. Stull in Ind. Eng. Chem., 39, 517 (1947). For information on fuels see Hibbard, N.A.C.A. Research Mem. E56I21, 1956. For methane see Johnson (ed.), WADD-TR-60-56, 1960. (Continued )

2-64

PHYSICAL AnD CHEMICAL DATA

TABLE 2-10

Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name

Benzylamine Benzyl bromide (α-bromotoluene) chloride (α-chlorotoluene) cinnamate Benzyldichlorosilane Benzyl ethyl ether phenyl ether isothiocyanate Biphenyl 1-Biphenyloxy-2,3-epoxypropane d-Bornyl acetate Bornyl n-butyrate formate isobutyrate propionate Brassidic acid Bromoacetic acid 4-Bromoanisole Bromobenzene 4-Bromobiphenyl 1-Bromo-2-butanol 1-Bromo-2-butanone cis-1-Bromo-1-butene trans-1-Bromo-1-butene 2-Bromo-1-butene cis-2-Bromo-2-butene trans-2-Bromo-2-butene 1,4-Bromochlorobenzene 1-Bromo-1-chloroethane 1-Bromo-2-chloroethane 2-Bromo-4,6-dichlorophenol 1-Bromo-4-ethyl benzene (2-Bromoethyl)-benzene 2-Bromoethyl 2-chloroethyl ether (2-Bromoethyl)-cyclohexane 1-Bromoethylene Bromoform (tribromomethane) 1-Bromonaphthalene 2-Bromo-4-phenylphenol 3-Bromopyridine 2-Bromotoluene 3-Bromotoluene 4-Bromotoluene 3-Bromo-2,4,6-trichlorophenol 2-Bromo-1,4-xylene 1,2-Butadiene (methyl allene) 1,3-Butadiene n-Butane iso-Butane (2-methylpropane) 1,3-Butanediol 1,2,3-Butanetriol 1-Butene cis-2-Butene trans-2-Butene 3-Butenenitrile iso-Butyl acetate n-Butyl acrylate alcohol iso-Butyl alcohol sec-Butyl alcohol tert-Butyl alcohol iso-Butyl amine n-Butylbenzene iso-Butylbenzene sec-Butylbenzene tert-Butylbenzene iso-Butyl benzoate n-Butyl bromide (1-bromobutane) iso-Butyl n-butyrate carbamate Butyl carbitol (diethylene glycol butyl ether) n-Butyl chloride (1-chlorobutane) iso-Butyl chloride

1

5

10

20

29.0 32.2 22.0 173.8 45.3 26.0 95.4 79.5 70.6 135.3 46.9 74.0 47.0 70.0 64.6 209.6 54.7 48.8 +2.9 98.0 23.7 +6.2 −44.0 −38.4 −47.3 −39.0 −45.0 32.0 −36.0 −28.8 84.0 30.4 48.0 36.5 38.7 −95.4

70.0

54.8 59.6 47.8 206.3 70.2 52.0 127.7 107.8 101.8 169.9 75.7 103.4 74.8 99.8 93.7 241.7 81.6 77.8 27.8 133.7 45.4 30.0 −23.2 −17.0 −27.0 −17.9 −24.1 59.5 −18.0 −7.0 115.6 42.5 76.2 63.2 66.6 −77.8 22.0 117.5 135.4 42.0 49.7 50.8 47.5 146.2 65.0 −72.7 −87.6 −85.7 −94.1 67.5 132.0 −89.4 −81.1 −84.0 +2.9 +1.4 +23.5 +20.0 +11.6 +7.2 −3.0 −31.0 48.8 40.5 44.2 39.0 93.6 −11.2 30.0 83.7 95.7

67.7 73.4 60.8 221.5 83.2 65.0 144.0 121.8 117.0 187.2 90.2 118.0 89.3 114.0 108.0 256.0 94.1 91.9 40.0 150.6 55.8 41.8 −12.8 −6.4 −16.8 −7.2 −13.8 72.7 −9.4 +4.1 130.8 74.0 90.5 76.3 80.5 −68.8 34.0 133.6 152.3 55.2 62.3 64.0 61.1 163.2 78.8 −64.2 −79.7 −77.8 −86.4 85.3 146.0 −81.6 −73.4 −76.3 14.1 12.8 35.5 30.2 21.7 16.9 +5.5 −21.0 62.0 53.7 57.0 51.7 108.6 −0.3 42.2 96.4 107.8

81.8 88.3 75.0 239.3 96.7 79.6 160.7 137.0 134.2 205.8 106.0 133.8 104.0 130.0 123.7 272.9 108.2 107.8 53.8 169.8 67.2 54.2 −1.4 +5.4 −5.3 +4.6 −2.4 87.8 0.0 16.0 147.7 90.2 105.8 90.8 95.8 −58.8 48.0 150.2 171.8 69.1 76.0 78.1 75.2 181.8 94.0 −54.9 −71.0 −68.9 −77.9 100.0 161.0 −73.0 −64.6 −67.5 26.6 25.5 48.6 41.5 32.4 27.3 14.3 −10.3 76.3 67.8 70.6 65.6 124.2 +11.6 56.1 110.1 120.5

97.3 104.8 90.7 255.8 111.8 95.4 180.1 153.0 152.5 226.3 123.7 150.7 121.2 147.2 140.4 290.0 124.0 125.0 68.6 190.8 79.5 68.2 +11.5 18.4 +7.2 17.7 +10.5 103.8 +10.4 29.7 165.8 108.5 123.2 106.6 113.0 −48.1 63.6 170.2 193.8 84.1 91.0 93.9 91.8 200.5 110.6 −44.3 −61.3 −59.1 −68.4 117.4 178.0 −63.4 −54.7 −57.6 40.0 39.2 63.4 53.4 44.1 38.1 24.5 +1.3 92.4 83.3 86.2 80.8 141.8 24.8 71.7 125.3 135.5

C4H9Cl C4H9Cl

−49.0 −53.8

−28.9 −34.3

−18.6 −24.5

−7.4 −13.8

+5.0 −1.9

60

100

200

400

760

107.3 115.6 100.5 267.0 121.3 105.5 192.6 163.8 165.2 239.7 135.7 161.8 131.7 157.6 151.2 301.5 133.8 136.0 78.1 204.5 87.0 77.3 19.8 27.2 15.4 26.2 18.7 114.8 17.0 38.0 177.6 121.0 133.8 116.4 123.7 −41.2 73.4 183.5 207.0 94.1 100.0 104.1 102.3 213.0 121.6 −37.5 −55.1 −52.8 −62.4 127.5 188.0 −57.2 −48.4 −51.3 48.8 48.0 72.6 60.3 51.7 45.2 31.0 8.8 102.6 93.3 96.0 90.6 152.0 33.4 81.3 134.6 146.0

120.0 129.8 114.2 281.5 133.5 118.9 209.2 177.7 180.7 255.0 149.8 176.4 145.8 172.2 165.7 316.2 146.3 150.1 90.8 221.8 97.6 89.2 30.8 38.1 26.3 37.5 29.9 128.0 28.0 49.5 193.2 135.5 148.2 129.8 138.0 −31.9 85.9 198.8 224.5 107.8 112.0 117.8 116.4 229.3 135.7 −28.3 −46.8 −44.2 −54.1 141.2 202.5 −48.9 −39.8 −42.7 60.2 59.7 85.1 70.1 61.5 54.1 39.8 18.8 116.2 107.0 109.5 103.8 166.4 44.7 94.0 147.2 159.8

140.0 150.8 134.0 303.8 152.0 139.6 233.2 198.0 204.2 280.4 172.0 198.0 166.4 194.2 187.5 336.8 165.8 172.7 110.1 248.2 112.1 107.0 47.8 55.7 42.8 54.5 46.5 149.5 44.7 66.8 216.5 156.5 169.8 150.0 160.0 −17.2 106.1 224.2 251.0 127.7 133.6 138.0 137.4 253.0 156.4 −14.2 −33.9 −31.2 −41.5 161.0 222.0 −36.2 −26.8 −29.7 78.0 77.6 104.0 84.3 75.9 67.9 52.7 32.0 136.9 127.2 128.8 123.7 188.2 62.0 113.9 165.7 181.2

161.3 175.2 155.8 326.7 173.0 161.5 259.8 220.4 229.4 309.8 197.5 222.2 190.2 218.2 211.2 359.6 186.7 197.5 132.3 277.7 128.3 126.3 66.8 75.0 61.9 74.0 66.0 172.6 63.4 86.0 242.0 182.0 194.0 172.3 186.2 −1.1 127.9 252.0 280.2 150.0 157.3 160.0 160.2 278.0 181.0 +1.8 −19.3 −16.3 −27.1 183.8 243.5 −21.7 −12.0 −14.8 98.0 97.5 125.2 100.8 91.4 83.9 68.0 50.7 159.2 149.6 150.3 145.8 212.8 81.7 135.7 186.0 205.0

184.5 198.5 179.4 350.0 194.3 185.0 287.0 243.0 254.9 340.0 223.0 247.0 214.0 243.0 235.0 382.5 208.0 223.0 156.2 310.0 145.0 147.0 86.2 94.7 81.0 93.9 85.5 196.9 82.7 106.7 268.0 206.0 219.0 195.8 213.0 +15.8 150.5 281.1 311.0 173.4 181.8 183.7 184.5 305.8 206.7 18.5 −4.5 −0.5 −11.7 206.5 264.0 −6.3 +3.7 +0.9 119.0 118.0 147.4 117.5 108.0 99.5 82.9 68.6 183.1 172.8 173.5 168.5 237.0 101.6 156.9 206.5 231.2

13.0 +5.9

24.0 16.0

40.0 32.0

58.8 50.0

77.8 68.9

Temperature, °C

Formula C7H9N C7H7Br C7H7Cl C16H14O2 C7H8Cl2Si C9H12O C13H12O C8H7NS C12H10 C15H14O2 C12H20O2 C14H24O2 C11H18O2 C14H24O2 C13H22O2 C22H42O2 C2H3BrO2 C7H7BrO C6H5Br C12H9Br C4H9BrO C4H7BrO C4H7Br C4H7Br C4H7Br C4H7Br C4H7Br C6H4BrCl C2H4BrCl C2H4BrCl C6H3BrCl2O C8H9Br C8H9Br C4H8BrClO C8H15Br C2H3Br CHBr3 C10H7Br C12H9BrO C5H4BrN C7H7Br C7H7Br C7H7Br C6H2BrCl3O C8H9Br C 4H 6 C 4H 6 C4H10 C4H10 C4H10O2 C4H10O3 C4H8 C4H8 C4H8 C4H5N C6H12O2 C7H12O2 C4H10O C4H10O C4H10O C4H10O C4H11N C10H14 C10H14 C10H14 C10H14 C11H14O2 C4H9Br C8H16O2 C5H11NO2 C8H18O3

40

84.2 100.0 16.8 24.4 14.8 10.3 112.4 37.5 −89.0 −102.8 −101.5 −109.2 22.2 102.0 −104.8 −96.4 −99.4 −19.6 −21.2 −0.5 −1.2 −9.0 −12.2 −20.4 −50.0 22.7 14.1 18.6 13.0 64.0 −33.0 +4.6

Melting point, °C −4 −39 39

69.5 29

61.5 49.5 12.5 −30.7 90.5

−100.3 −133.4 −111.2 −114.6 16.6 −16.6 68 −45.0

−138 8.5 5.5 95 −28 39.8 28.5 +9.5 −108.9 −135 −145 77 −130 −138.9 −105.4 −98.9 −64.6 −79.9 −108 −114.7 25.3 −85.0 −88.0 −51.5 −75.5 −58 −112.4 65 −123.1 −131.2

VAPOR PRESSURES

2-65

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name

Formula

sec-Butyl chloride (2-Chlorobutane) tert-Butyl chloride sec-Butyl chloroacetate 2-tert-Butyl-4-cresol 4-tert-Butyl-2-cresol iso-Butyl dichloroacetate 2,3-Butylene glycol (2,3-butanediol) 2-Butyl-2-ethylbutane-1,3-diol 2-tert-Butyl-4-ethylphenol n-Butyl formate iso-Butyl formate sec-Butyl formate sec-Butyl glycolate iso-Butyl iodide (1-iodo-2-methylpropane) isobutyrate isovalerate levulinate naphthylketone (1-isovaleronaphthone) 2-sec-Butylphenol 2-tert-Butylphenol 4-iso-Butylphenol 4-sec-Butylphenol 4-tert-Butylphenol 2-(4-tert-Butylphenoxy)ethyl acetate 4-tert-Butylphenyl dichlorophosphate

C4H9Cl C4H9Cl C6H11ClO2 C11H16O C11H16O C6H10Cl2O2 C4H10O2 C10H22O2 C12H15O C5H10O2 C5H10O2 C5H10O2 C6H12O3 C4H9I C8H16O2 C9H18O2 C9H16O3 C15H16O C10H14O C10H14O C10H14O C10H14O C10H14O C14H20O3 C10H13Cl2 O2P C11H14O C7H14O2 C12H18O C12H18O C12H18O C12H18O C4H8O2 C4H8O2 C4H7N C11H14O C10H16 C10H16O2 C10H16O C10H19N C10H20O C10H20O2 C6H12O2 C6H12O2 C6H10O2 C6H11N C8H18O C8H16O C8H16O2 C8H15N C12H9N CO2 CS2 CO COSe COS CBr4 CCl4 CF4 C10H14O C10H14O C10H12O2 C2HCl3O C2H3Cl3O2 C6Cl4O2 C2H3ClO2 C4H4Cl2O3 C6H6ClN C6H6ClN C6H6ClN C6H5Cl

tert-Butyl phenyl ketone (pivalophenone) iso-Butyl propionate 4-tert-Butyl-2,5-xylenol 4-tert-Butyl-2,6-xylenol 6-tert-Butyl-2,4-xylenol 6-tert-Butyl-3,4-xylenol Butyric acid iso-Butyric acid Butyronitrile iso-Valerophenone Camphene Campholenic acid d-Camphor Camphylamine Capraldehyde Capric acid n-Caproic acid iso-Caproic acid iso-Caprolactone Capronitrile Capryl alcohol (2-octanol) Caprylaldehyde Caprylic acid (octanoic acid) Caprylonitrile Carbazole Carbon dioxide disulfide monoxide oxyselenide (carbonyl selenide) oxysulfide (carbonyl sulfide) tetrabromide tetrachloride tetrafluoride Carvacrol Carvone Chavibetol Chloral (trichloroacetaldehyde) hydrate (trichloroacetaldehyde hydrate) Chloranil Chloroacetic acid anhydride 2-Chloroaniline 3-Chloroaniline 4-Chloroaniline Chlorobenzene 2-Chlorobenzotrichloride (2-α,α,α-tetrachlorotoluene)

C7H4Cl4

1

5

10

20

−60.2

−39.8

−29.2

−17.7

17.0 70.0 74.3 28.6 44.0 94.1 76.3 −26.4 −32.7 −34.4 28.3 −17.0 +4.1 16.0 65.0 136.0 57.4 56.6 72.1 71.4 70.0 118.0 96.0

41.8 98.0 103.7 54.3 68.4 122.6 106.2 −4.7 −11.4 −13.3 53.6 +5.8 28.0 41.2 92.1 167.9 86.0 84.2 100.9 100.5 99.2 150.0 129.6

54.6 112.0 118.0 67.5 80.3 136.8 121.0 +6.1 −0.8 −3.1 66.0 17.0 39.9 53.8 105.9 184.0 100.8 98.1 115.5 114.8 114.0 165.8 146.0

57.8 −2.3 88.2 74.0 70.3 83.9 25.5 14.7 −20.0 58.3

85.7 +20.9 119.8 103.9 100.2 113.6 49.8 39.3 +2.1 87.0

97.6 41.5 45.3 51.9 125.0 71.4 66.2 38.3 9.2 32.8 73.4 92.3 43.0

40

60

Melting point, °C

100

200

400

760

31.5 +14.6 124.1 187.8 197.8 139.2 145.6 212.0 200.3 67.9 60.0 56.8 135.5 81.0 106.3 124.8 181.8 269.7 179.7 173.8 192.1 194.3 191.5 250.3 240.0

50.0 32.6 146.0 210.0 221.8 160.0 164.0 233.5 223.8 86.2 79.0 75.2 155.6 100.3 126.3 146.4 205.5 294.0 203.8 196.3 214.7 217.6 214.0 277.6 268.2

68.0 51.0 167.8 232.6 247.0 183.0 182.0 255.0 247.8 106.0 98.2 93.6 177.5 120.4 147.5 168.7 229.9 320.0 228.0 219.5 237.0 242.1 238.0 304.4 299.0

Temperature, °C

68.2 127.2 134.0 81.4 93.4 151.2 137.0 18.0 +11.0 +8.4 79.8 29.8 52.4 67.7 120.2 201.6 116.1 113.0 130.3 130.3 129.5 183.3 164.0

−5.0 −19.0 83.6 143.9 150.8 96.7 107.8 167.8 154.0 31.6 24.1 21.3 94.2 42.8 67.2 82.7 136.2 219.7 133.4 129.2 147.2 147.8 146.0 201.5 184.3

+3.4 −11.4 93.0 153.7 161.7 106.6 116.3 178.0 165.4 39.8 32.4 29.6 104.0 51.8 75.9 92.4 147.0 231.5 143.9 140.0 157.0 157.9 156.0 212.8 197.2

14.2 −1.0 105.5 167.0 176.2 119.8 127.8 191.9 179.0 51.0 43.4 40.2 116.4 63.5 88.0 105.2 160.2 246.7 157.3 153.5 171.2 172.4 170.2 228.0 214.3

125.7 68.6 74.0 78.8 142.0 89.5 83.0 66.4 34.6 57.6 92.0 114.1 67.6

99.0 32.3 135.0 119.0 115.0 127.0 61.5 51.2 13.4 101.4 47.2 139.8 82.3 83.7 92.0 152.2 99.5 94.0 80.3 47.5 70.0 101.2 124.0 80.4

114.3 44.8 151.0 135.0 131.0 143.0 74.0 64.0 25.7 116.8 60.4 153.9 97.5 97.6 106.3 165.0 111.8 107.0 95.7 61.7 83.3 110.2 136.4 94.6

130.4 58.5 169.8 152.2 148.5 159.7 88.0 77.8 38.4 133.8 75.7 170.0 114.0 112.5 122.2 179.9 125.0 120.4 112.3 76.9 98.0 120.0 150.6 110.6

−134.3 −73.8 −222.0 −117.1 −132.4

−124.4 −54.3 −217.2 −102.3 −119.8

−119.5 −44.7 −215.0 −95.0 −113.3

−114.4 −34.3 −212.8 −86.3 −106.0

−50.0 −184.6 70.0 57.4 83.6 −37.8 −9.8

−30.0 −174.1 98.4 86.1 113.3 −16.0 +10.0

−19.6 −169.3 113.2 100.4 127.0 −5.0 19.5

−8.2 −164.3 127.9 116.1 143.2 +7.2 29.2

−108.6 −22.5 −210.0 −76.4 −98.3 96.3 +4.3 −158.8 145.2 133.0 159.8 20.2 39.7

140.8 67.6 180.3 163.6 158.2 170.0 96.5 86.3 47.3 144.6 85.0 180.0 124.0 122.0 132.0 189.8 133.3 129.6 123.2 86.8 107.4 126.0 160.0 121.2 248.2 −104.8 −15.3 −208.1 −70.2 −93.0 106.3 12.3 −155.4 155.3 143.8 170.7 29.1 46.2

154.0 79.5 195.0 176.0 172.0 184.0 108.0 98.0 59.0 158.0 97.9 193.7 138.0 134.6 145.3 200.0 144.0 141.4 137.2 99.8 119.8 133.9 172.2 134.8 265.0 −100.2 −5.1 −205.7 −61.7 −85.9 119.7 23.0 −150.7 169.7 157.3 185.5 40.2 55.0

70.7 43.0 67.2 46.3 63.5 59.3 −13.0

89.3 68.3 94.1 72.3 89.8 87.9 +10.6

97.8 81.0 108.0 84.8 102.0 102.1 22.2

106.4 94.2 122.4 99.2 116.7 117.8 35.3

116.1 109.2 138.2 115.6 133.6 135.0 49.7

122.0 118.3 148.0 125.7 144.1 145.8 58.3

129.5 130.7 159.8 139.5 158.0 159.9 70.7

140.3 149.0 177.8 160.0 179.5 182.3 89.4

151.3 169.0 197.0 183.7 203.5 206.6 110.0

162.6 189.5 217.0 208.8 228.5 230.5 132.2

290 61.2 46 0 −10.4 70.5 −45.2

69.0

101.8

117.9

135.8

155.0

167.8

185.0

208.0

233.0

262.1

28.7

175.0 197.7 220.0 97.0 116.4 136.8 217.5 241.3 265.3 196.0 217.8 239.8 192.3 214.2 236.5 204.5 226.7 249.5 125.5 144.5 163.5 115.8 134.5 154.5 76.7 96.8 117.5 180.1 204.2 228.0 117.5 138.7 160.5 212.7 234.0 256.0 157.9 182.0 209.2 153.0 173.8 195.0 164.8 186.3 208.5 217.1 240.3 268.4 160.8 181.0 202.0 158.3 181.0 207.7 157.8 182.1 207.0 119.7 141.0 163.7 138.0 157.5 178.5 145.4 156.5 168.5 190.3 213.9 237.5 155.2 179.5 204.5 292.5 323.0 354.8 −93.0 −85.7 −78.2 +10.4 28.0 46.5 −201.3 −196.3 −191.3 −49.8 −35.6 −21.9 −75.0 −62.7 −49.9 139.7 163.5 189.5 38.3 57.8 76.7 −143.6 −135.5 −127.7 191.2 213.8 237.0 179.6 203.5 227.5 206.8 229.8 254.0 57.8 77.5 97.7 68.0 82.1 96.2

−131.3 −26.5

22.5

−95.3 −90.7 −80.7

99

−71

−74 −47 50 178.5 31.5 −1.5 −35 −38.6 16 244.8 −57.5 −110.8 −205.0 −138.8 90.1 −22.6 −183.7 +0.5 −57 51.7

(Continued )

2-66

PHYSICAL AnD CHEMICAL DATA

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name 2-Chlorobenzotrifluoride (2-chloro-α,α,α-trifluorotoluene) 2-Chlorobiphenyl 4-Chlorobiphenyl α-Chlorocrotonic acid Chlorodifluoromethane Chlorodimethylphenylsilane 1-Chloro-2-ethoxybenzene 2-(2-Chloroethoxy) ethanol bis-2-Chloroethyl acetacetal 1-Chloro-2-ethylbenzene 1-Chloro-3-ethylbenzene 1-Chloro-4-ethylbenzene 2-Chloroethyl chloroacetate 2-Chloroethyl 2-chloroisopropyl ether 2-Chloroethyl 2-chloropropyl ether 2-Chloroethyl α-methylbenzyl ether Chloroform (trichloromethane) 1-Chloronaphthalene 4-Chlorophenethyl alcohol 2-Chlorophenol 3-Chlorophenol 4-Chlorophenol 2-Chloro-3-phenylphenol 2-Chloro-6-phenylphenol Chloropicrin (trichloronitromethane) 1-Chloropropene 2-Chloropyridine 3-Chlorostyrene 4-Chlorostyrene 1-Chlorotetradecane 2-Chlorotoluene 3-Chlorotoluene 4-Chlorotoluene Chlorotriethylsilane 1-Chloro-1,2,2-trifluoroethylene Chlorotrifluoromethane Chlorotrimethylsilane trans-Cinnamic acid Cinnamyl alcohol Cinnamylaldehyde Citraconic anhydride cis-α-Citral d-Citronellal Citronellic acid Citronellol Citronellyl acetate Coumarin o-Cresol (2-cresol; 2-methylphenol) m-Cresol (3-cresol; 3-methylphenol) p-Cresol (4-cresol; 4-methylphenol) cis-Crotonic acid trans-Crotonic acid cis-Crotononitrile trans-Crotononitrile Cumene 4-Cumidene Cuminal Cuminyl alcohol 2-Cyano-2-n-butyl acetate Cyanogen bromide chloride iodide Cyclobutane Cyclobutene Cyclohexane Cyclohexaneethanol Cyclohexanol Cyclohexanone 2-Cyclohexyl-4,6-dinitrophenol Cyclopentane Cyclopropane Cymene

1

5

10

20

60

100

200

400

760

88.3 197.0 212.5 155.9 −76.4 124.7 141.8 139.5 150.7 110.0 113.6 116.0 140.0 115.8 125.6 164.8 10.4 180.4 188.1 106.0 143.0 150.0 237.0 237.1 53.8 −15.1 104.6 121.2 122.0 215.5 94.7 96.3 96.6 82.3 −66.7 −111.7 +6.0 232.4 177.8 177.7 145.4 160.0 140.1 195.4 159.8 161.0 216.5 127.4 138.0 140.0 116.3 128.0 50.1 62.8 88.1 158.0 160.0 176.2 133.8 −51.8 22.6 −24.9 97.6 −32.8 −41.2 25.5 142.7 103.7 90.4 229.0 −1.3 −70.0 110.8

108.3 219.6 237.8 173.8 −65.8 145.5 162.0 157.2 169.8 130.2 133.8 137.0 159.8 135.7 146.3 186.3 25.9 204.2 210.0 126.4 164.8 172.0 261.3 261.6 71.8 +1.3 125.0 142.2 143.5 240.3 115.0 116.6 117.1 101.6 −55.0 −102.5 21.9 253.3 199.8 199.3 165.8 181.8 160.0 214.5 179.8 178.8 240.0 146.7 157.3 157.3 133.9 146.0 68.0 81.1 107.3 180.0 182.8 197.9 152.2 −42.6 33.8 −14.1 111.5 −18.9 −27.8 42.0 161.7 121.7 110.3 248.7 +13.8 −59.1 131.4

130.0 243.8 264.5 193.2 −53.6 168.6 185.5 176.5 190.5 152.2 156.7 159.8 182.2 156.5 169.8 210.8 42.7 230.8 234.5 149.8 188.7 196.0 289.4 289.5 91.8 18.0 147.7 165.7 166.0 267.5 137.1 139.7 139.8 123.6 −41.7 −92.7 39.4 276.7 224.6 222.4 189.8 205.0 183.8 236.6 201.0 197.8 264.7 168.4 179.0 179.4 152.2 165.5 88.0 101.5 129.2 203.2 206.7 221.7 173.4 −33.0 46.0 −2.3 126.1 −3.4 −12.2 60.8 183.5 141.4 132.5 269.8 31.0 −46.9 153.5

152.2 267.5 292.9 212.0 −40.8 193.5 208.0 196.0 212.6 177.6 181.1 184.3 205.0 180.0 194.1 235.0 61.3 259.3 259.3 174.5 214.0 220.0 317.5 317.0 111.9 37.0 170.2 190.0 191.0 296.0 159.3 162.3 162.3 146.3 −27.9 −81.2 57.9 300.0 250.0 246.0 213.5 228.0 206.5 257.0 221.5 217.0 291.0 190.8 202.8 201.8 171.9 185.0 108.0 122.8 152.4 227.0 232.0 246.6 195.2 −21.0 61.5 +13.1 141.1 +12.9 +2.4 80.7 205.4 161.0 155.6 291.5 49.3 −33.5 177.2

Temperature, °C

Formula C7H4ClF3 C12H9Cl C12H9Cl C4H5ClO2 CHClF2 C8H11ClSi C8H9ClO C4H9ClO2 C6H12Cl2O2 C8H9Cl C8H9Cl C8H9Cl C4H6Cl2O2 C5H10Cl2O C5H10Cl2O C10H13ClO CHCl3 C10H7Cl C8H9ClO C6H5ClO C6H5ClO C6H5ClO C12H9ClO C12H9ClO CCl3NO2 C3H5Cl C5H4ClN C8H7Cl C8H7Cl C14H29Cl C7H7Cl C7H7Cl C7H7Cl C6H15ClSi C2ClF3 CClF3 C3H9ClSi C9H8O2 C9H10O C9H8O C5H4O3 C10H16O C10H18O C10H18O2 C10H20O C12H22O2 C9H6O2 C7H8O C7H8O C7H8O C4H6O2 C4H6O2 C4H5N C4H5N C9H12 C9H13N C10H12O C10H14O C7H11NO2 C2N2 CBrN CClN CIN C4H8 C4H6 C6H12 C8H16O C6H12O C6H10O C12H14N2O5 C5H10 C3H6 C10H14

40

0.0 89.3 96.4 70.0 −122.8 29.8 45.8 53.0 56.2 17.2 18.6 19.2 46.0 24.7 29.8 62.3 −58.0 80.6 84.0 12.1 44.2 49.8 118.0 119.8 −25.5 −81.3 13.3 25.3 28.0 98.5 +5.4 +4.8 +5.5 −4.9 −116.0 −149.5 −62.8 127.5 72.6 76.1 47.1 61.7 44.0 99.5 66.4 74.7 106.0 38.2 52.0 53.0 33.5

24.7 109.8 129.8 95.6 −110.2 56.7 72.8 78.3 83.7 43.0 45.2 46.4 72.1 50.1 56.5 91.4 −39.1 104.8 114.3 38.2 72.0 78.2 152.2 153.7 −3.3 −63.4 38.8 51.3 54.5 131.8 30.6 30.3 31.0 +19.8 −102.5 −139.2 −43.6 157.8 102.5 105.8 74.8 90.0 71.4 127.3 93.6 100.2 137.8 64.0 76.0 76.5 57.4

−29.0 −19.5 +2.9 60.0 58.0 74.2 42.0 −95.8 −35.7 −76.7 25.2 −92.0 −99.1 −45.3 50.4 21.0 +1.4 132.8 −68.0 −116.8 17.3

−7.1 +3.5 26.8 88.2 87.3 103.7 68.7 −83.2 −18.3 −61.4 47.2 −76.0 −83.4 −25.4 77.2 44.0 26.4 161.8 −49.6 −104.2 43.9

37.1 134.7 146.0 108.0 −103.7 70.0 86.5 90.7 97.6 56.1 58.1 60.0 86.0 63.0 70.0 106.0 −29.7 118.6 129.0 51.2 86.1 92.2 169.7 170.7 +7.8 −54.1 51.7 65.2 67.5 148.2 43.2 43.2 43.8 32.0 −95.9 −134.1 −34.0 173.0 117.8 120.0 88.9 103.9 84.8 141.4 107.0 113.0 153.4 76.7 87.8 88.6 69.0 80.0 +4.0 15.0 38.3 102.2 102.0 118.0 82.0 −76.8 −10.0 −53.8 57.7 −67.9 −75.4 −15.9 90.0 56.0 38.7 175.9 −40.4 −97.5 57.0

50.6 151.2 164.0 121.2 −96.5 84.7 101.5 104.1 112.2 70.3 73.0 75.5 100.0 77.2 84.8 121.8 −19.0 134.4 145.0 65.9 101.7 108.1 186.7 189.8 20.0 −44.0 65.8 80.0 82.0 166.2 56.9 57.4 57.8 45.5 −88.2 −128.5 −23.2 189.5 133.7 135.7 103.8 119.4 99.8 155.6 121.5 126.0 170.0 90.5 101.4 102.3 82.0 93.0 16.4 27.8 51.5 117.8 117.9 133.8 96.2 −70.1 −1.0 −46.1 68.6 −58.7 −66.6 −5.0 104.0 68.8 52.5 191.2 −30.1 −90.3 71.1

65.9 169.9 183.8 135.6 −88.6 101.2 117.8 118.4 127.8 86.2 89.2 91.8 116.0 92.4 101.5 139.6 −7.1 153.2 162.0 82.0 118.0 125.0 207.4 208.2 33.8 −32.7 81.7 96.5 98.0 187.0 72.0 73.0 73.5 60.2 −79.7 −121.9 −11.4 207.1 151.0 152.2 120.3 135.9 116.1 171.9 137.2 140.5 189.0 105.8 116.0 117.7 96.0 107.8 30.0 41.8 66.1 134.2 135.2 150.3 111.8 −62.7 +8.6 −37.5 80.3 −48.4 −56.4 +6.7 119.8 83.0 67.8 206.7 −18.6 −82.3 87.0

75.4 182.1 196.0 144.4 −83.4 111.5 127.8 127.5 138.0 96.4 99.6 102.0 126.2 102.2 111.8 150.0 +0.5 165.6 173.5 92.0 129.4 136.1 219.6 220.0 42.3 −25.1 91.6 107.2 108.5 199.8 81.8 83.2 83.3 69.5 −74.1 −117.3 −4.0 217.8 162.0 163.7 131.3 146.3 126.2 182.1 147.2 149.7 200.5 115.5 125.8 127.0 104.5 116.7 38.5 50.9 75.4 145.0 146.0 161.7 121.5 −57.9 14.7 −32.1 88.0 −41.8 −50.0 14.7 129.8 91.8 77.5 216.0 −11.3 −77.0 97.2

Melting point, °C −6.0 34 75.5 −160

−80.2 −53.3 −62.6

−63.5 −20 7 32.5 42 +6 −64 −99.0 −15.0 +0.9 +7.3 −157.5 133 33 −7.5

70 30.8 10.9 35.5 15.5 72 −96.0

−34.4 58 −6.5 −50 +6.6 23.9 −45.0 −93.7 −126.6 −68.2

VAPOR PRESSURES

2-67

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name cis-Decalin trans-Decalin Decane Decan-2-one 1-Decene Decyl alcohol Decyltrimethylsilane Dehydroacetic acid Desoxybenzoin Diacetamide Diacetylene (1,3-butadiyne) Diallyldichlorosilane Diallyl sulfide Diisoamyl ether oxalate sulfide Dibenzylamine Dibenzyl ketone (1,3-diphenyl2-propanone) 1,4-Dibromobenzene 1,2-Dibromobutane dl-2,3-Dibromobutane meso-2,3-Dibromobutane 1,2-Dibromodecane Di(2-bromoethyl) ether α,β-Dibromomaleic anhydride 1,2-Dibromo-2-methylpropane 1,3-Dibromo-2-methylpropane 1,2-Dibromopentane 1,2-Dibromopropane 1,3-Dibromopropane 2,3-Dibromopropene 2,3-Dibromo-1-propanol Diisobutylamine 2,6-Ditert-butyl-4-cresol 4,6-Ditert-butyl-2-cresol 4,6-Ditert-butyl-3-cresol 2,6-Ditert-butyl-4-ethylphenol 4,6-Ditert-butyl-3-ethylphenol Diisobutyl oxalate 2,4-Ditert-butylphenol Dibutyl phthalate sulfide Diisobutyl d-tartrate Dicarvacryl-mono-(6-chloro-2-xenyl) phosphate Dicarvacryl-2-tolyl phosphate Dichloroacetic acid 1,2-Dichlorobenzene 1,3-Dichlorobenzene 1,4-Dichlorobenzene 1,2-Dichlorobutane 2,3-Dichlorobutane 1,2-Dichloro-1,2-difluoroethylene Dichlorodifluoromethane Dichlorodiphenyl silane Dichlorodiisopropyl ether Di(2-chloroethoxy) methane Dichloroethoxymethylsilane 1,2-Dichloro-3-ethylbenzene 1,2-Dichloro-4-ethylbenzene 1,4-Dichloro-2-ethylbenzene cis-1,2-Dichloroethylene trans-1,2-Dichloro ethylene Di(2-chloroethyl) ether Dichlorofluoromethane 1,5-Dichlorohexamethyltrisiloxane Dichloromethylphenylsilane 1,1-Dichloro-2-methylpropane 1,2-Dichloro-2-methylpropane 1,3-Dichloro-2-methylpropane 2,4-Dichlorophenol 2,6-Dichlorophenol

1

5

10

20

40

C10H18 C10H18 C10H22 C10H20O C10H20 C10H22O C13H30Si C8H8O4 C14H12O C4H7NO2 C4H2 C6H10Cl2Si C6H10S C10H22O C12H22O4 C10H22S C14H15N C15H14O

22.5 −0.8 16.5 44.2 14.7 69.5 67.4 91.7 123.3 70.0 −82.5 +9.5 −9.5 18.6 85.4 43.0 118.3 125.5

50.1 +30.6 42.3 71.9 40.3 97.3 96.4 122.0 156.2 95.0 −68.0 34.8 +14.4 44.3 116.0 73.0 149.8 159.8

64.2 47.2 55.7 85.8 53.7 111.3 111.0 137.3 173.5 108.0 −61.2 47.4 26.6 57.0 131.4 87.6 165.6 177.6

79.8 65.3 69.8 100.7 67.8 125.8 126.5 153.0 192.0 122.6 −53.8 61.3 39.7 70.7 147.7 102.7 182.2 195.7

97.2 85.7 85.5 117.1 83.3 142.1 144.0 171.0 212.0 138.2 −45.9 76.4 54.2 86.3 165.7 120.0 200.2 216.6

C6H4Br2 C4H8Br2 C4H8Br2 C4H8Br2 C10H20Br2 C4H8Br2O C4H2Br2O3 C4H8Br2 C4H8Br2 C5H10Br2 C3H6Br2 C3H6Br2 C3H4Br2 C3H6Br2O C8H19N C15H24O C15H24O C15H24O C16H26O C16H26O C10H18O4 C14H22O C16H22O4 C8H18S C12H22O6 C32H34ClO4P

61.0 7.5 +5.0 +1.5 95.7 47.7 50.0 −28.8 14.0 19.8 −7.0 +9.7 −6.0 57.0 −5.1 85.8 86.2 103.7 89.1 111.5 63.2 84.5 148.2 +21.7 117.8 204.2

79.3 33.2 30.0 26.6 123.6 75.3 78.0 −3.0 40.0 45.4 +17.3 35.4 +17.9 84.5 +18.4 116.2 117.3 135.2 121.4 142.6 91.2 115.4 182.1 51.8 151.8 234.5

87.7 46.1 41.6 39.3 137.3 88.5 92.0 +10.5 53.0 58.0 29.4 48.0 30.0 98.2 30.6 131.0 132.4 150.0 137.0 157.4 105.3 130.0 198.2 66.4 169.0 249.3

103.6 60.0 56.4 53.2 151.0 103.6 106.7 25.7 67.5 72.0 42.3 62.1 43.2 113.5 43.7 147.0 149.0 167.0 154.0 174.0 120.3 146.0 216.2 80.5 188.0 264.5

C27H33O4P C2H2Cl2O2 C6H4Cl2 C6H4Cl2 C6H4Cl2 C4H8Cl2 C4H8Cl2 C2Cl2F2 CCl2F2 C12H10Cl2Si C6H12Cl2O C5H10Cl2O2 C8H8Cl2OSi C8H8Cl2 C8H8Cl2 C8H8Cl2 C2H2Cl2 C2H2Cl2 C4H8Cl2O CHCl2F C6H18Cl2 O2Si3 C7H8Cl2Si C4H8Cl2 C4H8Cl2 C4H8Cl2 C6H4Cl2O C6H4Cl2O

180.2 44.0 20.0 12.1

209.3 69.8 46.0 39.0

−23.6 −25.2 −82.0 −118.5 109.6 29.6 53.0 −33.8 46.0 47.0 38.5 −58.4 −65.4 23.5 −91.3 26.0

−0.3 −3.0 −65.6 −104.6 142.4 55.2 80.4 −12.1 75.0 77.2 68.0 −39.2 −47.2 49.3 −75.5 52.0

221.8 82.6 59.1 52.0 54.8 +11.5 +8.5 −57.3 −97.8 158.0 68.2 94.0 −1.3 90.0 92.3 83.2 −29.9 −38.0 62.0 −67.5 65.1

35.7 −31.0 −25.8 −3.0 53.0 59.5

63.5 −8.4 −4.2 +20.6 80.0 87.6

77.4 +2.6 +6.7 32.0 92.8 101.0

60

Melting point, °C

100

200

400

760

108.0 98.4 95.5 127.8 93.5 152.0 154.3 181.5 224.5 148.0 −41.0 86.3 63.7 96.0 177.0 130.6 212.2 229.4

123.2 114.6 108.6 142.0 106.5 165.8 169.5 197.5 241.3 160.6 −34.0 99.7 75.8 109.6 192.2 145.3 227.3 246.6

145.4 136.2 128.4 163.2 126.7 186.2 191.0 219.5 265.2 180.8 −20.9 119.4 94.8 129.0 215.0 166.4 249.8 272.3

169.9 160.1 150.6 186.7 149.2 208.8 215.5 244.5 293.0 202.0 −6.1 142.0 116.1 150.3 240.0 191.0 274.3 301.7

194.6 186.7 174.1 211.0 172.0 231.0 240.0 269.0 321.0 223.0 +9.7 165.3 138.6 173.4 265.0 216.0 300.0 330.5

120.8 76.0 72.0 68.0 167.4 119.8 123.5 42.3 83.5 87.4 57.2 77.8 57.8 129.8 57.8 164.1 167.4 185.3 172.1 192.3 137.5 164.3 235.8 96.0 208.5 280.5

131.6 86.0 82.0 78.0 177.5 130.0 133.8 53.7 93.7 97.4 66.4 87.8 67.0 140.0 67.0 175.2 179.0 196.1 183.9 204.4 147.8 175.8 247.8 105.8 221.6 290.7

146.5 99.8 95.3 91.7 190.2 144.0 147.7 68.8 107.4 110.1 78.7 101.3 79.5 153.0 79.2 190.0 194.0 211.0 198.0 218.0 161.8 190.0 263.7 118.6 239.5 304.9

168.5 120.2 115.7 111.8 209.6 165.0 168.0 92.1 117.8 130.2 97.8 121.7 98.0 173.8 97.6 212.8 217.5 233.0 220.0 241.7 183.5 212.5 287.0 138.0 264.7 323.8

192.5 143.5 138.0 134.2 229.8 188.0 192.0 119.8 150.6 151.8 118.5 144.1 119.5 196.0 118.0 237.6 243.4 257.1 244.0 264.6 205.8 237.0 313.5 159.0 294.0 342.0

218.6 166.3 160.5 157.3 250.4 212.5 215.0 149.0 174.6 175.0 141.6 167.5 141.2 219.0 139.5 262.5 269.3 282.0 268.6 290.0 229.5 260.8 340.0 182.0 324.0 361.0

237.0 96.3 73.4 66.2 69.2 24.5 21.2 −48.3 −90.1 176.0 82.2 109.5 +11.3 105.9 109.6 99.8 −19.4 −28.0 76.0 −58.6 79.0

251.5 111.8 89.4 82.0 84.8 37.7 35.0 −38.2 −81.6 195.5 97.3 125.5 24.4 123.8 127.5 118.0 −7.9 −17.0 91.5 −48.8 94.8

260.3 121.5 99.5 92.2 95.2 47.8 43.9 −31.8 −76.1 207.5 106.9 135.8 32.6 135.0 139.0 129.0 −0.5 −10.0 101.5 −42.6 105.0

272.5 134.0 112.9 105.0 108.4 60.2 56.0 −23.0 −68.6 223.8 119.7 149.6 44.1 149.8 153.3 144.0 +9.5 −0.2 114.5 −33.9 118.2

290.0 152.3 133.4 125.9 128.3 79.7 74.0 −10.0 −57.0 248.0 139.0 170.0 61.0 172.0 176.0 166.2 24.6 +14.3 134.0 −20.9 138.3

309.8 173.7 155.8 149.0 150.2 100.8 94.2 +5.0 −43.9 275.5 159.8 192.0 80.3 197.0 201.7 191.5 41.0 30.8 155.4 −6.2 160.2

330.0 194.4 179.0 173.0 173.9 123.5 116.0 20.9 −29.8 304.0 182.7 215.0 100.6 222.1 226.6 216.3 59.0 47.8 178.5 +8.9 184.0

92.4 14.6 18.7 44.8 107.7 115.5

109.5 28.2 32.0 58.6 123.4 131.6

120.0 37.0 40.2 67.5 133.5 141.8

134.2 48.2 51.7 78.8 146.0 154.6

155.5 65.8 68.9 96.1 165.2 175.5

180.2 85.4 87.8 115.4 187.5 197.7

205.5 106.0 108.0 135.0 210.0 220.0

Temperature, °C

Formula

−43.3 −30.7 −29.7 +3.5 +7 60 78.5 −34.9 −83

−26 34.5 87.5 −64.5 −34.5

−70.3 −55.5 −34.4 −70

−79.7 73.5

9.7 −17.6 −24.2 53.0 −80.4 −112

−40.8 −76.4 −61.2 −80.5 −50.0 −135 −53.0

45.0

(Continued )

2-68

PHYSICAL AnD CHEMICAL DATA

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name α,α-Dichlorophenylacetonitrile Dichlorophenylarsine 1,2-Dichloropropane 2,3-Dichlorostyrene 2,4-Dichlorostyrene 2,5-Dichlorostyrene 2,6-Dichlorostyrene 3,4-Dichlorostyrene 3,5-Dichlorostyrene 1,2-Dichlorotetraethylbenzene 1,4-Dichlorotetraethylbenzene 1,2-Dichloro-1,1,2,2-tetrafluoroethane Dichloro-4-tolylsilane 3,4-Dichloro-α,α,α-trifluorotoluene Dicyclopentadiene Diethoxydimethylsilane Diethoxydiphenylsilane Diethyl adipate Diethylamine N-Diethylaniline Diethyl arsanilate 1,2-Diethylbenzene 1,3-Diethylbenzene 1,4-Diethylbenzene Diethyl carbonate cis-Diethyl citraconate Diethyl dioxosuccinate Diethylene glycol Diethyleneglycol-bis-chloroacetate Diethylene glycol dimethyl ether Di(2-methoxyethyl) ether glycol ethyl ether Diethyl ether ethylmalonate fumarate glutarate Diethylhexadecylamine Diethyl itaconate ketone (3-pentanone) malate maleate malonate mesaconate oxalate phthalate sebacate 2,5-Diethylstyrene Diethyl succinate isosuccinate sulfate sulfide sulfite d-Diethyl tartrate dl-Diethyl tartrate 3,5-Diethyltoluene Diethylzinc 1-Dihydrocarvone Dihydrocitronellol 1,4-Dihydroxyanthraquinone Dimethylacetylene (2-butyne) Dimethylamine N,N-Dimethylaniline Dimethyl arsanilate Di(α-methylbenzyl) ether 2,2-Dimethylbutane 2,3-Dimethylbutane Dimethyl citraconate 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane trans-1,3-Dimethylcyclohexane cis-1,3-Dimethylcyclohexane cis-1,4-Dimethylcyclohexane trans-1,4-Dimethylcyclohexane

1

5

10

20

40

56.0 61.8 −38.5 61.0 53.5 55.5 47.8 57.2 53.5 105.6 91.7 −95.4 46.2 11.0 −19.1 111.5 74.0

84.0 100.0 −17.0 90.1 82.2 83.9 75.7 86.0 82.2 138.7 126.1 −80.0 71.7 38.3 34.1 +2.4 142.8 106.6

113.8 133.1 +6.0 120.5 111.8 114.0 105.5 116.2 111.8 172.5 162.0 −63.5 97.8 67.3 62.0 25.3 174.3 138.3 −22.6 107.2

130.0 151.0 19.4 137.8 129.2 131.0 122.4 133.7 129.2 192.2 183.2 −53.7 113.2 84.0 77.9 38.0 193.2 154.6 −11.3 123.6

60

100

200

400

760

141.0 163.2 28.0 149.0 140.0 142.0 133.3 144.6 140.0 204.8 195.8 −47.5 122.6 95.0 88.0 46.3 205.0 165.8 −4.0 133.8

154.5 178.9 39.4 163.5 153.8 155.8 147.6 158.2 153.8 220.7 212.0 −39.1 135.5 109.2 101.7 57.6 220.0 179.0 +6.0 147.3

176.2 202.8 57.0 185.7 176.0 178.0 169.0 181.5 176.0 245.6 238.5 −26.3 153.5 129.0 121.8 74.2 243.8 198.2 21.0 168.2

199.5 228.8 76.0 210.0 200.0 202.5 193.5 205.7 200.0 272.8 265.8 −12.0 175.2 150.5 144.2 93.2 259.7 219.1 38.0 192.4

223.5 256.5 96.8 235.0 225.0 227.0 217.0 230.0 225.0 302.0 296.5 +3.5 196.3 172.8 166.6 113.5 296.0 240.0 55.5 215.5

Temperature, °C

Formula C8H5Cl2N C6H5AsCl2 C3H6Cl2 C8H6Cl2 C8H6Cl2 C8H6Cl2 C8H6Cl2 C8H6Cl2 C8H6Cl2 C14H20Cl2 C14H20Cl2 C2Cl2F4 C7H8Cl2Si C7H3Cl2F3 C10H8 C6H16O2Si C16H20O2Si C10H18O4 C4H11N C10H15N C10H16As NO3 C10H14 C10H14 C10H14 C5H10O3 C9H14O4 C8H10O6 C4H10O3 C8H12Cl2O5

49.7

78.0

98.1 116.0 −6.1 104.6 97.4 98.2 90.0 100.4 97.4 155.0 143.8 −72.3 84.2 52.2 47.6 13.3 157.6 123.0 −33.0 91.9

38.0 22.3 20.7 20.7 −10.1 59.8 70.0 91.8 148.3

62.6 48.7 46.8 47.1 +12.3 88.3 98.0 120.0 180.0

74.8 62.0 59.9 60.3 23.8 103.0 112.0 133.8 195.8

88.0 76.4 74.5 74.7 36.0 118.2 126.8 148.0 212.0

102.6 92.5 90.4 91.1 49.5 135.7 143.8 164.3 229.0

111.8 102.6 100.7 101.3 57.9 146.2 153.7 174.0 239.5

123.8 116.2 114.4 115.3 69.7 160.0 167.7 187.5 252.0

141.9 136.7 134.8 136.1 86.5 182.3 188.0 207.0 271.5

161.0 159.0 156.9 159.0 105.8 206.5 210.8 226.5 291.8

181.0 183.5 181.1 183.8 125.8 230.3 233.5 244.8 313.0

C6H14O3 C6H14O3 C4H10O C9H16O4 C8H12O4 C9H16O4 C20H43N C9H14O4 C5H10O C8H14O5 C8H12O4 C7H12O4 C9H14O4 C6H10O4 C12H14O4 C14H26O4 C12H16 C8H14O4 C8H14O4 C4H10O4S C4H10S C4H10O3S C8H14O6 C8H14O6 C11H16 C4H10Zn C10H16O C10H22O C14H8O4 C4H6 C2H7N C8H11N C8H12AsNO3 C16H18O C6H14 C6H14 C7H10O4 C8H16 C8H16 C8H16 C8H16 C8H16 C8H16 C8H16

13.0 45.3 −74.3 50.8 53.2 65.6 139.8 51.3 −12.7 80.7 57.3 40.0 62.8 47.4 108.8 125.3 49.7 54.6 39.8 47.0 −39.6 10.0 102.0 100.0 34.0 −22.4 46.6 68.0 196.7 −73.0 −87.7 29.5 15.0 96.7 −69.3 −63.6 50.8 −24.4 −15.9 −21.1 −19.4 −22.7 −20.0 −24.3

37.6 72.0 −56.9 77.8 81.2 94.7 175.8 80.2 +7.5 110.4 85.6 67.5 91.0 71.8 140.7 156.2 78.4 83.0 66.7 74.0 −18.6 34.2 133.0 131.7 61.5 0.0 75.5 91.7 239.8 −57.9 −72.2 56.3 39.6 128.3 −50.7 −44.5 78.2 −1.4 +7.3 +1.7 +3.4 0.0 +3.2 −1.7

50.0 85.8 −48.1 91.6 95.3 109.7 194.0 95.2 17.2 125.3 100.0 81.3 105.3 83.8 156.0 172.1 92.6 96.6 80.0 87.7 −8.0 46.4 148.0 147.2 75.3 +11.7 90.0 103.0 259.8 −50.5 −64.6 70.0 51.8 144.0 −41.5 −34.9 91.8 +10.3 18.4 13.0 14.9 +11.2 14.5 +10.1

63.0 100.3 −38.5 106.0 110.2 125.4 213.5 111.0 27.9 141.2 115.3 95.9 120.3 96.8 173.6 189.8 108.5 111.7 94.7 102.1 +3.5 59.7 164.2 163.8 90.2 24.2 106.0 115.0 282.0 −42.5 −56.0 84.8 65.0 160.3 −31.1 −24.1 106.5 23.0 31.1 25.6 27.4 23.6 27.1 22.6

77.5 116.7 27.7 122.4 126.7 142.8 235.0 128.2 39.4 157.8 131.8 113.3 137.3 110.6 192.1 207.5 125.8 127.8 111.0 118.0 16.1 74.2 182.3 181.7 107.0 38.0 123.7 127.6 307.4 −33.9 −46.7 101.6 79.7 179.6 −19.5 −12.4 122.6 37.3 45.3 39.7 41.4 37.5 41.1 36.5

86.8 126.8 −21.8 132.4 137.7 153.2 248.5 139.9 46.7 169.0 142.4 123.0 147.9 119.7 204.1 218.4 136.8 138.2 121.4 128.6 24.2 83.8 194.0 193.2 117.7 47.2 134.7 136.7 323.3 −27.8 −40.7 111.9 88.6 191.5 −12.1 −4.9 132.7 45.7 54.4 48.7 50.4 46.4 50.1 45.4

99.5 140.3 −11.5 146.0 151.1 167.8 265.5 154.3 56.2 183.9 156.0 136.2 161.6 130.8 219.5 234.4 151.0 151.1 134.8 142.5 35.0 96.3 208.5 208.0 131.7 59.1 149.7 145.9 344.5 −18.8 −32.6 125.8 101.0 206.8 −2.0 +5.4 145.8 57.9 66.8 61.0 62.5 58.5 62.3 57.6

118.0 159.0 +2.2 166.0 172.2 189.5 292.8 177.5 70.6 205.3 177.8 155.5 183.2 147.9 243.0 255.8 173.2 171.7 155.1 162.5 51.3 115.8 230.4 230.0 152.4 77.0 171.8 160.2 377.8 −5.0 −20.4 146.5 119.8 229.7 +13.4 21.1 165.8 76.2 85.6 79.6 81.0 76.9 80.8 76.0

138.5 180.3 17.9 188.7 195.8 212.8 324.6 203.1 86.3 229.5 201.7 176.8 205.8 166.2 267.5 280.3 198.0 193.8 177.7 185.5 69.7 137.0 254.8 254.3 176.5 97.3 197.0 176.8 413.0 +10.6 −7.1 169.2 140.3 254.8 31.0 39.0 188.0 97.2 107.0 100.9 102.1 97.8 101.9 97.0

159.8 201.9 34.6 211.5 218.5 237.0 355.0 227.9 102.7 253.4 225.0 198.9 229.0 185.7 294.0 305.5 223.0 216.5 201.3 209.5 88.0 159.0 280.0 280.0 200.7 118.0 223.0 193.5 450.0 27.2 +7.4 193.1 160.5 281.0 49.7 58.0 210.5 119.5 129.7 123.4 124.4 120.1 124.3 119.3

Melting point, °C

−94 −12.1 32.9 −21 −38.9 −34.4 −31.4 −83.9 −43.2 −43

−116.3 +0.6

−42 −49.8 −40.6 1.3 −20.8 −25.0 −99.5 17 −28 194 −32.5 −96 +2.5 −99.8 −128.2 −34 −50.0 −88.0 −92.0 −76.2 −87.4 −36.9

VAPOR PRESSURES

2-69

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Dimethyl ether 2,2-Dimethylhexane 2,3-Dimethylhexane 2,4-Dimethylhexane 2,5-Dimethylhexane 3,3-Dimethylhexane 3,4-Dimethylhexane Dimethyl itaconate 1-Dimethyl malate Dimethyl maleate malonate trans-Dimethyl mesaconate 2,7-Dimethyloctane Dimethyl oxalate 2,2-Dimethylpentane 2,3-Dimethylpentane 2,4-Dimethylpentane 3,3-Dimethylpentane 2,3-Dimethylphenol (2,3-xylenol) 2,4-Dimethylphenol (2,4-xylenol) 2,5-Dimethylphenol (2,5-xylenol) 3,4-Dimethylphenol (3,4-xylenol) 3,5-Dimethylphenol (3,5-xylenol) Dimethylphenylsilane Dimethyl phthalate 3,5-Dimethyl-1,2-pyrone 4,6-Dimethylresorcinol Dimethyl sebacate 2,4-Dimethylstyrene 2,5-Dimethylstyrene α,α-Dimethylsuccinic anhydride Dimethyl sulfide d-Dimethyl tartrate dl-Dimethyl tartrate N,N-Dimethyl-2-toluidine N,N-Dimethyl-4-toluidine Di(nitrosomethyl) amine Diosphenol 1,4-Dioxane Dipentene Diphenylamine Diphenyl carbinol (benzhydrol) chlorophosphate disulfide 1,2-Diphenylethane (dibenzyl) Diphenyl ether 1,1-Diphenylethylene trans-Diphenylethylene 1,1-Diphenylhydrazine Diphenylmethane Diphenyl sulfide Diphenyl-2-tolyl thiophosphate 1,2-Dipropoxyethane 1,2-Diisopropylbenzene 1,3-Diisopropylbenzene Dipropylene glycol Dipropyleneglycol monobutyl ether isopropyl ether Di-n-propyl ether Diisopropyl ether Di-n-propyl ketone (4-heptanone) Di-n-propyl oxalate Diisopropyl oxalate Di-n-propyl succinate Di-n-propyl d-tartrate Diisopropyl d-tartrate Divinyl acetylene (1,5-hexadiene-3-yne) 1,3-Divinylbenzene Docosane n-Dodecane 1-Dodecene n-Dodecyl alcohol Dodecylamine Dodecyltrimethylsilane Elaidic acid

1

5

10

20

40

−101.1 −7.9 −1.1 −5.3 −5.5 −4.4 +0.2 94.0 104.0 73.0 59.8 74.0 30.5 44.0 −28.7 −20.8 −27.4 −25.0 83.8 78.0 78.0 93.8 89.2 30.3 131.8 107.6 76.8 139.8 61.9 55.9 88.1 −58.0 133.2 131.8 54.1 74.3 27.8 95.4 −12.8 40.4 141.7 145.0 160.5 164.0 119.8 97.8 119.6 145.8 159.3 107.4 129.0 179.8 −10.3 67.8 62.3 102.1 92.0 72.8 −22.3 −37.4 44.4 80.2 69.0 107.6 147.7 133.7 −24.4 60.0 195.4 75.8 74.0 120.2 111.8 122.1 206.7

−93.3 +3.1 +9.9 +5.2 +5.3 +6.1 11.3 106.6 118.3 86.4 72.0 87.8 42.3 56.0 −18.7 −10.3 −17.1 −14.4 97.6 91.3 91.3 107.7 102.4 42.6 147.6 122.0 90.7 156.2 75.8 69.0 102.0 −49.2 148.2 147.5 66.2 86.7 40.0 109.0 −1.2 53.8 157.0 162.0 182.0 180.0 136.0 114.0 135.0 161.0 176.1 122.8 145.0 201.6 +5.0 81.8 76.0 116.2 106.0 86.2 −11.8 −27.4 55.0 93.9 81.9 122.2 163.5 148.2 −14.0 73.8 213.0 90.0 87.8 134.7 127.8 137.7 223.5

−85.2 15.0 22.1 17.2 17.2 18.2 23.5 119.7 133.8 101.3 85.0 102.1 55.8 69.4 −7.5 +1.1 −5.9 −2.9 112.0 105.0 105.0 122.0 117.0 56.2 164.0 136.4 105.8 175.8 90.8 84.0 116.3 −39.4 164.3 164.0 80.2 100.0 53.7 124.0 +12.0 68.2 175.2 180.9 203.8 197.0 153.7 130.8 151.8 179.8 194.0 139.8 162.0 215.5 22.3 96.8 91.2 131.3 120.4 100.8 0.0 −16.7 66.2 108.6 95.6 138.0 180.4 164.0 −2.8 88.7 233.5 104.6 102.4 150.0 141.6 153.8 242.3

−76.2 28.2 35.6 30.5 30.4 31.7 37.1 133.7 150.1 117.2 100.0 118.0 71.2 83.6 +5.0 13.9 +6.5 +9.9 129.2 121.5 121.5 138.0 133.3 71.4 182.8 152.7 122.5 196.0 107.7 100.2 132.3 −28.4 182.4 182.4 95.0 116.3 68.2 141.2 25.2 84.3 194.3 200.0 227.9 214.8 173.7 150.0 170.8 199.0 213.5 157.8 182.8 230.6 42.3 114.0 107.9 147.4 136.3 117.0 +13.2 −4.5 78.1 124.6 110.5 154.8 199.7 181.8 +10.0 105.5 254.5 121.7 118.6 167.2 157.4 172.1 260.8

Melting point, °C

100

200

400

760

−62.7 48.2 56.0 50.6 50.5 52.5 57.7 153.7 175.1 140.4 121.9 141.5 93.9 104.8 23.9 33.3 25.4 29.3 152.2 143.0 143.0 161.0 156.0 94.2 210.0 177.5 147.3 222.6 132.3 124.7 155.3 −12.0 208.8 209.5 118.1 140.3 90.3 165.6 45.1 108.3 222.8 227.5 265.0 241.3 202.8 178.8 198.6 227.4 242.5 186.3 211.8 252.5 74.2 138.7 132.3 169.9 159.8 140.3 33.0 13.7 96.0 148.1 132.6 180.3 227.0 207.3 29.5 130.0 286.0 146.2 142.3 192.0 182.1 199.5 288.0

−50.9 65.7 73.8 68.1 68.0 70.0 75.6 171.0 196.3 160.0 140.0 161.0 114.0 123.3 40.3 50.1 41.8 46.2 173.0 161.5 161.5 181.5 176.2 114.2 232.7 198.0 167.8 245.0 153.2 145.6 175.8 +2.6 230.5 232.3 138.3 161.6 110.0 186.2 62.3 128.2 247.5 250.0 299.5 262.6 227.8 203.3 222.8 251.7 267.2 210.7 236.8 270.3 103.8 159.8 153.7 189.9 180.0 160.0 50.3 30.0 111.2 168.0 151.2 202.5 250.1 228.2 46.0 151.4 314.2 167.2 162.2 213.0 203.0 222.0 312.4

−37.8 85.6 94.1 88.2 87.9 90.4 96.0 189.8 219.5 182.2 159.8 183.5 136.0 143.3 59.2 69.4 60.6 65.5 196.0 184.2 184.2 203.6 197.8 136.4 257.8 221.0 192.0 269.6 177.5 168.7 197.5 18.7 255.0 257.4 161.5 185.4 131.3 209.5 81.8 150.5 274.1 275.6 337.2 285.8 255.0 230.7 249.8 278.3 294.0 237.5 263.9 290.0 140.0 184.3 177.6 210.5 203.8 183.1 69.5 48.2 127.3 190.3 171.8 226.5 275.6 251.8 64.4 175.2 343.5 191.0 185.5 235.7 225.0 248.0 337.0

−23.7 106.8 115.6 109.4 109.1 112.0 117.7 208.0 242.6 205.0 180.7 206.0 159.7 163.3 79.2 89.8 80.5 86.1 218.0 211.5 211.5 225.2 219.5 159.3 283.7 245.0 215.0 293.5 202.0 193.0 219.5 36.0 280.0 282.0 184.8 209.5 153.0 232.0 101.1 174.6 302.0 301.0 378.0 310.0 284.0 258.5 277.0 306.5 322.2 264.5 292.5 310.0 180.0 209.0 202.0 231.8 227.0 205.6 89.5 67.5 143.7 213.5 193.5 250.8 303.0 275.0 84.0 199.5 376.0 216.2 208.0 259.0 248.0 273.0 362.0

Temperature, °C

Formula C2H6O −115.7 −29.7 C8H18 −23.0 C8H18 C8H18 −26.9 −26.7 C8H18 −25.8 C8H18 C8H18 −22.1 69.3 C7H10O4 75.4 C6H10O5 C6H8O4 45.7 35.0 C5H8O4 46.8 C7H10O4 C10H22 +6.3 20.0 C4H6O4 −49.0 C7H16 C7H16 −42.0 −48.0 C7H16 −45.9 C7H16 C8H10O 56.0 51.8 C8H10O 51.8 C8H10O C8H10O 66.2 62.0 C8H10O +5.3 C8H12Si C10H10O4 100.3 78.6 C7H8O2 49.0 C8H10O2 C12H22O4 104.0 34.2 C10H12 29.0 C10H12 C6H8O3 61.4 −75.6 C2H6S 102.1 C6H10O6 C6H10O6 100.4 28.8 C9H13N 50.1 C9H13N C2H5N3O2 +3.2 66.7 C10H16O2 −35.8 C4H8O2 C10H16 14.0 108.3 C12H11N 110.0 C13H12O C12H10ClPO3 121.5 131.6 C12H10S2 86.8 C14H14 C12H10O 66.1 87.4 C14H12 113.2 C14H12 C12H12N2 126.0 76.0 C13H12 96.1 C12H10S C18H17O3PS 159.7 −38.8 C8H18O2 40.0 C12H18 C12H18 34.7 73.8 C6H14O3 64.7 C10H22O3 C9H20O3 46.0 −43.3 C6H14O −57.0 C6H14O C7H14O 23.0 53.4 C8H14O4 43.2 C8H14O4 C10H18O4 77.5 115.6 C10H18O6 103.7 C10H18O6 C6H6 −45.1 32.7 C10H10 157.8 C22H46 C12H26 47.8 47.2 C12H24 91.0 C12H26O C12H27N 82.8 91.2 C15H34Si 171.3 C18H34O2

60 −70.4 36.7 44.2 39.0 38.9 40.4 45.8 142.6 160.4 127.1 109.7 127.8 80.8 92.8 13.0 22.1 14.5 18.1 139.5 131.0 131.0 148.0 143.5 81.3 194.0 163.8 133.2 208.0 118.0 110.7 142.4 −21.4 193.8 193.8 105.2 126.4 77.7 151.3 33.8 94.6 206.9 212.0 244.2 226.2 186.0 162.0 183.4 211.5 225.9 170.2 194.8 240.4 55.8 124.3 118.2 156.5 146.3 126.8 21.6 +3.4 85.8 134.8 120.0 166.0 211.7 192.6 18.1 116.0 268.3 132.1 128.5 177.8 168.0 184.2 273.0

−138.5

−90.7 38 −62 −52.8 −123.7 −135 −119.5 −135.0 75 25.5 74.5 62.5 68 51.5 38

−83.2 61.5 89 −61

10 52.9 68.5 61 51.5 27 124 44 26.5

−105

−122 −60 −32.6

−66.9 44.5 −9.6 −31.5 24 51.5

(Continued )

2-70

PHYSICAL AnD CHEMICAL DATA

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Epichlorohydrin 1,2-Epoxy-2-methylpropane Erucic acid Estragole (p-methoxy allyl benzene) Ethane Ethoxydimethylphenylsilane Ethoxytrimethylsilane Ethoxytriphenylsilane Ethyl acetate acetoacetate Ethylacetylene (1-butyne) Ethyl acrylate α-Ethylacrylic acid α-Ethylacrylonitrile Ethyl alcohol (ethanol) Ethylamine 4-Ethylaniline N-Ethylaniline 2-Ethylanisole 3-Ethylanisole 4-Ethylanisole Ethylbenzene Ethyl benzoate benzoylacetate bromide α-bromoisobutyrate n-butyrate isobutyrate Ethylcamphoronic anhydride Ethyl isocaproate carbamate carbanilate Ethylcetylamine Ethyl chloride chloroacetate chloroglyoxylate α-chloropropionate trans-cinnamate 3-Ethylcumene 4-Ethylcumene Ethyl cyanoacetate Ethylcyclohexane Ethylcyclopentane Ethyl dichloroacetate N,N-diethyloxamate N-Ethyldiphenylamine Ethylene Ethylene-bis-(chloroacetate) Ethylene chlorohydrin (2-chloroethanol) diamine (1,2-ethanediamine) dibromide (1,2-dibromethane) dichloride (1,2-dichloroethane) glycol (1,2-ethanediol) glycol diethyl ether (1,2-diethoxyethane) glycol dimethyl ether (1,2-dimethoxyethane) glycol monomethyl ether (2-methoxyethanol) oxide Ethyl α-ethylacetoacetate fluoride formate 2-furoate glycolate 3-Ethylhexane 2-Ethylhexyl acrylate Ethylidene chloride (1,1-dichloroethane) fluoride (1,1-difluoroethane) Ethyl iodide Ethyl l-leucinate Ethyl levulinate Ethyl mercaptan (ethanethiol) Ethyl methylcarbamate Ethyl methyl ether

1

5

10

20

−16.5 −69.0 206.7 52.6 −159.5 36.3 −50.9 167.0 −43.4 28.5 −92.5 −29.5 47.0 −29.0 −31.3 −82.3 52.0 38.5 29.7 33.7 33.5 −9.8 44.0 107.6 −74.3 10.6 −18.4 −24.3 118.2 11.0 107.8 133.2 −89.8 +1.0 −5.1 +6.6 87.6 28.3 31.5 67.8 −14.5 −32.2 9.6 76.0 98.3 −168.3 112.0 −4.0 −11.0 −27.0 −44.5 53.0 −33.5

+5.6 −50.0 239.7 80.0 −148.5 63.1 −31.0 198.2 −23.5 54.0 −76.7 −8.7 70.7 −6.4 −12.0 −66.4 80.0 66.4 55.9 60.3 60.2 +13.9 72.0 136.4 −56.4 35.8 +4.0 −2.4 149.8 35.8 65.8 131.8 168.2 −73.9 25.4 +18.0 30.2 108.5 55.5 58.4 93.5 +9.2 −10.8 34.0 106.3 130.2 −158.3 142.4 +19.0 +10.5 +4.7 −24.0 79.7 −10.2

16.6 −40.3 254.5 93.7 −142.9 76.2 −20.7 213.5 −13.5 67.3 −68.7 +2.0 82.0 +5.0 −2.3 −58.3 93.8 80.6 69.0 73.9 73.9 25.9 86.0 150.3 −47.5 48.0 15.3 +8.4 165.0 48.0 77.8 143.7 186.0 −65.8 37.5 29.9 41.9 134.0 68.8 72.0 106.0 20.6 −0.1 46.3 121.7 146.0 −153.2 158.0 30.3 21.5 18.6 −13.6 92.1 +1.6

29.0 −29.5 270.6 108.4 −136.7 91.0 −9.8 230.0 −3.0 81.1 −59.9 13.0 94.4 17.7 +8.0 −48.6 109.0 96.0 83.1 88.5 88.5 38.6 101.4 166.8 −37.8 61.8 27.8 20.6 181.8 61.7 91.0 155.5 205.5 −56.8 50.4 42.0 54.3 150.3 83.6 86.7 119.8 33.4 +11.7 59.5 137.7 162.8 −147.6 173.5 42.5 33.0 32.7 −2.4 105.8 14.7

42.0 −17.3 289.1 124.6 −129.8 107.2 +3.7 247.0 +9.1 96.2 −50.0 26.0 108.1 31.8 19.0 −39.8 125.7 113.2 98.8 104.8 104.7 52.8 118.2 181.8 −26.7 77.0 41.5 33.8 199.8 76.3 105.6 168.8 226.5 −47.0 65.2 56.0 68.2 169.2 99.9 103.3 133.8 47.6 25.0 74.0 154.4 182.0 −141.3 191.0 56.0 45.8 48.0 +10.0 120.0 29.7

50.6 −9.7 300.2 135.2 −125.4 127.5 11.5 258.3 16.6 106.0 −43.4 33.5 116.7 40.6 26.0 −33.4 136.0 123.6 109.0 115.5 115.4 61.8 129.0 191.9 −19.5 86.7 50.1 42.3 211.5 85.8 114.8 177.3 239.8 −40.6 74.0 65.2 77.3 181.2 110.2 113.8 142.1 56.7 33.4 83.6 166.0 193.7 −137.3 201.8 64.1 53.8 57.9 18.1 129.5 39.0

62.0 +1.2 314.4 148.5 −119.3 131.4 22.1 273.5 27.0 118.5 −34.9 44.5 127.5 53.0 34.9 −25.1 149.8 137.3 122.3 129.2 128.4 74.1 143.2 205.0 −10.0 99.8 62.0 53.5 226.6 98.4 126.2 187.9 256.8 −32.0 86.0 76.6 89.3 196.0 124.3 127.2 152.8 69.0 45.0 96.1 180.3 209.8 −131.8 215.0 75.0 62.5 70.4 29.4 141.8 51.8

C4H10O2

−48.0

−26.2

−15.3

−3.0

+10.7

19.7

31.8

50.0

70.8

93.0

C3H8O2

−13.5

+10.2

22.0

34.3

47.8

56.4

68.0

85.3

104.3

124.4

−89.7 40.5 −117.0 −60.5 37.6 14.3 −20.0 50.0 −60.7 −112.5 −54.4 27.8 47.3 −76.7 26.5 −91.0

−73.8 67.3 −103.8 −42.2 63.8 38.8 +2.1 77.7 −41.9 −98.4 −34.3 57.3 74.0 −59.1 51.0 −75.6

−65.7 80.2 −97.7 −33.0 77.1 50.5 12.8 91.8 −32.3 −91.7 −24.3 72.1 87.3 −50.2 63.2 −67.8

−56.6 94.6 −90.0 −22.7 91.5 63.9 25.0 106.3 −21.9 −84.1 −13.1 88.0 101.8 −40.7 76.1 −59.1

−46.9 110.3 −81.8 −11.5 107.5 78.1 38.5 123.7 −10.2 −75.8 −0.9 106.0 117.7 −29.8 91.0 −49.4

−40.7 120.6 −76.4 −4.3 117.5 87.6 47.1 134.0 −2.9 −70.4 +7.2 117.8 127.6 −22.4 100.0 −43.3

−32.1 133.8 −69.3 −5.4 130.4 99.8 58.9 147.9 +7.2 −63.2 18.0 131.8 141.3 −13.0 112.0 −34.8

−19.5 153.2 −58.0 20.0 150.1 117.8 76.7 168.2 22.4 −52.0 34.1 149.8 160.2 +1.5 130.0 −22.0

−4.9 175.6 −45.5 37.1 172.5 138.0 97.0 192.2 39.8 −39.5 52.3 167.3 183.0 17.7 149.8 −7.8

+10.7 198.0 −32.0 54.3 195.0 158.2 118.5 216.0 57.4 −26.5 72.4 184.0 206.2 35.0 170.0 +7.5

C2H4O C8H14O3 C2H5F C3H6O2 C7H8O3 C4H8O3 C8H18 C11H20O2 C2H4Cl2 C2H4F2 C2H5I C8H17NO2 C7H12O3 C2H6S C4H9NO2 C3H8O

60

100

200

400

760

Temperature, °C

Formula C3H5ClO C4H8O C22H42O2 C10H12O C2H6 C10H16OSi C5H14OSi C20H20OSi C4H8O2 C6H10O3 C4H6 C5H8O2 C5H8O2 C5H7N C2H6O C2H7N C8H11N C8H11N C9H12O C9H12O C9H12O C8H10 C9H10O2 C11H12O3 C2H5Br C6H11BrO2 C6H12O2 C6H12O2 C11H16O5 C8H16O2 C3H7NO2 C9H11NO2 C18H39N C2H5Cl C4H7ClO2 C4H5ClO3 C5H9ClO2 C11H12O2 C11H16 C11H16 C5H7NO2 C8H16 C7H14 C4H6Cl2O2 C8H15NO3 C14H15N C2H4 C6H8Cl2O4 C2H5ClO C2H8N2 C2H4Br2 C2H4Cl2 C2H6O2 C6H14O2

40

79.3 98.0 117.9 17.5 36.0 55.5 336.5 358.8 381.5 168.7 192.0 215.0 −110.2 −99.7 −88.6 151.5 175.0 199.5 38.1 56.3 75.7 295.0 319.5 344.0 42.0 59.3 77.1 138.0 158.2 180.8 −21.6 −6.9 +8.7 61.5 80.0 99.5 144.0 160.7 179.2 71.6 92.2 114.0 48.4 63.5 78.4 −12.3 +2.0 16.6 170.6 194.2 217.4 156.9 180.8 204.0 142.1 164.2 187.1 149.7 172.8 196.5 149.2 172.3 196.5 92.7 113.8 136.2 164.8 188.4 213.4 223.8 244.7 265.0 +4.5 21.0 38.4 119.7 141.2 163.6 79.8 100.0 121.0 71.0 90.0 110.0 248.5 272.8 298.0 117.8 139.2 160.4 144.2 164.0 184.0 203.8 220.0 237.0 283.3 313.0 342.0 −18.6 −3.9 +12.3 103.8 123.8 144.2 94.5 114.7 135.0 107.2 126.2 146.5 219.3 245.0 271.0 145.4 168.2 193.0 148.3 171.8 195.8 169.8 187.8 206.0 87.8 109.1 131.8 62.4 82.3 103.4 115.2 135.9 156.5 202.8 226.5 252.0 233.0 258.8 286.0 −123.4 −113.9 −103.7 237.3 259.5 283.5 91.8 110.0 128.8 81.0 99.0 117.2 89.8 110.1 131.5 45.7 64.0 82.4 158.5 178.5 197.3 71.8 94.1 119.5

Melting point, °C −25.6 33.5 −183.2

−82.4 −45 −130 −71.2 −112 −80.6 −4 −63.5

−94.9 −34.6 −117.8 −93.3 −88.2 49 52.5 −139 −26 12

−111.3 −138.6

−169 −69 8.5 10 −35.3 −15.6

−111.3 −79 34

−96.7 −117 −105 −121

VAPOR PRESSURES

2-71

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name 1-Ethylnaphthalene Ethyl α-naphthyl ketone (1-propionaphthone) Ethyl 3-nitrobenzoate 3-Ethylpentane 4-Ethylphenetole 2-Ethylphenol 3-Ethylphenol 4-Ethylphenol Ethyl phenyl ether (phenetole) Ethyl propionate Ethyl propyl ether Ethyl salicylate 3-Ethylstyrene 4-Ethylstyrene Ethylisothiocyanate 2-Ethyltoluene 3-Ethyltoluene 4-Ethyltoluene Ethyl trichloroacetate Ethyltrimethylsilane Ethyltrimethyltin Ethyl isovalerate 2-Ethyl-1,4-xylene 4-Ethyl-1,3-xylene 5-Ethyl-1,3-xylene Eugenol iso-Eugenol Eugenyl acetate Fencholic acid d-Fenchone dl-Fenchyl alcohol Fluorene Fluorobenzene 2-Fluorotoluene 3-Fluorotoluene 4-Fluorotoluene Formaldehyde Formamide Formic acid trans-Fumaryl chloride Furfural (2-furaldehyde) Furfuryl alcohol Geraniol Geranyl acetate Geranyl n-butyrate Geranyl isobutyrate Geranyl formate Glutaric acid Glutaric anhydride Glutaronitrile Glutaryl chloride Glycerol Glycerol dichlorohydrin (1,3-dichloro-2-propanol) Glycol diacetate Glycolide (1,4-dioxane-2,6-dione) Guaicol (2-methoxyphenol) Heneicosane Heptacosane Heptadecane Heptaldehyde (enanthaldehyde) n-Heptane Heptanoic acid (enanthic acid) 1-Heptanol Heptanoyl chloride (enanthyl chloride) 2-Heptene Heptylbenzene Heptyl cyanide (enanthonitrile) Hexachlorobenzene Hexachloroethane Hexacosane Hexadecane 1-Hexadecene n-Hexadecyl alcohol (cetyl alcohol)

1

C13H12O C9H9NO4 C7H16 C10H14O C8H10O C8H10O C8H10O C8H10O C5H10O2 C5H12O C9H10O3 C10H12 C10H12 C3H5NS C9H12 C9H12 C9H12 C4H5Cl3O2 C5H14Si C5H14Sn C7H14O2 C10H14 C10H14 C10H14 C10H12O2 C10H12O2 C12H14O3 C10H16O2 C10H16O C10H18O C13H10 C6H5F C7H7F C7H7F C7H7F CH2O CH3NO CH2O2 C4H2Cl2O2 C5H4O2 C5H6O2 C10H18O C12H20O2 C14H24O2 C14H24O2 C11H18O2 C5H8O4 C5H6O3 C5H6N2 C5H6Cl2O2 C3H8O3 C3H6Cl2O C6H10O4 C4H4O4 C7H8O2 C21H44 C27H56 C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H13ClO C7H14 C13H20 C7H13N C6Cl6 C2Cl6 C26H54 C16H34 C16H32 C16H34O

200

400

760

Melting point, °C

164.1

180.0

204.6

230.8

258.1

−27

206.9 192.6 17.5 119.8 117.9 130.0 131.3 86.6 27.2 −12.0 136.7 99.2 97.3 50.8 76.4 73.3 73.6 85.5 −9.0 30.0 55.2 96.0 97.2 92.6 155.8 167.0 183.0 171.8 99.5 110.8 185.2 +11.5 34.7 37.0 37.8 −70.6 137.5 24.0 79.5 82.1 95.7 141.8 150.0 170.1 164.0 136.2 226.3 185.5 176.4 128.3 198.0 93.0

218.2 205.0 25.7 129.8 127.9 139.8 141.7 95.4 35.1 −4.0 147.6 109.6 107.6 59.8 86.0 82.9 83.2 94.4 −1.2 38.4 64.0 106.2 107.4 103.0 167.3 178.2 194.0 181.5 109.8 120.2 197.8 19.6 43.7 45.8 46.5 −65.0 147.0 32.4 89.0 91.5 104.0 151.5 160.3 180.2 174.0 147.2 235.5 196.2 189.5 139.1 208.0 102.0

233.5 220.3 36.9 143.5 141.8 152.0 154.2 108.4 45.2 +6.8 161.5 123.2 121.5 71.9 99.0 95.9 96.3 107.4 +9.2 50.0 75.9 120.0 121.2 116.5 182.2 194.0 209.7 194.0 123.6 132.3 214.7 30.4 55.3 57.5 58.1 −57.3 157.5 43.8 101.0 103.4 115.9 165.3 175.2 193.8 187.7 160.7 247.0 212.5 205.5 151.8 220.1 114.8

255.5 244.6 53.8 163.2 161.6 171.8 175.0 127.9 61.7 23.3 183.7 144.0 142.0 90.0 119.0 115.5 116.1 125.8 25.0 67.3 93.8 140.2 141.8 137.4 204.7 217.2 232.5 215.0 144.0 150.0 240.3 47.2 73.0 75.4 76.0 −46.0 175.5 61.4 120.0 121.8 133.1 185.6 196.3 214.0 207.6 182.6 265.0 236.5 230.0 172.4 240.0 133.3

280.2 270.6 73.0 185.7 184.5 193.3 197.4 149.8 79.8 41.6 207.0 167.2 165.0 110.1 141.4 137.8 136.4 146.0 42.8 87.6 114.0 163.1 164.4 159.6 228.3 242.3 257.4 237.8 166.8 173.2 268.6 65.7 92.8 95.4 96.1 −33.0 193.5 80.3 140.0 141.8 151.8 207.8 219.8 235.0 228.5 205.8 283.5 261.0 257.3 195.3 263.0 153.5

306.0 298.0 93.5 208.0 207.5 214.0 219.0 172.0 99.1 61.7 231.5 191.5 189.0 131.0 165.1 161.3 162.0 167.0 62.0 108.8 134.3 186.9 188.4 183.7 253.5 267.5 282.0 264.1 191.0 201.0 295.0 84.7 114.0 116.0 117.0 −19.5 210.5 100.6 160.0 161.8 170.0 230.0 243.3 257.4 251.0 230.0 303.0 287.0 286.2 217.0 290.0 174.3

106.1 148.6 121.6 243.4 305.7 195.8 66.3 22.3 139.5 99.8 86.4 21.5 144.0 92.6 206.0 102.3 295.2 181.3 178.8 219.8

115.8 158.2 131.0 255.3 318.3 207.3 74.0 30.6 148.5 108.0 93.5 30.0 154.8 103.0 219.0 112.0 307.8 193.2 190.8 234.3

128.0 173.2 144.0 272.0 333.5 223.0 84.0 41.8 160.0 119.5 102.7 41.3 170.2 116.8 235.5 124.2 323.2 208.5 205.3 251.7

147.8 194.0 162.7 296.5 359.4 247.8 102.0 58.7 179.5 136.6 116.3 58.6 193.3 137.7 258.5 143.1 348.4 231.7 226.8 280.2

168.3 217.0 184.1 323.8 385.0 274.5 125.5 78.0 199.6 155.6 130.7 78.1 217.8 160.0 283.5 163.8 374.6 258.3 250.0 312.7

190.5 240.0 205.0 350.5 410.6 303.0 155.0 98.4 221.5 175.8 145.0 98.5 244.0 184.6 309.4 185.6 399.8 287.5 274.0 344.0

10

20

70.0

101.4

116.8

133.8

40 152.0

124.0 108.1 −37.8 48.5 46.2 60.0 59.3 18.1 −28.0 −64.3 61.2 28.3 26.0 −13.2 9.4 7.2 7.6 20.7 −60.6 −30.0 −6.1 25.7 26.3 22.1 78.4 86.3 101.6 101.7 28.0 45.8 −43.4 −24.2 −22.4 −21.8

155.5 140.2 −17.0 75.7 73.4 86.8 86.5 43.7 −7.2 −45.0 90.0 55.0 52.7 +10.6 34.8 32.3 32.7 45.5 −41.4 −7.6 +17.0 52.0 53.0 48.8 108.1 117.0 132.3 128.7 54.7 70.3 129.3 −22.8 −2.2 −0.3 +0.3

70.5 −20.0 +15.0 18.5 31.8 69.2 73.5 96.8 90.9 61.8 155.5 100.8 91.3 56.1 125.5 28.0

96.3 −5.0 38.5 42.6 56.0 96.8 102.7 125.2 119.6 90.3 183.8 133.3 123.7 84.0 153.8 52.2

171.0 155.0 −6.8 89.5 87.0 100.2 100.2 56.4 +3.4 −35.0 104.2 68.3 66.3 22.8 47.6 44.7 44.9 57.7 −31.8 +3.8 28.7 65.6 66.4 62.1 123.0 132.4 148.0 142.3 68.3 82.1 146.0 −12.4 +8.9 +11.0 11.8 −88.0 109.5 +2.1 51.8 54.8 68.0 110.0 117.9 139.0 133.0 104.3 196.0 149.5 140.0 97.8 167.2 64.7

188.1 173.6 +4.7 103.8 101.5 114.5 115.0 70.3 14.3 −24.0 119.3 82.8 80.8 36.1 61.2 58.2 58.5 70.6 −21.0 16.1 41.3 79.8 80.6 76.5 138.7 149.0 164.2 155.8 83.0 95.6 164.2 −1.2 21.4 23.4 24.0 −79.6 122.5 10.3 65.0 67.8 81.0 125.6 133.0 153.8 147.9 119.8 210.5 166.0 156.5 112.3 182.2 78.0

38.3

64.1 103.0 79.1 188.0 248.6 145.2 32.7 −12.7 101.3 64.3 54.6 −14.1 94.6 47.8 149.3 49.8 240.0 135.2 131.7 158.3

77.1 116.6 92.0 205.4 266.8 160.0 43.0 −2.1 113.2 74.7 64.6 −3.5 110.0 61.6 166.4 73.5 257.4 149.8 146.2 177.8

90.8 132.0 106.0 223.2 284.6 177.7 54.0 +9.5 125.6 85.8 75.0 +8.3 126.0 76.3 185.7 87.6 275.8 164.7 162.0 197.8

60

Temperature, °C

Formula C12H12

100

5

52.4 152.6 211.7 115.0 12.0 −34.0 78.0 42.4 34.2 −35.8 64.0 21.0 114.4 32.7 204.0 105.3 101.6 122.7

47 −118.6 −45 −4 46.5 −30.2 −72.6 1.3 −5.9 −95.5

−99.3

−10 295 19 5 35 113 −42.1 −80 −110.8 −92 8.2

97.5

17.9 −31 97 28.3 40.4 59.5 22.5 −42 −90.6 −10 34.6

230 186.6 56.6 18.5 4 49.3

(Continued )

2-72

PHYSICAL AnD CHEMICAL DATA

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name n-Hexadecylamine (cetylamine) Hexaethylbenzene n-Hexane 1-Hexanol 2-Hexanol 3-Hexanol 1-Hexene n-Hexyl levulinate n-Hexyl phenyl ketone (enanthophenone) Hydrocinnamic acid Hydrogen cyanide (hydrocyanic acid) Hydroquinone 4-Hydroxybenzaldehyde α-Hydroxyisobutyric acid α-Hydroxybutyronitrile 4-Hydroxy-3-methyl-2-butanone 4-Hydroxy-4-methyl-2-pentanone 3-Hydroxypropionitrile Indene Iodobenzene Iodononane 2-Iodotoluene α-Ionone Isoprene Lauraldehyde Lauric acid Levulinaldehyde Levulinic acid d-Limonene Linalyl acetate Maleic anhydride Menthane 1-Menthol Menthyl acetate benzoate formate Mesityl oxide Methacrylic acid Methacrylonitrile Methane Methanethiol Methoxyacetic acid N-Methylacetanilide Methyl acetate acetylene (propyne) acrylate alcohol (methanol) Methylamine N-Methylaniline Methyl anthranilate benzoate 2-Methylbenzothiazole α-Methylbenzyl alcohol Methyl bromide 2-Methyl-1-butene 2-Methyl-2-butene Methyl isobutyl carbinol (2-methyl4-pentanol) n-butyl ketone (2-hexanone) isobutyl ketone (4-methyl-2-pentanone) n-butyrate isobutyrate caprate caproate caprylate chloride chloroacetate cinnamate α-Methylcinnamic acid Methylcyclohexane Methylcyclopentane Methylcyclopropane Methyl n-decyl ketone (n-dodecan-2-one) dichloroacetate N-Methyldiphenylamine

1

5

10

20

123.6

157.8 134.3 −34.5 47.2 34.8 25.7 −38.0 120.0 130.3 133.5 −55.3 153.3 153.2 98.5 65.8 69.3 46.7 87.8 44.3 50.6 96.2 65.9 108.8 −62.3 108.4 150.6 54.9 128.1 40.4 82.5 63.4 35.7 83.2 85.8 154.2 75.8 +14.1 48.5 −23.3 −199.0 −75.3 79.3 103.8 −38.6 −97.5 −23.6 −25.3 −81.3 62.8 109.0 64.4 97.5 75.2 −80.6 −72.8 −57.0 +22.1

176.0 150.3 −25.0 58.2 45.0 36.7 −28.1 134.7 145.5 148.7 −47.7 163.5 169.7 110.5 77.8 81.0 58.8 102.0 58.5 64.0 109.0 79.8 123.0 −53.3 123.7 166.0 68.0 141.8 53.8 96.0 78.7 48.3 96.0 100.0 170.0 90.0 26.0 60.0 −12.5 −195.5 −67.5 92.0 118.6 −29.3 −90.5 −13.5 −16.2 −73.8 76.2 124.2 77.3 111.2 88.0 −72.8 −64.3 −47.9 33.3

195.7 168.0 −14.1 70.3 55.9 49.0 −17.2 150.2 161.0 165.0 −39.7 174.6 186.8 123.8 90.7 94.0 72.0 117.9 73.9 78.3 123.0 95.6 139.0 −43.5 140.2 183.6 82.7 154.1 68.2 111.4 95.0 62.7 110.3 115.4 186.3 105.8 37.9 72.7 −0.6 −191.8 −58.8 106.5 135.1 −19.1 −82.9 −2.7 −6.0 −65.9 90.5 141.5 91.8 125.5 102.1 −64.0 −54.8 −37.9 45.4

C6H12O C6H12O C5H10O2 C5H10O2 C11H22O2 C7H14O2 C9H18O2 CH3Cl C3H5ClO2 C10H10O2 C10H10O2 C7H14 C6H12 C4H8 C12H24O C3H4Cl2O2 C13H13N

60

100

215.7 187.7 −2.3 83.7 67.9 62.2 −5.0 167.8 178.9 183.3 −30.9 192.0 206.0 138.0 104.8 108.2 86.7 134.1 90.7 94.4 138.1 112.4 155.6 −32.6 157.8 201.4 98.3 169.5 84.3 127.7 111.8 78.3 126.1 132.1 204.3 123.0 51.7 86.4 +12.8 −187.7 −49.2 122.0 152.2 −7.9 −74.3 +9.2 +5.0 −56.9 106.0 159.7 107.8 141.2 117.8 −54.2 −44.1 −26.7 58.2

228.8 199.7 +5.4 92.0 76.0 70.7 +2.8 179.0 189.8 194.0 −25.1 203.0 217.5 146.4 113.9 117.4 96.0 144.7 100.8 105.0 147.7 123.8 166.3 −25.4 168.7 212.7 108.4 178.0 94.6 138.1 122.0 88.6 136.1 143.2 215.8 133.8 60.4 95.3 21.5 −185.1 −43.1 131.8 164.2 −0.5 −68.8 17.3 12.1 −51.3 115.8 172.0 117.4 150.4 127.4 −48.0 −37.3 −19.4 67.0

245.8 216.0 15.8 102.8 87.3 81.8 13.0 193.6 204.2 209.0 −17.8 216.5 233.5 157.7 125.0 129.0 108.2 157.7 114.7 118.3 159.8 138.1 181.2 −16.0 184.5 227.5 121.8 190.2 108.3 151.8 135.8 102.1 149.4 156.7 230.4 148.0 72.1 106.6 32.8 −181.4 −34.8 144.5 179.8 +9.4 −61.3 28.0 21.2 −43.7 129.8 187.8 130.8 163.9 140.3 −39.4 −28.0 −9.9 78.0

28.8 +19.7 −5.5 −13.0 93.5 30.0 61.7 −99.5 19.0 108.1 155.0 −14.0 −33.8 −80.6 106.0 26.7 134.0

38.8 30.0 +5.0 −2.9 108.0 42.0 74.9 −92.4 30.0 123.0 169.8 −3.2 −23.7 −72.8 120.4 38.1 149.7

50.0 40.8 16.7 +8.4 123.0 55.4 89.0 −84.8 41.5 140.0 185.2 +8.7 −12.8 −64.0 136.0 50.7 165.8

62.0 52.8 29.6 21.0 139.0 70.0 105.3 −76.0 54.5 157.9 201.8 22.0 −0.6 −54.2 152.4 64.7 184.0

69.8 60.4 37.4 28.9 148.6 79.7 115.3 −70.4 63.0 170.0 212.0 30.5 +7.2 −48.0 163.8 73.6 195.4

79.8 70.4 48.0 39.6 161.5 91.4 128.0 −63.0 73.5 185.8 224.8 42.1 17.9 −39.3 177.5 85.4 210.1

200

400

760

Temperature, °C

Formula C16H35N C18H30 C6H14 C6H14O C6H14O C6H14O C6H12 C11H20O3 C13H18O C9H10O2 CHN C6H6O2 C7H6O2 C4H8O3 C5H9NO C5H10O2 C6H12O2 C3H5NO C9H8 C6H5I C9H19I C7H7I C13H20O C5H8 C12H24O C12H24O2 C5H8O2 C5H8O3 C10H16 C12H20O2 C4H2O3 C10H20 C10H20O C12H22O2 C17H24O2 C11H20O2 C6H10O C4H6O2 C4H5N CH4 CH4S C3H6O3 C9H11NO C3H6O2 C3H4 C4H6O2 CH4O CH5N C7H9N C8H9NO2 C8H8O2 C8H7NS C8H10O CH3Br C5H10 C5H10 C6H14O

40

−53.9 24.4 14.6 +2.5 −57.5 90.0 100.0 102.2 −71.0 132.4 121.2 73.5 41.0 44.6 22.0 58.7 16.4 24.1 70.0 37.2 79.5 −79.8 77.7 121.0 28.1 102.0 14.0 55.4 44.0 +9.7 56.0 57.4 123.2 47.3 −8.7 25.5 −44.5 −205.9 −90.7 52.5 −57.2 −111.0 −43.7 −44.0 −95.8 36.0 77.6 39.0 70.0 49.0 −96.3 −89.1 −75.4 −0.3 +7.7 −1.4 −26.8 −34.1 63.7 +5.0 34.2 −2.9 77.4 125.7 −35.9 −53.7 −96.0 77.1 3.2 103.5

272.2 300.4 330.0 241.7 268.5 298.3 31.6 49.6 68.7 119.6 138.0 157.0 103.7 121.8 139.9 98.3 117.0 135.5 29.0 46.8 66.0 215.7 241.0 266.8 225.0 248.3 271.3 230.8 255.0 279.8 −5.3 +10.2 25.9 238.0 262.5 286.2 256.8 282.6 310.0 175.2 193.8 212.0 142.0 159.8 178.8 146.5 165.5 185.0 126.8 147.5 167.9 178.0 200.0 221.0 135.6 157.8 181.6 139.8 163.9 188.6 179.0 199.3 219.5 160.0 185.7 211.0 202.5 225.2 250.0 −1.2 +15.4 32.6 207.8 231.8 257.0 249.8 273.8 299.2 142.0 164.0 187.0 208.3 227.4 245.8 128.5 151.4 175.0 173.3 196.2 220.0 155.9 179.5 202.0 122.7 146.0 169.5 168.3 190.2 212.0 178.8 202.8 227.0 253.2 277.1 301.0 169.8 194.2 219.0 90.0 109.8 130.0 123.9 142.5 161.0 50.0 70.3 90.3 −175.5 −168.8 −161.5 −22.1 −7.9 +6.8 163.5 184.2 204.0 202.3 227.4 253.0 24.0 40.0 57.8 −49.8 −37.2 −23.3 43.9 61.8 80.2 34.8 49.9 64.7 −32.4 −19.7 −6.3 149.3 172.0 195.5 212.4 238.5 266.5 151.4 174.7 199.5 183.2 204.5 225.5 159.0 180.7 204.0 −26.5 −11.9 +3.6 −13.8 +2.5 20.2 +4.9 21.6 38.5 94.9 113.5 131.7 94.3 85.6 64.3 55.7 181.6 109.8 148.1 −51.2 90.5 209.6 245.0 59.6 34.0 −26.0 199.0 103.2 232.8

111.0 102.0 83.1 73.6 202.9 129.8 170.0 −38.0 109.5 235.0 266.8 79.6 52.3 −11.3 222.5 122.6 257.0

127.5 119.0 102.3 92.6 224.0 150 193.0 −24.0 130.3 263.0 288.0 100.9 71.8 +4.5 246.5 143.0 282.0

Melting point, °C 130 −95.3 −51.6 −98.5 48.5 −13.2 170.3 115.5 79 −47 −2 −28.5

−146.7 44.5 48 33.5 −96.9 58 42.5 54.5 −59 15 −182.5 −121 102 −98.7 −102.7 −97.8 −93.5 −57 24 −12.5 15.4 −93 −135 −133 −56.9 −84.7 −84.7 −18 −40 −97.7 −31.9 33.4 −126.4 −142.4

−7.6

VAPOR PRESSURES

2-73

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Methyl n-dodecyl ketone (2-tetradecanone) Methylene bromide (dibromomethane) chloride (dichloromethane) Methyl ethyl ketone (2-butanone) 2-Methyl-3-ethylpentane 3-Methyl-3-ethylpentane Methyl fluoride formate α-Methylglutaric anhydride Methyl glycolate 2-Methylheptadecane 2-Methylheptane 3-Methylheptane 4-Methylheptane 2-Methyl-2-heptene 6-Methyl-3-hepten-2-ol 6-Methyl-5-hepten-2-ol 2-Methylhexane 3-Methylhexane Methyl iodide laurate levulinate methacrylate myristate α-naphthyl ketone (1-acetonaphthone) β-naphthyl ketone (2-acetonaphthone) n-nonyl ketone (undecan-2-one) palmitate n-pentadecyl ketone (2-heptdecanone) 2-Methylpentane 3-Methylpentane 2-Methyl-1-pentanol 2-Methyl-2-pentanol Methyl n-pentyl ketone (2-heptanone) phenyl ether (anisole) 2-Methylpropene Methyl propionate 4-Methylpropiophenone 2-Methylpropionyl bromide Methyl propyl ether n-propyl ketone (2-pentanone) isopropyl ketone (3-Methyl-2-butanone) 2-Methylquinoline Methyl salicylate α-Methyl styrene 4-Methyl styrene Methyl n-tetradecyl ketone (2-hexadecanone) thiocyanate isothiocyanate undecyl ketone (2-tridecanone) isovalerate Monovinylacetylene (butenyne) Myrcene Myristaldehyde Myristic acid (tetradecanoic acid) Naphthalene 1-Naphthoic acid 2-Naphthoic acid 1-Naphthol 2-Naphthol 1-Naphthylamine 2-Naphthylamine Nicotine 2-Nitroaniline 3-Nitroaniline 4-Nitroaniline 2-Nitrobenzaldehyde 3-Nitrobenzaldehyde Nitrobenzene Nitroethane Nitroglycerin Nitromethane 2-Nitrophenol 2-Nitrophenyl acetate

1

5

10

20

99.3 −35.1 −70.0 −48.3 −24.0 −23.9 −147.3 −74.2 93.8 +9.6 119.8 −21.0 −19.8 −20.4 −16.1 41.6 41.9 −40.4 −39.0

130.0 −13.2 −52.1 −28.0 −1.8 −1.4 −137.0 −57.0 125.4 33.7 152.0 +1.3 +2.6 +1.5 +6.7 65.0 66.0 −19.5 −18.1 −55.0 117.9 66.4 −10.0 145.7 146.3 152.3 95.5 166.8 161.6 −41.7 −39.8 38.0 +16.8 43.6 30.0 −96.5 −21.5 89.3 38.4 −54.3 +8.0 −1.0 104.0 81.6 34.0 42.0

145.5 −2.4 −43.3 −17.7 +9.5 +9.9 −131.6 −48.6 141.8 45.3 168.7 12.3 13.3 12.4 17.8 76.7 77.8 −9.1 −7.8 −45.8 133.2 79.7 +1.0 160.8 161.5 168.5 108.9 184.3 178.0 −32.1 −30.1 49.6 27.6 55.5 42.2 −81.9 −11.8 103.8 50.6 −45.4 17.9 +8.3 119.0 95.3 47.1 55.1

161.3 +9.7 −33.4 −6.5 21.7 22.3 −125.9 −39.2 157.7 58.1 186.0 24.4 25.4 24.5 30.4 89.3 90.4 +2.3 +3.6 −35.6 149.0 93.7 11.0 177.8 178.4 185.7 123.1 202.0 196.4 −21.4 −19.4 61.6 38.8 67.7 55.8 −73.4 −1.0 120.2 64.1 −35.4 28.5 18.3 134.0 110.0 61.8 69.2

179.8 23.3 −22.3 +6.0 35.2 36.2 −119.1 −28.7 177.5 72.3 204.8 37.9 38.9 38.0 44.0 102.7 104.0 14.9 16.4 −24.2 166.0 109.5 25.5 195.8 196.8 203.8 139.0

C16H32O C2H3NS C2H3NS C13H26O C6H12O2 C4H4 C10H16 C14H28O C14H28O2 C10H8 C11H8O2 C11H8O2 C10H8O C10H8O C10H9N C10H9N C10H14N2 C6H6N2O2 C6H6N2O2 C6H6N2O2 C7H5NO3 C7H5NO3 C6H5NO2 C2H5NO2 C3H5N3O9 CH3NO2 C6H5NO3 C8H7NO4

151.5 +9.8 −8.3 117.0 +2.9 −77.7 40.0 132.0 174.1 74.2 184.0 189.7 125.5 128.6 137.7 141.6 91.8 135.7 151.5 177.6 117.7 127.4 71.6 +1.5 167 −7.9 76.8 128.0

167.3 21.6 +5.4 131.8 14.0 −70.0 53.2 148.3 190.8 85.8 196.8 202.8 142.0 145.5 153.8 157.6 107.2 150.4 167.8 194.4 133.4 142.8 84.9 12.5 188 +2.8 90.4 142.0

184.6 34.5 20.4 147.8 26.4 −61.3 67.0 166.2 207.6 101.7 211.2 216.9 158.0 161.8 171.6 175.8 123.7 167.7 185.5 213.2 150.0 159.0 99.3 24.8 210 14.1 105.8 155.8

60

100

200

400

760

191.4 31.6 −15.7 14.0 43.9 45.0 −115.0 −21.9 189.9 81.8 216.3 46.6 47.6 46.6 52.8 111.5 112.8 23.0 24.5 −16.9 176.8 119.3 34.5 207.5 208.6 214.7 148.6

206.0 42.3 −6.3 25.0 55.7 57.1 −109.0 −12.9 205.0 93.7 231.5 58.3 59.4 58.3 64.6 122.6 123.8 34.1 35.6 −7.0 190.8 133.0 47.0 222.6 223.8 229.8 161.0

228.2 58.5 +8.0 41.6 73.6 75.3 −99.9 +0.8 229.1 111.8 254.5 76.0 77.1 76.1 82.3 139.5 140.0 50.8 52.4 +8.0

253.3 79.0 24.1 60.0 94.0 96.2 −89.5 16.0 255.5 131.7 279.8 96.2 97.4 96.3 102.2 156.6 156.6 69.8 71.6 25.3

278.0 98.6 40.7 79.6 115.6 118.3 −78.2 32.0 282.5 151.5 306.5 117.6 118.9 117.7 122.5 175.5 174.3 90.0 91.9 42.4

153.4 63.0 245.3 246.7 251.6 181.2

175.8 82.0 269.8 270.5 275.8 202.3

197.7 101.0 295.8 295.5 301.0 224.0

214.3 −9.7 −7.3 74.7 51.3 81.2 70.7 −63.8 +11.0 138.0 79.4 −24.3 39.8 29.6 150.8 126.2 77.8 85.0

226.7 −1.9 +0.1 83.4 58.8 89.8 80.1 −57.7 18.7 149.3 88.8 −17.4 47.3 36.2 161.7 136.7 88.3 95.0

242.0 +8.1 10.5 94.2 69.2 100.0 93.0 −49.3 29.0 164.2 101.6 −8.1 56.8 45.5 176.2 150.0 102.2 108.6

265.8 24.1 26.5 111.3 85.0 116.1 112.3 −36.7 44.2 187.4 120.5 +6.0 71.0 59.0 197.8 172.6 121.8 128.7

291.7 41.6 44.2 129.8 102.6 133.2 133.8 −22.2 61.8 212.7 141.7 22.5 86.8 73.8 211.7 197.5 143.0 151.2

319.5 60.3 63.3 147.9 121.2 150.2 155.5 −6.9 79.8 238.5 163.0 39.1 103.3 88.9 246.5 223.2 165.4 175.0

203.7 49.0 38.2 165.7 39.8 −51.7 82.6 186.0 223.5 119.3 225.0 231.5 177.8 181.7 191.5 195.7 142.1 186.0 204.2 234.2 168.8 177.7 115.4 38.0 235 27.5 122.1 172.8

215.0 58.1 47.5 176.6 48.2 −45.3 92.6 198.3 237.2 130.2 234.5 241.3 190.0 193.7 203.8 208.1 154.7 197.8 216.5 245.9 180.7 189.5 125.8 46.5 251 35.5 132.6 181.7

230.5 70.4 59.3 191.5 59.8 −37.1 106.0 214.5 250.5 145.5 245.8 252.7 206.0 209.8 220.0 224.3 169.5 213.0 232.1 261.8 196.2 204.3 139.9 57.8

254.4 89.8 77.5 214.0 77.3 −24.1 126.0 240.4 272.3 167.7 263.5 270.3 229.6 234.0 244.9 249.7 193.8 236.3 255.3 284.5 220.0 227.4 161.2 74.8

279.8 110.8 97.8 238.3 96.7 −10.1 148.3 267.9 294.6 193.2 281.4 289.5 255.8 260.6 272.2 277.4 219.8 260.0 280.2 310.2 246.8 252.1 185.8 94.0

307.0 132.9 119.0 262.5 116.7 +5.3 171.5 297.8 318.0 217.9 300.0 308.5 282.5 288.0 300.8 306.1 247.3 284.5 305.7 336.0 273.5 278.3 210.6 114.0

46.6 146.4 194.1

63.5 167.6 213.0

82.0 191.0 233.5

101.2 214.5 253.0

Temperature, °C

Formula C14H28O CH2Br2 CH2Cl2 C4H8O C8H18 C8H18 CH3F C2H4O2 C6H8O3 C3H6O3 C18H38 C8H18 C8H18 C8H18 C8H16 C8H16O C8H16O C7H16 C7H16 CH3I C13H26O2 C6H10O3 C5H8O2 C15H30O2 C12H10O C12H10O C11H22O C17H34O2 C17H34O C6H14 C6H14 C6H14O C6H14O C7H14O C7H8O C4H8 C4H8O2 C10H12O C4H7BrO C4H10O C5H10O C5H10O C10H9N C8H8O3 C9H10 C9H10

40

87.8 39.8 −30.5 115.0 115.6 120.2 68.2 134.3 129.6 −60.9 −59.0 15.4 −4.5 19.3 +5.4 −105.1 −42.0 59.6 13.5 −72.2 −12.0 −19.9 75.3 54.0 7.4 16.0 109.8 −14.0 −34.7 86.8 −19.2 −93.2 14.5 99.0 142.0 52.6 156.0 160.8 94.0 104.3 108.0 61.8 104.0 119.3 142.4 85.8 96.2 44.4 −21.0 127 −29.0 49.3 100.0

Melting point, °C −52.8 −96.7 −85.9 −114.5 −90 −99.8

−109.5 −120.8 −121.1

−118.2 −64.4 5 18.5 55.5 15 30 −154 −118 −103 −37.3 −140.3 −87.5

−77.8 −92 −1 −8.3 −23.2

−51 35.5 28.5

23.5 57.5 80.2 160.5 184 96 122.5 50 111.5 71.5 114 146.5 40.9 58 +5.7 −90 11 −29 45

(Continued )

2-74

PHYSICAL AnD CHEMICAL DATA

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name 1-Nitropropane 2-Nitropropane 2-Nitrotoluene 3-Nitrotoluene 4-Nitrotoluene 4-Nitro-1,3-xylene (4-nitro-m-xylene) Nonacosane Nonadecane n-Nonane 1-Nonanol 2-Nonanone Octacosane Octadecane n-Octane n-Octanol (1-octanol) 2-Octanone n-Octyl acrylate iodide (1-Iodooctane) Oleic acid Palmitaldehyde Palmitic acid Palmitonitrile Pelargonic acid Pentachlorobenzene Pentachloroethane Pentachloroethylbenzene Pentachlorophenol Pentacosane Pentadecane 1,3-Pentadiene 1,4-Pentadiene Pentaethylbenzene Pentaethylchlorobenzene n-Pentane iso-Pentane (2-methylbutane) neo-Pentane (2,2-dimethylpropane) 2,3,4-Pentanetriol 1-Pentene α-Phellandrene Phenanthrene Phenethyl alcohol (phenyl cellosolve) 2-Phenetidine Phenol 2-Phenoxyethanol 2-Phenoxyethyl acetate Phenyl acetate Phenylacetic acid Phenylacetonitrile Phenylacetyl chloride Phenyl benzoate 4-Phenyl-3-buten-2-one Phenyl isocyanate isocyanide Phenylcyclohexane Phenyl dichlorophosphate m-Phenylene diamine (1,3-phenylenediamine) Phenylglyoxal Phenylhydrazine N-Phenyliminodiethanol 1-Phenyl-1,3-pentanedione 2-Phenylphenol 4-Phenylphenol 3-Phenyl-1-propanol Phenyl isothiocyanate Phorone iso-Phorone Phosgene (carbonyl chloride) Phthalic anhydride Phthalide Phthaloyl chloride 2-Picoline Pimelic acid α-Pinene β-Pinene

1

5

10

20

−9.6 −18.8 50.0 50.2 53.7 65.6 234.2 133.2 +1.4 59.5 32.1 226.5 119.6 −14.0 54.0 23.6 58.5 45.8 176.5 121.6 153.6 134.3 108.2 98.6 +1.0 96.2

+13.5 +4.1 79.1 81.0 85.0 95.0 269.8 166.3 25.8 86.1 59.0 260.3 152.1 +8.3 76.5 48.4 87.7 74.8 208.5 154.6 188.1 168.3 126.0 129.7 27.2 130.0

25.3 15.8 93.8 96.0 100.5 109.8 286.4 183.5 38.0 99.7 72.3 277.4 169.6 19.2 88.3 60.9 102.0 90.0 223.0 171.8 205.8 185.8 137.4 144.3 39.8 148.0

194.2 91.6 −71.8 −83.5 86.0 90.0 −76.6 −82.9 −102.0 155.0 −80.4 20.0 118.2 58.2 67.0 40.1 78.0 82.6 38.2 97.0 60.0 48.0 106.8 81.7 10.6 12.0 67.5 66.7

230.0 121.0 −53.8 −66.2 120.0 123.8 −62.5 −65.8 −85.4 189.3 −63.3 45.7 154.3 85.9 94.7 62.5 106.6 113.5 64.8 127.0 89.0 75.3 141.5 112.2 36.0 37.0 96.5 95.9

248.2 135.4 −45.0 −57.1 135.8 140.7 −50.1 −57.0 −76.7 204.5 −54.5 58.0 173.0 100.0 108.6 73.8 121.2 128.0 78.0 141.3 103.5 89.0 157.8 127.4 48.5 49.7 111.3 110.0

37.9 28.2 109.6 112.8 117.7 125.8 303.6 200.8 51.2 113.8 87.2 295.4 187.5 31.5 101.0 74.3 117.8 105.9 240.0 190.0 223.8 204.2 149.8 160.0 53.9 166.0 192.2 266.1 150.2 −34.8 −47.7 152.4 158.1 −40.2 −47.3 −67.2 220.5 −46.0 72.1 193.7 114.8 123.7 86.0 136.0 144.5 92.3 156.0 119.4 103.6 177.0 143.8 62.5 63.4 126.4 125.9

51.8 41.8 126.3 130.7 136.0 143.3 323.2 220.0 66.0 129.0 103.4 314.2 207.4 45.1 115.2 89.8 135.6 123.8 257.2 210.0 244.4 223.8 163.7 178.5 69.9 186.2 211.2 285.6 167.7 −23.4 −37.0 171.9 178.2 −29.2 −36.5 −56.1 239.6 −34.1 87.8 215.8 130.5 139.9 100.1 152.2 162.3 108.1 173.6 136.3 119.8 197.6 161.3 77.7 78.3 144.0 143.4

C6H8N2 C8H6O2 C6H8N2 C10H15NO2 C11H12O2 C12H10O C12H10O C9H12O C7H5NS C9H14O C9H14O CCl2O C8H4O3 C8H6O2 C8H4Cl2O2 C6H7N C7H12O4 C10H16 C10H16

99.8 71.8 145.0 98.0 100.0

131.2 75.0 101.6 179.2 128.5 131.6

74.7 47.2 42.0 38.0 −92.9 96.5 95.5 86.3 −11.1 163.4 −1.0 +4.2

102.4 75.6 68.3 66.7 −77.0 121.3 127.7 118.3 +12.6 196.2 +24.6 30.0

147.0 87.8 115.8 195.8 144.0 146.2 176.2 116.0 89.8 81.5 81.2 −69.3 134.0 144.0 134.2 24.4 212.0 37.3 42.3

163.8 100.7 131.5 213.4 159.9 163.3 193.8 131.2 115.5 95.6 96.8 −60.3 151.7 161.3 151.0 37.4 229.3 51.4 58.1

182.5 115.5 148.2 233.0 178.0 180.3 213.0 147.4 122.5 111.3 114.5 −50.3 172.0 181.0 170.0 51.2 247.0 66.8 71.5

60

100

200

400

760

60.5 50.3 137.6 142.5 147.9 153.8 334.8 232.8 75.5 139.0 113.8 326.8 219.7 53.8 123.8 99.0 145.6 135.4 269.8 222.6 256.0 236.6 172.3 190.1 80.0 199.0 223.4 298.4 178.4 −16.5 −30.0 184.2 191.0 −22.2 −29.6 −49.0 249.8 −27.1 97.6 229.9 141.2 149.8 108.4 163.2 174.0 118.1 184.5 147.7 129.8 210.8 172.6 87.7 88.0 154.2 153.6

72.3 62.0 151.5 156.9 163.0 168.5 350.0 248.0 88.1 151.3 127.4 341.8 236.0 65.7 135.2 111.7 159.1 150.0 286.0 239.5 271.5 251.5 184.4 205.5 93.5 216.0 239.6 314.0 194.0 −6.7 −20.6 200.0 208.0 −12.6 −20.2 −39.1 263.5 −17.7 110.6 249.0 154.0 163.5 121.4 176.5 189.2 131.6 198.2 161.8 143.5 227.8 187.8 100.6 101.0 169.3 168.0

90.2 80.0 173.7 180.3 186.7 191.7 373.2 271.8 107.5 170.5 148.2 364.8 260.6 83.6 152.0 130.4 180.2 173.3 309.8 264.1 298.7 277.1 203.1 227.0 114.0 241.8 261.8 339.0 216.1 +8.0 −6.7 224.1 230.3 +1.9 −5.9 −23.7 284.5 −3.4 130.6 277.1 175.0 184.0 139.0 197.6 211.3 151.2 219.5 184.2 163.8 254.0 211.0 120.8 120.8 191.3 189.8

110.6 99.8 197.7 206.8 212.5 217.5 397.2 299.8 128.2 192.1 171.2 388.9 288.0 104.0 173.8 151.0 204.0 199.3 334.7 292.3 326.0 304.5 227.5 251.6 137.2 269.3 285.0 365.4 242.8 24.7 +8.3 250.2 257.2 18.5 +10.5 −7.1 307.0 +12.8 152.0 308.0 197.5 207.0 160.0 221.0 235.0 173.5 243.0 208.5 186.0 283.5 235.4 142.7 142.3 214.6 213.0

131.6 120.3 222.3 231.9 238.3 244.0 421.8 330.0 150.8 213.5 195.0 412.5 317.0 125.6 195.2 172.9 227.0 225.5 360.0 321.0 353.8 332.0 253.5 276.0 160.5 299.0 309.3 390.3 270.5 42.1 26.1 277.0 285.0 36.1 27.8 +9.5 327.2 30.1 175.0 340.2 219.5 228.0 181.9 245.3 259.7 195.9 265.5 233.5 210.0 314.0 261.0 165.6 165.0 240.0 239.5

194.0 124.2 158.7 245.3 189.8 192.2 225.3 156.8 133.3 121.4 125.6 −44.0 185.3 193.5 182.2 59.9 258.2 76.8 81.2

209.9 136.2 173.5 260.6 204.5 205.9 240.9 170.3 147.7 134.0 140.6 −35.6 202.3 210.0 197.8 71.4 272.0 90.1 94.0

233.0 153.8 195.4 284.5 226.7 227.9 263.2 191.2 169.6 153.5 163.3 −22.3 228.0 234.5 222.0 89.0 294.5 110.2 114.1

259.0 173.5 218.2 311.3 251.2 251.8 285.5 212.8 194.0 175.3 188.7 −7.6 256.8 261.8 248.3 108.4 318.5 132.3 136.1

285.5 193.5 243.5 337.8 276.5 275.0 308.0 235.0 218.5 197.2 215.2 +8.3 284.5 290.0 275.8 128.8 342.1 155.0 158.3

Temperature, °C

Formula C3H7NO2 C3H7NO2 C7H7NO2 C7H7NO2 C7H7NO2 C8H9NO2 C29H60 C19H40 C9H20 C9H20O C9H18O C28H58 C18H38 C8H18 C8H18O C8H16O C11H20O2 C8H17I C18H34O2 C16H32O C16H32O2 C16H31N C9H18O2 C6HCl5 C2HCl5 C8H5Cl5 C6HCl5O C25H52 C15H32 C5H8 C5H8 C16H26 C16H25Cl C5H12 C5H12 C5H12 C5H12O3 C5H10 C10H16 C14H10 C8H10O2 C8H11NO C6H6O C8H10O2 C10H12O3 C8H8O2 C8H8O2 C8H7N C8H7ClO C13H10O2 C10H10O C7H5NO C7H5N C12H16 C6H5Cl2O2P

40

Melting point, °C −108 −93 −4.1 15.5 51.9 +2 63.8 32 −53.7 −5 −19 61.6 28 −56.8 −15.4 −16 −45.9 14 34 64.0 31 12.5 85.5 −22 188.5 53.3 10

−129.7 −159.7 −16.6

99.5 40.6 11.6 −6.7 76.5 −23.8 70.5 41.5 +7.5 62.8 73 19.5 56.5 164.5 −21.0 28 −104 130.8 73 88.5 −70 103 −55

VAPOR PRESSURES TABLE 2-10

2-75

Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name

Piperidine Piperonal Propane Propenylbenzene Propionamide Propionic acid anhydride Propionitrile Propiophenone n-Propyl acetate iso-Propyl acetate n-Propyl alcohol (1-propanol) iso-Propyl alcohol (2-propanol) n-Propylamine Propylbenzene Propyl benzoate n-Propyl bromide (1-bromopropane) iso-Propyl bromide (2-bromopropane) n-Propyl n-butyrate isobutyrate iso-Propyl isobutyrate Propyl carbamate n-Propyl chloride (1-chloropropane) iso-Propyl chloride (2-chloropropane) iso-Propyl chloroacetate Propyl chloroglyoxylate Propylene Propylene glycol (1,2-Propanediol) Propylene oxide n-Propyl formate iso-Propyl formate 4,4′-iso-Propylidenebisphenol n-Propyl iodide (1-iodopropane) iso-Propyl iodide (2-iodopropane) n-Propyl levulinate iso-Propyl levulinate Propyl mercaptan (1-propanethiol) 2-iso-Propylnaphthalene iso-Propyl β-naphthyl ketone (2-isobutyronaphthone) 2-iso-Propylphenol 3-iso-Propylphenol 4-iso-Propylphenol Propyl propionate 4-iso-Propylstyrene Propyl isovalerate Pulegone Pyridine Pyrocatechol Pyrocaltechol diacetate (1,2-phenylene diacetate) Pyrogallol Pyrotartaric anhydride Pyruvic acid Quinoline iso-Quinoline Resorcinol Safrole Salicylaldehyde Salicylic acid Sebacic acid Selenophene Skatole Stearaldehyde Stearic acid Stearyl alcohol (1-octadecanol) Styrene Styrene dibromide [(1,2-dibromoethyl) benzene] Suberic acid Succinic anhydride Succinimide Succinyl chloride α-Terpineol Terpenoline

1

5

10

20

87.0 −128.9 17.5 65.0 4.6 20.6 −35.0 50.0 −26.7 −38.3 −15.0 −26.1 −64.4 6.3 54.6 −53.0 −61.8 −1.6 −6.2 −16.3 52.4 −68.3 −78.8 +3.8 9.7 −131.9 45.5 −75.0 −43.0 −52.0 193.0 −36.0 −43.3 59.7 48.0 −56.0 76.0

−7.0 117.4 −115.4 43.8 91.0 28.0 45.3 −13.6 77.9 −5.4 −17.4 +5.0 −7.0 −46.3 31.3 83.8 −33.4 −42.5 +22.1 +16.8 +5.8 77.6 −50.0 −61.1 28.1 32.3 −120.7 70.8 −57.8 −22.7 −32.7 224.2 −13.5 −22.1 86.3 74.5 −36.3 107.9

+3.9 132.0 −108.5 57.0 105.0 39.7 57.7 −3.0 92.2 +5.0 −7.2 14.7 +2.4 −37.2 43.4 98.0 −23.3 −32.8 34.0 28.3 17.0 90.0 −41.0 −52.0 40.2 43.5 −112.1 83.2 −49.0 −12.6 −22.7 240.8 −2.4 −11.7 99.9 88.0 −26.3 123.4

15.8 148.0 −100.9 71.5 119.0 52.0 70.4 +8.8 107.6 16.0 +4.2 25.3 12.7 −27.1 56.8 114.3 −12.4 −22.0 47.0 40.6 29.0 103.2 −31.0 −42.0 53.9 55.6 −104.7 96.4 −39.3 −1.7 −12.1 255.5 +10.0 0.0 114.0 102.4 −15.4 140.3

29.2 165.7 −92.4 87.7 134.8 65.8 85.6 22.0 124.3 28.8 17.0 36.4 23.8 −16.0 71.6 131.8 −0.3 −10.1 61.5 54.3 42.4 117.7 −19.5 −31.0 68.7 68.8 −96.5 111.2 −28.4 +10.8 −0.2 273.0 23.6 +13.2 130.1 118.1 −3.2 159.0

60

Melting point, °C

100

200

400

760

37.7 177.0 −87.0 97.8 144.3 74.1 94.5 30.1 135.0 37.0 25.1 43.5 30.5 −9.0 81.1 143.3 +7.5 −2.5 70.3 63.0 51.4 126.5 −12.1 −23.5 78.0 77.2 −91.3 119.9 −21.3 18.8 +7.5 282.9 32.1 21.6 140.6 127.8 +4.6 171.4

49.0 191.7 −79.6 111.7 156.0 85.8 107.2 41.4 149.3 47.8 35.7 52.8 39.5 +0.5 94.0 157.4 18.0 +8.0 82.6 73.9 62.3 138.3 −2.5 −13.7 90.3 88.0 −84.1 132.0 −12.0 29.5 17.8 297.0 43.8 32.8 154.0 141.8 15.3 187.6

66.2 214.3 −68.4 132.0 174.2 102.5 127.8 58.2 170.2 64.0 51.7 66.8 53.0 15.0 113.5 180.1 34.0 23.8 101.0 91.8 80.2 155.8 +12.2 +1.3 108.8 104.7 −73.3 149.7 +2.1 45.3 33.6 317.5 61.8 50.0 175.6 161.6 31.5 211.8

85.7 238.5 −55.6 154.7 194.0 122.0 146.0 77.7 194.2 82.0 69.8 82.0 67.8 31.5 135.7 205.2 52.0 41.5 121.7 112.0 100.0 175.8 29.4 18.1 128.0 123.0 −60.9 168.1 17.8 62.6 50.5 339.0 81.8 69.5 198.0 185.2 49.2 238.5

106.0 263.0 −42.1 179.0 213.0 141.1 167.0 97.1 218.0 101.8 89.0 97.8 82.5 48.5 159.2 231.0 71.0 60.0 142.7 133.9 120.5 195.0 46.4 36.5 148.6 150.0 −47.7 188.2 34.5 81.3 68.3 360.5 102.5 89.5 221.2 208.2 67.4 266.0

Temperature, °C

Formula C5H11N C8H6O3 C3H8 C9H10 C3H7NO C3H6O2 C6H10O3 C3H5N C9H10O C5H10O2 C5H10O2 C3H8O C3H8O C3H9N C9H12 C10H12O2 C3H7Br C3H7Br C7H14O2 C7H14O2 C7H14O2 C4H9NO2 C3H7Cl C3H7Cl C5H9ClO2 C5H7ClO3 C3H6 C3H8O2 C3H6O C4H8O2 C4H8O2 C15H16O2 C3H7I C3H7I C8H14O3 C8H14O3 C3H8S C13H14

40

C14H14O C9H12O C9H12O C9H12O C6H12O2 C11H14 C8H16O2 C10H16O C5H5N C6H6O2

133.2 56.6 62.0 67.0 −14.2 34.7 +8.0 58.3 −18.9

165.4 83.8 90.3 94.7 +8.0 62.3 32.8 82.5 +2.5 104.0

181.0 97.0 104.1 108.0 19.4 76.0 45.1 94.0 13.2 118.3

197.7 111.7 119.8 123.4 31.6 91.2 58.0 106.8 24.8 134.0

215.6 127.5 136.2 139.8 45.0 108.0 72.8 121.7 38.0 150.6

227.0 137.7 146.6 149.7 53.8 118.4 82.3 130.2 46.8 161.7

242.3 150.3 160.2 163.3 65.2 132.8 95.0 143.1 57.8 176.0

264.0 170.1 182.0 184.0 82.7 153.9 113.9 162.5 75.0 197.7

288.2 192.6 205.0 206.1 102.0 178.0 135.0 189.8 95.6 221.5

313.0 214.5 228.0 228.2 122.4 202.5 155.9 221.0 115.4 245.5

C10H10O4 C6H6O3 C5H6O3 C3H4O3 C9H7N C9H7N C6H6O2 C10H10O2 C7H6O2 C7H6O3 C10H18O4 C4H4Se C9H9N C18H36O C18H36O2 C18H36O C8H8

98.0 69.7 21.4 59.7 63.5 108.4 63.8 33.0 113.7 183.0 −39.0 95.0 140.0 173.7 150.3 −7.0

129.8 151.7 99.7 45.8 89.6 92.7 138.0 93.0 60.1 136.0 215.7 −16.0 124.2 174.6 209.0 185.6 +18.0

145.7 167.7 114.2 57.9 103.8 107.8 152.1 107.6 73.8 146.2 232.0 −4.0 139.6 192.1 225.0 202.0 30.8

161.8 185.3 130.0 70.8 119.8 123.7 168.0 123.0 88.7 156.8 250.0 +9.1 154.3 210.6 243.4 220.0 44.6

179.8 204.2 147.8 85.3 136.7 141.6 185.3 140.1 105.2 172.2 268.2 24.1 171.9 230.8 263.3 240.4 59.8

191.6 216.3 158.6 94.1 148.1 152.0 195.8 150.3 115.7 182.0 279.8 33.8 183.6 244.2 275.5 252.7 69.5

206.5 232.0 173.8 106.5 163.2 167.6 209.8 165.1 129.4 193.4 294.5 47.0 197.4 260.0 291.0 269.4 82.0

228.7 255.3 196.1 124.7 186.2 190.0 230.8 186.2 150.0 210.0 313.2 66.7 218.8 285.0 316.5 293.5 101.3

253.3 281.5 221.0 144.7 212.3 214.5 253.4 210.0 173.7 230.5 332.8 89.8 242.5 313.8 343.0 320.3 122.5

278.0 309.0 247.4 165.0 237.7 240.5 276.5 233.0 196.5 256.0 352.3 114.3 266.2 342.5 370.0 349.5 145.2

C8H8Br2 C8H14O4 C4H4O3 C4H5NO2 C4H4Cl2O2 C10H18O C10H16

86.0 172.8 92.0 115.0 39.0 52.8 32.3

115.6 205.5 115.0 143.2 65.0 80.4 58.0

129.8 219.5 128.2 157.0 78.0 94.3 70.6

145.2 238.2 145.3 174.0 91.8 109.8 84.8

161.8 254.6 163.0 192.0 107.5 126.0 100.0

172.2 265.4 174.0 203.0 117.2 136.3 109.8

186.3 279.8 189.0 217.4 130.0 150.1 122.7

207.8 300.5 212.0 240.0 149.3 171.2 142.0

230.0 322.8 237.0 263.5 170.0 194.3 163.5

254.0 345.5 261.0 287.5 192.5 217.5 185.0

−9 37 −187.1 −30.1 79 −22 −45 −91.9 21 −92.5 −127 −85.8 −83 −99.5 −51.6 −109.9 −89.0 −95.2

−122.8 −117 −185 −112.1 −92.9 −98.8 −90 −112

15.5 26 61 −76

−42 105 133 13.6 −15 24.6 110.7 11.2 −7 159 134.5 95 63.5 69.3 58.5 −30.6 142 119.6 125.5 17 35

(Continued )

2-76

PHYSICAL AnD CHEMICAL DATA

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name

Formula

1,1,1,2-Tetrabromoethane 1,1,2,2-Tetrabromoethane Tetraisobutylene Tetracosane 1,2,3,4-Tetrachlorobenzene 1,2,3,5-Tetrachlorobenzene 1,2,4,5-Tetrachlorobenzene 1,1,2,2-Tetrachloro-1,2-difluoroethane 1,1,1,2-Tetrachloroethane 1,1,2,2-Tetrachloroethane 1,2,3,5-Tetrachloro-4-ethylbenzene Tetrachloroethylene 2,3,4,6-Tetrachlorophenol 3,4,5,6-Tetrachloro-1,2-xylene Tetradecane Tetradecylamine Tetradecyltrimethylsilane Tetraethoxysilane 1,2,3,4-Tetraethylbenzene Tetraethylene glycol Tetraethylene glycol chlorohydrin Tetraethyllead Tetraethylsilane Tetralin 1,2,3,4-Tetramethylbenzene 1,2,3,5-Tetramethylbenzene 1,2,4,5-Tetramethylbenzene 2,2,3,3-Tetramethylbutane Tetramethylene dibromide (1,4-dibromobutane) Tetramethyllead Tetramethyltin Tetrapropylene glycol monoisopropyl ether Thioacetic acid (mercaptoacetic acid) Thiodiglycol (2,2′-thiodiethanol) Thiophene Thiophenol (benzenethiol) α-Thujone Thymol Tiglaldehyde Tiglic acid Tiglonitrile Toluene Toluene-2,4-diamine 2-Toluic nitrile (2-tolunitrile) 4-Toluic nitrile (4-tolunitrile) 2-Toluidine 3-Toluidine 4-Toluidine 2-Tolyl isocyanide 4-Tolylhydrazine Tribromoacetaldehyde 1,1,2-Tribromobutane 1,2,2-Tribromobutane 2,2,3-Tribromobutane 1,1,2-Tribromoethane 1,2,3-Tribromopropane Triisobutylamine Triisobutylene 2,4,6-Tritertbutylphenol Trichloroacetic acid Trichloroacetic anhydride Trichloroacetyl bromide 2,4,6-Trichloroaniline 1,2,3-Trichlorobenzene 1,2,4-Trichlorobenzene 1,3,5-Trichlorobenzene 1,2,3-Trichlorobutane 1,1,1-Trichloroethane 1,1,2-Trichloroethane Trichloroethylene Trichlorofluoromethane 2,4,5-Trichlorophenol 2,4,6-Trichlorophenol

C2H2Br4 C2H2Br4 C16H32 C24H50 C6H2Cl4 C6H2Cl4 C6H2Cl4 C2Cl4F2 C2H2Cl4 C2H2Cl4 C8H6Cl4 C2Cl4 C6H2Cl4O C8H6Cl4 C14H30 C14H31N C17H38Si C8H20O4Si C14H22 C8H18O5 C8H17ClO4 C8H20Pb C8H20Si C10H12 C10H14 C10H14 C10H14 C8H18 C4H8Br2 C4H12Pb C4H12Sn C15H32O5 C2H4O2S C4H10O2S C4H4S C6H6S C10H16O C10H14O C5H8O C5H8O2 C5H7N C7H8 C7H10N2 C8H7N C8H7N C7H9N C7H9N C7H9N C8H7N C7H10N2 C2HBr3O C4H7Br3 C4H7Br3 C4H7Br3 C2H3Br3 C3H5Br3 C12H27N C12H24 C18H30O C2HCl3O2 C4Cl6O3 C2BrCl3O C6H4Cl3N C6H3Cl3 C6H3Cl3 C6H3Cl3 C4H7Cl3 C2H3Cl3 C2H3Cl3 C2HCl3 CCl3F C6H3Cl3O C6H3Cl3O

1

5

10

20

58.0 65.0 63.8 183.8 68.5 58.2

83.3 95.5 93.7 219.6 99.6 89.0

95.7 110.0 108.5 237.6 114.7 104.1

108.5 126.0 124.5 255.3 131.2 121.6

−37.5 −16.3 −3.8 77.0 −20.6 100.0 94.4 76.4 102.6 120.0 16.0 65.7 153.9 110.1 38.4 −1.0 38.0 42.6 40.6 45.0 −17.4

−16.0 +7.4 +20.7 110.0 +2.4 130.3 125.0 106.0 135.8 150.7 40.3 96.2 183.7 141.8 63.6 +23.9 65.3 68.7 65.8 65.0 +3.2

−5.0 19.3 33.0 126.0 13.8 145.3 140.3 120.7 152.0 166.2 52.6 111.6 197.1 156.1 74.8 36.3 79.0 81.8 77.8 74.6 13.5

32.0 −29.0 −51.3 116.6 60.0 42.0 −40.7 18.6 38.3 64.3 −25.0 52.0 −25.5 −26.7 106.5 36.7 42.5 44.0 41.0 42.0 25.2 82.4 18.5 45.0 41.0 38.2 32.6 47.5 32.3 18.0 95.2 51.0 56.2 −7.4 134.0 40.0 38.4

58.8 −6.8 −31.0 147.8 87.7 96.0 −20.8 43.7 65.7 92.8 −1.6 77.8 −2.4 −4.4 137.2 64.0 71.3 69.3 68.0 68.2 51.0 110.0 45.0 73.5 69.0 66.0 58.0 75.8 57.4 44.0 126.1 76.0 85.3 +16.7 157.8 70.0 67.3 63.8 27.2 −32.0 −2.0 −22.8 −67.6 102.1 105.9

72.4 +4.4 −20.6 163.0 101.5 128.0 −10.9 56.0 79.3 107.4 +10.0 90.2 +9.2 +6.4 151.7 77.9 85.8 81.4 82.0 81.8 64.0 123.8 58.0 87.8 83.2 79.8 70.6 90.0 69.8 56.5 142.0 88.2 99.6 29.3 170.0 85.6 81.7 78.0 40.0 −21.9 +8.3 −12.4 −59.0 117.3 120.2

40

60

100

200

400

760

Temperature, °C

+0.5 −52.0 −24.0 −43.8 −84.3 72.0 76.5

+6.7 32.1 46.2 143.7 26.3 161.0 156.0 135.6 170.0 183.5 65.8 127.7 212.3 172.6 88.0 50.0 93.8 95.8 91.0 88.0 24.6

123.2 144.0 142.2 276.3 149.2 140.0 146.0 19.8 46.7 60.8 162.1 40.1 179.1 174.2 152.7 189.0 201.5 81.1 145.8 228.0 190.0 102.4 65.3 110.4 111.5 105.8 104.2 36.8

132.0 155.1 152.6 288.4 160.0 152.0 157.7 28.1 56.0 70.0 175.0 49.2 190.0 185.8 164.0 200.2 213.3 90.7 156.7 237.8 200.5 111.7 74.8 121.3 121.8 115.4 114.8 44.5

144.0 170.0 167.5 305.2 175.7 168.0 173.5 38.6 68.0 83.2 191.6 61.3 205.2 200.5 178.5 215.7 227.8 103.6 172.4 250.0 214.7 123.8 88.0 135.3 135.7 128.3 128.1 54.8

161.5 192.5 190.0 330.5 198.0 193.7 196.0 55.0 87.2 102.2 215.3 79.8 227.2 223.0 201.8 239.8 250.0 123.5 196.0 268.4 236.5 142.0 108.0 157.2 155.7 149.9 149.5 70.2

181.0 217.5 214.6 358.0 225.5 220.0 220.5 73.1 108.2 124.0 243.0 100.0 250.4 248.3 226.8 264.6 275.0 146.2 221.4 288.0 258.2 161.8 130.2 181.8 180.0 173.7 172.1 87.4

200.0 243.5 240.0 386.4 254.0 246.0 245.0 92.0 130.5 145.9 270.0 120.8 275.0 273.5 252.5 291.2 300.0 168.5 248.0 307.8 281.5 183.0 153.0 207.2 204.4 197.9 195.9 106.3

87.6 16.6 −9.3 179.8 115.8 165.0 0.0 69.7 93.7 122.6 23.2 103.8 22.1 18.4 167.9 93.0 101.7 95.1 96.7 95.8 78.2 138.6 72.1 103.2 98.6 94.6 84.2 105.8 83.0 70.0 158.0 101.8 114.3 42.1 182.6 101.8 97.2 93.7 55.0 −10.8 21.6 −1.0 −49.7 134.0 135.8

104.0 30.3 +3.5 197.7 131.8 210.0 +12.5 84.2 110.0 139.8 37.0 119.0 36.7 31.8 185.7 110.0 109.5 110.0 113.5 111.5 94.0 154.1 87.8 120.2 116.0 111.8 100.0 122.8 97.8 86.7 177.4 116.3 131.2 57.2 195.8 119.8 114.8 110.8 71.5 +1.6 35.2 +11.9 −39.0 151.5 152.2

115.1 39.2 11.7 209.0 142.0 240.5 20.1 93.9 120.2 149.8 45.8 127.8 46.0 40.3 196.2 120.8 130.0 119.8 123.8 121.5 104.0 165.0 97.5 131.6 127.0 122.2 110.0 134.0 107.3 96.7 188.0 125.9 141.8 66.7 204.5 131.5 125.7 121.8 82.0 9.5 44.0 20.0 −32.3 162.5 163.5

128.7 50.8 22.8 223.3 154.0 285 30.5 106.6 134.0 164.1 57.7 140.5 58.2 51.9 211.5 135.0 145.2 133.0 136.7 133.7 117.7 178.0 110.2 146.0 141.8 136.3 123.5 148.0 119.7 110.0 203.0 137.8 155.2 79.5 214.6 146.0 140.0 136.0 96.2 20.0 55.7 31.4 −23.0 178.0 177.8

149.8 68.8 39.8 245.0

173.8 89.0 58.5 268.3

197.5 110.0 78.0 292.7

46.5 125.8 154.2 185.5 75.4 158.0 77.8 69.5 232.8 156.0 167.3 153.0 157.6 154.0 137.8 198.0 130.0 167.8 163.5 157.8 143.5 170.0 138.0 130.2 226.2 155.4 176.2 98.4 229.8 168.2 162.0 157.7 118.0 36.2 73.3 48.0 −9.1 201.5 199.0

64.7 146.7 177.8 209.2 95.5 179.2 99.7 89.5 256.0 180.0 193.0 176.2 180.6 176.9 159.9 219.5 151.6 192.0 188.0 182.2 165.4 195.0 157.8 153.0 250.6 175.2 199.8 120.2 246.4 193.5 187.7 183.0 143.0 54.6 93.0 67.0 +6.8 226.5 222.5

84.4 168.0 201.0 231.8 116.4 198.5 122.0 110.6 280.0 205.2 217.6 199.7 203.3 200.4 183.5 242.0 174.0 216.2 213.8 206.5 188.4 220.0 179.0 179.0 276.3 195.6 223.0 143.0 262.0 218.5 213.0 208.4 169.0 74.1 113.9 86.7 23.7 251.8 246.0

Melting point, °C

51.1 46.5 54.5 139 26.5 −68.7 −36 −19.0 69.5 5.5

11.6 −136 −31.0 −6.2 −24.0 79.5 −102.2 −20 −27.5 −16.5 −38.3 51.5 64.5 −95.0 99 −13 29.5 −16.3 −31.5 44.5 65.5

−26 16.5 −22 57 78 52.5 17 63.5 −30.6 −36.7 −73 62 68.5

VAPOR PRESSURES

2-77

TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Tri-2-chlorophenylthiophosphate 1,1,1-Trichloropropane 1,2,3-Trichloropropane 1,1,2-Trichloro-1,2,2-trifluoroethane Tricosane Tridecane Tridecanoic acid Triethoxymethylsilane Triethoxyphenylsilane 1,2,4-Triethylbenzene 1,3,4-Triethylbenzene Triethylborine Triethyl camphoronate citrate Triethyleneglycol Triethylheptylsilane Triethyloctylsilane Triethyl orthoformate phosphate Triethylthallium Trifluorophenylsilane Trimethallyl phosphate 2,3,5-Trimethylacetophenone Trimethylamine 2,4,5-Trimethylaniline 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 1,3,5-Trimethylbenzene 2,2,3-Trimethylbutane Trimethyl citrate Trimethyleneglycol (1,3-propanediol) 1,2,4-Trimethyl-5-ethylbenzene 1,3,5-Trimethyl-2-ethylbenzene 2,2,3-Trimethylpentane 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 2,3,4-Trimethylpentane 2,2,4-Trimethyl-3-pentanone Trimethyl phosphate 2,4,5-Trimethylstyrene 2,4,6-Trimethylstyrene Trimethylsuccinic anhydride Triphenylmethane Triphenylphosphate Tripropyleneglycol Tripropyleneglycol monobutyl ether Tripropyleneglycol monoisopropyl ether Tritolyl phosphate Undecane Undecanoic acid 10-Undecenoic acid Undecan-2-ol n-Valeric acid iso-Valeric acid γ-Valerolactone Valeronitrile Vanillin Vinyl acetate 2-Vinylanisole 3-Vinylanisole 4-Vinylanisole Vinyl chloride (1-chloroethylene) cyanide (acrylonitrile) fluoride (1-fluoroethylene) Vinylidene chloride (1,1-dichloroethene) 4-Vinylphenetole 2-Xenyl dichlorophosphate 2,4-Xyaldehyde 2-Xylene (2-xylene) 3-Xylene (3-xylene) 4-Xylene (4-xylene) 2,4-Xylidine 2,6-Xylidine

1

5

10

20

188.2

217.2

231.2

246.7

261.7

−28.8 +9.0 −68.0 170.0 59.4 137.8 −1.5 71.0 46.0 47.9

−7.0 33.7 −49.4 206.3 98.3 166.3 +22.8 98.8 74.2 76.0

107.0 114.0 70.0 73.7 +5.5 39.6 +9.3 −31.0 93.7 79.0 −97.1 68.4 16.8 13.6 9.6

150.2 138.7 144.0 99.8 104.8 29.2 67.8 37.6 −9.7 131.0 108.0 −81.7 95.9 42.9 38.3 34.7

106.2 59.4 43.7 38.8 −29.0 −36.5 −25.8 −26.3 14.7 26.0 48.1 37.5 53.5 169.7 193.5 96.0 101.5 82.4 154.6 32.7 101.4 114.0 71.1 42.2 34.5 37.5 −6.0 107.0 −48.0 41.9 43.4 45.2 −105.6 −51.0 −149.3 −77.2 64.0 138.2 59.0 −3.8 −6.9 −8.1 52.6 44.0

146.2 87.2 71.2 67.0 −7.1 −15.0 −3.9 −4.1 36.0 53.7 77.0 65.7 82.6 188.4 230.4 125.7 131.6 112.4 184.2 59.7 133.1 142.8 99.0 67.7 59.6 65.8 +18.1 138.4 −28.0 68.0 69.9 72.0 −90.8 −30.7 −138.0 −60.0 91.7 171.1 85.9 +20.2 +16.8 +15.5 79.8 72.6

+4.2 46.0 −40.3 223.0 104.0 181.0 34.6 112.6 88.5 90.2 −148.0 166.0 144.0 158.1 114.6 120.6 40.5 82.1 51.7 +0.8 149.8 122.3 −73.8 109.0 55.9 50.7 47.4 −18.8 160.4 100.6 84.6 80.5 +3.9 −4.3 +6.9 +7.1 46.4 67.8 91.6 79.7 97.4 197.0 249.8 140.5 147.0 127.3 198.0 73.9 149.0 156.3 112.8 79.8 71.3 79.8 30.0 154.0 −18.0 81.0 83.0 85.7 −83.7 −20.3 −132.2 −51.2 105.6 187.0 99.0 32.1 28.3 27.3 93.0 87.0

16.2 59.3 −30.0 242.0 120.2 195.8 47.2 127.2 104.0 105.8 −140.6 183.6 171.1 174.0 130.3 137.7 53.4 97.8 67.7 12.3 169.8 137.5 −65.0 123.7 69.9 64.5 61.0 −7.5 177.2 115.5 99.7 96.0 16.0 +7.5 19.2 19.3 57.6 83.0 107.1 94.8 113.8 206.8 269.7 155.8 161.8 143.7 213.2 85.6 166.0 172.0 127.5 93.1 84.0 95.2 43.3 170.5 −7.0 94.7 97.2 100.0 −75.7 −9.0 −125.4 −41.7 120.3 205.0 114.0 45.1 41.1 40.1 107.6 102.7

29.9 74.0 −18.5 261.3 137.7 212.4 61.7 143.5 121.7 122.6 −131.4 201.8 190.4 191.3 148.0 155.7 67.5 115.7 85.4 25.4 192.0 154.2 −55.2 139.8 85.4 79.8 76.1 +5.2 194.2 131.0 106.0 113.2 29.5 20.7 33.0 32.9 69.8 100.0 124.2 111.8 131.0 215.5 290.3 173.7 179.8 161.4 229.7 104.4 185.6 188.7 143.7 107.8 98.0 101.9 57.8 188.7 +5.3 110.0 112.5 116.0 −66.8 +3.8 −118.0 −31.1 136.3 223.8 129.7 59.5 55.3 54.4 123.8 120.2

60

100

200

400

760

271.5

283.8

302.8

322.0

341.3

38.3 83.6 −11.2 273.8 148.2 222.0 70.4 153.2 132.2 133.4 −125.2 213.5 202.5 201.5 158.2 168.0 76.0 126.3 95.7 33.2 207.0 165.7 −48.8 149.5 95.3 89.5 85.8 13.3 205.5 141.1 126.3 123.8 38.1 29.1 41.8 41.6 77.3 110.0 135.5 122.3 142.2 221.2 305.2 184.6 190.2 173.2 239.8 115.2 197.2 199.5 153.7 116.6 107.3 122.4 66.9 199.8 13.0 119.8 122.3 126.1 −61.1 11.8 −113.0 −24.0 146.4 236.0 139.8 68.8 64.4 63.5 133.7 131.5

50.0 96.1 −1.7 289.8 162.5 236.0 82.7 167.5 146.8 147.7 −116.0 228.6 217.8 214.6 174.0 184.3 88.0 141.6 112.1 44.2 225.7 179.7 −40.3 162.0 108.8 102.8 98.9 24.4 219.6 153.4 140.3 137.9 49.9 40.7 53.8 53.4 87.6 124.0 149.8 136.8 156.5 228.4 322.5 199.0 204.4 187.8 252.2 128.1 212.5 213.5 167.2 128.3 118.9 136.5 78.6 214.5 23.3 132.3 135.3 139.7 −53.2 22.8 −106.2 −15.0 159.8 251.5 152.2 81.3 76.8 75.9 146.8 146.0

67.7 115.6 +13.5 313.5 185.0 255.2 101.0 188.0 168.3 168.3 −101.0 250.8 242.2 235.2 196.0 208.0 106.0 163.7 136.0 60.1 255.0 201.3 −27.0 182.3 129.0 122.7 118.6 41.2 241.3 172.8 160.3 158.4 67.8 58.1 72.0 71.3 102.2 145.0 171.8 157.8 179.8 239.7 349.8 220.2 224.4 209.7 271.8 149.3 237.8 232.8 187.7 146.0 136.2 157.7 97.7 237.3 38.4 151.0 154.0 159.0 −41.3 38.7 −95.4 −1.0 180.0 275.3 172.3 100.2 95.5 94.6 166.4 168.0

87.5 137.0 30.2 339.8 209.4 276.5 121.8 210.5 193.7 193.2 −81.0 276.0 267.5 256.6 221.0 235.0 125.7 187.0 163.5 78.7 288.5 224.3 −12.5 203.7 152.0 145.4 141.0 60.4 264.2 193.8 184.5 183.5 88.2 78.0 92.7 91.8 118.4 167.8 196.1 182.3 205.5 249.8 379.2 244.3 247.0 232.8 292.7 171.9 262.8 254.0 209.8 165.0 155.2 182.3 118.7 260.0 55.5 172.1 175.8 182.0 −28.0 58.3 −84.0 +14.8 202.8 301.5 194.1 121.7 116.7 115.9 188.3 193.7

108.2 158.0 47.6 366.5 234.0 299.0 143.5 233.5 218.0 217.5 −56.2 301.0 294.0 278.3 247.0 262.0 146.0 211.0 192.1 98.3 324.0 247.5 +2.9 234.5 176.1 169.2 164.7 80.9 287.0 214.2 208.1 208.0 109.8 99.2 114.8 113.5 135.0 192.7 221.2 207.0 231.0 259.2 413.5 267.2 269.5 256.6 313.0 195.8 290.0 275.0 232.0 184.4 175.1 207.5 140.8 285.0 72.5 194.0 197.5 204.5 −13.8 78.5 −72.2 31.7 225.0 328.5 215.5 144.4 139.1 138.3 211.5 217.9

Temperature, °C

Formula C18H12Cl3O3 PS C3H5Cl3 C3H5Cl3 C2Cl3F3 C23H48 C13H28 C13H26O2 C7H18O3Si C12H20O3Si C12H18 C12H18 C6H15B C15H26O6 C12H20O7 C6H14O4 C13H30Si C14H32Si C7H16O3 C6H15O4P C6H15Tl C6H5F3Si C12H21PO4 C11H14O C3H9N C9H13N C9H12 C9H12 C9H12 C7H16 C9H14O7 C3H8O2 C11H16 C11H16 C8H18 C8H18 C8H18 C8H18 C8H16O C3H9O4P C11H14 C11H14 C7H10O3 C19H16 C18H15O4P C9H20O4 C13H28O4 C12H26O4 C21H21O4P C11H24 C11H22O2 C11H20O2 C11H24O C5H10O2 C5H10O2 C5H8O2 C5H9N C8H8O3 C4H6O2 C9H10O C9H10O C9H10O C2H3Cl C3H3N C2H3F C2H2Cl2 C10H12O C12H9Cl2PO C9H10O C8H10 C8H10 C8H10 C8H11N C8H11N

40

Melting point, °C

−77.7 −14.7 −35 47.7 −6.2 41

135

−63.0

−117.1 67 −25.5 −44.1 −44.8 −25.0 78.5

−112.3 −107.3 −101.5 −109.2

93.4 49.4

−25.6 29.5 24.5 −34.5 −37.6 81.5

−153.7 −82 −160.5 −122.5 75 −25.2 −47.9 +13.3

2-78

PHYSICAL AnD CHEMICAL DATA

VAPOR PRESSURES OF SOLUTIOnS TABLE 2-11 Partial Pressures of Water over Aqueous Solutions of HCl* log10 pmm = A − B/T, (T in K), which, however, agrees only approximately with the table. The table is more nearly correct. Partial pressure of H2O, mmHg, °C % HCl

A

B

0°

5°

10°

15°

20°

25°

30°

35°

40°

45°

50°

60°

6 10 14 18 20

8.99156 8.99864 8.97075 8.98014 8.97877

2282 2295 2300 2323 2334

4.18 3.84 3.39 2.87 2.62

6.04 5.52 4.91 4.21 3.83

8.45 7.70 6.95 5.92 5.40

11.7 10.7 9.65 8.26 7.50

15.9 14.6 13.1 11.3 10.3

21.8 20.0 18.0 15.4 14.1

29.1 26.8 24.1 20.6 19.0

39.4 35.5 31.9 27.5 25.1

50.6 47.0 42.1 36.4 33.3

66.2 61.5 55.3 47.9 43.6

86.0 80.0 72.0 62.5 57.0

139 130 116 102 93.5

22 24 26 28 30

9.02708 8.96022 9.01511 8.97611 9.00117

2363 2356 2390 2395 2422

2.33 2.05 1.76 1.50 1.26

3.40 3.04 2.60 2.24 1.90

4.82 4.31 3.71 3.21 2.73

6.75 6.03 5.21 4.54 3.88

9.30 8.30 7.21 6.32 5.41

12.6 11.4 9.95 8.75 7.52

17.1 15.4 13.5 11.8 10.2

22.8 20.4 18.0 15.8 13.7

30.2 27.1 24.0 21.1 18.4

39.8 35.7 31.7 27.9 24.3

52.0 46.7 41.5 36.5 32.0

32 34 36 38 40 42

9.03317 9.07143 9.11815 9.20783 9.33923 9.44953

2453 2487 2526 2579 2647 2709

1.04 0.85 0.68 0.53 0.41 0.31

1.57 1.29 1.03 0.81 0.63 0.48

2.27 1.87 1.50 1.20 0.94 0.72

3.25 2.70 2.19 1.75 1.37 1.06

4.55 3.81 3.10 2.51 2.00 1.56

6.37 5.35 4.41 3.60 2.88 2.30

11.7 9.95 8.33 6.92 5.68 4.60

15.7 13.5 11.4 9.52 7.85 6.45

21.0 18.1 15.4 13.0 10.7 8.90

27.7 24.0 20.4 17.4 14.5 12.1

8.70 7.32 6.08 5.03 4.09 3.28

70°

80°

90°

100° 110°

220 204 185 162 150

333 310 273 248 230

492 463 425 374 345

715 677 625 550 510

960 892 783 729

85.6 77.0 69.0 60.7 53.5

138 124 112 99.0 87.5

211 194 173 154 136

317 290 261 234 207

467 426 387 349 310

670 611 555 499 444

46.5 40.5 34.8 29.6 25.0 21.2

76.5 66.5 57.0 49.1 42.1 35.8

120 104 90.0 77.5 67.3 57.2

184 161 140 120 105 89.2

275 243 212 182 158 135

396 355 311 266 230 195

∗Uncertainty, ca. 2 percent for solutions of 15 to 30 percent HCl between 0 and 100°; for solutions of > 30 percent HCl the accuracy is ca. 5 percent at the lower temperatures and ca. 15 percent at the higher temperatures. Below 15 percent HCl, the uncertainty is ca. 5 percent at the lower temperatures and higher strengths to ca. 15 to 20 percent at the lower strengths and perhaps 15 to 20 percent at the higher temperatures and lower strengths. International Critical Tables, vol. 3, p. 301.

FIG. 2-1 Vapor pressures of H3PO4 aqueous: partial pressure of H2O vapor. (Courtesy of Victor Chemical Works, Stauffer Chemical Company; measurements by W. H. Woodstock.)

VAPOR PRESSURES OF SOLUTIOnS

2-79

TABLE 2-12 Water Partial Pressure, Bar, over Aqueous Sulfuric Acid Solutions* Weight percent, H2SO4 °C 0 10 20 30 40 50 60 70 80 90

10.0

20.0

.582E−02 .117E−01 .223E−01 .404E−01 .703E−01 .117 .189 .296 .449 .664

.534E−02 .107E−01 .205E−01 .373E−01 .649E−01 .109 .175 .275 .417 .617

30.0 .448E−02 .909E−02 .174E−01 .319E−01 .558E−01 .939E−01 .152 .239 .365 .542

40.0 .326E−02 .670E−02 .130E−01 .241E−01 .427E−01 .725E−01 .119 .188 .290 .434

50.0

60.0

70.0

75.0

80.0

85.0

.193E−02 .405E−02 .802E−02 .151E−01 .272E−01 .470E−01 .782E−01 .126 .196 .298

.836E−03 .180E−02 .367E−02 .710E−02 .131E−01 .232E−01 .395E−01 .651E−01 .104 .161

.207E−03 .467E−03 .995E−03 .201E−02 .387E−02 .715E−02 .127E−01 .217E−01 .360E−01 .578E−01

.747E−04 .175E−03 .388E−03 .811E−03 .162E−02 .309E−02 .565E−02 .997E−02 .170E−01 .281E−01

.197E−04 .490E−04 .115E−04 .253E−03 .531E−03 .106E−02 .204E−02 .376E−02 .668E−02 .115E−01

.343E−05 .952E−05 .245E−04 .589E−04 .133E−03 .286E−03 .584E−03 .114E−02 .213E−02 .383E−02

.905E−01 .138 .206 .301 .481 .605 .837 1.138 1.525 2.017

.452E−01 .708E−01 .108 .162 .236 .339 .478 .662 .902 1.212

.192E−01 .312E−01 .493E−01 .760E−01 .115 .170 .246 .350 .489 .673

.666E−02 .112E−01 .183E−01 .291E−01 .451E−01 .682E−01 .101 .147 .208 .291

100 110 120 130 140 150 160 170 180 190

.957 1.349 1.863 2.524 3.361 4.404 5.685 7.236 9.093 11.289

.891 1.258 1.740 2.361 3.149 4.132 5.342 6.810 8.571 10.658

.786 1.113 1.544 2.101 2.810 3.697 4.793 6.127 7.731 9.640

.634 .904 1.264 1.732 2.333 3.090 4.031 5.185 6.584 8.259

.441 .638 .903 1.253 1.708 2.289 3.021 3.930 5.045 6.397

.244 .360 .519 .734 1.020 1.392 1.870 2.475 3.233 4.169

200 210 220 230 240 250 260 270 280 290

13.861 16.841 20.264 24.160 28.561 33.494 38.984 45.055 51.726 59.015

13.107 15.951 19.225 22.960 27.188 31.939 37.240 43.116 49.590 56.681

11.887 14.505 17.529 20.992 24.927 29.364 34.334 39.865 45.984 52.715

10.245 12.576 15.287 18.414 21.992 26.056 30.642 35.784 41.514 47.865

8.020 9.948 12.217 14.864 17.929 21.452 25.472 30.030 35.168 40.926

5.312 6.696 8.354 10.322 12.641 15.351 18.496 22.121 26.274 31.003

2.632 3.395 4.331 5.466 6.831 8.458 10.382 12.640 15.269 18.311

1.606 2.101 2.714 3.467 4.381 5.480 6.788 8.333 10.142 12.242

.913 1.220 1.609 2.096 2.699 3.435 4.326 5.395 6.663 8.155

.401 .542 .724 .952 1.237 1.587 2.012 2.525 3.136 3.857

300 310 320 330 340 350

66.934 75.495 84.705 94.567 105.083 116.251

64.407 72.781 81.816 91.518 101.894 112.946

60.081 68.100 76.792 86.172 96.252 107.043

54.868 62.553 70.947 80.077 89.969 100.646

47.346 54.470 62.337 70.988 80.463 90.802

36.360 42.395 49.164 56.721 65.123 74.426

21.808 25.804 30.343 35.473 41.240 47.692

14.665 17.438 20.591 24.153 28.154 32.622

9.897 11.912 14.227 16.867 19.855 23.217

4.701 5.680 6.806 8.093 9.551 11.193

Weight percent, H2SO4 °C

90.0

92.0

94.0

96.0

97.0

99.0

99.5

100.0

0 10 20 30 40 50 60 70 80 90

.518E−06 .159E−05 .448E−05 .117E−04 .285E−04 .652E−04 .141E−03 .290E−03 .569E−03 .107E−02

.242E−06 .762E−06 .220E−05 .587E−05 .146E−04 .341E−04 .754E−04 .158E−03 .316E−03 .606E−03

.107E−06 .344E−06 .101E−05 .275E−05 .696E−05 .166E−04 .372E−04 .795E−04 .162E−03 .315E−03

.401E−07 .130E−06 .390E−06 .108E−05 .278E−05 .672E−05 .154E−04 .334E−04 .691E−04 .137E−03

.218E−07 .713E−07 .215E−06 .598E−06 .155E−05 .379E−05 .875E−05 .192E−04 .400E−04 .801E−04

.980E−08 .323E−07 .978E−07 .275E−06 .720E−06 .177E−05 .413E−05 .912E−05 .192E−04 .388E−04

.569E−08 .188E−07 .572E−07 .161E−06 .424E−06 .105E−05 .245E−05 .544E−05 .115E−04 .234E−04

.268E−08 .888E−08 .271E−07 .766E−07 .202E−06 .503E−06 .118E−05 .263E−05 .559E−05 .114E−04

.775E−09 .258E−08 .789E−08 .224E−07 .595E−07 .149E−06 .350E−06 .784E−06 .168E−05 .343E−05

.196E−09 .655E−09 .201E−08 .575E−08 .153E−07 .384E−07 .910E−07 .205E−06 .439E−06 .903E−06

100 110 120 130 140 150 160 170 180 190

.194E−02 .338E−02 .571E−02 .938E−02 .150E−01 .233E−01 .354E−01 .526E−01 .766E−01 .110

.112E−02 .198E−02 .341E−02 .569E−02 .923E−02 .146E−01 .225E−01 .340E−01 .502E−01 .729E−01

.590E−03 .107E−02 .186E−02 .315E−02 .519E−02 .832E−02 .130E−01 .199E−01 .298E−01 .438E−01

.261E−03 .479E−03 .851E−03 .146E−02 .245E−02 .399E−02 .633E−02 .983E−02 .149E−01 .222E−01

.154E−03 .285E−03 .511E−03 .886E−03 .149E−02 .245E−02 .393E−02 .614E−02 .941E−02 .141E−01

.752E−04 .141E−03 .254E−03 .445E−03 .757E−03 .125E−02 .202E−02 .319E−02 .492E−02 .744E−02

.455E−04 .855E−04 .155E−03 .278E−03 .467E−03 .776E−03 .126E−02 .199E−02 .309E−02 .469E−02

.223E−04 .420E−04 .766E−04 .135E−03 .232E−03 .387E−03 .629E−03 .999E−03 .155E−02 .236E−02

.674E−05 .128E−04 .233E−04 .414E−04 .711E−04 .119E−03 .194E−03 .309E−03 .482E−03 .735E−03

.178E−05 .339E−05 .623E−05 .111E−04 .191E−04 .321E−04 .526E−04 .840E−04 .131E−03 .201E−03

.631E−01 .894E−01 .125 .171 .232 .310 .409 .534 .689 .880

.325E−01 .467E−01 .660E−01 .918E−01 .126 .170 .227 .300 .391 .505

.208E−01 .300E−01 .427E−01 .598E−01 .825E−01 .112 .151 .200 .263 .341

.110E−01 .161E−01 .230E−01 .325E−01 .451E−01 .618E−01 .835E−01 .111 .147 .192

.698E−02 .102E−01 .147E−01 .208E−01 .290E−01 .398E−01 .540E−01 .723E−01 .957E−01 .125

.352E−02 .516E−02 .743E−02 .105E−01 .147E−01 .202E−01 .274E−01 .366E−01 .485E−01 .634E−01

.110E−02 .161E−02 .232E−02 .329E−02 .460E−02 .633E−02 .858E−02 .115E−01 .152E−01 .199E−01

.300E−03 .442E−03 .638E−03 .906E−03 .127E−02 .174E−02 .237E−02 .317E−02 .420E−02 .548E−02

.248 .316 .400 .502 .624 .770

.162 .208 .264 .331 .413 .511

.820E−01 .105 .133 .167 .208 .256

.257E−01 .328E−01 .415E−01 .520E−01 .646E−01 .795E−01

.708E−02 .905E−02 .114E−01 .143E−01 .178E−01 .218E−01

200 210 220 230 240 250 260 270 280 290

.154 .213 .290 .389 .514 .673 .870 1.112 1.407 1.763

.104 .146 .201 .273 .366 .485 .635 .822 1.052 1.335

300 310 320 330 340 350

2.190 2.696 3.292 3.990 4.801 5.738

1.676 2.088 2.578 3.159 3.843 4.641

1.112 1.394 1.732 2.133 2.608 3.164

.646 .817 1.025 1.274 1.571 1.922

.437 .556 .701 .875 1.083 1.331

98.0

98.5

∗Vermeulen, Dong, Robinson, Nguyen, and Gmitro, AIChE meeting, Anaheim, Calif., 1982; and private communication from Prof. Theodore Vermeulen, Chemical Engineering Dept., University of California, Berkeley.

2-80

PHYSICAL AnD CHEMICAL DATA TABLE 2-13 Partial Vapor Pressure of Sulfur Dioxide over Water, mmHg g SO2 / 100 g H2O

Temperature, °C 0

10

0.01 0.05 0.10 0.15 0.20

0.02 0.38 1.15 2.10 3.17

0.04 0.66 1.91 3.44 5.13

0.25 0.30 0.40 0.50 1.00

4.34 5.57 8.17 10.9 25.8

6.93 8.84 12.8 17.0 39.5

2.00 3.00 4.00 5.00 6.00 8.00 10.00 15.00 20.00

20 0.07 1.07 3.03 5.37 7.93 10.6 13.5 19.4 25.6 58.4

30

40

50

60

90

120

0.12 1.68 4.62 8.07 11.8

0.19 2.53 6.80 11.7 17.0

0.29 3.69 9.71 16.5 23.8

0.43 5.24 13.5 22.7 32.6

1.21 12.9 31.7 52.2 73.7

2.82 27.0 63.9 104 145

15.7 19.8 28.3 37.1 83.7

58.6 93.2 129 165 202

88.5 139 192 245 299

129 202 277 353 430

183 285 389 496 602

275 351 542 735

407 517 796

585 741

818

22.5 28.2 40.1 52.3 117

31.4 39.2 55.3 72.0 159

42.8 53.3 74.7 96.8 212

95.8 118 164 211 454

253 393 535 679 824

342 530 720

453 700

955

186 229 316 404 856

Condensed from Rabe, A. E. and Harris, J. F., J. Chem. Eng. Data, 8 (3), 333–336, 1963. Copyright © American Chemical Society and reproduced by permission of the copyright owner.

TABLE 2-14 Partial Pressures of HnO3 and H2O over Aqueous Solutions of HnO3* mmHg Percentages are weight % HNO3 in solution. 20% °C

HNO3

25% H2O

HNO3

30% H2O

HNO3

35% H2O

0 5 10 15 20

4.1 5.7 8.0 10.9 15.2

3.8 5.4 7.6 10.3 14.2

3.6 5.0 7.1 9.7 13.2

25 30 35 40 45

20.6 27.6 36.5 47.5 62

19.2 25.7 33.8 44 57.5

17.8 23.8 31.1 41 53

0.09

0.11 .17

HNO3

40% H2O

HNO3

3.3 4.6 6.5 8.9 12.0 0.09 .13 .20 .28

16.2 21.7 28.3 37.7 48

0.12 .17 .25 .36 .52

45% H2O

50%

HNO3

H2O

HNO3

H2O

3.0 4.2 5.8 8.0 10.8

0.10 .15

2.6 3.6 5.0 6.9 9.4

0.12 .18 .27

2.1 3.0 4.2 5.8 7.9

14.6 19.5 25.5 33.5 43

.23 .33 .48 .68 .96

12.7 16.9 22.3 29.3 38.0

.39 .56 .80 1.13 1.57

10.7 14.4 19.0 25.0 32.5

49.5 62.5 80 100 126

2.18 2.95 4.05 5.46 7.25

42.5 54 70 88 110

50 55 60 65 70

0.09 .13 .19 .27

80 100 128 162 200

.13 .18 .28 .40 .54

75 94 121 151 187

.25 .35 .51 .71 1.00

69 87 113 140 174

.42 .59 .85 1.18 1.63

63 79 102 127 159

.75 1.04 1.48 2.05 2.80

56 71 90 114 143

1.35 1.83 2.54 3.47 4.65

75 80 85 90 95

.38 .53 .74 1.01 1.37

250 307 378 458 555

.77 1.05 1.44 1.95 2.62

234 287 352 426 517

1.38 1.87 2.53 3.38 4.53

217 267 325 393 478

2.26 3.07 4.15 5.50 7.32

198 243 297 359 436

3.80 5.10 6.83 9.0 11.7

178 218 268 325 394

6.20 8.15 10.7 13.7 17.8

158 195 240 292 355

9.6 12.5 16.3 20.9 26.8

138 170 211 258 315

6.05 7.90

580 690

530 631 755

15.5 20.0 25.7 32.5

480 573 688 810

23.0 29.2 37.0 46

430 520 625 740

34.2 43.0 54.5 67 84

383 463 560 665 785

100 1.87 675 3.50 628 105 2.50 800 4.65 745 110 115 120 ∗International Critical Tables, vol. 3, pp. 304–305.

9.7 12.7 16.5

(Continued )

VAPOR PRESSURES OF SOLUTIOnS

2-81

TABLE 2-14 Partial Pressures of HnO3 and H2O over Aqueous Solutions of HnO3 (Continued ) mmHg Percentages are weight % HNO3 in solution. 55% °C

60%

65%

70%

80%

HNO3

H2O

HNO3

H2O

HNO3

H2O

HNO3

H2O

0 5 10 15 20

0.14 .21 .31 .45

1.8 2.5 3.5 4.9 6.7

0.19 .28 .41 .59 .84

1.5 2.1 3.0 4.1 5.6

0.41 .60 .86 1.21 1.68

1.3 1.8 2.6 3.5 4.9

0.79 1.12 1.58 2.18 3.00

1.1 1.6 2.2 3.0 4.1

25 30 35 40 45

.66 .93 1.30 1.82 2.50

9.1 12.2 16.1 21.3 28.0

1.21 1.66 2.28 3.10 4.20

7.7 10.3 13.6 18.1 23.7

2.32 3.17 4.26 5.70 7.55

6.6 8.8 11.6 15.5 20.0

4.10 5.50 7.30 9.65 12.6

5.5 7.4 9.8 12.8 16.7

50 55 60 65 70

3.41 4.54 6.15 8.18 10.7

36.3 46 60 76 95

5.68 7.45 9.9 13.0 16.8

31 39 51 64 81

10.0 12.8 16.8 21.7 27.5

26.0 33.0 43.0 54.5 68

16.5 21.0 27.1 34.5 43.3

21.8 27.3 35.3 44.5 56

75 80 85 90 95

13.9 18.0 23.0 29.4 37.3

120 148 182 223 272

21.8 27.5 34.8 43.7 55.0

102 126 156 192 233

35.0 43.5 54.5 67.5 83.5

100 105 110 115 120 125

47 58.5 73 90 110

331 400 485 575 685

69.5 84.5 103 126 156 187

285 345 417 495 590 700

103 124 152 181 218 260

HNO3

90%

100%

H 2O

HNO3

H 2O

2 3 4 6 8

1.2 1.7 2.4

5.5 8 11 15 20

10.5 14 18.5 24.5 32

3.2 4 5.5 7 9.5

27 36 47 62 80

1 1.3 1.8 2.4 3

57 77 102 133 170

11 15 22 30 42

41 52 67 85 106

12 15 20 25 31

103 127 157 192 232

4 5 6.5 8 10

215 262 320 385 460 540 625 720 820

86 106 131 160 195

54.5 67.5 83 103 125

70 86 107 130 158

130 158 192 230 278

38 48 60 73 89

282 338 405 480 570

13 16 20 24 29

238 288 345 410 490 580

152 183 221 262 312 372

192 231 278 330 393 469

330 392 465 545 640

108 129 155 185 219

675 790

35 42

TABLE 2-15 Total Vapor Pressures of Aqueous Solutions of CH3COOH* Percentages of weight % acetic acid in the solution mmHg °C

25%

50%

75%

20 25 30 35 40

16.3 22.1 29.6 39.4 51.7

15.7 21.4 28.8 38.3 50.2

15.3 20.8 27.8 36.6 48.1

45 50 55 60 65

67.0 87.2 110 141 178

65.0 85.0 107 138 172

62.0 80.1 102 130 162

70 75 80 85 90

223 277 342 419 510

216 269 331 407 497

203 251 310 376 458

95 100

618 743

602 725

550 666

∗International Critical Tables, vol. 3, p. 306.

HNO3

2-82 TABLE 2-16 Partial Pressure of H2O over Aqueous Solutions of nH3 (psia) Liquid mole percent NH3 (liquid weight percent NH3) 0

5

10

15

(0)

(4.74)

(9.5)

(14.29)

32 40 50 60 70

0.089 0.122 0.178 0.256 0.363

0.083 0.115 0.168 0.242 0.343

0.077 0.106 0.156 0.225 0.320

0.071 0.097 0.143 0.207 0.294

80 90 100 110 120

0.507 0.699 0.951 1.277 1.695

0.479 0.661 0.899 1.209 1.607

0.448 0.618 0.843 1.135 1.510

130 140 150 160 170

2.226 2.893 3.723 4.747 6.000

2.112 2.748 3.540 4.519 5.717

180 190 200 210 220

7.520 9.350 11.538 14.136 17.201

230 240 250

20.796 24.986 29.844

t, °F

20

25

30

35

40

45

80

85

90

(23.94)

(28.81)

(33.71)

(38.64)

(43.59)

(48.57)

(53.58)

(58.62)

(63.69)

(68.79)

(73.91)

(79.07)

(84.26)

(89.47)

(94.72)

0.063 0.087 0.129 0.186 0.266

0.055 0.077 0.113 0.164 0.235

0.047 0.065 0.097 0.142 0.204

0.039 0.054 0.081 0.119 0.172

0.031 0.044 0.066 0.098 0.143

0.025 0.035 0.053 0.079 0.116

0.019 0.027 0.041 0.062 0.093

0.014 0.021 0.032 0.049 0.073

0.011 0.016 0.025 0.038 0.058

0.008 0.012 0.019 0.030 0.045

0.006 0.009 0.014 0.023 0.036

0.004 0.007 0.011 0.018 0.028

0.003 0.005 0.008 0.014 0.022

0.002 0.004 0.006 0.010 0.016

0.002 0.002 0.004 0.007 0.011

0.001 0.001 0.002 0.004 0.006

0.413 0.571 0.780 1.052 1.402

0.374 0.518 0.710 0.960 1.283

0.332 0.462 0.634 0.861 1.154

0.289 0.403 0.556 0.758 1.021

0.245 0.345 0.479 0.656 0.889

0.205 0.290 0.405 0.559 0.763

0.168 0.240 0.338 0.470 0.647

0.136 0.196 0.279 0.392 0.544

0.109 0.159 0.228 0.324 0.455

0.087 0.128 0.186 0.268 0.380

0.069 0.103 0.152 0.220 0.316

0.055 0.083 0.123 0.181 0.263

0.043 0.066 0.100 0.148 0.217

0.034 0.052 0.079 0.119 0.176

0.025 0.040 0.061 0.092 0.137

0.018 0.028 0.043 0.065 0.099

0.010 0.015 0.024 0.036 0.056

1.988 2.591 3.343 4.273 5.416

1.850 2.415 3.122 4.000 5.079

1.696 2.221 2.879 3.698 4.709

1.532 2.012 2.618 3.374 4.312

1.361 1.796 2.347 3.039 3.902

1.192 1.582 2.078 2.706 3.493

1.030 1.376 1.821 2.387 3.101

0.881 1.186 1.582 2.090 2.736

0.747 1.016 1.367 1.821 2.405

0.632 0.867 1.177 1.584 2.110

0.532 0.738 1.013 1.376 1.851

0.448 0.628 0.870 1.194 1.622

0.376 0.532 0.746 1.033 1.418

0.313 0.448 0.634 0.887 1.229

0.257 0.371 0.529 0.748 1.047

0.202 0.295 0.425 0.607 0.858

0.147 0.216 0.314 0.453 0.647

0.083 0.124 0.183 0.267 0.386

7.174 8.931 11.035 13.538 16.496

6.807 8.488 10.504 12.910 15.758

6.397 7.994 9.916 12.213 14.941

5.947 7.452 9.270 11.449 14.047

5.465 6.873 8.580 10.635 13.095

4.968 6.275 7.869 9.796 12.115

4.472 5.680 7.160 8.962 11.141

3.995 5.107 6.479 8.160 10.205

3.551 4.573 5.842 7.410 9.331

3.148 4.086 5.262 6.725 8.534

2.787 3.650 4.740 6.110 7.817

2.468 3.262 4.275 5.559 7.175

2.184 2.914 3.856 5.061 6.592

1.928 2.598 3.470 4.598 6.045

1.688 2.297 3.098 4.146 5.504

1.451 1.994 2.718 3.675 4.932

1.201 1.669 2.300 3.147 4.277

0.917 1.290 1.802 2.502 3.455

0.555 0.793 1.129 1.600 2.262

19.971 24.029 28.744

19.111 23.037 27.607

18.162 21.943 26.358

17.124 20.748 24.996

16.020 19.479 23.549

14.886 18.179 22.070

13.760 16.889 20.608

12.679 15.654 19.212

11.672 14.506 17.917

10.754 13.463 16.748

9.930 12.530 15.708

9.192 11.696 14.783

8.522 10.938 13.946

7.889 10.221 13.153

7.255 9.496 12.346

6.573 8.703 11.452

5.777 7.759 10.369

4.751 6.508 8.891

3.196 4.520 6.413

(19.1)

50

55

60

65

70

75

95

The values in Table 2-16 were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002). The primary source for the properties of aqueous ammonia mixtures is R. Tillner-Roth and D. G. Friend, “A Helmholtz Free Energy Formulation of the Thermodynamic Properties of the Mixture {Water + Ammonia},” J. Phys. Chem. Ref. Data 27:63–96 (1998).

VAPOR PRESSURES OF SOLUTIOnS TABLE 2-17 Partial Pressures of H2O over Aqueous Solutions of Sodium Carbonate*

TABLE 2-18 Partial Pressures of H2O and CH3OH over Aqueous Solutions of Methyl Alcohol*

mmHg %Na2CO3 t, °C

0

5

10

0 10 20 30 40 50 60 70 80 90 100

4.5 9.2 17.5 31.8 55.3 92.5 149.5 239.8 355.5 526.0 760.0

4.5 9.0 17.2 31.2 54.2 90.7 146.5 235 348 516 746

8.8 16.8 30.4 53.0 88.7 143.5 230.5 342 506 731

15

20

16.3 29.6 57.6 86.5 139.9 225 334 494 715

25

28.8 50.2 84.1 136.1 219 325 482 697

27.8 48.4 81.2 131.6 211.5 315 467 676

2-83

30

39.9°C

Mole fraction CH3OH

PH2O, mmHg

PCH3OH , mmHg

0 14.99 17.85 21.07 27.31 31.06 40.1 47.0 55.8 68.9 86.0 100.0

54.7 39.2 38.5 37.2 35.8 34.9 32.8 31.5 27.3 20.7 10.1 0

0 66.1 75.5 85.2 100.6 108.8 127.7 141.6 158.4 186.6 225.2 260.7

26.4 46.1 77.5 125.7 202.5 301 447 648

∗International Critical Tables, vol. 3, p. 372.

59.4°C

Mole fraction CH3OH

PH2O, mmHg

PCH3OH , mmHg

0 22.17 27.40 33.24 39.80 47.08 55.5 69.2 78.5 85.9 100.0

145.4 106.9 102.2 96.6 91.7 84.8 76.9 57.8 43.8 30.1 0

0 210.1 240.2 272.1 301.9 335.6 373.7 439.4 486.6 526.9 609.3

∗International Critical Tables, vol. 3, p. 290.

TABLE 2-19 Partial Pressures of H2O over Aqueous Solutions of Sodium Hydroxide* mmHg Conc. g NaOH/ 100 g H2O

Temperature, °C 0

20

40

0 4.6 17.5 55.3 5 4.4 16.9 53.2 10 4.2 16.0 50.6 20 3.6 13.9 44.2 30 2.9 11.3 36.6 40 2.2 8.7 28.7 50 6.3 20.7 60 4.4 15.5 70 3.0 10.9 80 2.0 7.6 90 1.3 5.2 100 0.9 3.6 120 1.7 140 160 180 200 250 300 350 400 500 700 1000 2000 4000 8000 ∗International Critical Tables, vol. 3, p. 370.

60

80

100

120

160

200

250

300

350

149.5 143.5 137.0 120.5 101.0 81.0 62.5 47.0 34.5 24.5 17.5 12.5 6.3 3.0 1.5

355.5 341.5 325.5 288.5 246.0 202.0 160.5 124.0 94.0 70.5 53.0 38.5 20.5 11.0 6.0 3.5 2.0 0.5 0.1

760.0 730.0 697.0 621.0 537.0 450.0 368.0 294.0 231.0 179.0 138.0 105.0 61.0 35.5 20.5 12.0 7.0 2.0 0.5

1,489 1,430 1,365 1,225 1,070 920 770 635 515 415 330 262 164 102 63 40 25 8 2.7 0.9

4,633 4,450 4,260 3,860 3,460 3,090 2,690 2,340 2,030 1,740 1,490 1,300 915 765 470 340 245 110 50 23 11

11,647 11,200 10,750 9,800 8,950 8,150 7,400 6,750 6,100 5,500 5,000 4,500 3,650 2,980 2,430 1,980 1,620 985 610 380 240 100

29,771 28,600 27,500 25,300 23,300 21,500 19,900 18,400 17,100 15,800 14,700 13,650 11,800 10,300 8,960 7,830 6,870 5,000 3,690 2,750 2,080 1,210 440

64,200 61,800 59,300 54,700 50,800 47,200 44,100 41,200 38,700 36,300 34,200 32,200 28,800 25,900 23,300 21,200 19,200 15,400 12,500 10,300 8,600 6,100 3,300 1,470 150

123,600 118,900 114,100 105,400 98,000 91,600 85,800 80,700 76,000 71,900 68,100 64,600 58,600 53,400 49,000 45,100 41,800 35,000 29,800 25,700 22,400 17,500 11,500 6,800 1,760 120 7

2-84

PHYSICAL AnD CHEMICAL DATA

WATER VAPOR COnTEnT In GASES The accompanying figure is useful in determining the water vapor content of air at high pressure in contact with liquid water.

FIG. 2-2 Water content in air at pressures over atmospheric. (Landsbaum, E.M., W.S. Dodds, and L.F. Stutzman. Reprinted from vol. 47, January 1955 issue of Ind. Eng. Chem. [p. 192]. Copyright 1955 by the American Chemical Society and reproduced by permission of the copyright owner.) For other water-in-air data, see Table 2-111, Fig. 2-3 and Section 12 figures and tables.

SOLUBILITIES Unit Conversions For this subsection, the following unit conversions are applicable: °F = 9⁄5°C + 32. To convert cubic centimeters to cubic feet, multiply by 3.532 × 10−5. To convert millimeters of mercury to pounds-force per square inch, multiply by 0.01934. To convert grams per liter to pounds per cubic foot, multiply by 6.243 × 10−2. Introduction The database containing solubilities was originally published in the International Union for Pure and Applied Chemistry (IUPAC)National Institute of Standards and Technology (NIST) Solubility Data Series. It is available at no cost online at http://srdata.nist.gov/solubility. The H in the following tables is the proportionality constant in Henry’s law, p = Hx, where x is the mole fraction of the solute in the aqueous liquid phase; p is the partial pressure in atm of the solute in the gas phase; and H is a proportionality constant, generally referred to as Henry’s constant. Values of H often have considerable uncertainty and are strong functions of

temperature. To convert values of H at 25°C from atm to atm/(mol/m3), divide by the molar density of water at 25°C, which is 55,342 mol/m3. Henry’s law is valid only for dilute solutions. Additional values of Henry’s constant can be found in “Environmental Simulation Program,” OLI Systems, Inc., Morris Plains, N.J.; “Estimated Henry’s Law Constant,” EPA Online Tools for Site Assessment Calculation (http://www.epa .gov/athens/learn2model/part-two/onsite/esthenry.htm); Rolf Sander, “Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry,” Air Chemistry Department, Max-Planck Institute of Chemistry, Mainz, Germany; Rolf Sander, “Modeling Atmospheric Chemistry: Interactions between Gas-Phase Species and Liquid Cloud/Aerosol Particles,” Surv. Geophys. 20: 1–31, 1999 (http:// www.henrys-law.org).

TABLE 2-20 Solubilities of Inorganic Compounds in Water at Various Temperatures* This table shows the grams of anhydrous substance that are soluble in 100 g of water at the temperature in degrees Celsius as indicated; when the name is followed by †, the value is expressed in grams of substance in 100 cm3 of saturated solution. Solid phase gives the hydrated form in equilibrium with the saturated solution. Substance

Formula

Solid phase

AlCl3 Al2(SO4)3 (NH4)2Al2(SO4)4

6H2O 18H2O 24H2O

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Aluminum chloride sulfate Ammonium aluminum sulfate bicarbonate bromide chloride chloroplatinate chromate chromium sulfate dichromate dihydrogen phosphite hydrogen phosphate iodide magnesium phosphate manganese phosphate nitrate oxalate perchlorate† persulfate sulfate thiocyanate vanadate (meta) Antimonious fluoride sulfide Arsenic oxide Arsenious sulfide

NH4HCO3 NH4Br NH4Cl (NH4)2PtCl6 (NH4)2CrO4 (NH4)2Cr2(SO4)4 (NH4)2Cr2O7 NH4H2PO3 (NH4)2HPO4 NH4I NH4MgPO4 NH4MnPO4 NH4NO3 (NH4)2C2O4 NH4ClO4† (NH4)2S2O8 (NH4)2SO4 NH4CNS NH4VO3 SbF3 Sb2S3 As2O5 As2S3

27 28 29

Barium acetate acetate carbonate

Ba(C2H3O2)2 Ba(C2H3O2)2 BaCO3

3H2O 1H2O

30 31 32 33 34 35 36 37 38

chlorate chloride chromate hydroxide iodide iodide nitrate nitrite oxalate

Ba(ClO3)2 BaCl2 BaCrO4 Ba(OH)2 BaI2 BaI2 Ba(NO3)2 Ba(NO2)2 BaC2O4

1H2O 2H2O

1 2 3

39 40 41 42 43 44 45 46 47 48 49 50 51

perchlorate sulfate Beryllium sulfate sulfate sulfate Boric acid Boron oxide Bromine Cadmium chloride chloride chloride cyanide hydroxide

Ba(ClO4)2 BaSO4 BeSO4 BeSO4 BeSO4 H3BO3 B2O3 Br2 CdCl2 CdCl2 CdCl2 Cd(CN)2 Cd(OH)2

52 53 54

sulfate Calcium acetate acetate

CdSO4 Ca(C2H3O2)2 Ca(C2H3O2)2

0°C

10°C

31.2 2.1

33.5 4.99

11.9 60.6 29.4

15.8 68 33.3 0.7

171

1H2O

154.2 0.023 118.3 2.2 11.56 58.2 70.6 119.8

163.2

3.1 73.0 144

384.7

8H2O 6H2O 2H2O 1H2O 3H2O 6H2O 4H2O 2H2O

4H2O 2½H2O 1H2O

2H2O 1H2O

30°C

40°C

50°C

60°C

70°C

80°C

90°C

100°C

40.4 10.94

46.1 14.88

52.2 20.10

59.2 26.70

66.1

73.0

80.8

89.0 109.796°

21 75.5 37.2

27 83.2 41.4

91.1 45.8

99.2 50.4

107.8 55.2

116.8 60.2

126 65.6

135.6 71.3

145.6 77.3 1.25

190.5 0.036 0 297.0 8.0 30.58

199.6 0.030

208.9 0.040 0 421.0

218.7 0.016 0.005 499.0

228.8 0.019 0.007 580.0

10.7825°

24II2O

6H2O 7H2O

20°C 69.8615° 36.4 7.74

59.5 5.17 × 10−5 at 18° 59

62.1 63 0.00168°

20.34 31.6 0.0002 1.67 170.2 5.0

26.95 33.3 0.00028 2.48 185.7 7.0 0.00168°

205.8 1.15 × 10−4

2.66 1.1 4.22 97.59 90.01

76.48 37.4

2.0 × 10−4

19014.5° 13115 172.3 0.052 0 192 4.4 20.85 75.4 170 0.48 444.7 0.00017518° 65.8 71 0.002218° 33.80 35.7 0.00037 3.89 203.1 9.2 67.5 0.002218° 289.1 2.4 × 10−4

3.57 1.5 3.4 125.1

5.04 2.2 3.20

135.1

134.5 1.715°

76.00 36.0

76.60 34.7

40.4 47.17 26031° 181.4 241.8 5.9 78.0 207.7 0.84 563.6

81.0

69.5

71.2

1.32

75 0.0024 at 24.2° 41.70 38.2 0.00046 5.59 219.6 11.6 0.0024 at 24.2° 2.85 × 10−4 52 43.78 6.60 3.13

48.19 95.3

103.3

75.1

76.7

77

74

74

49.61 40.7

43.6

66.81 46.4

49.4

8.22

13.12

20.94

358.7

426.3

46.74

135.3

75 84.84 52.4

261.0 27.0 205.8 495.2 62

14.81 6.2

136.5

104.9 58.8

101.4

247.3 20.3

60.67 11.54

57.01

3.05 73.0

17.1

871.0

88.0 1.78

231.9 14.2

740.0

39.05

79

8.72 4.0

132.1

344.0 10.3

250.3

16.73

271.7 34.2 300 562.3

84.76 23.75 9.5

83 98 30.38

140.4

100 110 40.25 15.7

147.0

−4

2.6 × 10 at 25° 33.8

78.54 33.2

83.68 32.7

33.5

63.13

60.77

31.1

29.7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

2-85

(Continued )

2-86

TABLE 2-20 Solubilities of Inorganic Compounds in Water at Various Temperatures* (Continued ) This table shows the grams of anhydrous substance that are soluble in 100 g of water at the temperature in degrees Celsius as indicated; when the name is followed by †, the value is expressed in grams of substance in 100 cm3 of saturated solution. Solid phase gives the hydrated form in equilibrium with the saturated solution. Substance

Formula

1 2 3 4 5 6 7 8 9 10 11

Calcium bicarbonate chloride chloride fluoride hydroxide nitrate nitrate nitrate nitrite nitrite oxalate

Ca(HCO3)2 CaCl2 CaCl2 CaF2 Ca(OH)2 Ca(NO3)2 Ca(NO3)2 Ca(NO3)2 Ca(NO2)2 Ca(NO2)2 CaC2O4

12 13 14 15 16 17 18 19 20 21 22 23 24

sulfate Carbon dioxide, 760 mm ‡ monoxide, 760 mm ‡ Cesium chloride nitrate sulfate Chlorine, 760 mm ‡ Chromic anhydride Cuprio chloride nitrate nitrate sulfate sulfide

CaSO4 CO2 CO CsCl CsNO3 Cs2SO4 Cl2 CrO3 CuCl2 Cu(NO3)2 Cu(NO3)2 CuSO4 CuS

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

Cuprous chloride Ferric chloride Ferrous chloride chloride nitrate sulfate sulfate Hydrobromic acid, 760 mm Hydrochloric acid, 760 mm Iodine Lead acetate bromide carbonate chloride chromate fluoride nitrate sulfate Magnesium bromide chloride hydroxide nitrate sulfate sulfate sulfate Manganous sulfate sulfate sulfate sulfate Mercurous chloride Molybdic oxide Nickel chloride nitrate nitrate sulfate sulfate Nitric oxide, 760 mm Nitrous oxide

CuCl FeCl3 FeCl2 FeCl2 Fe(NO3)2 FeSO4 FeSO4 HBr HCl I2 Pb(C2H3O2)2 PbBr2 PbCO3 PbCl2 PbCrO4 PbF2 Pb(NO3)2 PbSO4 MgBr2 MgCl2 Mg(OH)2 Mg(NO3)2 MgSO4 MgSO4 MgSO4 MnSO4 MnSO4 MnSO4 MnSO4 HgCl MoO3 NiCl2 Ni(NO3)2 Ni(NO3)2 NiSO4 NiSO4 NO N2O

Solid phase 6H2O 2H2O 4H2O 3H2O

0°C 16.15 59.5

65.0

0.185 102.0

0.176 115.3

4H2O 2H2O

62.07

2H2O

0.1759 0.3346 0.0044 161.4 9.33 167.1 1.46 164.9 70.7 81.8

2H2O 6H2O 3H2O 5H2O

4H2O 6H2O 7H2O 1H2O

3H2O

10°C

6.7 × 10−4 at 13° 0.1928 0.2318 0.0035 174.7 14.9 173.1 0.980 73.76 95.28 17.4

74.4

81.9 64.5

221.2 82.3

20.51 210.3

0.6728

6H2O 6H2O 6H2O 7H2O 6H2O 1H2O 7H2O 5H2O 4H2O 1H2O 2H2O 6H2O 6H2O 3H2O 7H2O 6H2O

66.55 40.8 53.23

0.060 48.3 0.0035 94.5 53.5 30.9 42.2 60.01 59.5

0.00014 53.9 79.58

59.5

27.22

32

0.00984

0.001618° 0.165 129.3

6.8 × 10−4 at 25° 0.1688 0.0028 186.5 23.0 178.7 0.716 77.0 125.1 20.7 3.3 × 10−5 at 18° 1.5225° 91.8 83.8 26.5 198 0.029

0.4554

38.8 0.0028 91.0 52.8

16.60 74.5

30°C 102 0.001726° 0.153 152.6

40°C

50°C

17.05

0.00757 0.1705

0.85 0.00011 0.99 7 × 10−6 0.064 56.5 0.0041 96.5 54.5 0.000918°

9.5 × 10−4 at 50° 0.2090 0.1257 0.0024 197.3 33.9 184.1 0.562

0.141 195.9 237.5

70°C

17.50

0.128

0.116

80.34 25

159.8 28.5

33.3

73.0

77.3

315.1 82.5

32.9

40.2

48.6

90°C

0.106

147.0 0.094

0.2047 0.0576 0.0015 229.7 83.8 199.9 0.324

151.9

0.085

0.077

244.8

0.0010 250.0 134.0 210.3 0.219

91.2

99.2

178.8 40

207.8 55

88.7

525.8 100

165.6 50.9

159

363.6

0.1966 0.0013 239.5 107.0 205.0 0.274

100°C 18.40

152.7

358.7 132.6

0.0761 0.0018 218.5 64.4 194.9 0.386 182.1 87.44

80°C 17.95

141.7

281.5

14 × 10−4 at 95° 0.2097 0.0973 0.0021 208.0 47.2 189.9 0.451 174.0 83.8

43.6

0.0006 260.1 163.0 214.9 0.125 217.5

0.1619 0 0 270.5 197.0 220.3 0 206.8 107.9 75.4

535.7 105.3 37.3

105.8

67.3 0.04 55.0425° 1.15

63.3 0.056

171.5 59.6 0.078

1.53

1.94

2.36

3.34

4.75

1.20

1.45

1.70

1.98

2.62

3.34

0.068 66 0.0049 99.2

35.5 44.5

40.8 45.3

62.9 64.5

67.76 66.44

0.0002 0.138 64.2 96.31

0.264 68.9

75 0.0056 101.6 57.5 84.74 45.6

68.8 0.0007 0.476 73.3 122.2

42.46 0.00618 0.1211

60°C

136.8

76.68

14.3

71.02 15.65

20°C

0.00517

0.00440

56.1

85

95

104.1

107.5 61.0

115

130

38.8

113.7 66.0

120.2 73.0 137.0

50.4

53.5

59.5

64.2 62.9

69.0

74.0 68.3

72.6 58.17

55.0

52.0

48.0

42.5

34.0

0.687 78.3

1.206 82.2

2.055 85.2

163.1 50.15 0.00376

54.80 0.00324

2.106

169.1 59.44 0.00267

87.6 235.1

63.17 0.00199

0.00114

76.7 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

Potassium acetate acetate alum bicarbonate bisulfate bitartrate carbonate chlorate chloride chromate dichromate ferricyanide hydroxide hydroxide nitrate nitrite perchlorate permanganate persulfate† sulfate thiocyanate Silver cyanide nitrate sulfate Sodium acetate acetate bicarbonate carbonate carbonate chlorate chloride chromate chromate chromate dichromate dichromate dihydrogen phosphate dihydrogen phosphate dihydrogen phosphate hydrogen arsenate hydrogen phosphate hydrogen phosphate hydrogen phosphate hydrogen phosphate hydroxide hydroxide hydroxide hydroxide nitrate nitrite oxalate phosphate, tripyrophosphate sulfate sulfate sulfate sulfide sulfide sulfide sulfite sulfite tetraborate tetraborate vanadate (meta)

KC2H3O2 KC2H3O2 K2SO4⋅Al2(SO4)3 KHCO3 KHSO4 KHC4H4O6 K2CO3 KClO3 KCl K2CrO4 K2Cr2O7 K3Fe(CN)6 KOH KOH KNO3 KNO2 KClO4 KMnO4 K2S2O8† K2SO4 KCNS AgCN AgNO3 Ag2SO4 NaC2H3O2 NaC2H3O2 NaHCO3 Na2CO3 Na2CO3 NaClO8 NaCl Na2CrO4 Na2CrO4 Na2CrO4 Na2Cr2O7 Na2Cr2O7 NaH2PO4 NaH2PO4 NaH2PO4 Na2HAsO4 Na2HPO4 Na2HPO4 Na2HPO4 Na2HPO4 NaOH NaOH NaOH NaOH NaNO3 NaNO2 Na2C2O4 Na3PO4 Na4P2O7 Na2SO4 Na2SO4 Na2SO4 Na2S Na2S Na2S Na2SO3 Na2SO3 Na2B4O7 Na2B4O7 NaVO8

1½H2O ½H2O 24H2O

2H2O

2H2O 1H2O

†

3H2O 10H2O 1H2O 10H2O 4H2O

216.7

233.9

255.6

3.0 22.4 36.3 0.32 105.5 3.3 27.6 58.2 5 31 97

4.0 27.7

5.9 33.2 51.4 0.53 110.5 7.4 34.0 61.7 12 43 112

13.3 278.8 0.75 2.83 1.62 7.35 177.0

20.9

122 0.573 36.3 119 6.9 7

170 0.695 40.8 121 8.15 12.5

31.6 298.4 1.80 6.4 4.49 11.11 217.5 2.2 × 10−5 222 0.796 46.5 123.5 9.6 21.5

79 35.65 31.70

89 35.72 50.17

101 35.89 88.7

2H2O

163.0

2H2O 1H2O

57.9

12H2O 12H2O 7H2O 2H2O 4H2O 3½H2O 1H2O

12H2O 10H2O 10H2O 7H2O 9H2O 5½H2O 6H2O 7H2O 10H2O 5H2O 2H2O

0.40 108 5 31.0 60.0 7 36 103

7.3 1.67

42

1.05 4.4 2.60 9.22

0.90 113.7 10.5 37.0 63.4 20 50 126 45.8 2.6 9.0 7.19 12.97

11.70 45.4 67.3 1.32 116.9 14 40.0 65.2 26 60 63.9 334.9 4.4 12.56 9.89 14.76

4.1 3.95 9.0 30 15.42

18.8

22.5

20

26.9

36

20 9.95 40.8

3.9

202

16.50

18.17

19.75

21.4

22.8

1.22

669 1.30

114.6

96 91.6

169

54.0 73.9 70

18

158.6

80.2

1.36

146

153

172 37.46

45.8 189 37.93

123.0 316.7

124.8 376.2

179.3 65

190.3

207.3 85

225.3

82.9

88.1

92.4

102.9

244.8

88 84.5 3.7 11 6.23 19.4 44

138

147.5

14.8

104

119

48.3 70.4 52

4.6 139.8 38.5 51.1 72.1 61

396.3 109.0

11.8

95.96

51.8

133.1

380.1 71.0

9 22.2

88.7

47

364.8 40.0

6.5 16.89

46.4 155 37.04

37 20.8

15.325°

110.0

140 36.69

26.5 7.7

2.7

140 85.5

48.5 126 36.37

15.5 3.6

1.6

2.46 126.8 24.5 45.5 68.6 43 66

525 1.15 139 139.5 16.4

138.2

1.5 3.16 5.0 19.5

1.83 121.2 19.3 42.6 66.8 34

455 1.08 83 134 14.45

106.5

109

350 24.75 60.0

376 0.979 65.5 129.5 12.7

85.2

51.5

337.3 17.00

300 0.888 54.5 126 11.1 38.8 50.5 113 36.09

69.9

80 78.0

1.3

8.39 39.1

323.3

177.8

73 72.1

13.9

283.8

129

145

174

104 98.4

114 104.1

124

161

38.47

121.6 6.95 155.7 57 56.7 75.6 80 82.6104 178 246 412.8 21.8 24.1 952 1.41 170 45.5 230 38.99 125.9 426.3

102.2

31 13.50

43 17.45

55 21.83

81 30.04

347 180 163.2 6.33 108 40.26

48.8 28.5

46.7

45.3

43.7

42.5

39.82 36.4

42.69 39.1

28

28.2 10.5

28.8 20.3

30.2

68.4

148 132.6

45.73 43.31

51.40 49.14

313

246.6

59.23 57.28

28.3 24.4

31.5

41

52.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

2-87

∗By N. A. Lange; abridged from “Table of Solubilities of Inorganic Compounds in Water at Various Temperatures” in Lange’s Handbook of Chemistry, 10th ed., McGraw-Hill, New York, 1961 (except for NaCl, which is from CRC Handbook of Chemistry and Physics, 86th ed., CRC Press, 2005). For tables of the solubility of gases in water at various temperatures, Atack (Handbook of Chemical Data, Reinhold, New York, 1957) gives values at closer temperature intervals, usually 1 or 5°C, than are tabulated here. For materials marked by ‡, additional data are given in tables subsequent to this one. For the solubility of various hydrocarbons in water at high pressures see J. Chem. Eng. Data, 4, 212 (1959).

2-88 TABLE 2-20 Solubilities of Inorganic Compounds in Water at Various Temperatures (Continued ) This table shows the grams of anhydrous substance that are soluble in 100 g of water at the temperature in degrees Celsius as indicated; when the name is followed by †, the value is expressed in grams of substance in 100 cm3 of saturated solution. Solid phase gives the hydrated form in equilibrium with the saturated solution. Substance 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Sodium vanadate (meta) Stannous chloride sulfate Strontium acetate acetate chloride chloride nitrate nitrate nitrate sulfate Sulfur dioxide, 760 mm† Thallium sulfate Thorium sulfate sulfate sulfate sulfate Zinc chlorate chlorate nitrate nitrate sulfate sulfate sulfate

Formula NaVO3 SnCl2 SnSO4 Sr(C2H3O2)2 Sr(C2H3O2)2 SrCl2 SrCl2 Sr(NO3)2 Sr(NO3)2 Sr(NO3)2 SrSO4 SO2 Tl2SO4 Th(SO4)2 Th(SO4)2 Th(SO4)2 Th(SO4)2 ZnClO3 ZnClO3 Zn(NO3)2 Zn(NO3)2 ZnSO4 ZnSO4 ZnSO4

Solid phase

0°C

10°C

20°C

30°C

21.10 ° 269.815° 19 25

83.9 4H2O ½H2O 6H2O 2H2O 1H2O 4H2O

9H2O 8H2O 6H2O 4H2O 6H2O 4H2O 6H2O 3H2O 7H2O 6H2O 1H2O

36.9 43.5

43.61 42.95 47.7

41.6 52.9

52.7 40.1

64.0 70.5

0.0113 22.83 2.70 0.74 1.0 1.50

0.0114 11.29 4.87 1.38 1.62 1.90

145.0

16.21 3.70 0.98 1.25 152.5

94.78 41.9

47

200.3 118.3 54.4

40°C

50°C

26.23

60°C

70°C

80°C

36.9

38.8 °

36.24

36.10

85.9

90.5

93.8

96

98

10.92

12.74

14.61

16.53

18.45

6.64 1.63

1.09

86.6

83.7

80.8

32.97

90°C

100°C

75

18 39.5 58.7

88.6 0.0114 7.81 6.16 1.995 2.45 209.2

65.3

37.35 72.4

81.8

83.8

97.2

90.1

2.998

5.41

4.5 9.21 5.22

4.04

2.54

223.2

36.4 130.4

100.8 139

100

273.1

206.9 70.1

76.8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

SOLUBILITIES

2-89

TABLE 2-21 Solubility as a Function of Temperature and Henry’s Constant at 25çC for Gases in Water Name Acetylene Carbon dioxide Carbon monoxide Ethane Ethylene Helium Hydrogen Methane Nitrogen Oxygen

Formula

A −156.51 −159.854 −171.764 −250.812 −153.027 −105.9768 −125.939 −338.217 −181.587 −171.2542

C2H2 CO2 CO C2H6 C2H4 He H2 CH4 N2 O2

C

D

T range, K

H at 25°C, atm

21.403 21.6694 23.3376 34.7413 20.5248 14.0094 16.8893 51.9144 24.7981 23.24323

0 −1.10261E-03 0 0 0 0 0 −0.0425831 0 0

274–343 273–353 273–353 275–323 287–346 273–348 273–345 273–523 273–350 273–333

1,330 1,635 58,000 29,400 11,726 142,900 70,800 39,200 84,600 43,400

B 8,160.2 8,741.68 8,296.9 12,695.6 7,965.2 4,259.62 5,528.45 13,282.1 8,632.13 8,391.24

The constants can be used to calculate solubility by the equation ln x = A + B/T + C ln T + DT, where T is in K and x is the mole fraction of the solute dissolved in water when the solute partial pressure is 1 atm. With the assumption that Henry’s law is valid up to 1 atm, H = 1/x. Values of the constants are from P. G. T. Fogg and W. Gerrard, Solubility of Gases in Liquids, Wiley, 1991, New York, and Solubility Data Series, vol. 1, Helium and Neon, IUPAC, Pergamon Press, Oxford, 1979. For higher-temperature behavior and an up-to-date reference list, see R. Fernandez-Prini, J. L. Alvarez, and A. H. Harvey, J. Phys. Chem. Ref. Data 32(2):903, 2003. To find H at temperatures other than 25°C, first find the solubility and then take the reciprocal.

TABLE 2-22 Henry’s Constant H for Various Compounds in Water at 25çC Group Paraffin hydrocarbons

Olefins Aromatics

Aldehydes Ketones Esters

Chlorine containing Alcohols

Miscellaneous

Compound Methane Ethane Propane Butane Pentane Octane Nonane Ethylene Propylene Benzene Toluene o-Xylene Cumene Phenol Acetaldehyde Propionaldehyde Methylethyl ketone Methyl formate Ethyl formate Methyl acetate Butyl acetate Chloromethane Chloroethane Chlorobenzene Methanol Ethanol 1-Propanol 1-Butanol Acrylonitrile Dimethyl sulfide Dimethyl disulfide Methyl mercaptan Ethyl mercaptan Pyridine

Formula CH4 C2H6 C3H8 C4H10 C5H12 C8H18 C9H20 C2H4 C3H6 C6H6 C7H8 C8H10 C9H12 C6H6O C2H4O C3H6O C4H8O C2H4O2 C3H6O2 C3H6O2 C6H12O2 CH3Cl C2H5Cl C6H5Cl CH4O C2H6O C3H8O C4H10O C3H3N C2H6S C2H6S2 CH4S C2H6S C5H5N

CAS 74-82-8 74-84-0 74-98-6 106-97-8 109-66-0 111-65-9 111-84-2 74-85-1 115-07-1 71-43-2 108-88-3 95-47-6 98-82-8 108-95-2 75-07-0 123-38-6 78-93-3 107-31-3 109-94-4 79-20-9 123-86-4 74-87-3 75-00-3 108-90-7 67-56-1 64-17-5 71-23-8 71-36-3 107-13-1 75-18-3 624-92-0 74-93-1 75-08-1 110-86-1

H, atm† 36,600 26,700 37,800 51,100 70,000 2,74,000 3,29,000 11,700 11,700 299 354 272 724 0.0394 5.56 4.36 2.59 13.6 13.6 5.04 13.6 556 681 204 0.272 0.272 0.507 0.482 5.54 121 68.1 177 161 0.817

Rating∗ 4 3 3 3 3 3 3 3 4 10 10 10 9 7 3 4 5 3 3 3 3 ? 10 10 4 4 3 3 3 3 3 3 3 3

Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York (2016). ∗The ratings reflect DIPPR ESP’s effort to provide a critical evaluation and quality assessment of each data point with 15 being the highest score possible. The rating is not directly correlated with the estimated experimental uncertainty. † Henry’s constant is a strong nonlinear function of temperature. A single value measured at one temperature, if used for calculation at a different temperature, can lead to serious errors. Procedures for extrapolation of singlepoint values over the ambient temperature range (4°C < T < 50°C) are presented in Sec. 22, under “Air Pollution Control” > “Biological APC Technologies” > “Estimating Henry’s law constants”. Estimation procedures for the larger range (4°C < T < 200°C) are presented in F. L. Smith and A. H. Harvey, “Avoid Common Pitfalls When Using Henry’s Law,” Chem. Eng. Prog., 103(9), 2007. See also Y.-L. Huang, J. D. Olson, and G. E. Keller II, “Steam Stripping for Removal of Organic Pollutants from Water. 2. Vapor-Liquid Equilibrium Data,” Ind. Eng. Chem. Res., 31, pp. 1759–1768, 1992. (Also see the Supplementary Material, which contains the databank of 404 compounds of environmental interest and other useful property data.)

2-90

PHYSICAL AnD CHEMICAL DATA

TABLE 2-23 Henry’s Constant H for Various Compounds in Water at 25çC from Infinite Dilution Activity Coefficients Compound

CAS no.

Formula

H = γ ∞Pvp, atm

Pentane Hexane Heptane Benzene Toluene o-Xylene Cumene Styrene Formaldehyde Acetaldehyde Propanal Acetone Methyl ethyl ketone Methyl n-propyl ketone Formic acid Methyl acetate Ethyl acetate Butyl acetate Chloroethane 1-Chloropropane Chlorobenzene Methanol Ethanol Pyridine Diethyl ether Thiophene

109660 1100543 142825 71432 108883 95476 98,828 100425 50000 75070 123386 67641 78933 107879 64186 79209 141786 123864 75003 74986 108907 67561 64175 110861 60297 110021

C5H12 C6H14 C7H16 C6H6 C7H8 C8H10 C9H12 C8H8 CH2O C2H4O C3H6O C3H6O C4H8O C5H10O CH2O2 C3H6O2 C4H8O2 C6H12O2 C2H5Cl C3H7Cl C6H5Cl CH4O C2H6O C5H5N C4H10O C4H4S

63700 84600 120000 309 344 267 613 145 14.3 4.54 5.45 2.13 3.11 4.60 0.0404 6.38 8.01 12.3 626 792 219 0.263 0.293 0.544 48.7 160

TABLE 2-24

Air*

t, °C

0

5

10

15

20

25

30

35

10−4 × H †

4.32

4.88

5.49

6.07

6.64

7.20

7.71

8.23

t, °C

40

45

50

60

70

80

90

100

10−4 × H †

8.70

9.11

9.46

10.1

10.5

10.7

10.8

10.7

∗International Critical Tables, vol. 3, p. 257. † H is calculated from the absorption coefficients of O2 and N2, taking into consideration the correction for constant argon content.

TABLE 2-25 Ammonia-Water at 10 and 20çC* 10°C Mass fraction NH3 in liquid 0.0 0.00467 0.00495 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Henry’s constant H at 25°C is the vapor pressure at 25°C times the infinite dilution activity coefficient, also at 25°C. Infinite dilution activity coefficients are from Mitchell and Jurs, J. Chem. Inf. Comput. Sci. 38: 200 (1998). Henry’s constant is a strong nonlinear function of temperature. A single value measured at one temperature, if used for calculation at a different temperature, can lead to serious errors. Procedures for extrapolation of single-point values over the ambient temperature range (4°C < T < 50°C) are presented in Sec. 22, pp. 22–49, under “Estimating Henry’s law constants.” Estimation procedures for the larger range (4°C < T < 200°C) are presented in F. L. Smith and A. H. Harvey, “Avoid Common Pitfalls When Using Henry’s Law,” Chem. Eng. Prog., 103(9), 2007. See also Y.-L. Huang, J. D. Olson, and G. E. Keller II, “Steam Stripping for Removal of Organic Pollutants from Water. 2. Vapor-Liquid Equilibrium Data,” Ind. Eng. Chem. Res., 31, pp. 1759–1768, 1992. (Also see the Supplementary Material, which contains the databank of 404 compounds of environmental interest and other useful property data.)

P, kPa 1.23 1.37 7.07 20.07 47.37 99.84 184.44 292.15 399.03 486.44 554.33 615.05

20°C

Mass fraction NH3 in vapor 0.0 0.1

P, kPa 2.34

0.84164 0.95438 0.98565 0.99544 0.99848 0.99943 0.99975 0.99988 0.99995 1.0

2.60 11.95 32.34 73.85 150.56 269.50 416.63 560.61 678.61 771.87 857.48

Mass fraction NH3 in vapor 0.0 0.1 0.82096 0.94541 0.98199 0.99393 0.99783 0.99913 0.99960 0.99980 0.99991 1.0

∗Selected values from R. Tillner-Roth and D. G. Friend, J. Phys. Chem. Ref. Data 27:63 (1998). This reference lists solubilities for temperatures from −70 to 340°C. Densities, enthalpies, and entropies are listed for both the two-phase and single-phase regions for pressures up to 40 MPa.

TABLE 2-26 Carbon Dioxide (CO2)* Liquid mol fraction CO2 × 103 Total pressure, atm 1 2 10 20 30 36

0°C

10°C

15°C

20°C

25°C

35°C

50°C

75°C

100°C

1.445 2.89 12.71 21.23 25.79

0.985 1.946 8.81 15.38 19.80 21.45

0.802 1.587 7.32 13.13 17.49 19.42

0.692 1.374 6.44 11.84 16.22 18.30

0.608 1.207 5.74 10.75 15.05 17.29

0.473 0.943 4.54 8.64 12.80 14.80

0.342 0.683 3.30 6.34 9.10 10.63

0.248 0.495 2.41 4.65 6.78 7.90

0.187 0.373 1.841 3.62 5.35 6.35

∗Values selected from G. Houghton, A. M. McLean, and P. D. Ritchie, Chem. Eng. Sci. 6:132–137, 1957.

SOLUBILITIES TABLE 2-27 Chlorine (Cl2) Partial pressure of Cl2, mmHg

TABLE 2-28 Chlorine Dioxide (ClO2)

Solubility, g of Cl2 per liter 10°C

20°C

30°C

40°C

50°C

5 10 30 50 100

0.488 0.679 1.221 1.717 2.79

0.451 0.603 1.024 1.354 2.08

0.438 0.575 0.937 1.210 1.773

0.424 0.553 0.873 1.106 1.573

0.412 0.532 0.821 1.025 1.424

0.398 0.512 0.781 0.962 1.313

150 200 250 300 350

3.81 4.78 5.71

2.73 3.35 3.95 4.54 5.13

2.27 2.74 3.19 3.63 4.06

1.966 2.34 2.69 3.03 3.35

1.754 2.05 2.34 2.61 2.86

1.599 1.856 2.09 2.31 2.53

400 450 500 550 600

5.71 6.26 6.85 7.39 7.97

4.48 4.88 5.29 5.71 6.12

3.69 3.98 4.30 4.60 4.91

3.11 3.36 3.61 3.84 4.08

2.74 2.94 3.14 3.33 3.52

650 700 750 800 900

8.52 9.09 9.65 10.21

6.52 6.90 7.29 7.69 8.46

5.21 5.50 5.80 6.08 6.68

4.32 4.54 4.77 4.99 5.44

3.71 3.89 4.07 4.27 4.62

9.27 10.84 13.23 17.07 21.0

7.27 8.42 10.14 13.02 15.84

5.89 6.81 8.05 10.22 12.32

4.97 5.67 6.70 8.38 10.03

18.73 21.7 24.7 27.7 30.8

14.47 16.62 18.84 20.7 23.3

11.70 13.38 15.04 16.75 18.46

Cl2.8H2O2 separates

3000 3500 4000 4500 5000 Partial pressure of Cl2, mmHg

Weight of ClO2, grams per liter of solution

Vol % of ClO2 in gas phase

0°C

1000 1200 1500 2000 2500

2-91

1 3 5 7 10 11 12 13 14 15 16

0°C

5°C

10°C

15°C

20°C

30°C

40°C

2.00 6.00 10.0 14.0 20.0

1.50 4.7 7.8 10.9 15.5 17.0 18.6 20.3

1.25 3.85 6.30 8.95 12.8 14.0 15.3 16.6 18.0 19.2 20.3

1.00 3.20 5.25 7.35 10.5 11.7 12.8 13.8 14.9 16.0 17.0

0.90 2.70 4.30 6.15 8.80 9.70 10.55 11.5 12.3 13.2 14.2

0.60 1.95 3.20 4.40 6.30 7.00 7.50 8.20 8.80 9.50 10.1

0.46 1.30 2.25 3.20 4.50 5.00 5.45 5.85 6.35 6.80 7.20

Ishi, Chem. Eng. (Japan), 22:153 (1958).

TABLE 2-29 Hydrogen Chloride (HCl) Weights of HCl per 100 weights of H2O 78.6 66.7 56.3 47.0 38.9 31.6 25.0 19.05 13.64 8.70 4.17 2.04

Partial pressure of HCl, mmHg 0°C

10°C

20°C

30°C

510 130 29.0 5.7 1.0 0.175 0.0316 0.0056 0.00099 0.000118 0.000018

840 233 56.4 11.8 2.27 0.43 0.084 0.016 0.00305 0.000583 0.000069 0.0000117

399 105.5 23.5 4.90 1.00 0.205 0.0428 0.0088 0.00178 0.00024 0.000044

627 188 44.5 9.90 2.17 0.48 0.106 0.0234 0.00515 0.00077 0.000151

Weights of HCl per 100 weights of H2O

Solubility, g of Cl2 per liter 60°C

70°C

80°C

90°C

100°C

110°C

5 10 30 50 100

0.383 0.492 0.743 0.912 1.228

0.369 0.470 0.704 0.863 1.149

0.351 0.447 0.671 0.815 1.085

0.339 0.431 0.642 0.781 1.034

0.326 0.415 0.627 0.747 0.987

0.316 0.402 0.598 0.722 0.950

150 200 250 300 350

1.482 1.706 1.914 2.10 2.28

1.382 1.580 1.764 1.932 2.10

1.294 1.479 1.642 1.793 1.940

1.227 1.396 1.553 1.700 1.831

1.174 1.333 1.480 1.610 1.736

1.137 1.276 1.413 1.542 1.661

400 450 500 550 600

2.47 2.64 2.80 2.97 3.13

2.25 2.41 2.55 2.69 2.83

2.08 2.22 2.35 2.47 2.59

1.965 2.09 2.21 2.32 2.43

1.854 1.972 2.08 2.19 2.29

1.773 1.880 1.986 2.09 2.19

650 700 750 800 900

3.29 3.44 3.59 3.75 4.04

2.97 3.10 3.23 3.37 3.63

2.72 2.84 2.96 3.08 3.30

2.55 2.66 2.76 2.87 3.08

2.41 2.50 2.60 2.69 2.89

2.28 2.37 2.47 2.56 2.74

1000 1200 1500 2000 2500

4.36 4.92 5.76 7.14 8.48

3.88 4.37 5.09 6.26 7.40

3.53 3.95 4.58 5.63 6.61

3.28 3.67 4.23 5.17 6.05

3.07 3.43 3.95 4.78 5.59

2.91 3.25 3.74 4.49 5.25

3000 3500 4000 4500 5000

9.83 11.22 12.54 13.88 15.26

8.52 9.65 10.76 11.91 13.01

7.54 8.53 9.52 10.46 11.42

6.92 7.79 8.65 9.49 10.35

6.38 7.16 7.94 8.72 9.48

5.97 6.72 7.42 8.13 8.84

78.6 66.7 56.3 47.0 38.9 31.6 25.0 19.05 13.64 8.70 4.17 2.04

50°C

Partial pressure of HCl, mm Hg 80°C

535 141 35.7 8.9 2.21 0.55 0.136 0.0344 0.0064 0.00140

623 188 54.5 15.6 4.66 1.34 0.39 0.095 0.0245

110°C

760 253 83 28 9.3 3.10 0.93 0.280

Enthalpy and phase-equilibrium data for the binary system HCl-H2O are given by Van Nuys, Trans. Am. Inst. Chem. Engrs., 39, 663 (1943).

TABLE 2-30 Hydrogen Sulfide (H2S) t, °C

0

5

10

15

20

25

30

35

10−2 × H

2.68

3.15

3.67

4.23

4.83

5.45

6.09

6.76

t, °C

40

45

50

60

70

80

90

100

10−2 × H

7.45

8.14

8.84

10.3

11.9

13.5

14.4

14.8

International Critical Tables, vol. 3, p. 259.

2-92

PHYSICAL AnD CHEMICAL DATA

DEnSITIES Unit Conversions Unless otherwise noted, densities are given in grams per cubic centimeter. To convert to pounds per cubic foot, multiply by 62.43. Temperature conversion: °F = 9⁄5°C + 32. Additional References and Comments The aqueous solution data tables are from International Critical Tables, vol. 3, pp. 115–129, unless otherwise stated. All compositions are in weight percent in vacuo. All density

values are d 4t = g/mL in vacuo. For more detailed data on densities, see also the CRC Handbook of Chemistry and Physics, Chemical Rubber Publishing Co., 97th ed.; or http://hbcponline.com. DEnSITIES OF PURE SUBSTAnCES

TABLE 2-31 Density (kg/m3) of Saturated Liquid Water from the Triple Point to the Critical Point T, K

ρ, kg/m3

T, K

ρ, kg/m3

T, K

ρ, kg/m3

T, K

ρ, kg/m3

T, K

ρ, kg/m3

273.160∗ 274 276 278 280 282 284 286 288 290 292 294 296 298 300 302 304 306 308 310 312 314 316 318 320 322 324 326 328 330 332 334 336 338 340 342 344 346 348 350

999.793 999.843 999.914 999.919 999.862 999.746 999.575 999.352 999.079 998.758 998.392 997.983 997.532 997.042 996.513 995.948 995.346 994.711 994.042 993.342 992.610 991.848 991.056 990.235 989.387 988.512 987.610 986.682 985.728 984.750 983.747 982.721 981.671 980.599 979.503 978.386 977.247 976.086 974.904 973.702

352 354 356 358 360 362 364 366 368 370 372 374 376 378 380 382 384 386 388 390 392 394 396 398 400 402 404 406 408 410 412 414 416 418 420 422 424 426 428 430

972.479 971.235 969.972 968.689 967.386 966.064 964.723 963.363 961.984 960.587 959.171 957.737 956.285 954.815 953.327 951.822 950.298 948.758 947.199 945.624 944.030 942.420 940.793 939.148 937.486 935.807 934.111 932.398 930.668 928.921 927.157 925.375 923.577 921.761 919.929 918.079 916.212 914.328 912.426 910.507

432 434 436 438 440 442 444 446 448 450 452 454 456 458 460 462 464 466 468 470 472 474 476 478 480 482 484 486 488 490 492 494 496 498 500 502 504 506 508 510

908.571 906.617 904.645 902.656 900.649 898.624 896.580 894.519 892.439 890.341 888.225 886.089 883.935 881.761 879.569 877.357 875.125 872.873 870.601 868.310 865.997 863.664 861.310 858.934 856.537 854.118 851.678 849.214 846.728 844.219 841.686 839.130 836.549 833.944 831.313 828.658 825.976 823.269 820.534 817.772

512 514 516 518 520 522 524 526 528 530 532 534 536 538 540 542 544 546 548 550 552 554 556 558 560 562 564 566 568 570 572 574 576 578 580 582 584 586 588 590

814.982 812.164 809.318 806.441 803.535 800.597 797.629 794.628 791.594 788.527 785.425 782.288 779.115 775.905 772.657 769.369 766.042 762.674 759.263 755.808 752.308 748.762 745.169 741.525 737.831 734.084 730.283 726.425 722.508 718.530 714.489 710.382 706.206 701.959 697.638 693.238 688.757 684.190 679.533 674.781

592 594 596 598 600 602 604 606 608 610 612 614 616 618 620 622 624 626 628 630 632 634 636 638 640 641 642 643 644 645 646 647 647.096†

669.930 664.974 659.907 654.722 649.411 643.97 638.38 632.64 626.74 620.65 614.37 607.88 601.15 594.16 586.88 579.26 571.25 562.81 553.84 544.25 533.92 522.71 510.42 496.82 481.53 473.01 463.67 453.14 440.73 425.05 402.96 357.34 322

∗Triple point † Critical point From Wagner, W., and Pruss, A., “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2):387–535, 2002.

TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) Eqn

2-93

105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105

Cmpd. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Chlorine

Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4 CF4 Cl2

CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5 75-73-0 7782-50-5

Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 153.8227 88.0043 70.906

C1 1.711365 1.016 1.4486 0.79388 1.2332 1.0693 2.4507 1.3261 1.2414 1.0379 2.8963 3.5383 0.77488 3.8469 0.7371 1.0259 0.83573 0.71587 0.72184 0.43743 0.59867 0.60917 0.70797 0.52257 2.1872 0.8226 1.3285 1.796 1.187 1.2346 1.0677 0.81696 0.81856 0.98279 0.97552 1.0877 1.1591 1.1448 0.67794 0.50812 0.89458 0.89137 1.3409 1.033873 0.88443 0.79716 2.768 1.7968 2.897 0.99835 1.955 2.23

C2 0.26355 0.21845 0.25892 0.24119 0.25886 0.20656 0.27448 0.26124 0.25822 0.22465 0.26733 0.25443 0.26114 0.2881 0.25487 0.26666 0.26326 0.24812 0.24606 0.24833 0.22849 0.26925 0.25982 0.25833 0.29527 0.26632 0.2708 0.27065 0.26114 0.27216 0.27188 0.24755 0.24967 0.2683 0.26339 0.26454 0.27085 0.27154 0.2637 0.25238 0.27463 0.27365 0.27892 0.266739 0.25828 0.23168 0.26212 0.28749 0.27532 0.274 0.27884 0.27645

C3 466 761 591.95 606 508.2 545.5 308.3 506 615 540 132.45 405.65 645.6 150.86 824 562.05 689 751 702.3 830 720.15 662 718 773 584.15 670.15 503.8 464 452 425 425.12 680 676 563.1 535.9 419.5 435.5 428.6 575.4 660.5 570.1 554 440 537.2 615.7 585.4 304.21 552 132.92 556.35 227.51 417.15

C4 0.28571 0.26116 0.2529 0.29817 0.2913 0.24699 0.28752 0.2489 0.30701 0.28921 0.27341 0.2888 0.28234 0.29783 0.28571 0.28394 0.30798 0.2857 0.28789 0.27555 0.23567 0.2632 0.32144 0.27026 0.3295 0.2821 0.3012 0.28947 0.3065 0.28707 0.28688 0.24535 0.22023 0.25488 0.26864 0.2843 0.28116 0.28419 0.29318 0.29373 0.28512 0.2953 0.29661 0.28571 0.248 0.28071 0.2908 0.3226 0.2813 0.287 0.28571 0.2926

C5

C6

C7

Tmin, K 149.78 353.33 289.81 200.15 178.45 229.32 192.40 185.45 286.15 189.63 59.15 195.41 235.65 83.78 403.00 278.68 258.27 395.45 260.28 321.35 257.85 275.65 243.95 342.20 265.85 242.43 154.25 173.00 136.95 164.25 134.86 220.00 196.15 183.85 158.45 87.80 134.26 167.62 199.65 185.30 157.46 133.02 147.43 176.80 267.95 161.30 216.58 161.11 68.15 250.33 89.56 172.12

Density at Tmin 21.423 16.936 17.492 11.626 15.683 20.544 23.692 16.822 14.693 17.254 33.279 43.141 9.6675 35.491 8.9381 11.422 10.074 8.8935 10.008 5.9496 9.9051 7.0651 8.8623 6.4251 20.109 9.9087 15.809 20.787 15.123 14.058 12.62 11.734 11.872 12.035 12.473 14.264 13.894 13.08 8.3365 7.0264 10.585 10.761 14.901 12.602 11.087 13.087 26.828 19.064 30.18 10.843 21.211 24.242

Tmax, K 466.00 761.00 591.95 606.00 508.20 545.50 308.30 506.00 615.00 540.00 132.45 405.65 645.60 150.86 824.00 562.05 689.00 751.00 702.30 830.00 720.15 662.00 718.00 773.00 584.15 670.15 503.80 464.00 452.00 425.00 425.12 680.00 676.00 563.10 535.90 419.50 435.50 428.60 575.40 660.50 570.10 554.00 440.00 537.20 615.70 585.40 304.21 552.00 132.92 556.35 227.51 417.15

Density at Tmax 6.4935 4.6509 5.5948 3.2915 4.7640 5.1767 8.9285 5.0762 4.8075 4.6201 10.8340 13.9070 2.9673 13.3530 2.8921 3.8472 3.1745 2.8852 2.9336 1.7615 2.6201 2.2625 2.7248 2.0229 7.4075 3.0888 4.9058 6.6359 4.5455 4.5363 3.9271 3.3002 3.2786 3.6630 3.7037 4.1117 4.2795 4.2160 2.5709 2.0133 3.2574 3.2573 4.8075 3.8760 3.4243 3.4408 10.5600 6.2500 10.5220 3.6436 7.0112 8.0666 (Continued )

2-94

TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) (Continued ) Eqn

Cmpd. no.

105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104

Name Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Di–sopropyl amine Di–sopropyl ether Di–sopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane

Formula C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2

CAS 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0

Mol. wt. 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19 102.17476 114.18546 90.121 104.14758

C1 0.8711 1.39625 1.0841 1.8651 1.12465 1.1202 0.9061 0.95937 1.1503 0.58711 1.7805 1.3931 0.88998 0.8243 0.86464 0.92997 1.0897 1.1035 1.7411 0.78578 0.478542 0.41084 0.39348 0.38208 0.43981 0.44289 0.46877 5.2115 0.95523 1.0132 1.1136 0.55941 0.74495 0.74404 0.74858 1.1055 1.2591 1.3897 0.9551 0.89833 0.68184 0.85379 0.9554 0.82227 1.4345 1.173 1.9973 0.6181 0.69213 0.64619 0.89368 0.76327

C2 0.26805 0.26867 0.2581 0.2627 0.2728 0.27669 0.28268 0.2882 0.31861 0.25583 0.26846 0.29255 0.27376 0.26545 0.26888 0.27056 0.28356 0.27035 0.28205 0.27882 0.275162 0.25175 0.2492 0.24645 0.25661 0.27636 0.25875 0.315 0.26364 0.26634 0.24834 0.27243 0.26147 0.26112 0.26276 0.26533 0.27698 0.25678 0.27794 0.26142 0.23796 0.25675 0.26847 0.26314 0.25774 0.22856 0.24653 0.25786 0.26974 0.26881 0.26599 0.26742

C3 632.35 460.35 536.4 416.25 503.15 489 705.85 697.55 704.65 631 400.15 459.93 553.8 650.1 653 560.4 511.7 507 398 664 674 617.7 722.1 688 616.6 696 619.85 38.35 628 650.15 611 584.1 683.95 705 684.75 523 561.6 510 560 572 736.6 496.6 466.7 557.15 386.44 445 351.26 523.1 500.05 576 507.8 543

C4 0.2799 0.28571 0.2741 0.28571 0.28571 0.27646 0.2707 0.2857 0.30104 0.28498 0.26079 0.24913 0.28571 0.28495 0.29943 0.28943 0.25142 0.28699 0.29598 0.31067 0.28571 0.28571 0.28571 0.26125 0.29148 0.27668 0.29479 0.28571 0.29825 0.28571 0.27583 0.29932 0.31526 0.30815 0.30788 0.287 0.30492 0.2902 0.24132 0.2868 0.2062 0.27027 0.2814 0.27369 0.28178 0.28571 0.28153 0.271 0.28571 0.28036 0.28571 0.28571

C5

C6

C7

Tmin, K 227.95 136.75 209.63 175.43 150.35 155.97 285.39 304.19 307.93 177.14 245.25 182.48 279.69 296.60 242.00 169.67 179.28 138.13 145.59 189.64 285.00 243.51 304.55 280.05 206.89 247.56 229.15 18.73 210.15 282.85 220.60 175.30 248.39 256.15 326.14 176.19 237.49 178.01 192.50 172.71 301.15 223.35 156.85 169.20 154.56 179.60 136.95 176.85 187.65 204.81 159.95 226.10

Density at Tmin 10.385 17.055 13.702 22.272 13.333 12.855 9.6115 9.5725 9.4494 7.9387 18.517 14.074 9.3804 9.4693 10.09 11.16 11.906 13.47 18.658 8.9048 5.2396 5.3927 5.1809 5.2609 5.7328 5.0048 5.8954 42.945 11.799 11.704 15.358 6.6071 9.1207 9.1658 8.5175 13.549 13.462 17.974 10.925 11.526 10.39 10.575 11.487 10.47 18.006 18.336 27.399 8.0541 8.0673 7.6796 11.029 8.8431

Tmax, K 632.35 460.35 536.40 416.25 503.15 489.00 705.85 697.55 704.65 631.00 400.15 459.93 553.80 650.10 653.00 560.40 511.70 507.00 398.00 664.00 674.00 617.70 722.10 688.00 616.60 696.00 619.85 38.35 628.00 650.15 611.00 584.10 683.95 705.00 684.75 523.00 561.60 510.00 560.00 572.00 736.60 496.60 466.70 557.15 386.44 445.00 351.26 523.10 500.05 576.00 507.80 543.00

Density at Tmax 3.2498 5.1969 4.2003 7.0997 4.1226 4.0486 3.2054 3.3288 3.6104 2.2949 6.6323 4.7619 3.2509 3.1053 3.2157 3.4372 3.8429 4.0817 6.1730 2.8182 1.7391 1.6319 1.5790 1.5503 1.7139 1.6026 1.8117 16.5440 3.6232 3.8042 4.4842 2.0534 2.8491 2.8494 2.8489 4.1665 4.5458 5.4120 3.4364 3.4363 2.8654 3.3254 3.5587 3.1248 5.5657 5.1321 8.1017 2.3970 2.5659 2.4039 3.3598 2.8542

105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105

105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159

Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal

C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O

503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7

54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026 240.46774 114.18546

1.1717 1.5436 0.7565 0.55873 0.52953 0.54405 1.1058 1.5693 0.89615 0.72352 0.47977 1.0214 1.4029 1.1096 0.48611 1.1819 0.52133 0.659 0.33267 0.18166 1.9122 1.6288 0.8996 1.0936 0.70041 0.48864 0.66085 0.63566 0.61587 0.71751 2.0961 0.7842 1.315 1.3462 1.836 1.1343 0.47428 0.55729 0.8185 0.68162 1.3047 0.7405 0.7908 0.61243 4.2895 1.0146 1.693858 2.2261 3.897011 1.2486 1.938 1.1339 7.2475 0.21897 0.577362

0.25895 0.27784 0.27305 0.25143 0.24358 0.25026 0.27866 0.2679 0.23478 0.28629 0.25428 0.26351 0.27991 0.25189 0.25715 0.2813 0.26218 0.26428 0.24664 0.23351 0.27937 0.27469 0.25856 0.22636 0.26162 0.23894 0.25707 0.25613 0.26477 0.26903 0.27657 0.20702 0.25125 0.23289 0.26024 0.26168 0.25028 0.2714 0.26929 0.25152 0.2694 0.25563 0.266 0.24681 0.28587 0.27277 0.269323 0.25072 0.331636 0.20352 0.24225 0.24741 0.41865 0.23642 0.250575

473.2 437.2 500 591.15 606.15 596.15 615 400.1 649.6 537.3 766 402 503.04 729 777.4 587 766.8 550 658 768 305.32 514 523.3 456.15 617.15 698 655 571 609.15 569.5 282.34 593 720 537 469.15 508.4 674.6 583 489 567 499.15 546 500.23 559.95 144.12 560.09 375.31 317.42 420 771 588 490.15 5.2 736 620

0.27289 0.2572 0.27408 0.27758 0.26809 0.2658 0.31082 0.2882 0.28091 0.27121 0.30722 0.28421 0.2741 0.3311 0.28571 0.3047 0.31033 0.2766 0.28571 0.28571 0.29187 0.23178 0.278 0.25522 0.28454 0.28421 0.31103 0.27829 0.28054 0.27733 0.29147 0.20254 0.21868 0.23357 0.2696 0.2791 0.25442 0.29538 0.30621 0.3182 0.27866 0.2795 0.292 0.30858 0.28776 0.28291 0.28571 0.27343 0.28571 0.25178 0.24435 0.2612 0.24096 0.28571 0.28571

240.91 180.96 145.19 239.66 223.16 184.99 188.44 131.65 212.72 141.23 274.18 122.93 174.88 291.67 413.79 284.95 300.03 210.15 263.57 309.58 90.35 159.05 189.60 192.15 178.20 238.45 258.15 175.15 161.84 134.71 104.00 284.29 260.15 195.20 160.65 193.55 155.15 180.00 140.00 204.15 125.26 199.25 145.65 167.55 53.48 230.94 129.95 131.35 155.15 275.60 281.45 187.55 2.20 295.13 229.80

13.767 16.964 9.031 7.3417 7.5783 7.6258 12.413 18.95 13.954 7.9932 6.2334 12.898 15.556 14.111 5.6397 11.838 6.2648 7.9929 4.5205 2.7293 21.64 19.41 11.478 17.588 9.0407 7.2908 8.2198 8.4912 7.8679 9.0179 23.326 15.055 18.31 21.45 23.477 14.006 6.926 6.612 9.9236 8.9749 16.242 9.6317 9.8474 8.6934 44.888 11.374 20.099 29.345 30.92 25.488 26.806 15.702 37.115 3.2189 7.7462

473.20 437.20 500.00 591.15 606.15 596.15 615.00 400.10 649.60 537.30 766.00 402.00 503.04 729.00 777.40 587.00 766.80 550.00 658.00 768.00 305.32 514.00 523.30 456.15 617.15 698.00 655.00 571.00 609.15 569.50 282.34 593.00 720.00 537.00 469.15 508.40 674.60 583.00 489.00 567.00 499.15 546.00 500.23 559.95 144.12 560.09 375.31 317.42 420.00 771.00 588.00 490.15 5.20 736.00 620.00

4.5248 5.5557 2.7706 2.2222 2.1739 2.1739 3.9683 5.8578 3.8170 2.5272 1.8868 3.8761 5.0120 4.4051 1.8904 4.2016 1.9884 2.4936 1.3488 0.7780 6.8447 5.9296 3.4793 4.8312 2.6772 2.0450 2.5707 2.4818 2.3261 2.6670 7.5789 3.7880 5.2338 5.7804 7.0550 4.3347 1.8950 2.0534 3.0395 2.7100 4.8430 2.8968 2.9729 2.4814 15.0050 3.7196 6.2893 8.8788 11.7510 6.1350 8.0000 4.5831 17.3120 0.9262 2.3041

2-95

(Continued )

2-96

TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) (Continued ) Eqn

Cmpd. no.

105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105

160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211

Name Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate

Formula C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2

CAS 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7

Mol. wt. 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317

C1 0.61259 0.53066 0.55687 0.59339 0.59268 0.58247 0.66016 0.58622 0.67304 0.23289 0.668504 0.70824 0.62833 0.70093 0.67393 0.67816 0.67666 0.76925 0.78045 0.66372 0.84427 0.76277 1.0516 5.414 2.832 3.342 1.3413 2.8061 2.7672 0.88575 1.2801 0.87969 0.87025 2.9214 2.3267 0.88268 1.13 1.6085 0.97286 1.39 0.53382 0.84623 0.91991 0.72762 0.8189 0.91619 0.93391 1.1157 0.8363 0.75509 0.94575 0.76983

C2 0.26211 0.24729 0.24725 0.2602 0.25663 0.25279 0.26657 0.2726 0.26045 0.23659 0.252695 0.26411 0.25598 0.26776 0.25948 0.25634 0.25578 0.26809 0.26065 0.27345 0.27185 0.25248 0.16613 0.34893 0.2832 0.2729 0.18589 0.19362 0.27369 0.25736 0.2828 0.24543 0.24383 0.28976 0.27073 0.23568 0.2593 0.26436 0.26267 0.21405 0.23274 0.24625 0.27815 0.25244 0.26974 0.26752 0.27275 0.27671 0.27514 0.27183 0.26008 0.26173

C3 540.2 677.3 632.3 608.3 606.6 611.4 537.4 645 547 723 594 507.6 660.2 611.3 585.3 587.61 582.82 504 544 623 516.2 549 653.15 33.19 363.15 324.65 456.65 461.15 373.53 605 471.85 834 662 190.56 512.5 718 506.55 402.4 536 430.05 693 490 460.4 643 577.2 465 470 492 512.74 593 463.2 554.5

C4 0.28141 0.28289 0.31471 0.26968 0.27766 0.29818 0.28571 0.29644 0.28388 0.28571 0.28571 0.27537 0.25304 0.24919 0.26552 0.28365 0.27746 0.28571 0.28571 0.29185 0.2771 0.31611 0.1898 0.2706 0.28571 0.3217 0.28206 0.29847 0.29015 0.26265 0.2972 0.28571 0.28571 0.28881 0.24713 0.27379 0.2764 0.27987 0.2508 0.2275 0.28147 0.29041 0.28667 0.28571 0.23573 0.28164 0.2578 0.30821 0.27553 0.29127 0.30807 0.26879

C5

C6

C7

Tmin, K 182.57 265.83 239.15 220.00 234.15 238.15 154.12 229.92 192.22 291.31 214.93 177.83 269.25 228.55 223.00 217.35 217.50 133.39 170.05 192.62 141.25 183.65 274.69 13.95 185.15 158.97 259.83 189.79 187.68 227.15 177.95 409.15 288.15 90.69 175.47 301.15 175.15 170.45 196.32 179.69 260.75 159.53 113.25 193.00 155.95 135.58 139.39 160.15 157.48 175.30 183.45 187.35

Density at Tmin 7.6998 7.2212 7.5022 7.5173 7.5751 7.5514 8.2257 6.7277 8.4922 3.415 8.8708 8.747 8.0964 8.456 8.5181 8.7319 8.7631 9.5815 10.021 7.7733 10.23 10.133 31.934 38.487 27.985 34.854 27.202 58.861 29.13 11.42 13.561 11.417 11.834 28.18 27.915 13.012 14.475 19.031 12.203 25.378 8.2202 11.994 10.764 9.9915 10.248 11.332 11.216 12.581 9.7581 9.0056 11.519 9.7638

Tmax, K 540.20 677.30 632.30 608.30 606.60 611.40 537.40 645.00 547.00 723.00 594.00 507.60 660.20 611.30 585.30 587.61 582.82 504.00 544.00 623.00 516.20 549.00 653.15 33.19 363.15 324.65 456.65 461.15 373.53 605.00 471.85 834.00 662.00 190.56 512.50 718.00 506.55 402.40 536.00 430.05 693.00 490.00 460.40 643.00 577.20 465.00 470.00 492.00 512.74 593.00 463.20 554.50

Density at Tmax 2.3371 2.1459 2.2523 2.2805 2.3095 2.3042 2.4765 2.1505 2.5841 0.9844 2.6455 2.6816 2.4546 2.6178 2.5972 2.6455 2.6455 2.8694 2.9942 2.4272 3.1056 3.0211 6.3300 15.5160 10.0000 12.2460 7.2156 14.4930 10.1110 3.4417 4.5265 3.5843 3.5691 10.0820 8.5942 3.7452 4.3579 6.0845 3.7037 6.4938 2.2936 3.4365 3.3072 2.8823 3.0359 3.4248 3.4241 4.0320 3.0395 2.7778 3.6364 2.9413

105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105

212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266

Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid

CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N CH3NO2 N2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2

993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2

80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211

1.0674 0.73109 0.7013 0.70973 0.72836 0.84758 0.88824 0.9109 0.97608 1.2635 0.93767 1.067 1.525 0.84005 0.71687 1.0228 0.97887 0.86567 0.78912 1.9323 0.7761 0.4416 0.72701 0.71004 1.0631 0.92128 1.1446 0.9147 0.96145 0.87496 1.3052 0.64856 0.817948 1.2587 0.6348 7.3718 1.0024 3.2091 2.3736 1.3728 2.781 5.246 0.19199 0.473233 0.46321 0.41582 0.43682 0.419258 0.48661 0.47377 0.52152 0.20448 0.525901 0.5266 0.48251

0.26257 0.26971 0.266 0.26544 0.27241 0.27037 0.26914 0.276 0.28209 0.27878 0.25035 0.27102 0.2634 0.27638 0.26453 0.20692 0.27017 0.26836 0.25915 0.28018 0.25068 0.2521 0.26754 0.26981 0.27506 0.25442 0.2724 0.2594 0.26536 0.26862 0.26757 0.25877 0.269105 0.26433 0.25838 0.3067 0.23655 0.2861 0.2817 0.23793 0.27244 0.3044 0.23337 0.256918 0.25444 0.24284 0.25161 0.241912 0.25722 0.27052 0.25918 0.23474 0.25664 0.25693 0.25196

442 572.1 686 614 617 532.7 542 526 483 437.8 535.5 533 487.2 497 574.6 488 464.48 553.4 553.1 469.95 566 694 497.7 546.49 407.8 506.2 417.9 530.6 476.25 565 352.5 654 497.1 437 748.4 44.4 593 126.2 234 588.15 309.57 180.15 758 658.5 594.6 710.7 670.9 649.5 593.1 681 598.05 747 638.9 568.7 694.26

0.26569 0.29185 0.28571 0.26016 0.2478 0.28258 0.27874 0.26756 0.22529 0.2744 0.29964 0.29364 0.2806 0.27645 0.28918 0.28571 0.28998 0.28364 0.26512 0.28523 0.29773 0.28532 0.28268 0.29974 0.2758 0.27586 0.28172 0.2774 0.30088 0.30259 0.28799 0.31444 0.28571 0.25819 0.27727 0.2786 0.278 0.2966 0.29529 0.29601 0.2882 0.242 0.28571 0.28571 0.28571 0.30036 0.2498 0.28571 0.28571 0.30284 0.29177 0.28571 0.28571 0.28571 0.26842

139.05 146.58 285.15 280.15 269.15 130.73 146.62 168.54 182.55 160.00 186.48 167.23 174.15 188.00 189.15 256.15 127.93 180.15 171.64 150.18 224.95 240.00 119.55 176.00 113.54 298.97 132.81 185.65 133.97 160.17 116.34 249.95 164.55 151.15 333.15 24.56 183.63 63.15 66.46 244.60 182.30 109.50 305.04 267.30 219.66 285.55 268.15 238.15 191.91 253.05 223.15 301.31 251.65 216.38 289.65

13.626 9.0173 8.2091 8.2931 8.2628 10.491 10.98 10.538 10.789 13.995 12.663 12.671 18.811 9.3871 8.8617 17.666 11.933 10.46 10.352 21.564 10.176 5.938 9.2041 8.445 12.574 10.556 13.507 11.678 12.043 10.689 15.791 8.0099 9.7955 15.691 7.7545 61.796 15.556 31.063 26.555 19.632 27.928 44.487 2.8889 5.9415 6.0427 5.7592 5.8496 6.0223 6.3717 5.4532 6.5369 3.0418 6.6608 6.7049 6.3107

442.00 572.10 686.00 614.00 617.00 532.70 542.00 526.00 483.00 437.80 535.50 533.00 487.20 497.00 574.60 488.00 464.48 553.40 553.10 469.95 566.00 694.00 497.70 546.49 407.80 506.20 417.90 530.60 476.25 565.00 352.50 654.00 497.10 437.00 748.40 44.40 593.00 126.20 234.00 588.15 309.57 180.15 758.00 658.50 594.60 710.70 670.90 649.50 593.10 681.00 598.05 747.00 638.90 568.70 694.26

4.0652 2.7107 2.6365 2.6738 2.6738 3.1349 3.3003 3.3004 3.4602 4.5322 3.7454 3.9370 5.7897 3.0395 2.7100 4.9430 3.6232 3.2258 3.0450 6.8966 3.0960 1.7517 2.7174 2.6316 3.8650 3.6211 4.2019 3.5262 3.6232 3.2572 4.8780 2.5063 3.0395 4.7619 2.4568 24.0360 4.2376 11.2170 8.4260 5.7698 10.2080 17.2340 0.8227 1.8420 1.8205 1.7123 1.7361 1.7331 1.8918 1.7513 2.0122 0.8711 2.0492 2.0496 1.9150

2-97

(Continued )

2-98 TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) (Continued ) Eqn

Cmpd. no.

105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105

267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312

Name 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene

Formula C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8

CAS 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5

Mol. wt. 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912

C1 0.48979 0.52497 0.50006 0.5108 0.55449 0.52577 0.58945 1.1911 3.9143 3.3592 0.25142 0.85658 0.84947 0.73455 0.81754 0.81577 0.90411 0.71811 0.89816 0.65858 0.75345 0.8491 0.92099 0.45554 1.3798 0.63163 0.5393 1.6087 1.3757 1.2457 1.1799 0.61255 1.2861 1.0969 0.91281 0.73041 0.9195 0.57233 1.4403 0.915 1.093 1.0714 1.0923 0.83228 1.1945 0.7397

C2 0.24931 0.26186 0.24851 0.25386 0.25952 0.27234 0.26052 0.27038 0.28772 0.29884 0.23837 0.26811 0.26726 0.25636 0.26732 0.26594 0.27207 0.24129 0.26608 0.25367 0.27047 0.2352 0.25419 0.2523 0.31598 0.23373 0.22704 0.26543 0.27453 0.27281 0.2644 0.26769 0.26236 0.25568 0.22125 0.25456 0.23878 0.25171 0.26852 0.26134 0.27762 0.27214 0.26106 0.25385 0.24128 0.2603

C3 652.3 629.8 632.7 627.7 566.9 667.3 574 828 154.58 261 708 566.1 469.7 639.16 588.1 561 561.08 560.95 464.8 584.3 598 481.2 519 869 694.25 653 791 394 369.83 536.8 508.3 636 503.6 600.81 561.3 549.73 496.95 638.35 364.85 538 517 536.6 626 683 259 636

C4 0.27824 0.25257 0.29942 0.26735 0.28571 0.30063 0.28532 0.28571 0.2924 0.28523 0.28571 0.27354 0.27789 0.25522 0.25348 0.25551 0.30669 0.27996 0.28571 0.28571 0.30583 0.353 0.31077 0.24841 0.32768 0.28571 0.248 0.29895 0.29359 0.23994 0.24653 0.28571 0.3004 0.26857 0.26811 0.27666 0.2461 0.29616 0.28775 0.28 0.29781 0.29481 0.20459 0.23658 0.16693 0.3009

C5

C6

C7

Tmin, K 257.65 241.55 252.85 255.55 171.45 223.95 193.55 462.65 54.35 80.15 283.07 191.59 143.42 239.15 195.56 200.00 196.29 234.18 108.02 160.75 197.45 167.45 163.83 372.38 314.06 243.15 404.15 136.87 85.47 146.95 185.26 199.00 165.00 252.45 180.37 178.15 188.36 173.55 87.89 180.25 142.61 159.95 213.15 388.85 186.35 242.54

Density at Tmin 6.5738 6.5625 6.6477 6.6283 7.2155 6.0987 7.4832 12.405 40.77 33.361 3.6423 10.353 10.474 9.5869 10.061 10.017 10.398 10.102 11.521 9.073 8.8575 12.532 12.24 5.9853 11.244 9.6466 8.2218 19.479 16.583 15.206 14.663 7.4763 16.075 13.935 16.067 9.7941 13.764 7.9821 18.07 11.59 12.61 12.716 14.363 10.082 15.635 9.1088

Tmax, K 652.30 629.80 632.70 627.70 566.90 667.30 574.00 828.00 154.58 261.00 708.00 566.10 469.70 639.16 588.10 561.00 561.08 560.95 464.80 584.30 598.00 481.20 519.00 869.00 694.25 653.00 791.00 394.00 369.83 536.80 508.30 636.00 503.60 600.81 561.30 549.73 496.95 638.35 364.85 538.00 517.00 536.60 626.00 683.00 259.00 636.00

Density at Tmax 1.9646 2.0048 2.0122 2.0121 2.1366 1.9306 2.2626 4.4053 13.6050 11.2410 1.0547 3.1949 3.1784 2.8653 3.0583 3.0675 3.3231 2.9761 3.3755 2.5962 2.7857 3.6101 3.6232 1.8055 4.3667 2.7024 2.3754 6.0607 5.0111 4.5662 4.4626 2.2883 4.9020 4.2901 4.1257 2.8693 3.8508 2.2738 5.3638 3.5012 3.9370 3.9369 4.1841 3.2786 4.9507 2.8417

105 105 105 105 105 105 100 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 100 119 105 105 105

313 314 315 316 317 318 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 342 343 344 345

Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water Water m-Xylene o-Xylene p-Xylene

C4H6O4 O2S F6S O3S C8H6O4 C18H14 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O H2O C8H10 C8H10 C8H10

110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 7732-18-5 108-38-3 95-47-6 106-42-3

118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 18.01528 106.165 106.165 106.165

0.65882 2.106 1.3587 1.4969 0.41922 0.3448 5.7136 0.27248 1.2543 0.67717 1.1628 0.58988 1.2874 0.8792 0.9062 0.29934 0.7035 1.0116 0.6531 0.60394 0.59059 0.6028 0.48195 0.37378 0.36703 0.33113 0.9591 1.2703 1.5115 0.59595 –13.851 17.874 0.68902 0.69962 0.67752

0.21741 0.25842 0.2701 0.19013 0.17775 0.25116 –0.003474 0.24007 0.28084 0.27772 0.28954 0.27201 0.28194 0.27136 0.25475 0.2433 0.27386 0.25683 0.27002 0.25956 0.27424 0.27446 0.23093 0.21379 0.24876 0.23676 0.2593 0.26041 0.2707 0.24314 0.64038 35.618 0.26086 0.26143 0.25887

838 430.75 318.69 490.85 883.6 857

0.28571 0.2895 0.2921 0.4359 0.28571 0.29268

693 540.15 720 631.95 568 579.35 591.75 602 675 535.15 433.25 664.5 649.1 543.8 573.5 846 828 639 703.9 519.13 454 432 543.15 –0.0019124 19.655 617 630.3 616.2

0.28571 0.2912 0.2878 0.28674 0.27341 0.30781 0.29241 0.31 0.28571 0.2872 0.2696 0.26268 0.27713 0.2847 0.2741 0.28571 0.29905 0.28571 0.2762 0.27448 0.297 0.2716 0.24856 1.8211E-06 –9.1306 0.27479 0.27365 0.27596

–31.367 –813.56 – 17421000

460.85 197.67 223.15 289.95 700.15 329.35 288.15 279.01 164.65 237.38 176.99 373.96 234.94 178.18 236.50 267.76 158.45 156.08 243.15 229.33 165.78 172.22 398.40 354.00 247.57 288.45 180.35 173.15 119.36 178.35 273.16 273.16 225.30 247.98 286.41

10.21 25.298 12.631 24.241 7.102 4.5526 4.7126 3.889 13.998 7.638 12.408 5.7242 13.43 10.487 11.478 4.1817 8.2843 13.144 7.7278 7.689 6.9146 7.0934 7.0825 6.4521 4.9453 4.8594 12.287 15.664 18.481 8.8236 55.497 55.487 8.648 8.6229 8.1614

838.00 430.75 318.69 490.85 883.60 857.00 313.19 693.00 540.15 720.00 631.95 568.00 579.35 591.75 602.00 675.00 535.15 433.25 664.50 649.10 543.80 573.50 846.00 828.00 639.00 703.90 519.13 454.00 432.00 543.15 353.15 647.096 617.00 630.30 616.20

3.0303 8.1495 5.0304 7.8730 2.3585 1.3728 4.6256 1.1350 4.4662 2.4383 4.0160 2.1686 4.5662 3.2400 3.5572 1.2303 2.5688 3.9388 2.4187 2.3268 2.1536 2.1963 2.0870 1.7484 1.4754 1.3986 3.6988 4.8781 5.5837 2.4511 54.0010 17.8740 2.6413 2.6761 2.6172

Except for o-terphenyl and water, liquid density ρ is calculated by Eqn 105: ρ = C1/(C2[1 + (1 – T/C3)^C4]) where ρ is in mol/dm3 and T is in K. The pressure is equal to the vapor pressure for pressures greater than 1 atm and equal to 1 atm when the vapor pressure is less than 1 atm. Equation (2-100), used for the limited temperature ranges as noted for o-terphenyl and water, is ρ = C1 + C2T + C3T 2 + C4T 3. Equation (2-119), used for water, is ρ = C1 + C2τ1/3 + C3τ2/3 + C4τ5/3 + C5τ16/3 + C6τ43/3 + C7τ110/3 where τ = 1 − T/TC, and TC = critical temperature (647.096 K). Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016).

2-99

2-100

PHYSICAL AnD CHEMICAL DATA

DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM TABLE 2-33

Ammonia (nH3)*

% −15°C −10°C 1 2 4 8 12 16 20 24 28 30

−5°C

0°C

5°C

10°C

20°C

25°C

TABLE 2-38 Ferric nitrate [Fe(nO3)3]*

d 415

%

0.9943 0.9954 0.9959 0.9958 0.9955 0.9939 0.993 32 0.889 .9906 .9915 .9919 .9917 .9913 .9895 .988 36 .877 .9834 .9840 .9842 .9837 .9832 .9811 .980 40 .865 0.970 .9701 .9701 .9695 .9686 .9677 .9651 .964 45 .849 .958 .9576 .9571 .9561 .9548 .9534 .9501 .948 50 .832 .947 .9461 .9450 .9435 .9420 .9402 .9362 .934 60 .796 .9353 .9335 .9316 .9296 .9275 .9229 70 .755 .9249 .9226 .9202 .9179 .9155 .9101 80 .711 .9150 .9122 .9094 .9067 .9040 .8980 90 .665 .9101 .9070 .9040 .9012 .8983 .8920 100 .618

0°C

10°C

20°C

30°C

50°C

80°C

100°C

1 2 4 8 12 16 20 24

1.0033 1.0067 1.0135 1.0266 1.0391 1.0510 1.0625 1.0736

1.0029 1.0062 1.0126 1.0251 1.0370 1.0485 1.0596 1.0705

1.0013 1.0045 1.0107 1.0227 1.0344 1.0457 1.0567 1.0674

0.9987 1.0018 1.0077 1.0195 1.0310 1.0422 1.0532 1.0641

0.9910 .9940 .9999 1.0116 1.0231 1.0343 1.0454 1.0564

0.9749 .9780 .9842 .9963 1.0081 1.0198 1.0312 1.0426

0.9617 .9651 .9718 .9849 .9975 1.0096 1.0213 1.0327

∗International Critical Tables, vol. 3, p. 60. TABLE 2-35 Calcium Chloride (CaCl2)* 2 4 8 12 16 20 25 30 35 40

1.0708 1.1083 1.1471 1.1874

1 2 4 8 12 16 20 25

1.0065 1.0144 1.0304 1.0636 1.0989 1.1359 1.1748 1.2281

Ammonium Chloride (nH4Cl)*

%

% −5°C

d4

∗International Critical Tables, vol. 3, p. 68.

∗International Critical Tables, vol. 3, p. 59. TABLE 2-34

18

%

0°C

20°C

30°C

40°C

60°C

80°C 100°C 120°C† 140°C

1.0171 1.0346 1.0703 1.1072 1.1454 1.1853 1.2376 1.2922

1.0148 1.0316 1.0659 1.1015 1.1386 1.1775 1.2284 1.2816 1.3373 1.3957

1.0120 1.0286 1.0626 1.0978 1.1345 1.1730 1.2236 1.2764 1.3316 1.3895

1.0084 1.0249 1.0586 1.0937 1.1301 1.1684 1.2186 1.2709 1.3255 1.3826

0.9994 1.0158 1.0492 1.0840 1.1202 1.1581 1.2079 1.2597 1.3137 1.3700

0.9881 1.0046 1.0382 1.0730 1.1092 1.1471 1.1965 1.2478 1.3013 1.3571

0.9748 0.9915 1.0257 1.0610 1.0973 1.1352 1.1846 1.2359 1.2893 1.3450

0.9596 0.9765 1.0111 1.0466 1.0835 1.1219

0.9428 0.9601 0.9954 1.0317 1.0691 1.1080

∗International Critical Tables, vol. 3, pp. 72–73. † Corrected to atmospheric pressure. TABLE 2-36 Ferric Chloride (FeCl3)* %

0°C

10°C

20°C

30°C

1 2 4 8 12 16 20 25 30 35 40 45 50

1.0086 1.0174 1.0347 1.0703 1.1088 1.1475 1.1870 1.2400 1.2970 1.3605 1.4280

1.0084 1.0168 1.0341 1.0692 1.1071 1.1449 1.1847 1.2380 1.2950 1.3580 1.4235 1.4920 1.5610

1.0068 1.0152 1.0324 1.0669 1.1040 1.1418 1.1820 1.2340 1.2910 1.3530 1.4175 1.4850 1.5510

1.0040 1.0122 1.0292 1.0636 1.1006 1.1386 1.1786 1.2290 1.2850 1.3475 1.4115

TABLE 2-37 Ferric Sulfate [Fe2(SO4)3]* 1 2 4 8 12 16 20 30 40 50 60

%

15°C

18°C

TABLE 2-40 Hydrogen Cyanide (HCn)*

20°C

0.2 1.00068 1.0002 0.4 1.00275 1.0022 0.8 1.00645 1.0062 1.0 1.0090 1.0085 1.0082 4.0 1.0380 1.0375 8.0 1.0790 1.0785 12.0 1.1235 1.1220 16.0 1.1690 1.1675 20.0 1.2150 1.2135 ∗International Critical Tables, vol. 3, p. 68.

17.5

d4

1.0072 1.0157 1.0327 1.0670 1.1028 1.1409 1.1811 1.3073 1.4487 1.6127 1.7983

∗International Critical Tables, vol. 3, p. 68.

15

%

d4

1 2 4 8 12 16 82 90 100

0.998 0.996 0.993 0.984 0.971 0.956 0.752 0.724 0.691

∗International Critical Tables, vol. 3, p. 61.

TABLE 2-41 Hydrogen Chloride (HCl) %

−5°C

0°C

10°C

20°C

40°C

60°C

80°C

100°C

1 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

1.0048 1.0104 1.0213 1.0321 1.0428 1.0536 1.0645 1.0754 1.0864 1.0975 1.1087 1.1200 1.1314 1.1426 1.1537 1.1648

1.0052 1.0106 1.0213 1.0319 1.0423 1.0528 1.0634 1.0741 1.0849 1.0958 1.1067 1.1177 1.1287 1.1396 1.1505 1.1613

1.0048 1.0100 1.0202 1.0303 1.0403 1.0504 1.0607 1.0711 1.0815 1.0920 1.1025 1.1131 1.1238 1.1344 1.1449 1.1553

1.0032 1.0082 1.0181 1.0279 1.0376 1.0474 1.0574 1.0675 1.0776 1.0878 1.0980 1.1083 1.1187 1.1290 1.1392 1.1493 1.1593 1.1691 1.1789 1.1885 1.1980

0.9970 1.0019 1.0116 1.0211 1.0305 1.0400 1.0497 1.0594 1.0692 1.0790 1.0888 1.0986 1.1085 1.1183 1.1280 1.1376

0.9881 0.9930 1.0026 1.0121 1.0215 1.0310 1.0406 1.0502 1.0598 1.0694 1.0790 1.0886 1.0982 1.1076 1.1169 1.1260

0.9768 0.9819 0.9919 1.0016 1.0111 1.0206 1.0302 1.0398 1.0494 1.0590 1.0685 1.0780 1.0874 1.0967 1.1058 1.1149

0.9636 0.9688 0.9791 0.9892 0.9992 1.0090 1.0188 1.0286 1.0383 1.0479 1.0574 1.0668 1.0761 1.0853 1.0942 1.1030

∗International Critical Tables, vol. 3, p. 54.

TABLE 2-42 Hydrogen Peroxide (H2O2)*

∗International Critical Tables, vol. 3, p. 68.

%

TABLE 2-39 Ferrous Sulfate (FeSO4)*

18

18

%

d4

%

d4

1 2 4 6 8 10 12 14 16 18 20 22 24

1.0022 1.0058 1.0131 1.0204 1.0277 1.0351 1.0425 1.0499 1.0574 1.0649 1.0725 1.0802 1.0880

26 28 30 35 40 45 50 55 60 70 80 90 100

1.0959 1.1040 1.1122 1.1327 1.1536 1.1749 1.1966 1.2188 1.2416 1.2897 1.3406 1.3931 1.4465

∗International Critical Tables, vol. 3, p. 54.

DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM

2-101

TABLE 2-43 nitric Acid (HnO3)* %

0°C

5°C

10°C

15°C

20°C

25°C

30°C

40°C

50°C

60°C

80°C

100°C

1 2 3 4

1.0058 1.0117 1.0176 1.0236

1.00572 1.01149 1.01730 1.02315

1.00534 1.01099 1.01668 1.02240

1.00464 1.01018 1.01576 1.02137

1.00364 1.00909 1.01457 1.02008

1.00241 1.00778 1.01318 1.01861

1.0009 1.0061 1.0114 1.0168

0.9973 1.0025 1.0077 1.0129

0.9931 0.9982 1.0033 1.0084

0.9882 0.9932 0.9982 1.0033

0.9767 0.9816 0.9865 0.9915

0.9632 0.9681 0.9730 0.9779

5 6 7 8 9

1.0296 1.0357 1.0418 1.0480 1.0543

1.02904 1.03497 1.0410 1.0471 1.0532

1.02816 1.03397 1.0399 1.0458 1.0518

1.02702 1.03272 1.0385 1.0443 1.0502

1.02563 1.03122 1.0369 1.0427 1.0485

1.02408 1.02958 1.0352 1.0409 1.0466

1.0222 1.0277 1.0333 1.0389 1.0446

1.0182 1.0235 1.0289 1.0344 1.0399

1.0136 1.0188 1.0241 1.0295 1.0349

1.0084 1.0136 1.0188 1.0241 1.0294

0.9965 1.0015 1.0066 1.0117 1.0169

0.9829 0.9879 0.9929 0.9980 1.0032

10 11 12 13 14

1.0606 1.0669 1.0733 1.0797 1.0862

1.0594 1.0656 1.0718 1.0781 1.0845

1.0578 1.0639 1.0700 1.0762 1.0824

1.0561 1.0621 1.0681 1.0742 1.0803

1.0543 1.0602 1.0661 1.0721 1.0781

1.0523 1.0581 1.0640 1.0699 1.0758

1.0503 1.0560 1.0618 1.0676 1.0735

1.0455 1.0511 1.0567 1.0624 1.0681

1.0403 1.0458 1.0513 1.0568 1.0624

1.0347 1.0401 1.0455 1.0509 1.0564

1.0221 1.0273 1.0326 1.0379 1.0432

1.0083 1.0134 1.0186 1.0238 1.0289

15 16 17 18 19

1.0927 1.0992 1.1057 1.1123 1.1189

1.0909 1.0973 1.1038 1.1103 1.1168

1.0887 1.0950 1.1014 1.1078 1.1142

1.0865 1.0927 1.0989 1.1052 1.1115

1.0842 1.0903 1.0964 1.1026 1.1088

1.0818 1.0879 1.0940 1.1001 1.1062

1.0794 1.0854 1.0914 1.0974 1.1034

1.0739 1.0797 1.0855 1.0913 1.0972

1.0680 1.0737 1.0794 1.0851 1.0908

1.0619 1.0675 1.0731 1.0787 1.0843

1.0485 1.0538 1.0592 1.0646 1.0700

1.0341 1.0393 1.0444 1.0496 1.0547

20 21 22 23 24

1.1255 1.1322 1.1389 1.1457 1.1525

1.1234 1.1300 1.1366 1.1433 1.1501

1.1206 1.1271 1.1336 1.1402 1.1469

1.1178 1.1242 1.1306 1.1371 1.1437

1.1150 1.1213 1.1276 1.1340 1.1404

1.1123 1.1185 1.1247 1.1310 1.1374

1.1094 1.1155 1.1217 1.1280 1.1343

1.1031 1.1090 1.1150 1.1210 1.1271

1.0966 1.1024 1.1083 1.1142 1.1201

1.0899 1.0956 1.1013 1.1070 1.1127

1.0754 1.0808 1.0862 1.0917 1.0972

1.0598 1.0650 1.0701 1.0753 1.0805

25 26 27 28 29

1.1594 1.1663 1.1733 1.1803 1.1874

1.1569 1.1638 1.1707 1.1777 1.1847

1.1536 1.1603 1.1670 1.1738 1.1807

1.1503 1.1569 1.1635 1.1702 1.1770

1.1469 1.1534 1.1600 1.1666 1.1733

1.1438 1.1502 1.1566 1.1631 1.1697

1.1406 1.1469 1.1533 1.1597 1.1662

1.1332 1.1394 1.1456 1.1519 1.1582

1.1260 1.1320 1.1381 1.1442 1.1503

1.1185 1.1244 1.1303 1.1362 1.1422

1.1027 1.1083 1.1139 1.1195 1.1251

1.0857 1.0910 1.0963 1.1016 1.1069

30 31 32 33 34

1.1945 1.2016 1.2088 1.2160 1.2233

1.1917 1.1988 1.2059 1.2131 1.2203

1.1876 1.1945 1.2014 1.2084 1.2155

1.1838 1.1906 1.1974 1.2043 1.2113

1.1800 1.1867 1.1934 1.2002 1.2071

1.1763 1.1829 1.1896 1.1963 1.2030

1.1727 1.1792 1.1857 1.1922 1.1988

1.1645 1.1708 1.1772 1.1836 1.1901

1.1564 1.1625 1.1687 1.1749 1.1812

1.1482 1.1542 1.1602 1.1662 1.1723

1.1307 1.1363 1.1419 1.1476 1.1533

1.1122 1.1175 1.1228 1.1281 1.1335

35 36 37 38 39

1.2306 1.2375 1.2444 1.2513 1.2581

1.2275 1.2344 1.2412 1.2479 1.2546

1.2227 1.2294 1.2361 1.2428 1.2494

1.2183 1.2249 1.2315 1.2381 1.2446

1.2140 1.2205 1.2270 1.2335 1.2399

1.2098 1.2163 1.2227 1.2291 1.2354

1.2055 1.2119 1.2182 1.2245 1.2308

1.1966 1.2028 1.2089 1.2150 1.2210

1.1876 1.1936 1.1995 1.2054 1.2112

1.1784 1.1842 1.1899 1.1956 1.2013

1.1591 1.1645 1.1699 1.1752 1.1805

1.1390 1.1440 1.1490 1.1540 1.1589

40 41 42 43 44

1.2649 1.2717 1.2786 1.2854 1.2922

1.2613 1.2680 1.2747 1.2814 1.2880

1.2560 1.2626 1.2692 1.2758 1.2824

1.2511 1.2576 1.2641 1.2706 1.2771

1.2463 1.2527 1.2591 1.2655 1.2719

1.2417 1.2480 1.2543 1.2606 1.2669

1.2370 1.2432 1.2494 1.2556 1.2618

1.2270 1.2330 1.2390 1.2450 1.2510

1.2170 1.2229 1.2287 1.2345 1.2403

1.2069 1.2126 1.2182 1.2238 1.2294

1.1858 1.1911 1.1963 1.2015 1.2067

1.1638 1.1687 1.1735 1.1783 1.1831

45 46 47 48 49

1.2990 1.3058 1.3126 1.3194 1.3263

1.2947 1.3014 1.3080 1.3147 1.3214

1.2890 1.2955 1.3021 1.3087 1.3153

1.2836 1.2901 1.2966 1.3031 1.3096

1.2783 1.2847 1.2911 1.2975 1.3040

1.2732 1.2795 1.2858 1.2921 1.2984

1.2680 1.2742 1.2804 1.2867 1.2929

1.2570 1.2630 1.2690 1.2750 1.2811

1.2461 1.2519 1.2577 1.2635 1.2693

1.2350 1.2406 1.2462 1.2518 1.2575

1.2119 1.2171 1.2223 1.2275 1.2328

1.1879 1.1927 1.1976 1.2024 1.2073

50 51 52 53 54

1.3327 1.3391 1.3454 1.3517 1.3579

1.3277 1.3339 1.3401 1.3462 1.3523

1.3215 1.3277 1.3338 1.3399 1.3459

1.3157 1.3218 1.3278 1.3338 1.3397

1.3100 1.3160 1.3219 1.3278 1.3336

1.3043 1.3102 1.3160 1.3218 1.3275

1.2987 1.3045 1.3102 1.3159 1.3215

1.2867 1.2923 1.2978 1.3033 1.3087

1.2748 1.2802 1.2856 1.2909 1.2961

1.2628 1.2680 1.2731 1.2782 1.2833

1.2377 1.2425 1.2473 1.2521 1.2568

1.2118 1.2163 1.2208 1.2252 1.2296

55 56 57 58 59

1.3640 1.3700 1.3759 1.3818 1.3875

1.3583 1.3642 1.3700 1.3757 1.3813

1.3518 1.3576 1.3634 1.3691 1.3747

1.3455 1.3512 1.3569 1.3625 1.3680

1.3393 1.3449 1.3505 1.3560 1.3614

1.3331 1.3386 1.3441 1.3495 1.3548

1.3270 1.3324 1.3377 1.3430 1.3482

1.3141 1.3194 1.3246 1.3298 1.3348

1.3013 1.3064 1.3114 1.3164 1.3213

1.2883 1.2932 1.2981 1.3029 1.3077

1.2615 1.2661 1.2706 1.2751 1.2795

1.2339 1.2382 1.2424 1.2466 1.2507

60 61 62 63 64

1.3931 1.3986 1.4039 1.4091

1.3868 1.3922 1.3975 1.4027 1.4078

1.3801 1.3855 1.3907 1.3958 1.4007

1.3734 1.3787 1.3838 1.3888 1.3936

1.3667 1.3719 1.3769 1.3818 1.3866

1.3600 1.3651 1.3700 1.3748 1.3795

1.3533 1.3583 1.3632 1.3679 1.3725

1.3398 1.3447 1.3494 1.3540

1.3261 1.3308 1.3354 1.3398

1.3124 1.3169 1.3213 1.3255

1.2839 1.2881 1.2922 1.2962

1.2547 1.2587 1.2625 1.2661 (Continued )

2-102

PHYSICAL AnD CHEMICAL DATA

TABLE 2-43 nitric Acid (HnO3) (Continued ) %

5°C

10°C

15°C

20°C

25°C

30°C

65 66 67 68 69

0°C

1.4128 1.4177 1.4224 1.4271 1.4317

1.4055 1.4103 1.4150 1.4196 1.4241

1.3984 1.4031 1.4077 1.4122 1.4166

1.3913 1.3959 1.4004 1.4048 1.4091

1.3841 1.3887 1.3932 1.3976 1.4019

1.3770 1.3814 1.3857 1.3900 1.3942

70 71 72 73 74

1.4362 1.4406 1.4449 1.4491 1.4532

1.4285 1.4328 1.4371 1.4413 1.4454

1.4210 1.4252 1.4294 1.4335 1.4376

1.4134 1.4176 1.4218 1.4258 1.4298

1.4061 1.4102 1.4142 1.4182 1.4221

1.3983 1.4023 1.4063 1.4103 1.4142

75 76 77 78 79

1.4573 1.4613 1.4652 1.4690 1.4727

1.4494 1.4533 1.4572 1.4610 1.4647

1.4415 1.4454 1.4492 1.4529 1.4565

1.4337 1.4375 1.4413 1.4450 1.4486

1.4259 1.4296 1.4333 1.4369 1.4404

1.4180 1.4217 1.4253 1.4288 1.4323

80 81 82 83 84

1.4764 1.4800 1.4835 1.4869 1.4903

1.4683 1.4718 1.4753 1.4787 1.4820

1.4601 1.4636 1.4670 1.4704 1.4737

1.4521 1.4555 1.4589 1.4622 1.4655

1.4439 1.4473 1.4507 1.4540 1.4572

1.4357 1.4391 1.4424 1.4456 1.4487

85 86 87 88 89

1.4936 1.4968 1.4999 1.5029 1.5058

1.4852 1.4883 1.4913 1.4942 1.4970

1.4769 1.4799 1.4829 1.4858 1.4885

1.4686 1.4716 1.4745 1.4773 1.4800

1.4603 1.4633 1.4662 1.4690 1.4716

1.4518 1.4548 1.4577 1.4605 1.4631

90 91 92 93 94

1.5085 1.5111 1.5136 1.5156 1.5177

1.4997 1.5023 1.5048 1.5068 1.5088

1.4911 1.4936 1.4960 1.4979 1.4999

1.4826 1.4850 1.4873 1.4892 1.4912

1.4741 1.4766 1.4789 1.4807 1.4826

1.4656 1.4681 1.4704 1.4722 1.4741

95 96 97 98 99 100

1.5198 1.5220 1.5244 1.5278 1.5327 1.5402

1.5109 1.5130 1.5152 1.5187 1.5235 1.5310

1.5019 1.5040 1.5062 1.5096 1.5144 1.5217

1.4932 1.4952 1.4974 1.5008 1.5056 1.5129

1.4846 1.4867 1.4889 1.4922 1.4969 1.5040

1.4761 1.4781 1.4802 1.4835 1.4881 1.4952

40°C

50°C

60°C

80°C

100°C

∗International Critical Tables, vol. 3, pp. 58–59.

TABLE 2-44 Perchloric Acid (HClO4)* 15

%

d4

1 2 4 6 8 10 12 14 16 18 20 22 24 26

1.0050 1.0109 1.0228 1.0348 1.0471 1.0597 1.0726 1.0589 1.0995 1.1135 1.1279 1.1428 1.1581 1.1738

20

d4

25

50

TABLE 2-46 Potassium Bicarbonate (KHCO3)* 15

20

50

d4

d4

%

d4

d4

d4

1.0020 1.0070 1.0169 1.0270 1.0372 1.0475

0.9933 0.9986 0.9906 1.0205 1.0320 1.0440 1.0560 1.0680 1.0810 1.0940 1.1070 1.1205 1.1345 1.1490

28 30 32 34 36 38 40 45 50 55 60 65 70

1.1900 1.2067 1.2239 1.2418 1.2603 1.2794 1.2991 1.3521 1.4103 1.4733 1.5389 1.6059 1.6736

1.1851 1.2013 1.2183 1.2359 1.2542 1.2732 1.2927 1.3450 1.4018 1.4636 1.5298 1.5986 1.6680

1.1645 1.1800 1.1960 1.2130 1.2310 1.2490 1.2680 1.3180 1.3730 1.4320 1.4950 1.5620 1.6290

1.1697 ∗International Critical Tables, vol. 3, p. 54.

2%

6%

14%

20%

26%

0 1.0113 1.0339 1.0811 1.1192 10 1.0109 1.0330 1.0792 1.1167 1.1567 20 1.0092 1.0309 1.0764 1.1134 1.1529 30 1.0065 1.0279 1.0728 1.1094 1.1484 40 1.0029 1.0241 1.0685 1.1048 ∗International Critical Tables, vol. 3, p. 61.

1%

2%

4%

0 1.0066 1.0134 1.0270 10 1.0064 1.0132 1.0268 15 1.0058 1.0125 1.0260 20 1.0049 1.0117 1.0252 30 1.0024 1.0092 1.0228 40 0.9990 1.0058 1.0195 50 0.9949 1.0017 1.0154 60 0.9901 0.9969 1.0106 80 0.9786 0.9855 0.9993 100 0.9653 0.9722 0.9860 ∗International Critical Tables, vol. 3, p. 90.

6%

8%

10%

1.0396

1.0534

1.0674

TABLE 2-47 Potassium Carbonate (K2CO3)*

TABLE 2-45 Phosphoric Acid (H3PO4)* °C

°C

35%

50%

75%

100%

1.221 1.216 1.211

1.341 1.335 1.329

1.579 1.572

1.870 1.862

%

0°C

10°C

20°C

40°C

60°C

80°C

100°C

1 2 4 8 12 16 20 24 28 30 35 40 45 50

1.0094 1.0189 1.0381 1.0768 1.1160 1.1562 1.1977 1.2405 1.2846 1.3071 1.3646 1.4244 1.4867 1.5517

1.0089 1.0182 1.0369 1.0746 1.1131 1.1530 1.1941 1.2366 1.2804 1.3028 1.3600 1.4195 1.4815 1.5462

1.0072 1.0163 1.0345 1.0715 1.1096 1.1490 1.1898 1.2320 1.2756 1.2979 1.3548 1.4141 1.4759 1.5404

1.0010 1.0098 1.0276 1.0640 1.1013 1.1399 1.1801 1.2219 1.2652 1.2873 1.3440 1.4029 1.4644 1.5285

0.9919 1.0005 1.0180 1.0538 1.0906 1.1290 1.1690 1.2106 1.2538 1.2759 1.3324 1.3913 1.4528 1.5169

0.9803 0.9889 1.0063 1.0418 1.0786 1.1170 1.1570 1.1986 1.2418 1.2640 1.3206 1.3795 1.4408 1.5048

0.9670 0.9756 0.9951 1.0291 1.0663 1.1049 1.1451 1.1869 1.2301 1.2522 1.3089 1.3678 1.4290 1.4928

∗International Critical Tables, vol. 3, p. 90.

DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM TABLE 2-48 Potassium Chloride (KCl)*

2-103

TABLE 2-52 Sodium Carbonate (na2CO3)*

%

0°C

20°C

25°C

40°C

60°C

80°C

100°C

%

0°C

10°C

20°C

30°C

40°C

60°C

80°C

100°C

1.0 2.0 4.0 8.0 12.0 16.0 20.0 24.0 28.0

1.00661 1.01335 1.02690 1.05431 1.08222 1.11068 1.13973

1.00462 1.01103 1.02391 1.05003 1.07679 1.10434 1.13280 1.16226

1.00342 1.00977 1.02255 1.04847 1.07506 1.10245 1.13072 1.15995

0.99847 1.00471 1.01727 1.04278 1.06897 1.09600 1.12399 1.15299 1.18304

0.9894 0.9956 1.0080 1.0333 1.0592 1.0861 1.1138 1.1425 1.1723

0.9780 0.9842 0.9966 1.0219 1.0478 1.0746 1.1024 1.1311 1.1609

0.9646 0.9708 0.9634 1.0888 1.0350 1.0619 1.0897 1.1185 1.1483

1 2 4 8 12 14 16 18 20 24 28 30

1.0109 1.0219 1.0439 1.0878 1.1319 1.1543

1.0103 1.0210 1.0423 1.0850 1.1284 1.1506

1.0086 1.0190 1.0398 1.0816 1.1244 1.1463

1.0058 1.0159 1.0363 1.0775 1.1200 1.1417 1.1636 1.1859 1.2086 1.2552 1.3031 1.3274

1.0022 1.0122 1.0323 1.0732 1.1150 1.1365

0.9929 1.0027 1.0223 1.0625 1.1039 1.1251

0.9814 0.9910 1.0105 1.0503 1.0914 1.1125

0.9683 0.9782 0.9980 1.0380 1.0787 1.0996

%

110°C

120°C

130°C

3.79 7.45 13.62

0.9733 0.9978 1.0388

0.9663 0.9899 1.0313

0.9583 0.9827 1.0238

140°C 0.9502 0.9745 1.0159

∗International Critical Tables, vol. 3, pp. 82–83.

∗International Critical Tables, vol. 3, p. 87.

TABLE 2-53 Sodium Chloride (naCl)*

TABLE 2-49 Potassium Hydroxide (KOH)* %

d

15 4

1.0 1.0083 2.0 1.0175 4.0 1.0359 6.0 1.0544 8.0 1.0730 10.0 1.0918 15.0 1.1396 20.0 1.1884 25.0 1.2387 30.0 1.2905 35.0 1.3440 40.0 1.3991 45.0 1.4558 50.0 1.5143 51.7 1.5355 (sat’d. soln.) ∗International Critical Tables, vol. 3, p. 86.

0°C

10°C

20°C

1 2 4 8 12 16 20 24

1.00654 1.01326 1.02677 1.05419 1.08221

1.00615 1.01262 1.02566 1.05226 1.07963

1.00447 1.01075 1.02344 1.04940 1.07620 1.10392 1.13261 1.16233

10°C

25°C

40°C

60°C

80°C

100°C

1.00747 1.01509 1.03038 1.06121 1.09244 1.12419 1.15663 1.18999 1.20709

1.00707 1.01442 1.02920 1.05907 1.08946 1.12056 1.15254 1.18557 1.20254

1.00409 1.01112 1.02530 1.05412 1.08365 1.11401 1.14533 1.17776 1.19443

0.99908 1.00593 1.01977 1.04798 1.07699 1.10688 1.13774 1.16971 1.18614

0.9900 0.9967 1.0103 1.0381 1.0667 1.0962 1.1268 1.1584 1.1747

0.9785 0.9852 0.9988 1.0264 1.0549 1.0842 1.1146 1.1463 1.1626

0.9651 0.9719 0.9855 1.0134 1.0420 1.0713 1.1017 1.1331 1.1492

TABLE 2-54 Sodium Hydroxide (naOH)*

40°C

60°C

80°C

100°C

0.99825 1.00430 1.01652 1.04152 1.06740 1.09432 1.12240 1.15175

0.9890 0.9949 1.0068 1.0313 1.0567 1.0831 1.1106 1.1391

0.9776 0.9834 0.9951 1.0192 1.0442 1.0703 1.0974 1.1256

0.9641 0.9699 0.9816 1.0056 1.0304 1.0562 1.0831 1.1110

∗International Critical Tables, vol. 3, p. 89.

0°C

1 2 4 8 12 16 20 24 26

∗International Critical Tables, vol. 3, p. 79.

TABLE 2-50 Potassium nitrate (KnO3)* %

%

%

0°C

15°C

20°C

40°C

60°C

80°C

100°C

1 2 4 8 12 16 20 24 28 32 36 40 44 48 50

1.0124 1.0244 1.0482 1.0943 1.1399 1.1849 1.2296 1.2741 1.3182 1.3614 1.4030 1.4435 1.4825 1.5210 1.5400

1.01065 1.02198 1.04441 1.08887 1.13327 1.17761 1.22183 1.26582 1.3094 1.3520 1.3933 1.4334 1.4720 1.5102 1.5290

1.0095 1.0207 1.0428 1.0869 1.1309 1.1751 1.2191 1.2629 1.3064 1.3490 1.3900 1.4300 1.4685 1.5065 1.5253

1.0033 1.0139 1.0352 1.0780 1.1210 1.1645 1.2079 1.2512 1.2942 1.3362 1.3768 1.4164 1.4545 1.4922 1.5109

0.9941 1.0045 1.0254 1.0676 1.1101 1.1531 1.1960 1.2388 1.2814 1.3232 1.3634 1.4027 1.4405 1.4781 1.4967

0.9824 0.9929 1.0139 1.0560 1.0983 1.1408 1.1833 1.2259 1.2682 1.3097 1.3498 1.3889 1.4266 1.4641 1.4827

0.9693 0.9797 1.0009 1.0432 1.0855 1.1277 1.1700 1.2124 1.2546 1.2960 1.3360 1.3750 1.4127 1.4503 1.4690

∗International Critical Tables, vol. 3, p. 79.

TABLE 2-51 Sodium Acetate (naC2H3O2)* 20

%

d4

1 2 4 8 12 18 20 26 28

1.0033 1.0084 1.0186 1.0392 1.0598 1.0807 1.1021 1.1351 1.1462

∗International Critical Tables, vol. 3, p. 83.

2-104

PHYSICAL AnD CHEMICAL DATA

TABLE 2-55 Sulfuric Acid (H2SO4)* %

0°C

10°C

15°C

20°C

25°C

30°C

40°C

50°C

60°C

80°C

100°C

1 2 3 4

1.0074 1.0147 1.0219 1.0291

1.0068 1.0138 1.0206 1.0275

1.0060 1.0129 1.0197 1.0264

1.0051 1.0118 1.0184 1.0250

1.0038 1.0104 1.0169 1.0234

1.0022 1.0087 1.0152 1.0216

0.9986 1.0050 1.0113 1.0176

0.9944 1.0006 1.0067 1.0129

0.9895 0.9956 1.0017 1.0078

0.9779 0.9839 0.9900 0.9961

0.9645 0.9705 0.9766 0.9827

5 6 7 8 9

1.0364 1.0437 1.0511 1.0585 1.0660

1.0344 1.0414 1.0485 1.0556 1.0628

1.0332 1.0400 1.0469 1.0539 1.0610

1.0317 1.0385 1.0453 1.0522 1.0591

1.0300 1.0367 1.0434 1.0502 1.0571

1.0281 1.0347 1.0414 1.0481 1.0549

1.0240 1.0305 1.0371 1.0437 1.0503

1.0192 1.0256 1.0321 1.0386 1.0451

1.0140 1.0203 1.0266 1.0330 1.0395

1.0022 1.0084 1.0146 1.0209 1.0273

0.9888 0.9950 1.0013 1.0076 1.0140

10 11 12 13 14

1.0735 1.0810 1.0886 1.0962 1.1039

1.0700 1.0773 1.0846 1.0920 1.0994

1.0681 1.0753 1.0825 1.0898 1.0971

1.0661 1.0731 1.0802 1.0874 1.0947

1.0640 1.0710 1.0780 1.0851 1.0922

1.0617 1.0686 1.0756 1.0826 1.0897

1.0570 1.0637 1.0705 1.0774 1.0844

1.0517 1.0584 1.0651 1.0719 1.0788

1.0460 1.0526 1.0593 1.0661 1.0729

1.0338 1.0403 1.0469 1.0536 1.0603

1.0204 1.0269 1.0335 1.0402 1.0469

15 16 17 18 19

1.1116 1.1194 1.1272 1.1351 1.1430

1.1069 1.1145 1.1221 1.1298 1.1375

1.1045 1.1120 1.1195 1.1271 1.1347

1.1020 1.1094 1.1168 1.1243 1.1318

1.0994 1.1067 1.1141 1.1215 1.1290

1.0968 1.1040 1.1113 1.1187 1.1261

1.0914 1.0985 1.1057 1.1129 1.1202

1.0857 1.0927 1.0998 1.1070 1.1142

1.0798 1.0868 1.0938 1.1009 1.1081

1.0671 1.0740 1.0809 1.0879 1.0950

1.0537 1.0605 1.0674 1.0744 1.0814

20 21 22 23 24

1.1510 1.1590 1.1670 1.1751 1.1832

1.1453 1.1531 1.1609 1.1688 1.1768

1.1424 1.1501 1.1579 1.1657 1.1736

1.1394 1.1471 1.1548 1.1626 1.1704

1.1365 1.1441 1.1517 1.1594 1.1672

1.1335 1.1410 1.1486 1.1563 1.1640

1.1275 1.1349 1.1424 1.1500 1.1576

1.1215 1.1288 1.1362 1.1437 1.1512

1.1153 1.1226 1.1299 1.1373 1.1448

1.1021 1.1093 1.1166 1.1239 1.1313

1.0885 1.0957 1.1029 1.1102 1.1176

25 26 27 28 29

1.1914 1.1996 1.2078 1.2160 1.2243

1.1848 1.1929 1.2010 1.2091 1.2173

1.1816 1.1896 1.1976 1.2057 1.2138

1.1783 1.1862 1.1942 1.2023 1.2104

1.1750 1.1829 1.1909 1.1989 1.2069

1.1718 1.1796 1.1875 1.1955 1.2035

1.1653 1.1730 1.1808 1.1887 1.1966

1.1588 1.1665 1.1742 1.1820 1.1898

1.1523 1.1599 1.1676 1.1753 1.1831

1.1388 1.1463 1.1539 1.1616 1.1693

1.1250 1.1325 1.1400 1.1476 1.1553

30 31 32 33 34

1.2326 1.2409 1.2493 1.2577 1.2661

1.2255 1.2338 1.2421 1.2504 1.2588

1.2220 1.2302 1.2385 1.2468 1.2552

1.2185 1.2267 1.2349 1.2432 1.2515

1.2150 1.2232 1.2314 1.2396 1.2479

1.2115 1.2196 1.2278 1.2360 1.2443

1.2046 1.2126 1.2207 1.2289 1.2371

1.1977 1.2057 1.2137 1.2218 1.2300

1.1909 1.1988 1.2068 1.2148 1.2229

1.1771 1.1849 1.1928 1.2008 1.2088

1.1630 1.1708 1.1787 1.1866 1.1946

35 36 37 38 39

1.2746 1.2831 1.2917 1.3004 1.3091

1.2672 1.2757 1.2843 1.2929 1.3016

1.2636 1.2720 1.2805 1.2891 1.2978

1.2599 1.2684 1.2769 1.2855 1.2941

1.2563 1.2647 1.2732 1.2818 1.2904

1.2526 1.2610 1.2695 1.2780 1.2866

1.2454 1.2538 1.2622 1.2707 1.2793

1.2383 1.2466 1.2550 1.2635 1.2720

1.2311 1.2394 1.2477 1.2561 1.2646

1.2169 1.2251 1.2334 1.2418 1.2503

1.2027 1.2109 1.2192 1.2276 1.2361

40 41 42 43 44

1.3179 1.3268 1.3357 1.3447 1.3538

1.3103 1.3191 1.3280 1.3370 1.3461

1.3065 1.3153 1.3242 1.3332 1.3423

1.3028 1.3116 1.3205 1.3294 1.3384

1.2991 1.3079 1.3167 1.3256 1.3346

1.2953 1.3041 1.3129 1.3218 1.3308

1.2880 1.2967 1.3055 1.3144 1.3234

1.2806 1.2893 1.2981 1.3070 1.3160

1.2732 1.2819 1.2907 1.2996 1.3086

1.2589 1.2675 1.2762 1.2850 1.2939

1.2446 1.2532 1.2619 1.2707 1.2796

45 46 47 48 49

1.3630 1.3724 1.3819 1.3915 1.4012

1.3553 1.3646 1.3740 1.3835 1.3931

1.3515 1.3608 1.3702 1.3797 1.3893

1.3476 1.3569 1.3663 1.3758 1.3854

1.3437 1.3530 1.3624 1.3719 1.3814

1.3399 1.3492 1.3586 1.3680 1.3775

1.3325 1.3417 1.3510 1.3604 1.3699

1.3251 1.3343 1.3435 1.3528 1.3623

1.3177 1.3269 1.3362 1.3455 1.3549

1.3029 1.3120 1.3212 1.3305 1.3399

1.2886 1.2976 1.3067 1.3159 1.3253

50 51 52 53 54

1.4110 1.4209 1.4310 1.4412 1.4515

1.4029 1.4128 1.4228 1.4329 1.4431

1.3990 1.4088 1.4188 1.4289 1.4391

1.3951 1.4049 1.4148 1.4248 1.4350

1.3911 1.4009 1.4109 1.4209 1.4310

1.3872 1.3970 1.4069 1.4169 1.4270

1.3795 1.3893 1.3991 1.4091 1.4191

1.3719 1.3816 1.3914 1.4013 1.4113

1.3644 1.3740 1.3837 1.3936 1.4036

1.3494 1.3590 1.3687 1.3785 1.3884

1.3348 1.3444 1.3540 1.3637 1.3735

55 56 57 58 59

1.4619 1.4724 1.4830 1.4937 1.5045

1.4535 1.4640 1.4746 1.4852 1.4959

1.4494 1.4598 1.4703 1.4809 1.4916

1.4453 1.4557 1.4662 1.4768 1.4875

1.4412 1.4516 1.4621 1.4726 1.4832

1.4372 1.4475 1.4580 1.4685 1.4791

1.4293 1.4396 1.4500 1.4604 1.4709

1.4214 1.4317 1.4420 1.4524 1.4629

1.4137 1.4239 1.4342 1.4446 1.4551

1.3984 1.4085 1.4187 1.4290 1.4393

1.3834 1.3934 1.4035 1.4137 1.4240

60 61 62 63 64

1.5154 1.5264 1.5375 1.5487 1.5600

1.5067 1.5177 1.5287 1.5398 1.5510

1.5024 1.5133 1.5243 1.5354 1.5465

1.4983 1.5091 1.5200 1.5310 1.5421

1.4940 1.5048 1.5157 1.5267 1.5378

1.4898 1.5006 1.5115 1.5225 1.5335

1.4816 1.4923 1.5031 1.5140 1.5250

1.4735 1.4842 1.4950 1.5058 1.5167

1.4656 1.4762 1.4869 1.4977 1.5086

1.4497 1.4602 1.4708 1.4815 1.4923

1.4344 1.4449 1.4554 1.4660 1.4766

DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM

2-105

TABLE 2-55 Sulfuric Acid (H2SO4) (Continued ) %

0°C

10°C

15°C

20°C

25°C

30°C

40°C

50°C

60°C

80°C

100°C

65 66 67 68 69

1.5714 1.5828 1.5943 1.6059 1.6176

1.5623 1.5736 1.5850 1.5965 1.6081

1.5578 1.5691 1.5805 1.5920 1.6035

1.5533 1.5646 1.5760 1.5874 1.5989

1.5490 1.5602 1.5715 1.5829 1.5944

1.5446 1.5558 1.5671 1.5785 1.5899

1.5361 1.5472 1.5584 1.5697 1.5811

1.5277 1.5388 1.5499 1.5611 1.5724

1.5195 1.5305 1.5416 1.5528 1.5640

1.5031 1.5140 1.5249 1.5359 1.5470

1.4873 1.4981 1.5089 1.5198 1.5307

70 71 72 73 74

1.6293 1.6411 1.6529 1.6648 1.6768

1.6198 1.6315 1.6433 1.6551 1.6670

1.6151 1.6268 1.6385 1.6503 1.6622

1.6105 1.6221 1.6338 1.6456 1.6574

1.6059 1.6175 1.6292 1.6409 1.6526

1.6014 1.6130 1.6246 1.6363 1.6480

1.5925 1.6040 1.6155 1.6271 1.6387

1.5838 1.5952 1.6067 1.6182 1.6297

1.5753 1.5867 1.5981 1.6095 1.6209

1.5582 1.5694 1.5806 1.5919 1.6031

1.5417 1.5527 1.5637 1.5747 1.5857

75 76 77 78 79

1.6888 1.7008 1.7128 1.7247 1.7365

1.6789 1.6908 1.7026 1.7144 1.7261

1.6740 1.6858 1.6976 1.7093 1.7209

1.6692 1.6810 1.6927 1.7043 1.7158

1.6644 1.6761 1.6878 1.6994 1.7108

1.6597 1.6713 1.6829 1.6944 1.7058

1.6503 1.6619 1.6734 1.6847 1.6959

1.6412 1.6526 1.6640 1.6751 1.6862

1.6322 1.6435 1.6547 1.6657 1.6766

1.6142 1.6252 1.6361 1.6469 1.6575

1.5966 1.6074 1.6181 1.6286 1.6390

80 81 82 83 84

1.7482 1.7597 1.7709 1.7815 1.7916

1.7376 1.7489 1.7599 1.7704 1.7804

1.7323 1.7435 1.7544 1.7649 1.7748

1.7272 1.7383 1.7491 1.7594 1.7693

1.7221 1.7331 1.7437 1.7540 1.7639

1.7170 1.7279 1.7385 1.7487 1.7585

1.7069 1.7177 1.7281 1.7382 1.7479

1.6971 1.7077 1.7180 1.7279 1.7375

1.6873 1.6978 1.7080 1.7179 1.7274

1.6680 1.6782 1.6882 1.6979 1.7072

1.6493 1.6594 1.6692 1.6787 1.6878

85 86 87 88 89

1.8009 1.8095 1.8173 1.8243 1.8306

1.7897 1.7983 1.8061 1.8132 1.8195

1.7841 1.7927 1.8006 1.8077 1.8141

1.7786 1.7872 1.7951 1.8022 1.8087

1.7732 1.7818 1.7897 1.7968 1.8033

1.7678 1.7763 1.7842 1.7914 1.7979

1.7571 1.7657 1.7736 1.7809 1.7874

1.7466 1.7552 1.7632 1.7705 1.7770

1.7364 1.7449 1.7529 1.7602 1.7669

1.7161 1.7245 1.7324 1.7397 1.7464

1.6966 1.7050 1.7129 1.7202 1.7269

90 91 92 93 94

1.8361 1.8410 1.8453 1.8490 1.8520

1.8252 1.8302 1.8346 1.8384 1.8415

1.8198 1.8248 1.8293 1.8331 1.8363

1.8144 1.8195 1.8240 1.8279 1.8312

1.8091 1.8142 1.8188 1.8227 1.8260

1.8038 1.8090 1.8136 1.8176 1.8210

1.7933 1.7986 1.8033 1.8074 1.8109

1.7829 1.7883 1.7932 1.7974 1.8011

1.7729 1.7783 1.7832 1.7876 1.7914

1.7525 1.7581 1.7633 1.7681

1.7331 1.7388 1.7439 1.7485

95 96 97 98 99 100

1.8544 1.8560 1.8569 1.8567 1.8551 1.8517

1.8439 1.8457 1.8466 1.8463 1.8445 1.8409

1.8388 1.8406 1.8414 1.8411 1.8393 1.8357

1.8337 1.8355 1.8364 1.8361 1.8342 1.8305

1.8286 1.8305 1.8314 1.8310 1.8292 1.8255

1.8236 1.8255 1.8264 1.8261 1.8242 1.8205

1.8137 1.8157 1.8166 1.8163 1.8145 1.8107

1.8040 1.8060 1.8071 1.8068 1.8050 1.8013

1.7944 1.7965 1.7977 1.7976 1.7958 1.7922

%

d 45.96

%

d 413.00

d 418.00

0.005 .01 .02 .03 .04

1.000 0140 1.000 0576 1.000 1434 1.000 2276 1.000 3104

0.05 0.1 0.2 0.3 0.4

0.999 810 1.000 185 1.000 912 1.001 623 1.002 326

0.999 028 0.999 400 1.000 119 1.000 820 1.001 512

.05 .06 .07 .08 .09

1.000 3920 1.000 4726 1.000 5523 1.000 6313 1.000 7098

0.5 0.6 0.8 1.0 1.2

1.003 023 1.003 716 1.005 090 1.006 452 1.007 807

1.002 197 1.002 877 1.004 227 1.005 570 1.006 909

.10 .15 .20 .25 .30

1.000 7880 1.001 1732 1.001 5514 1.001 9254 1.002 2961

1.4 1.6 1.8 2.0 2.2

1.009 159 1.010 510 1.011 860 1.013 209 1.014 557

1.008 247 1.009 583 1.010 918 1.012 252 1.013 586

.35 .40 .45 .50

1.002 6639 1.003 0292 1.003 3923 1.003 7534

2.4

1.015 904

1.014 919

∗International Critical Tables, vol. 3, pp. 56–57.

2-106

PHYSICAL AnD CHEMICAL DATA

DEnSITIES OF AQUEOUS ORGAnIC SOLUTIOnS

TABLE 2-56 Acetic Acid (CH3COOH) %

0°C

10°C

15°C

20°C

25°C

30°C

40°C

%

0°C

10°C

15°C

20°C

25°C

30°C

40°C

0 1 2 3 4

0.9999 1.0016 1.0033 1.0051 1.0070

0.9997 1.0013 1.0029 1.0044 1.0060

0.9991 1.0006 1.0021 1.0036 1.0051

0.9982 0.9996 1.0012 1.0025 1.0040

0.9971 0.9987 1.0000 1.0013 1.0027

0.9957 0.9971 0.9984 0.9997 1.0011

0.9922 0.9934 0.9946 0.9958 0.9970

50 51 52 53 54

1.0729 1.0738 1.0748 1.0757 1.0765

1.0654 1.0663 1.0671 1.0679 1.0687

1.0613 1.0622 1.0629 1.0637 1.0644

1.0575 1.0582 1.0590 1.0597 1.0604

1.0534 1.0542 1.0549 1.0555 1.0562

1.0492 1.0499 1.0506 1.0512 1.0518

1.0408 1.0414 1.0421 1.0427 1.0432

5 6 7 8 9

1.0088 1.0106 1.0124 1.0142 1.0159

1.0076 1.0092 1.0108 1.0124 1.0140

1.0066 1.0081 1.0096 1.0111 1.0126

1.0055 1.0069 1.0083 1.0097 1.0111

1.0041 1.0055 1.0068 1.0081 1.0094

1.0024 1.0037 1.0050 1.0063 1.0076

0.9982 0.9994 1.0006 1.0018 1.0030

55 56 57 58 59

1.0774 1.0782 1.0790 1.0798 1.0805

1.0694 1.0701 1.0708 1.0715 1.0722

1.0651 1.0658 1.0665 1.0672 1.0678

1.0611 1.0618 1.0624 1.0631 1.0637

1.0568 1.0574 1.0580 1.0586 1.0592

1.0525 1.0531 1.0536 1.0542 1.0547

1.0438 1.0443 1.0448 1.0453 1.0458

10 11 12 13 14

1.0177 1.0194 1.0211 1.0228 1.0245

1.0156 1.0171 1.0187 1.0202 1.0217

1.0141 1.0155 1.0170 1.0184 1.0199

1.0125 1.0139 1.0154 1.0168 1.0182

1.0107 1.0120 1.0133 1.0146 1.0159

1.0089 1.0102 1.0115 1.0127 1.0139

1.0042 1.0054 1.0065 1.0077 1.0088

60 61 62 63 64

1.0813 1.0820 1.0826 1.0833 1.0838

1.0728 1.0734 1.0740 1.0746 1.0752

1.0684 1.0690 1.0696 1.0701 1.0706

1.0642 1.0648 1.0653 1.0658 1.0662

1.0597 1.0602 1.0607 1.0612 1.0616

1.0552 1.0557 1.0562 1.0566 1.0571

1.0462 1.0466 1.0470 1.0473 1.0477

15 16 17 18 19

1.0262 1.0278 1.0295 1.0311 1.0327

1.0232 1.0247 1.0262 1.0276 1.0291

1.0213 1.0227 1.0241 1.0255 1.0269

1.0195 1.0209 1.0223 1.0236 1.0250

1.0172 1.0185 1.0198 1.0210 1.0223

1.0151 1.0163 1.0175 1.0187 1.0198

1.0099 1.0110 1.0121 1.0132 1.0142

65 66 67 68 69

1.0844 1.0850 1.0856 1.0860 1.0865

1.0757 1.0762 1.0767 1.0771 1.0775

1.0711 1.0716 1.0720 1.0725 1.0729

1.0666 1.0671 1.0675 1.0678 1.0682

1.0621 1.0624 1.0628 1.0631 1.0634

1.0575 1.0578 1.0582 1.0585 1.0588

1.0480 1.0483 1.0486 1.0489 1.0491

20 21 22 23 24

1.0343 1.0358 1.0374 1.0389 1.0404

1.0305 1.0319 1.0333 1.0347 1.0361

1.0283 1.0297 1.0310 1.0323 1.0336

1.0263 1.0276 1.0288 1.0301 1.0313

1.0235 1.0248 1.0260 1.0272 1.0283

1.0210 1.0222 1.0233 1.0244 1.0256

1.0153 1.0164 1.0174 1.0185 1.0195

70 71 72 73 74

1.0869 1.0874 1.0877 1.0881 1.0884

1.0779 1.0783 1.0786 1.0789 1.0792

1.0732 1.0736 1.0738 1.0741 1.0743

1.0685 1.0687 1.0690 1.0693 1.0694

1.0637 1.0640 1.0642 1.0644 1.0645

1.0590 1.0592 1.0594 1.0595 1.0596

1.0493 1.0495 1.0496 1.0497 1.0498

25 26 27 28 29

1.0419 1.0434 1.0449 1.0463 1.0477

1.0375 1.0388 1.0401 1.0414 1.0427

1.0349 1.0362 1.0374 1.0386 1.0399

1.0326 1.0338 1.0349 1.0361 1.0372

1.0295 1.0307 1.0318 1.0329 1.0340

1.0267 1.0278 1.0289 1.0299 1.0310

1.0205 1.0215 1.0225 1.0234 1.0244

75 76 77 78 79

1.0887 1.0889 1.0891 1.0893 1.0894

1.0794 1.0796 1.0797 1.0798 1.0798

1.0745 1.0746 1.0747 1.0747 1.0747

1.0696 1.0698 1.0699 1.0700 1.0700

1.0647 1.0648 1.0648 1.0648 1.0648

1.0597 1.0598 1.0598 1.0598 1.0597

1.0499 1.0499 1.0499 1.0498 1.0497

30 31 32 33 34

1.0491 1.0505 1.0519 1.0532 1.0545

1.0440 1.0453 1.0465 1.0477 1.0489

1.0411 1.0423 1.0435 1.0446 1.0458

1.0384 1.0395 1.0406 1.0417 1.0428

1.0350 1.0361 1.0372 1.0382 1.0392

1.0320 1.0330 1.0341 1.0351 1.0361

1.0253 1.0262 1.0272 1.0281 1.0289

80 81 82 83 84

1.0895 1.0895 1.0895 1.0895 1.0893

1.0798 1.0797 1.0796 1.0795 1.0793

1.0747 1.0745 1.0743 1.0741 1.0738

1.0700 1.0699 1.0698 1.0696 1.0693

1.0647 1.0646 1.0644 1.0642 1.0638

1.0596 1.0594 1.0592 1.0589 1.0585

1.0495 1.0493 1.0490 1.0487 1.0483

35 36 37 38 39

1.0558 1.0571 1.0584 1.0596 1.0608

1.0501 1.0513 1.0524 1.0535 1.0546

1.0469 1.0480 1.0491 1.0501 1.0512

1.0438 1.0449 1.0459 1.0469 1.0479

1.0402 1.0412 1.0422 1.0432 1.0441

1.0371 1.0380 1.0390 1.0399 1.0408

1.0298 1.0306 1.0314 1.0322 1.0330

85 86 87 88 89

1.0891 1.0887 1.0883 1.0877 1.0872

1.0790 1.0787 1.0783 1.0778 1.0773

1.0735 1.0731 1.0726 1.0721 1.0715

1.0689 1.0685 1.0680 1.0675 1.0668

1.0635 1.0630 1.0626 1.0620 1.0613

1.0582 1.0576 1.0571 1.0564 1.0557

1.0479 1.0473 1.0467 1.0460 1.0453

40 41 42 43 44

1.0621 1.0633 1.0644 1.0656 1.0667

1.0557 1.0568 1.0578 1.0588 1.0598

1.0522 1.0532 1.0542 1.0551 1.0561

1.0488 1.0498 1.0507 1.0516 1.0525

1.0450 1.0460 1.0469 1.0477 1.0486

1.0416 1.0425 1.0433 1.0441 1.0449

1.0338 1.0346 1.0353 1.0361 1.0368

90 91 92 93 94

1.0865 1.0857 1.0848 1.0838 1.0826

1.0766 1.0758 1.0749 1.0739 1.0727

1.0708 1.0700 1.0690 1.0680 1.0667

1.0661 1.0652 1.0643 1.0632 1.0619

1.0605 1.0597 1.0587 1.0577 1.0564

1.0549 1.0541 1.0530 1.0518 1.0506

1.0445 1.0436 1.0426 1.0414 1.0401

45 46 47 48 49

1.0679 1.0689 1.0699 1.0709 1.0720

1.0608 1.0618 1.0627 1.0636 1.0645

1.0570 1.0579 1.0588 1.0597 1.0605

1.0534 1.0542 1.0551 1.0559 1.0567

1.0495 1.0503 1.0511 1.0518 1.0526

1.0456 1.0464 1.0471 1.0479 1.0486

1.0375 1.0382 1.0389 1.0395 1.0402

95 96 97 98 99

1.0813 1.0798 1.0780 1.0759 1.0730

1.0714

1.0652 1.0632 1.0611 1.0590 1.0567

1.0605 1.0588 1.0570 1.0549 1.0524

1.0551 1.0535 1.0516 1.0495 1.0468

1.0491 1.0473 1.0454 1.0431 1.0407

1.0386 1.0368 1.0348 1.0325 1.0299

100

1.0697

1.0545

1.0498

1.0440

1.0380

1.0271

DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM

2-107

TABLE 2-57 Methyl Alcohol (CH3OH)* %

0°C

10°C

20°C

15°C

%

0°C

10°C

20°C

15°C

%

0°C

10°C

20°C

15°C

0 1 2 3 4

0.9999 0.9981 0.9963 0.9946 0.9930

0.9997 0.9980 0.9962 0.9945 0.9929

15.56°C 0.9990 0.9973 0.9955 0.9938 0.9921

0.9982 0.9965 0.9948 0.9931 0.9914

0.99913 0.99727 0.99543 0.99370 0.99198

35 36 37 38 39

0.9534 0.9520 0.9505 0.9490 0.9475

0.9484 0.9469 0.9453 0.9437 0.9420

15.56°C 0.9456 0.9440 0.9422 0.9405 0.9387

0.9433 0.9416 0.9398 0.9381 0.9363

0.94570 0.94404 0.94237 0.94067 0.93894

70 71 72 73 74

0.8869 0.8847 0.8824 0.8801 0.8778

0.8794 0.8770 0.8747 0.8724 0.8699

15.56°C 0.8748 0.8726 0.8702 0.8678 0.8653

0.8715 0.8690 0.8665 0.8641 0.8616

0.87507 0.87271 0.87033 0.86792 0.86546

5 6 7 8 9

0.9914 0.9899 0.9884 0.9870 0.9856

0.9912 0.9896 0.9881 0.9865 0.9849

0.9904 0.9889 0.9872 0.9857 0.9841

0.9896 0.9880 0.9863 0.9847 0.9831

0.99029 0.98864 0.98701 0.98547 0.98394

40 41 42 43 44

0.9459 0.9443 0.9427 0.9411 0.9395

0.9403 0.9387 0.9370 0.9352 0.9334

0.9369 0.9351 0.9333 0.9315 0.9297

0.9345 0.9327 0.9309 0.9290 0.9272

0.93720 0.93543 0.93365 0.93185 0.93001

75 76 77 78 79

0.8754 0.8729 0.8705 0.8680 0.8657

0.8676 0.8651 0.8626 0.8602 0.8577

0.8629 0.8604 0.8579 0.8554 0.8529

0.8592 0.8567 0.8542 0.8518 0.8494

0.86300 0.86051 0.85801 0.85551 0.85300

10 11 12 13 14

0.9842 0.9829 0.9816 0.9804 0.9792

0.9834 0.9820 0.9805 0.9791 0.9778

0.9826 0.9811 0.9796 0.9781 0.9766

0.9815 0.9799 0.9784 0.9768 0.9754

0.98241 0.98093 0.97945 0.97802 0.97660

45 46 47 48 49

0.9377 0.9360 0.9342 0.9324 0.9306

0.9316 0.9298 0.9279 0.9260 0.9240

0.9279 0.9261 0.9242 0.9223 0.9204

0.9252 0.9234 0.9214 0.9196 0.9176

0.92815 0.92627 0.92436 0.92242 0.92048

80 81 82 83 84

0.8634 0.8610 0.8585 0.8560 0.8535

0.8551 0.8527 0.8501 0.8475 0.8449

0.8503 0.8478 0.8452 0.8426 0.8400

0.8469 0.8446 0.8420 0.8394 0.8366

0.85048 0.84794 0.84536 0.84274 0.84009

15 16 17 18 19

0.9780 0.9769 0.9758 0.9747 0.9736

0.9764 0.9751 0.9739 0.9726 0.9713

0.9752 0.9738 0.9723 0.9709 0.9695

0.9740 0.9725 0.9710 0.9696 0.9681

0.97518 0.97377 0.97237 0.97096 0.96955

50 51 52 53 54

0.9287 0.9269 0.9250 0.9230 0.9211

0.9221 0.9202 0.9182 0.9162 0.9142

0.9185 0.9166 0.9146 0.9126 0.9106

0.9156 0.9135 0.9114 0.9094 0.9073

0.91852 0.91653 0.91451 0.91248 0.91044

85 86 87 88 89

0.8510 0.8483 0.8456 0.8428 0.8400

0.8422 0.8394 0.8367 0.8340 0.8314

0.8374 0.8347 0.8320 0.8294 0.8267

0.8340 0.8314 0.8286 0.8258 0.8230

0.83742 0.83475 0.83207 0.82937 0.82667

20 21 22 23 24

0.9725 0.9714 0.9702 0.9690 0.9678

0.9700 0.9687 0.9673 0.9660 0.9646

0.9680 0.9666 0.9652 0.9638 0.9624

0.9666 0.9651 0.9636 0.9622 0.9607

0.96814 0.96673 0.96533 0.96392 0.96251

55 56 57 58 59

0.9191 0.9172 0.9151 0.9131 0.9111

0.9122 0.9101 0.9080 0.9060 0.9039

0.9086 0.9065 0.9045 0.9024 0.9002

0.9052 0.9032 0.9010 0.8988 0.8968

0.90839 0.90631 0.90421 0.90210 0.89996

90 91 92 93 94

0.8374 0.8347 0.8320 0.8293 0.8266

0.8287 0.8261 0.8234 0.8208 0.8180

0.8239 0.8212 0.8185 0.8157 0.8129

0.8202 0.8174 0.8146 0.8118 0.8090

0.82396 0.82124 0.81849 0.81568 0.81285

25 26 27 28 29

0.9666 0.9654 0.9642 0.9629 0.9616

0.9632 0.9618 0.9604 0.9590 0.9575

0.9609 0.9595 0.9580 0.9565 0.9550

0.9592 0.9576 0.9562 0.9546 0.9531

0.96108 0.95963 0.95817 0.95668 0.95518

60 61 62 63 64

0.9090 0.9068 0.9046 0.9024 0.9002

0.9018 0.8998 0.8977 0.8955 0.8933

0.8980 0.8958 0.8936 0.8913 0.8890

0.8946 0.8924 0.8902 0.8879 0.8856

0.89781 0.89563 0.89341 0.89117 0.88890

95 96 97 98 99

0.8240 0.8212 0.8186 0.8158 0.8130

0.8152 0.8124 0.8096 0.8068 0.8040

0.8101 0.8073 0.8045 0.8016 0.7987

0.8062 0.8034 0.8005 0.7976 0.7948

0.80999 0.80713 0.80428 0.80143 0.79859

30 31 32 33 34

0.9604 0.9590 0.9576 0.9563 0.9549

0.9560 0.9546 0.9531 0.9516 0.9500

0.9535 0.9521 0.9505 0.9489 0.9473

0.9515 0.9499 0.9483 0.9466 0.9450

0.95366 0.95213 0.95056 0.94896 0.94734

65 66 67 68 69

0.8980 0.8958 0.8935 0.8913 0.8891

0.8911 0.8888 0.8865 0.8842 0.8818

0.8867 0.8844 0.8820 0.8797 0.8771

0.8834 0.8811 0.8787 0.8763 0.8738

0.88662 0.88433 0.88203 0.87971 0.87739

100

0.8102

0.8009

0.7959

0.7917

0.79577

∗It should be noted that the values for 100 percent do not agree with some data available elsewhere, e.g., American Institute of Physics Handbook, McGraw-Hill, New York, 1957. Also, see Atack, Handbook of Chemical Data, Reinhold, New York, 1957. Also, see Tables 2-120 and 2-135 for pure methanol and water densities.

2-108

PHYSICAL AnD CHEMICAL DATA

TABLE 2-58 Ethyl Alcohol (C2H5OH)* %

10°C

15°C

20°C

25°C

30°C

35°C

40°C

%

10°C

15°C

20°C

25°C

30°C

35°C

40°C

0 1 2 3 4

0.99973 785 602 426 258

0.99913 725 542 365 195

0.99823 636 453 275 103

0.99708 520 336 157 0.98984

0.99568 379 194 014 0.98839

0.99406 217 031 0.98849 672

0.99225 034 0.98846 663 485

50 51 52 53 54

0.92126 0.91943 723 502 279

0.91776 555 333 110 0.90885

0.91384 160 0.90936 711 485

0.90985 760 534 307 079

0.90580 353 125 0.89896 667

0.90168 0.89940 710 479 248

0.89750 519 288 056 0.88823

5 6 7 8 9

098 0.98946 801 660 524

032 0.98877 729 584 442

0.98938 780 627 478 331

817 656 500 346 193

670 507 347 189 031

501 335 172 009 0.97846

311 142 0.97975 808 641

55 56 57 58 59

055 0.90831 607 381 154

659 433 207 0.89980 752

258 031 0.89803 574 344

0.89850 621 392 162 0.88931

437 206 0.88975 744 512

016 0.88784 552 319 085

589 356 122 0.87888 653

10 11 12 13 14

393 267 145 026 0.97911

304 171 041 0.97914 790

187 047 0.97910 775 643

043 0.97897 753 611 472

0.97875 723 573 424 278

685 527 371 216 063

475 312 150 0.96989 829

60 61 62 63 64

0.89927 698 468 237 006

523 293 062 0.88830 597

113 0.88882 650 417 183

699 466 233 0.87998 763

278 044 0.87809 574 337

0.87851 615 379 142 0.86905

417 180 0.86943 705 466

15 16 17 18 19

800 692 583 473 363

669 552 433 313 191

514 387 259 129 0.96997

334 199 062 0.96923 782

133 0.96990 844 697 547

0.96911 760 607 452 294

670 512 352 189 023

65 66 67 68 69

0.88774 541 308 074 0.87839

364 130 0.87895 660 424

0.87948 713 477 241 004

527 291 054 0.86817 579

100 0.86863 625 387 148

667 429 190 0.85950 710

227 0.85987 747 507 266

20 21 22 23 24

252 139 024 0.96907 787

068 0.96944 818 689 558

864 729 592 453 312

639 495 348 199 048

395 242 087 0.95929 769

134 0.95973 809 643 476

0.95856 687 516 343 168

70 71 72 73 74

602 365 127 0.86888 648

187 0.86949 710 470 229

0.86766 527 287 047 0.85806

340 100 0.85859 618 376

0.85908 667 426 184 0.84941

470 228 0.84986 743 500

025 0.84783 540 297 053

25 26 27 28 29

665 539 406 268 125

424 287 144 0.95996 844

168 020 0.95867 710 548

0.95895 738 576 410 241

607 442 272 098 0.94922

306 133 0.94955 774 590

0.94991 810 625 438 248

75 76 77 78 79

408 168 0.85927 685 442

0.85988 747 505 262 018

564 322 079 0.84835 590

134 0.84891 647 403 158

698 455 211 0.83966 720

257 013 0.83768 523 277

0.83809 564 319 074 0.82827

30 31 32 33 34

0.95977 823 665 502 334

686 524 357 186 011

382 212 038 0.94860 679

067 0.94890 709 525 337

741 557 370 180 0.93986

403 214 021 0.93825 626

055 0.93860 662 461 257

80 81 82 83 84

197 0.84950 702 453 203

0.84772 525 277 028 0.83777

344 096 0.83848 599 348

0.83911 664 415 164 0.82913

473 224 0.82974 724 473

029 0.82780 530 279 027

578 329 079 0.81828 576

35 36 37 38 39

162 0.94986 805 620 431

0.94832 650 464 273 079

494 306 114 0.93919 720

146 0.93952 756 556 353

790 591 390 186 0.92979

425 221 016 0.92808 597

051 0.92843 634 422 208

85 86 87 88 89

0.83951 697 441 181 0.82919

525 271 014 0.82754 492

095 0.82840 583 323 062

660 405 148 0.81888 626

220 0.81965 708 448 186

0.81774 519 262 003 0.80742

322 067 0.80811 552 291

40 41 42 43 44

238 042 0.93842 639 433

0.93882 682 478 271 062

518 314 107 0.92897 685

148 0.92940 729 516 301

770 558 344 128 0.91910

385 170 0.91952 733 513

0.91992 774 554 332 108

90 91 92 93 94

654 386 114 0.81839 561

227 0.81959 688 413 134

0.81797 529 257 0.80983 705

362 094 0.80823 549 272

0.80922 655 384 111 0.79835

478 211 0.79941 669 393

028 0.79761 491 220 0.78947

45 46 47 48 49

226 017 0.92806 593 379

0.92852 640 426 211 0.91995

472 257 041 0.91823 604

085 0.91868 649 429 208

692 472 250 028 0.90805

291 069 0.90845 621 396

0.90884 660 434 207 0.89979

95 96 97 98 99

278 0.80991 698 399 094

0.80852 566 274 0.79975 670

424 138 0.79846 547 243

0.79991 706 415 117 0.78814

555 271 0.78981 684 382

114 0.78831 542 247 0.77946

670 388 100 0.77806 507

100

0.79784

360

0.78934

506

075

641

203

∗For data from −78° to 78°C, see p. 2-142, Table 2N-5, American Institute of Physics Handbook, McGraw-Hill, New York, 1957. See Tables 2-115 and 2-135 for pure ethanol and pure water densities.

DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM

2-109

TABLE 2-59 n-Propyl Alcohol (C3H7OH) %

0°C

15°C

30°C

%

0°C

15°C

30°C

%

0°C

15°C

30°C

%

0°C

15°C

30°C

%

0°C

15°C

30°C

0 1 2 3 4

0.9999 0.9982 0.9967 0.9952 0.9939

0.9991 0.9974 0.9960 0.9944 0.9929

0.9957 0.9940 0.9924 0.9908 0.9893

20 21 22 23 24

0.9789 0.9776 0.9763 0.9748 0.9733

0.9723 0.9705 0.9688 0.9670 0.9651

0.9643 0.9622 0.9602 0.9583 0.9563

40 41 42 43 44

0.9430 0.9411 0.9391 0.9371 0.9352

0.9331 0.9310 0.9290 0.9269 0.9248

0.9226 0.9205 0.9184 0.9164 0.9143

60 61 62 63 64

0.9033 0.9013 0.8994 0.8974 0.8954

0.8922 0.8902 0.8882 0.8861 0.8841

0.8807 0.8786 0.8766 0.8745 0.8724

80 81 82 83 84

0.8634 0.8614 0.8594 0.8574 0.8554

0.8516 0.8496 0.8475 0.8454 0.8434

0.8394 0.8373 0.8352 0.8332 0.8311

5 6 7 8 9

0.9926 0.9914 0.9904 0.9894 0.9883

0.9915 0.9902 0.9890 0.9877 0.9864

0.9877 0.9862 0.9848 0.9834 0.9819

25 26 27 28 29

0.9717 0.9700 0.9682 0.9664 0.9646

0.9633 0.9614 0.9594 0.9576 0.9556

0.9543 0.9522 0.9501 0.9481 0.9460

45 46 47 48 49

0.9332 0.9311 0.9291 0.9272 0.9252

0.9228 0.9207 0.9186 0.9165 0.9145

0.9122 0.9100 0.9079 0.9057 0.9036

65 66 67 68 69

0.8934 0.8913 0.8894 0.8874 0.8854

0.8820 0.8800 0.8779 0.8759 0.8739

0.8703 0.8682 0.8662 0.8641 0.8620

85 86 87 88 89

0.8534 0.8513 0.8492 0.8471 0.8450

0.8413 0.8393 0.8372 0.8351 0.8330

0.8290 0.8269 0.8248 0.8227 0.8206

10 11 12 13 14

0.9874 0.9865 0.9857 0.9849 0.9841

0.9852 0.9840 0.9828 0.9817 0.9806

0.9804 0.9790 0.9775 0.9760 0.9746

30 31 32 33 34

0.9627 0.9608 0.9589 0.9570 0.9550

0.9535 0.9516 0.9495 0.9474 0.9454

0.9439 0.9418 0.9396 0.9375 0.9354

50 51 52 53 54

0.9232 0.9213 0.9192 0.9173 0.9153

0.9124 0.9104 0.9084 0.9064 0.9044

0.9015 0.8994 0.8973 0.8952 0.8931

70 71 72 73 74

0.8835 0.8815 0.8795 0.8776 0.8756

0.8719 0.8700 0.8680 0.8659 0.8639

0.8600 0.8580 0.8559 0.8539 0.8518

90 91 92 93 94

0.8429 0.8408 0.8387 0.8364 0.8342

0.8308 0.8287 0.8266 0.8244 0.8221

0.8185 0.8164 0.8142 0.8120 0.8098

15 16 17 18 19

0.9833 0.9825 0.9817 0.9808 0.9800

0.9793 0.9780 0.9768 0.9752 0.9739

0.9730 0.9714 0.9698 0.9680 0.9661

35 36 37 38 39

0.9530 0.9511 0.9491 0.9471 0.9450

0.9434 0.9413 0.9392 0.9372 0.9351

0.9333 0.9312 0.9289 0.9269 0.9247

55 56 57 58 59

0.9132 0.9112 0.9093 0.9073 0.9053

0.9023 0.9003 0.8983 0.8963 0.8942

0.8911 0.8890 0.8869 0.8849 0.8828

75 76 77 78 79

0.8736 0.8716 0.8695 0.8675 0.8655

0.8618 0.8598 0.8577 0.8556 0.8536

0.8497 0.8477 0.8456 0.8435 0.8414

95 96 97 98 99

0.8320 0.8296 0.8272 0.8248 0.8222

0.8199 0.8176 0.8153 0.8128 0.8104

0.8077 0.8054 0.8031 0.8008 0.7984

100

0.8194

0.8077

0.7958

TABLE 2-60 Isopropyl Alcohol (C3H7OH) %

0°C

15°C∗

15°C∗

20°C

30°C

%

0°C

15°C∗

20°C

30°C

%

0°C

15°C∗

15°C∗

20°C

30°C

0 1 2 3 4

0.9999 0.9980 0.9962 0.9946 0.9930

0.9991 0.9973 0.9956 0.9938 0.9922

0.99913 0.9972 0.9954 0.9936 0.9920

0.9982 0.9962 0.9944 0.9926 0.9909

0.9957 0.9939 0.9921 0.9904 0.9887

35 36 37 38 39

0.9557 0.9536 0.9514 0.9493 0.9472

15°C∗

0.9446 0.9424 0.9401 0.9379 0.9356

0.9419 0.9399 0.9377 0.9355 0.9333

0.9338 0.9315 0.9292 0.9269 0.9246

70 71 72 73 74

0.8761 0.8738 0.8714 0.8691 0.8668

0.8639 0.8615 0.8592 0.8568 0.8545

0.86346 0.8611 0.8588 0.8564 0.8541

0.8584 0.8560 0.8537 0.8513 0.8489

0.8511 0.8487 0.8464 0.8440 0.8416

5 6 7 8 9

0.9916 0.9902 0.9890 0.9878 0.9866

0.9906 0.9892 0.9878 0.9864 0.9851

0.9904 0.9890 0.9875 0.9862 0.9849

0.9893 0.9877 0.9862 0.9847 0.9833

0.9871 0.9855 0.9839 0.9824 0.9809

40 41 42 43 44

0.9450 0.9428 0.9406 0.9384 0.9361

0.93333 0.9311 0.9288 0.9266 0.9243

0.9310 0.9287 0.9264 0.9239 0.9215

0.9224 0.9201 0.9177 0.9154 0.9130

75 76 77 78 79

0.8644 0.8621 0.8598 0.8575 0.8551

0.8521 0.8497 0.8474 0.8450 0.8426

0.8517 0.8493 0.8470 0.8446 0.8422

0.8464 0.8439 0.8415 0.8391 0.8366

0.8392 0.8368 0.8344 0.8321 0.8297

10 11 12 13 14

0.9856 0.9846 0.9838 0.9829 0.9821

0.9838 0.9826 0.9813 0.9802 0.9790

0.98362 0.9824 0.9812 0.9800 0.9788

0.9820 0.9808 0.9797 0.9876 0.9776

0.9794 0.9778 0.9764 0.9750 0.9735

45 46 47 48 49

0.9338 0.9315 0.9292 0.9270 0.9247

0.9220 0.9197 0.9174 0.9150 0.9127

0.9191 0.9165 0.9141 0.9117 0.9093

0.9106 0.9082 0.9059 0.9036 0.9013

80 81 82 83 84

0.8528 0.8503 0.8479 0.8456 0.8432

0.8403 0.8379 0.8355 0.8331 0.8307

0.83979 0.8374 0.8350 0.8326 0.8302

0.8342 0.8317 0.8292 0.8268 0.8243

0.8273 0.8248 0.8224 0.8200 0.8175

15 16 17 18 19

0.9814 0.9806 0.9799 0.9792 0.9784

0.9779 0.9768 0.9756 0.9745 0.9730

0.9777 0.9765 0.9753 0.9741 0.9728

0.9765 0.9754 0.9743 0.9731 0.9717

0.9720 0.9705 0.9690 0.9675 0.9658

50 51 52 53 54

0.9224 0.9201 0.9178 0.9155 0.9132

0.91043 0.9081 0.9058 0.9035 0.9011

0.9069 0.9044 0.9020 0.8996 0.8971

0.8990 0.8966 0.8943 0.8919 0.8895

85 86 87 88 89

0.8408 0.8384 0.8360 0.8336 0.8311

0.8282 0.8259 0.8234 0.8209 0.8184

0.8278 0.8254 0.8229 0.8205 0.8180

0.8219 0.8194 0.8169 0.8145 0.8120

0.8151 0.8127 0.8201 0.8078 0.8053

20 21 22 23 24

0.9777 0.9768 0.9759 0.9749 0.9739

0.9719 0.9704 0.9690 0.9675 0.9660

0.97158 0.9703 0.9689 0.9674 0.9659

0.9703 0.9688 0.9669 0.9651 0.9634

0.9642 0.9624 0.9606 0.9587 0.9569

55 56 57 58 59

0.9109 0.9086 0.9063 0.9040 0.9017

0.8988 0.8964 0.8940 0.8917 0.8893

0.8946 0.8921 0.8896 0.8874 0.8850

0.8871 0.8847 0.8823 0.8800 0.8777

90 91 92 93 94

0.8287 0.8262 0.8237 0.8212 0.8186

0.8161 0.8136 0.8110 0.8085 0.8060

0.81553 0.8130 0.8104 0.8079 0.8052

0.8096 0.8072 0.8047 0.8023 0.7998

0.8029 0.8004 0.7979 0.7954 0.7929

25 26 27 28 29

0.9727 0.9714 0.9699 0.9684 0.9669

0.9643 0.9626 0.9608 0.9590 0.9570

0.9642 0.9624 0.9605 0.9586 0.9568

0.9615 0.9597 0.9577 0.9558 0.9540

0.9549 0.9529 0.9509 0.9488 0.9467

60 61 62 63 64

0.8994 0.8970 0.8947 0.8924 0.8901

0.8829 0.8805 0.8781

0.88690 0.8845 0.8821 0.8798 0.8775

0.8825 0.8800 0.8776 0.8751 0.8727

0.8752 0.8728 0.8704 0.8680 0.8656

95 96 97 98 99

0.8160 0.8133 0.8106 0.8078 0.8048

0.8034 0.8008 0.7981 0.7954 0.7926

0.8026 0.7999 0.7972 0.7945 0.7918

0.7973 0.7949 0.7925 0.7901 0.7877

0.7904 0.7878 0.7852 0.7826 0.7799

30 31 32 33 34

0.9652 0.9634 0.9615 0.9596 0.9577

0.9551

0.95493 0.9530 0.9510 0.9489 0.9468

0.9520 0.9500 0.9481 0.9460 0.9440

0.9446 0.9426 0.9405 0.9383 0.9361

65 66 67 68 69

0.8878 0.8854 0.8831 0.8807 0.8784

0.8757 0.8733 0.8710 0.8686 0.8662

0.8752 0.8728 0.8705 0.8682 0.8658

0.8702 0.8679 0.8656 0.8632 0.8609

0.8631 0.8607 0.8583 0.8559 0.8535

100

0.8016

0.7896

0.78913

0.7854

0.7770

∗Two different observers; see International Critical Tables, vol. 3, p. 120.

2-110

PHYSICAL AnD CHEMICAL DATA

TABLE 2-61 Glycerol* Density

Density

Density

Glycerol, %

15°C

15.5°C

20°C

25°C

30°C

Glycerol, %

15°C

15.5°C

20°C

25°C

30°C

Glycerol, %

15°C

15.5°C

20°C

25°C

30°C

100 99 98 97 96

1.26415 1.26160 1.25900 1.25645 1.25385

1.26381 1.26125 1.25865 1.25610 1.25350

1.26108 1.25850 1.25590 1.25335 1.25080

1.15802 1.25545 1.25290 1.25030 1.24770

1.25495 1.25235 1.24975 1.24710 1.24450

65 64 63 62 61

1.17030 1.16755 1.16480 1.16200 1.15925

1.17000 1.16725 1.16445 1.16170 1.15895

1.16750 1.16475 1.16205 1.15930 1.15655

1.16475 1.16200 1.15925 1.15655 1.15380

1.16195 1.15925 1.15650 1.15375 1.15100

30 29 28 27 26

1.07455 1.07195 1.06935 1.06670 1.06410

1.07435 1.07175 1.06915 1.06655 1.06390

1.07270 1.07010 1.06755 1.06495 1.06240

1.07070 1.06815 1.06560 1.06305 1.06055

1.06855 1.06605 1.06355 1.06105 1.05855

95 94 93 92 91

1.25130 1.24865 1.24600 1.24340 1.24075

1.25095 1.24830 1.24565 1.24305 1.24040

1.24825 1.24560 1.24300 1.24035 1.23770

1.24515 1.24250 1.23985 1.23725 1.23460

1.24190 1.23930 1.23670 1.23410 1.23150

60 59 58 57 56

1.15650 1.15370 1.15095 1.14815 1.14535

1.15615 1.15340 1.15065 1.14785 1.14510

1.15380 1.15105 1.14830 1.14555 1.14280

1.15105 1.14835 1.14560 1.14285 1.14015

1.14830 1.14555 1.14285 1.14010 1.13740

25 24 23 22 21

1.06150 1.05885 1.05625 1.05365 1.05100

1.06130 1.05870 1.05610 1.05350 1.05090

1.05980 1.05720 1.05465 1.05205 1.04950

1.05800 1.05545 1.05290 1.05035 1.04780

1.05605 1.05350 1.05100 1.04850 1.04600

90 89 88 87 86

1.23810 1.23545 1.23280 1.23015 1.22750

1.23775 1.23510 1.23245 1.22980 1.22710

1.23510 1.23245 1.22975 1.22710 1.22445

1.23200 1.22935 1.22665 1.22400 1.22135

1.22890 1.22625 1.22360 1.22095 1.21830

55 54 53 52 51

1.14260 1.13980 1.13705 1.13425 1.13150

1.14230 1.13955 1.13680 1.13400 1.13125

1.14005 1.13730 1.13455 1.13180 1.12905

1.13740 1.13465 1.13195 1.12920 1.12650

1.13470 1.13195 1.12925 1.12650 1.12380

20 19 18 17 16

1.04840 1.04590 1.04335 1.04085 1.03835

1.04825 1.04575 1.04325 1.04075 1.03825

1.04690 1.04440 1.04195 1.03945 1.03695

1.04525 1.04280 1.04035 1.03790 1.03545

1.04350 1.04105 1.03860 1.03615 1.03370

85 84 83 82 81

1.22485 1.22220 1.21955 1.21690 1.21425

1.22445 1.22180 1.21915 1.21650 1.21385

1.22180 1.21915 1.21650 1.21380 1.21115

1.21870 1.21605 1.21340 1.21075 1.20810

1.21565 1.21300 1.21035 1.20770 1.20505

50 49 48 47 46

1.12870 1.12600 1.12325 1.12055 1.11780

1.12845 1.12575 1.12305 1.12030 1.11760

1.12630 1.12360 1.12090 1.11820 1.11550

1.12375 1.12110 1.11840 1.11575 1.11310

1.12110 1.11845 1.11580 1.11320 1.11055

15 14 13 12 11

1.03580 1.03330 1.03080 1.02830 1.02575

1.03570 1.03320 1.03070 1.02820 1.02565

1.03450 1.03200 1.02955 1.02705 1.02455

1.03300 1.03055 1.02805 1.02560 1.02315

1.03130 1.02885 1.02640 1.02395 1.02150

80 79 78 77 76

1.21160 1.20885 1.20610 1.20335 1.20060

1.21120 1.20845 1.20570 1.20300 1.20025

1.20850 1.20575 1.20305 1.20030 1.19760

1.20545 1.20275 1.20005 1.19735 1.19465

1.20240 1.19970 1.19705 1.19435 1.19170

45 44 43 42 41

1.11510 1.11235 1.10960 1.10690 1.10415

1.11490 1.11215 1.10945 1.10670 1.10400

1.11280 1.11010 1.10740 1.10470 1.10200

1.11040 1.10775 1.10510 1.10240 1.09975

1.10795 1.10530 1.10265 1.10005 1.09740

10 9 8 7 6

1.02325 1.02085 1.01840 1.01600 1.01360

1.02315 1.02075 1.01835 1.01590 1.01350

1.02210 1.01970 1.01730 1.01495 1.01255

1.02070 1.01835 1.01600 1.01360 1.01125

1.01905 1.01670 1.01440 1.01205 1.00970

75 74 73 72 71

1.19785 1.19510 1.19235 1.18965 1.18690

1.19750 1.19480 1.19205 1.18930 1.18655

1.19485 1.19215 1.18940 1.18670 1.18395

1.19195 1.18925 1.18650 1.18380 1.18110

1.18900 1.18635 1.18365 1.18100 1.17830

40 39 38 37 36

1.10145 1.09875 1.09605 1.09340 1.09070

1.10130 1.09860 1.09590 1.09320 1.09050

1.09930 1.09665 1.09400 1.09135 1.08865

1.09710 1.09445 1.09180 1.08915 1.08655

1.09475 1.09215 1.08955 1.08690 1.08430

5 4 3 2 1

1.01120 1.00875 1.00635 1.00395 1.00155

1.01110 1.00870 1.00630 1.00385 1.00145

1.01015 1.00780 1.00540 1.00300 1.00060

1.00890 1.00655 1.00415 1.00180 0.99945

1.00735 1.00505 1.00270 1.00035 0.99800

70 69 68 67 66

1.18415 1.18135 1.17860 1.17585 1.17305

1.18385 1.18105 1.17830 1.17555 1.17275

1.18125 1.17850 1.17575 1.17300 1.17025

1.17840 1.17565 1.17295 1.17020 1.16745

1.17565 1.17290 1.17020 1.16745 1.16470

35 34 33 32 31

1.08800 1.08530 1.08265 1.07995 1.07725

1.08780 1.08515 1.08245 1.07975 1.07705

1.08600 1.08335 1.08070 1.07800 1.07535

1.08390 1.08125 1.07860 1.07600 1.07335

1.08165 1.07905 1.07645 1.07380 1.07120

0

0.99913 0.99905 0.99823 0.99708 0.99568

∗Bosart and Snoddy, Ind. Eng. Chem., 20, (1928): 1378.

TABLE 2-62 Hydrazine (n2H4)* %

d 415

%

d 415

1 2 4 8 12 16 20 24 28

1.0002 1.0013 1.0034 1.0077 1.0121 1.0164 1.0207 1.0248 1.0286

30 40 50 60 70 80 90 100

1.0305 1.038 1.044 1.047 1.046 1.040 1.030 1.011

∗International Critical Tables, vol. 3, p. 55.

DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM

2-111

TABLE 2-63 Densities of Aqueous Solutions of Miscellaneous Organic Compounds* d, dw, and ds are the density of the solution, pure water, and pure liquid solute, respectively, all in g/mL. ps is the wt % solute. 0.03255 means 2.55 × 10−4. Section A Name Acetaldehyde Acetamide

Formula C2H4O C2H5NO

Acetone

C3H6O

Acetonitrile Allyl alcohol Benzenepentacarboxylic acid Butyl alcohol (n-)

C2H3N C3H6O C11H6O10 C4H10O

Butyric acid (n-)

C4H8O2

Chloral hydrate

C2H3Cl3O2

Chloroacetic acid

C2H3ClO2

Citric acid (hydrate)

C6H3O7 + H2O

Dichloroacetic acid

C2H2Cl2O2

Diethylamine hydrochloride Ethylamine hydrochloride

C4H12ClN C2H8ClN

Ethylene glycol

C2H6O2

Ethyl ether

C4H10O

tartrate Formaldehyde Formamide

C8H14O6 CH2O CH3NO

Furfural

C5H4O2

Isoamyl alcohol

C5H12O

Isobutyl alcohol

C4H10O

Isobutyric acid

C4H8O2

Isovaleric acid Lactic acid Maleic acid

C5H10O2 C3H6O C4H4O4

Malic acid

C4H6O5

Malonic acid Methyl acetate

C3H4O4 C3H6O2

glucoside (α-) Nicotine Nitrophenol (p-) Oxalic acid

C7H14O6 C10H14N2 C6H5NO3 C2H2O4

Phenol

C6H6O

Phenylglycolic acid Picoline (α-) (β-)

C8H8O3 C6H7N C6H7N

Propionic acid

C3H6O2

Pyridine Resorcinol Succinic acid

C5H5N C6H6O2 C4H6O4

Tartaric acid (d, l, or dl)

C4H6O6

∗From International Critical Tables, vol. 3, pp. 111–114.

d = d w + Aps + Bp s2 + Cps3

t, °C

Range, ps

A

B

18 15 0 4 15 20 25 15 0 25 20  18    25  0  15  30  20   25 18  20   25 21 21  0  15  20   25 15 15 25  20   25 20  15   20  15  18  25 25 25 25  20   25 20 20  0   30 20 15 0 15 17.5 20 25  15   80 25 25 25  18   25 25 18 25 15 17.5 20 30 40 50 60

0–30 0–6 0–100 0–100 0–100 0–100 0–100 0–16 0–89 0–0.6 0–7.9 0–10 0–62 0–70 0–78 0–90 0–32 0–86 0–50 0–30 0–97 0–36 0–65 0–100 0–6 0–5 0–4.5 0–95 0–40 22–96 0–8 0–8 0–2.5 0–8 0–8 0–9 0–9 0–12 0–5 0–9 0–40 0–40 0–40 0–40 0–20 26–51 26–51 0–60 0–1.5 0–4 0–4 0–9 0–4 0–4 0–5 0–65 0–11 0–70 0–60 0–10 0–40 0–60 0–52 0–5.5 0–15 0–50 0–50 0–50 0–50 0–50 0–50

+0.03255 +0.03639 −0.03856 −0.027648 −0.021009 −0.021233 −0.021171 −0.021175 −0.033729 +0.025615 −0.021651 +0.03414 +0.035135 +0.024489 +0.024455 +0.024401 +0.023648 +0.023602 +0.023824 +0.024427 +0.024427 +0.0334 +0.021193 +0.021483 +0.02133 −0.02221 −0.02221 +0.022367 +0.022518 +0.021217 +0.021827 +0.021664 +0.02155 −0.02146 −0.02169 +0.0352 +0.0345 +0.0337 +0.03253 +0.02231 +0.0234 +0.023933 +0.023736 +0.02389 +0.0340 +0.023336 +0.023151 +0.03642 +0.023216 +0.025898 +0.02494 +0.02494 +0.025264 +0.025108 +0.02111 +0.03462 +0.02207 −0.04386 −0.04683 +0.0395 +0.039245 +0.03229 +0.02201 +0.02304 +0.024482 +0.024455 +0.024432 +0.024335 +0.024265 +0.024205 +0.024155

−0.0516 +0.04171 −0.05449 −0.041193 −0.059682 −0.053529 −0.05904 −0.042024 −0.041232 −0.02117 +0.04285 +0.04131 −0.04166 +0.042802 +0.042198 +0.041887 +0.05302 +0.05552 +0.041141 +0.05537 +0.05537 +0.0676 −0.05307 +0.052992 −0.05108 +0.0448 +0.0435 +0.05358 −0.05658 +0.053199 +0.05366 +0.0421 +0.043 +0.056 +0.0438

  

  

  

−0.04282 +0.05186 +0.0575 +0.05957 +0.04175 +0.041066 −0.0574 +0.05996 +0.05975 +0.05454 −0.0455 −0.033185 −0.058 −0.058 −0.031996 −0.031607 −0.04283 −0.0686 +0.0423 −0.051405 −0.0513 −0.04172 −0.0599 −0.05204 +0.05519

C

−0.07588 +0.08272 −0.08624 −0.075327 −0.0856 +0.072984

+0.0611 −0.071291 +0.074366 +0.076549 +0.0722 +0.0717 +0.077534 +0.077534 −0.0747 −0.075248

−0.076005 +0.06542 −0.072529

+0.01544 +0.08978 −0.07687 +0.0441 +0.04254 +0.04208

−0.074167 +0.07361 −0.0828 −0.0819

+0.04185 +0.04185 +0.041837 +0.04185 +0.04185 +0.04185 +0.04185 (Continued )

2-112

PHYSICAL AnD CHEMICAL DATA

TABLE 2-63 Densities of Aqueous Solutions of Miscellaneous Organic Compounds (Continued ) d = d w + Aps + Bp s2 + Cps3 (Cont.)

Section A Name

t, °C

Formula

Tetraethyl ammonium chloride Thiourea

C8H20ClN CH4N2S

Trichloroacetic acid

C2HCl3O2

Triethylamine hydrochloride

C6H16ClN

Trimethyl carbinol

C4H10O

Urea

CH4N2O

Urethane Valeric acid (n-)

C3H7NO2 C5H10O2

Section B Name

Formula

Butyl alcohol (n-) Butyric acid (n-) Ethyl ether

C4H10O C4H8O2 C4H10O

Isobutyl alcohol

C4H10O

Isobutyric acid Nicotine Picoline (α-) (β-) Pyridine Trimethyl carbinol

C4H8O2 C10H14N2 C6H7N C6H7N C5H5N C4H10O

ds 0.8097 0.9534 0.7077  0.8170   0.8055 0.9425 1.0093 0.9404 0.9515 0.9776 0.7856 Section C

Name

Formula

Allyl alcohol Butyl alcohol (n-)

C3H6O C4H10O

Chloral hydrate

C2H3Cl3O2

Ethyl tartrate

C7H14O6

Furfural

C5H4O2

Pyridine

C5H5N

Range, ps

21 15  12.5  20  25 21  20   25 14.8  18  20  25 20 25

ps 76.60 80.95  2.00  10.00  5.00 10.00 25.00  4.62  5.69  6.56 9.34 21.20 29.50 40.40

0–63 0–7 0–61 10–30 0–94 0–54 0–100 0–100 0–12 0–51 0–35 0–10 0–56 0–3

A

B

C

+0.031884 +0.022995 +0.02499 +0.025053 +0.025051 +0.046 −0.02117 −0.021286 +0.023213 +0.022718 +0.022702 +0.022728 +0.021278 +0.0334

+0.056 +0.05374 +0.04153 +0.041387 +0.056119 +0.05558 −0.041908 −0.04176 −0.044802 +0.051552 +0.053712 −0.041817 −0.05245 −0.0427

+0.07122

+0.061038 −0.0869 +0.07957 +0.07887 +0.051216 +0.072573 −0.072285 +0.051379 −0.073437

d = ds + Apw + Bp w2 + Cp w3 t, °C

Range, pw

A

B

20 25 25 0 15 26 20 25 25 25 20

0–20 0–38 0–1.1 0–14 0–16 0–80 0–40 0–30 0–40 0–40 0–20

+0.022103 +0.021854 +0.0234 +0.022437 +0.02224 +0.021808 +0.02199 +0.022715 +0.021925 +0.021157 +0.022287

−0.04113 −0.042314 +0.0336 −0.04285 −0.04129 −0.042358 −0.04331 −0.04393 −0.04352 −0.05536 +0.05275

C

+0.061253 +0.07315 +0.0625 −0.062

dt = do + At + Bt2 do

Range, °C

A

B

0.9122 0.8614 1.0094 1.0476 1.0150 1.0270 1.0665 1.0125 1.0140 1.0155 1.0055 1.0115 1.0145 1.0182

0–45 0–43 7–80 7–80 15–80 15–80 15–80 22–74 22–74 22–74 11–73 14–73 12–72 9–74

−0.038 −0.037292 −0.042597 −0.047955 −0.032103 −0.032116 −0.03401 −0.03232 −0.03221 −0.03211 −0.03171 −0.03378 −0.03463 −0.03605

−0.0527 −0.0675 −0.054313 −0.054253 −0.052544 −0.062929 −0.0523 −0.05254 −0.05268 −0.05290 −0.053615 −0.05248 −0.05235 −0.05167

DEnSITIES OF MISCELLAnEOUS MATERIALS

2-113

DEnSITIES OF MISCELLAnEOUS MATERIALS TABLE 2-64 Approximate Specific Gravities and Densities of Miscellaneous Solids and Liquids* Water at 4°C and normal atmospheric pressure taken as unity. For more detailed data on any material, see the section dealing with the properties of that material.

Substance Metals, Alloys, Ores Aluminum, cast-hammered bronze Brass, cast-rolled Bronze, 7.9 to 14% Sn phosphor

Sp. gr.

Aver. density lb/ft 3

Substance

Sp. gr.

Aver. density lb/ft 3

Timber, Air-dry Apple Ash, black white Birch, sweet, yellow Cedar, white, red

0.66–0.74 0.55 0.64–0.71 0.71–0.72 0.35

44 34 42 44 22

2.55–2.80 7.7 8.4–8.7 7.4–8.9 8.88

165 481 534 509 554

Copper, cast-rolled ore, pyrites German silver Gold, cast-hammered coin (U.S.)

8.8–8.95 4.1–4.3 8.58 19.25–19.35 17.18–17.2

556 262 536 1205 1073

Cherry, wild red Chestnut Cypress Elm, white Fir, Douglas

0.43 0.48 0.45–0.48 0.56 0.48–0.55

27 30 29 35 32

Iridium Iron, gray cast cast, pig wrought spiegeleisen

21.78–22.42 7.03–7.13 7.2 7.6–7.9 7.5

1383 442 450 485 468

balsam Hemlock Hickory Locust Mahogany

0.40 0.45–0.50 0.74–0.80 0.67–0.77 0.56–0.85

25 29 48 45 44

ferro-silicon ore, hematite ore, limonite ore, magnetite slag

6.7–7.3 5.2 3.6–4.0 4.9–5.2 2.5–3.0

437 325 237 315 172

Maple, sugar white Oak, chestnut live red, black

0.68 0.53 0.74 0.87 0.64–0.71

43 33 46 54 42

Lead ore, galena Manganese ore, pyrolusite Mercury

11.34 7.3–7.6 7.42 3.7–4.6 13.6

710 465 475 259 849

8.97 8.9 21.5 10.4–10.6 7.83 7.80 7.70–7.73 7.2–7.5 6.4–7.0 19.22

555 537 1330 656 489 487 481 459 418 1200

white Pine, Norway Oregon red Southern white

0.77 0.55 0.51 0.48 0.61–0.67 0.43

48 34 32 30 38–42 27

Poplar Redwood, California Spruce, white, red Teak, African Indian Walnut, black Willow

0.43 0.42 0.45 0.99 0.66–0.88 0.59 0.42–0.50

27 26 28 62 48 37 28

6.9–7.2 3.9–4.2

440 253

Various Solids Cereals, oats, bulk barley, bulk corn, rye, bulk wheat, bulk Cork

0.51 0.62 0.73 0.77 0.22–0.26

26 39 45 48 15

Various Liquids Alcohol, ethyl (100%) methyl (100%) Acid, muriatic, 40% nitric, 91% sulfuric, 87%

0.789 0.796 1.20 1.50 1.80

49 50 75 94 112

Cotton, flax, hemp Fats Flour, loose pressed Glass, common

1.47–1.50 0.90–0.97 0.40–0.50 0.70–0.80 2.40–2.80

93 58 28 47 162

Chloroform Ether Lye, soda, 66% Oils, vegetable mineral, lubricants

1.500 0.736 1.70 0.91–0.94 0.88–0.94

95 46 106 58 57

plate or crown crystal dint Hay and straw, bales Leather

2.45–2.72 2.90–3.00 3.2–4.7 0.32 0.86–1.02

161 184 247 20 59

0.861–0.867 1.0 0.9584 0.88–0.92 0.125

54 62.428 59.830 56 8

1.02–1.03

64

Paper Potatoes, piled Rubber, caoutchouc goods Salt, granulated, piled

0.70–1.15 0.67 0.92–0.96 1.0–2.0 0.77

58 44 59 94 48

Ashlar Masonry Bluestone Granite, syenite, gneiss Limestone Marble Sandstone

2.3–2.6 2.4–2.7 2.1–2.8 2.4–2.8 2.0–2.6

153 159 153 162 143

Saltpeter Starch Sulfur Wool

1.07 1.53 1.93–2.07 1.32

67 96 125 82

Rubble Masonry Bluestone Granite, syenite, gneiss Limestone Marble Sandstone

2.2–2.5 2.3–2.6 2.0–2.7 2.3–2.7 1.9–2.5

147 153 147 156 137

Monel metal, rolled Nickel Platinum, cast-hammered Silver, cast-hammered Steel, cold-drawn machine tool Tin, cast-hammered cassiterite Tungsten Zinc, cast-rolled blende

Turpentine Water, 4°C max. density 100°C ice snow, fresh fallen sea water

∗From Marks’ Standard Handbook for Mechanical Engineers, 10th ed., McGraw-Hill, 1996.

Sp. gr.

Aver. density lb/ft 3

Dry Rubble Masonry Granite, syenite, gneiss Limestone, marble Sandstone, bluestone

1.9–2.3 1.9–2.1 1.8–1.9

130 125 110

Brick Masonry Hard brick Medium brick Soft brick Sand-lime brick

1.8–2.3 1.6–2.0 1.4–1.9 1.4–2.2

128 112 103 112

Concrete Masonry Cement, stone, sand slag, etc. cinder, etc.

2.2–2.4 1.9–2.3 1.5–1.7

144 130 100

0.64–0.72 1.5 0.85–1.00 1.4–1.9 2.08–2.25

40–45 94 53–64 103 94–135

Portland cement Slags, bank slag bank screenings machine slag slag sand

3.1–3.2 1.1–1.2 1.5–1.9 1.5 0.8–0.9

196 67–72 98–117 96 49–55

Earth, etc., Excavated Clay, dry damp plastic and gravel, dry Earth, dry, loose dry, packed moist, loose moist, packed mud, flowing mud, packed Riprap, limestone

1.0 1.76 1.6 1.2 1.5 1.3 1.6 1.7 1.8 1.3–1.4

63 110 100 76 95 78 96 108 115 80–85

1.4 1.7 1.4–1.7 1.6–1.9 1.89–2.16

90 105 90–105 100–120 126

1.28 1.44 0.96 1.00 1.12 1.00

80 90 60 65 70 65

Minerals Asbestos Barytes Basait Bauxite Bluestone

2.1–2.8 4.50 2.7–3.2 2.55 2.5–2.6

153 281 184 159 159

Borax Chalk Clay, marl Dolomite Feldspar, orthoclase

1.7–1.8 1.8–2.8 1.8–2.6 2.9 2.5–2.7

109 143 137 181 162

Gneiss Granite Greenstone, trap Gypsum, alabaster Hornblende Limestone Marble Magnesite Phosphate rock, apatite Porphyry

2.7–2.9 2.6–2.7 2.8–3.2 2.3–2.8 3.0 2.1–2.86 2.6–2.86 3.0 3.2 2.6–2.9

175 165 187 159 187 155 170 187 200 172

Substance

Various Building Materials Ashes, cinders Cement, Portland, loose Lime, gypsum, loose Mortar, lime, set Portland cement

Riprap, sandstone Riprap, shale Sand, gravel, dry, loose gravel, dry, packed gravel, wet Excavations in Water Clay River mud Sand or gravel and clay Soil Stone riprap

(Continued )

2-114

PHYSICAL AnD CHEMICAL DATA

TABLE 2-64 Approximate Specific Gravities and Densities of Miscellaneous Solids and Liquids (Continued ) Water at 4°C and normal atmospheric pressure taken as unity. For more detailed data on any material, see the section dealing with the properties of that material.

Substance

Aver. density lb/ft3

Substance

0.37–0.90 2.5–2.8 2.0–2.6 2.7–2.8 2.6–2.9

40 165 143 171 172

Bituminous Substances Asphaltum Coal, anthracite bituminous lignite peat, turf, dry

1.1–1.5 1.4–1.8 1.2–1.5 1.1–1.4 0.65–0.85

81 97 84 78 47

2.6–2.8 2.6–2.7

169 165

1.5 1.7 1.5 1.3 1.5

96 107 95 82 92

charcoal, pine charcoal, oak coke Graphite Paraffin

0.28–0.44 0.47–0.57 1.0–1.4 1.64–2.7 0.87–0.91

23 33 75 135 56

Sp. gr.

Minerals (Cont.) Pumice, natural Quartz, flint Sandstone Serpentine Shale, slate Soapstone, talc Syenite Stone, Quarried, Piled Basalt, granite, gneiss Greenstone, hornblende Limestone, marble, quartz Sandstone Shale

Aver. density lb/ft 3

Sp. gr.

Substance

Sp. gr.

Aver. density lb/ft3

Bituminous Substances (Cont.) Petroleum refined (kerosene) benzine gasoline Pitch Tar, bituminous

0.87 0.78–0.82 0.73–0.75 0.70–0.75 1.07–1.15 1.20

54 50 46 45 69 75

Coal and Coke, Piled Coal, anthracite bituminous, lignite peat, turf charcoal coke

0.75–0.93 0.64–0.87 0.32–0.42 0.16–0.23 0.37–0.51

47–58 40–54 20–26 10–14 23–32

note: To convert pounds per cubic foot to kilograms per cubic meter, multiply by 16.02. °F = 9⁄5°C + 32.

TABLE 2-65 Density (kg/m3) of Selected Elements as a Function of Temperature Element symbol

Temperature, K∗

Al

Be†

Cr

Cu

Au

Ir

Fe

Pb

Mo

Ni

Pt

Ag

Zn†

50 100 150 200 250

2736 2732 2726 2719 2710

3650 3640 3630 3620 3610

7160 7155 7150 7145 7140

9019 9009 8992 8973 8951

19,490 19,460 19,420 19,380 19,340

22,600 22,580 22,560 22,540 22,520

7910 7900 7890 7880 7870

11,570 11,520 11,470 11,430 11,380

10,260 10,260 10,250 10,250 10,250

8960 8950 8940 8930 8910

21,570 21,550 21,530 21,500 21,470

10,620 10,600 10,575 10,550 10,520

7280 7260 7230 7200 7170

300 400 500 600 800

2701 2681 2661 2639 2591

3600 3580 3555 3530

7135 7120 7110 7080 7040

8930 8885 8837 8787 8686

19,300 19,210 19,130 19,040 18,860

22,500 22,450 22,410 22,360 22,250

7860 7830 7800 7760 7690

11,330 11,230 11,130 11,010 10,430

10,240 10,220 10,210 10,190 10,160

8900 8860 8820 8780 8690

21,450 21,380 21,330 21,270 21,140

10,490 10,430 10,360 10,300 10,160

7135 7070 7000 6935 6430

1000 1200 1400 1600 1800

2365 2305 2255

7000 6945 6890 6760 6700

8568 8458 7920 7750 7600

18,660 18,440 17,230 16,950

22,140 22,030 21,920 21,790 21,660

7650 7620 7520 7420 7320

10,190 9,940

10,120 10,080 10,040 10,000 9,950

8610 8510 8410 8320 7690

21,010 20,870 20,720 20,570 20,400

10,010 9,850 9,170 8,980

6260

21,510

7030

9,900

7450

20,220

2000

7460

note: Above the horizontal line the condensed phase is solid; below the line, it is liquid. ∗°R = 9⁄ 5 K. † Polycrystalline form tabulated. Similar tables for an additional 45 elements appear in the Handbook of Heat Transfer, 2d ed., McGraw-Hill, New York, 1984.

LATEnT HEATS Unit Conversions For this subsection, the following unit conversions are applicable: °F = 9⁄ 5°C + 32. To convert calories per gram to British thermal units per pound, multiply by 1.799.

To convert millimeters of mercury to pounds-force per square inch, multiply by 1.934 × 10−2.

LATEnT HEATS

2-115

TABLE 2-66 Heats of Fusion and Vaporization of the Elements and Inorganic Compounds* Unless stated otherwise, the values have been taken from the compilations by K. K. Kelley on “Heats of Fusion of Inorganic Compounds,” U.S. Bur. Mines Bull. 393 (1936), and “The Free Energies of Vaporization and Vapor Pressures of Inorganic Substances,” U.S. Bur. Mines Bull. 383 (1935).

Substance

mp, °C

Heat of fusion,a,b cal/mol

bp at 1 atm, °C

Aluminum Al 660.0 2,550 Al2Br6 97.5 5,420 Al2Cl6 192.5 16,960 AlF3⋅3NaF 1000 16,380 Al2I6 191.0 7,960 Al2O3 2045 (26,000) Antimony Sb 630.5 4,770 SbBr3 97 3,510 SbCl3 73.4 3,030 SbCl5 4 2,400 Sb4O6 655 (27,000) Sb4S6 546 11,200 Argon A −189.3 290 Arsenic As 814 (6,620) AsBr3 31 2,810 AsCl3 −16 2,420 AsF5 −80.7 2,800 As4O6 313 8,000 Barium Ba 704 (1,400)e BaBr2 847 6,000 BaCl2 960 5,370 BaF2 1287 3,000 Ba(NO3)2 595 (5,980) Ba3(PO4)2 1730 18,600 BaSO4 1350 9,700 Beryllium Be 1280 2,500e Bismuth Bi 271.3 2,505 BiBr3 BiCl3 224 2,600 Bi2O3 817 6,800 Bi2S5 747 8,900 Boron BBr3 BCl3 BF3 −128 480 B2H6 −165.5 B3H10 −119.8 B5H9 −46.9 B5H11 B10H14 99.7 7,800 B2H5Br −104 B3N3H6 −58 Bromine Br2 −7.2 2,580 BrF5 −61.3 1,355 Cadmium Cd 320.9 1,460 CdBr2 568 (5,000) CdCl2 568 5,300 CdF2 1110 (5,400) CdI2 387 3,660 CdO CdSO4 1000 4,790 Calcium Ca 851 2,230 CaBr2 730 4,180 CaCO3 1282 (12,700) CaCl2 782 6,100 CaF2 1392 4,100 Ca(NO3)2 561 5,120 CaO 2707 (12,240) CaO⋅Al2O3⋅2SiO2 1550 29,400 CaO⋅MgO⋅2SiO2 1392 (18,200) CaO⋅SiO2 1512 13,400 CaSO4 1297 6,700 Carbon C (graphite) 3600 11,000e CBr4 90 1,050 CCl4 −24.0 644 CF4 CH4 −182.5 224 C2N2 −27.8 1,938u CNBr 52 CNCl −5 2,240 ∗See also subsection “Thermodynamic Properties.”

Heat of vaporization,a,b cal/mol

2057 256.4 180.2c

61,020 10,920 26,750c

385.5 3000

15,360

1440

46,670

219 172d 1425

10,360 11,570 17,820

−185.8

1,590

610c

31,000c

122 −52.8 457.2

7,570 4,980 14,300

1638

35,670

1420 461 441

18,020 17,350

91.3 12.5 −100.9 −92.4 16 58 67 f 16 50.4

7,300 5,680 4,620 3,685 6,470 7,700 8,500 11,600 6,230 7,670

58.0 40.4

7,420 7,470

765

23,870

967

29,860

796 1559c

25,400 53,820c

1487

36,580

77 −127.9 −161.4 −21.1 13

7,280 3,110 2,040 5,576u 11,010c 6,300

Substance Carbon (Cont.) CNF CNI CO CO2 COS COCl2 CS2 Cerium Ce Cesium Cs CsBr CsCl CsF CsI CsNO3 Chlorine Cl2 ClF ClF3 Cl2O ClO2 Cl2O7 Chromium Cr Cr O2Cl2 Cobalt Co CoCl2 Copper Cu Cu2Br2 Cu2Cl2 CuI Cu2(CN)2 Cu2O CuO Cu2S Fluorine F2 F2O Gallium Ga Germanium Ge GeH4 Ge2H6 Ge3H8 GeHCl3 GeBr4 GeCl4 Ge(CH3)4 Gold Au Helium He Hydrogen H2 HBr HCl HCN HF (HF)6 HI H2O H22O (= D2O) H2O2 HNO3 H3PO2 H3PO3 H3PO4 H4P2O6 H2S H2S2 H2SO4 H2Se H2SeO4 H2Te Indium In

mp, °C

Heat of fusion,a,b cal/mol

−205.0 −57.5 −138.8

200 1,900 1,129 k

−112.0

1,049 l

775

2,120

28.4

500

642 715

3,600 (2,450)

407

3,250

−101.0

1,531m

1550

3,930

1490 727

3,660 7,390

1083.0

3,110

430

4,890

473 1230 1447 1127

(5,400) (13,400) 2,820 5,500

−223 29.8

bp at 1 atm, °C −72.8 141 −191.5 −78.4c −50.2 8.0

5,780c 13,980c 1,444 6,030 c, r 4,423 k 5,990

690 1300 1300 1251 1280

16,320 35,990 35,690 34,330 35,930

−34.1 −101 11.3 2.0 10.9 79

959 −165 −109 −105.6 −71 26.1 −49.5 −88

(8,300)

1063.0

3,030

−271.4 −259.2 −86.9 −114.2 −13.2 −83.0

28 575 476 2,009i 1,094

−50.8 0.0 3.8 −2 −47 17.4 74 42.4 55 −85.5 −87.6 10.5

686 1,436 1,501s 2,520c 600 2,310 3,070 2,520 8,300 568t 1,805 2,360

58 −48.9

3,450 1,670

156.4

781

4,878 m 5,890 6,280 7,100 8,480

2475 117

8,250

1050

27,170

2595 1355 1490 1336

72,810 16,310 11,920 15,940

−188.2 −144.8 1,336

Heat of vaporization,a,b cal/mol

1,640 2,650

2071 −89.1 31.4 110.6 75g 189 84 44 2966

3,580 5,900 7,550 8,000 8,560 7,030 6,460 81,800

−268.4

22

−252.7 −66.7 −85.0 25.7 33.3 51.2

216 4,210 3,860 6,027i 7,460 5,020

100.0 101.4 158

9,729 h,q 9,945 r,q 10,270

−60.3

4,463 t

−41.3

4,880

−2.2

5,650

(Continued )

2-116

PHYSICAL AnD CHEMICAL DATA

TABLE 2-66 Heats of Fusion and Vaporization of the Elements and Inorganic Compounds (Continued )

Substance Iodine I2 ICl(α) ICl(β) IF7 Iron Fe FeCl2 Fe2Cl6 Fe(CO)5 FeO FeS Krypton Kr Lead Pb PbBr2 PbCl2 PbF2 PbI2 PbMoO4 PbO PbS PbSO4 PbWO4 Lithium Li LiBO2 LiBr LiCl LiF LiI LiOH Li2MoO4 LiNO3 Li2SiO3 Li4SiO4 Li2SO4 Li2WO4 Magnesium Mg MgBr2 MgCl2 MgF2 MgO Mg3(PO4)2 MgSiO3 MgSO4 MgZn2 Manganese Mn MnCl2 MnSiO3 MnTiO3 Mercury Hg HgBr2 HgCl2 HgI2 HgSO4 Molybdenum Mo MoF6 MoO3 Neon Ne Nickel Ni NiCl2 Ni(CO)4 Ni2S Ni3S2 Nitrogen N2 NF3 NH3 NH4CNS NH4NO3 N2O NO N2O4 N2O5 NOCl Osmium OsF8 OsO4 (yellow) OsO4 (white) Oxygen O2 O3

mp, °C 113.0 17.2 13.9 1530 677 304 −21 1380 1195 −157

Heat of fusion,a,b cal/mol

bp at 1 atm, °C

Heat of vaporization,a,b cal/mol

3,650 2,660 2,270

183 4c

7,460c

3,560 7,800 20,590 3,250 (7,700) 5,000

2735 1026 319 105

84,600 30,210 12,040 9,000

360

e

152.9

10,390

2,310

e

327.4 488 498 824 412 1065 890 1114 1087 1123

1,224 4,290 5,650 1,860 5,970 (25,800) 2,820 4,150 9,600 (15,200)

179 845 552 614 847 440 462 705

1,100 (5,570) 2,900 3,200 (2,360) (1,420) 2,480 4,200

1177 1249 857 742

7,210 7,430 3,040 (6,700)

650 711 712 1221 2642 1184 1524 1127 589

2,160 8,300 8,100 5,900 18,500 (11,300) 14,700 3,500 (8,270)

1107

32,520

1418

32,690

1220 650 1274 1404

3,450 7,340 (8,200) (7,960)

2152 1190

55,150 29,630

557 3,960 4,150 4,500 (1,440)

361 319 304 354

13,980 14,080 14,080 14,260

(6,660) 2,500 (2,500)

(4800) 36 1151

(128,000) 6,000

−38.9 241 277 250 850 2622 17 745 −248.5

1744 914 954 1293 872

42,060 27,700 29,600 38,300 24,850

1472 1281

51,310 (50,000)

1372

32,250

1310 1382 1681 1171

35,420 35,960 50,970 40,770

77

−246.0

440e

1455

4,200

645 790

(2,980) 5,800

2730 987c 42.5

87,300 48,360c 7,000

−195.8 −129.0 −33.4

1,336 3,000 5,581n

−88.5 −151.7 30 32.4 −6.4

3,950 3,307 7,040 13,800c 6,140

47.4 130

6,840 9,450

−183.0 −111

1,629 2,880

−210.0 −77.7 146 169.6 −90.8 −163.6 −13

56 42 −218.9

172 1,352 (4,700) 1,460 1,563 550 5,540 n

4,060 2,340 106

Substance Palladium Pd Phosphorus P4 (yellow) P4 (violet) P4 (black) PCl3 PH3 P 4 O6 P4O10(α) P4O10(β) POCl3 P 2S 3 Platinum Pt Potassium K KBO2 KBr KCl KCN KCNS K2CO3 K2Cr O4 K2Cr2O7 KF KI K2MoO4 KNO3 KOH KPO3 K3PO4 K4P2O7 K2SO4 K2TiO3 K2WO4 Praseodymium Pr Radon Rn Rhenium Re Re2O7 Re2O8 Rubidium Rb RbBr RbCl RbF RbI RbNO3 Selenium Se2 Se6 SeF6 SeO2 SeOCl2 Silicon Si SiCl4 Si2Cl6 Si3Cl8 (SiCl3)2O SiF4 Si2F6 SiF3Cl SiF2Cl2 SiH4 Si2H6 Si3H8 Si4H10 SiH3Br SiH2Br2 SiHCl3 (SiH3)3N (SiH3)2O SiO2 (quartz) SiO2 (cristobalite) Silver Ag AgBr AgCl AgCN AgI AgNO3 Ag2S Ag2SO4 Sodium Na NaBO2

mp, °C 1554

Heat of fusion,a,b cal/mol

bp at 1 atm, °C

Heat of vaporization,a,b cal/mol

4,120

44.2

615

−133.8 23.8 569

270o 3,360 17,080

1.1

3,110

1773.5

4,700

(4400)

(107,000)

63.5 947 742 770 623 179 897 984 398 857 682 922 338 360 817 1340 1092 1074 810 927

574 (5,700) 5,000 6,410 (3,500) 2,250 7,800 6,920 8,770 6,500 4,100 (4,000) 2,840 (2,000) 2,110 8,900 14,000 8,100 (10,600) (4,400)

776

18,920

1383 1407

37,060 38,840

1324

34,690

1327

30,850

932

2,700

−71 (3000) 296 147

15,340 3,800

39.1 677 717 833 638 305

525 3,700 4,400 4,130 2,990 1,340

217

1,220

10

1,010

1427 −67.6 −1

9,470 1,845

−33 −18.5 −138 −144 −185 −132.5 −117 −93.5 −93.8 −70.0 −126.5 −105.6 −144 1470 1700

3,400 2,100

960.5 430 455 350 557 209 842 657

2,700 2,180 3,155 2,750 2,250 2,755 3,360 (4,300)

97.7 966

630 8,660

3,900

280 417c 453c 74.2 −87.7 174 591 358c 105.1 508

12,520 25,600c 33,100 7,280 3,489 o 10,380 20,670 8,380

−61.8

4,010

362.4

18,060

679 1352 1381 1408 1304 753 736 −45.8c 317c 168 2290 56.8 139 211.4 135.6 −94.8c −18.9c −70.1 −31.5 −111.6 −14.3 53.1 100 2.4 70.5 31.8 48.7 −15.4 2230 2212

18,110 37,120 36,920 39,510 35,960 25,490 20,600 6,350c 20,900

6,860 12,340 8,820 6,130c 10,400c 4,460 5,080 2,960 5,110 6,780 8,890 5,650 6,840 6,360 6,850 5,350

60,720

1564

42,520

1506

34,450

914

23,120 (Continued )

LATEnT HEATS

2-117

TABLE 2-66 Heats of Fusion and Vaporization of the Elements and Inorganic Compounds (Continued )

Substance Sodium (Cont.) NaBr NaCl NaClO3 NaCN NaCNS Na2CO3 NaF NaI Na2MoO4 NaNO3 NaOH ½Na2O⋅½Al2O3⋅3SiO2 NaPO3 Na4P2O7 Na2S Na2SiO3 Na2Si2O5 Na2SO4 Na2WO4 Strontium Sr SrBr2 SrCl2 SrF2 Sr3(PO4)2 Sulfur S (rhombic) S (monoclinic) S2Cl2 SF6 SO2 SO3(α) SO3(β) SO3(γ) SOBr2 SOCl2 SO2Cl2 Tellurium Te TeCl4 TeF6

mp, °C

Heat of fusion,a,b cal/mol

747 800 255 562 323 854 992 662 687 310 322 1107 988 970 920 1087 884 884 702

6,140 7,220 5,290 (4,400) 4,450 7,000 7,000 5,240 3,600 3,760 2,000 13,150 (5,000) (13,700) (1,200) 10,300 8,460 5,830 5,800

757 643 872 1400 1770

2,190 4,780 4,100 4,260 18,500

112.8 119.2 −75.5 17 32.4 62.2

453

1,769p 2,060 2,890 6,310

3,230

bp at 1 atm, °C

Heat of vaporization,a,b cal/mol

1392 1465

37,950 40,810

1500

37,280

1704

53,260

1378

1384

33,610

444.6

2,200

138 −63.5c −5.0 44.8

8,720 5,600c 5,960p 10,190

139.5 75.4 69.2

9,920 7,600 7,760

1090 392 −38.6c

16,830 6,700c

Values in parentheses are uncertain. For the freezing point or the normal boiling point unless otherwise stated. c Sublimation. d Decomposes at about 75°C; value obtained by extrapolation. e Bichowsky and Rossini, Thermochemistry of the Chemical Substances, Reinhold, New York (1936). f Decomposes before the normal boiling point is reached. g Decomposes at about 40°C; value obtained by extrapolation. h See also pp. 2-304 through 2-307 on steam table. i Giauque and Ruehrwein, J. Am. Chem. Soc., 61 (1939): 2626. j Giauque and Egan, J. Chem. Phys., 5 (1937): 45. a b

Substance Thallium Tl TlBr TlCl Tl2CO3 TlI TlNO3 Tl2S Tl2SO4 Tin Sn4 SnBr2 SnBr4 SnCl2 SnCl4 Sn(CH3)4 SnH4 SnI4 Titanium TiBr4 TiCl4 TiO2 Tungsten W WF6 Uranium UF6 Xenon Xe Zinc Zn ZnCl2 Zn(C2H5)2 ZnO ZnS Zirconium ZrBr4 Zr Cl4 ZrI4 Zr O2

mp, °C

Heat of fusion,a,b cal/mol

302.5 460 427 273 440 207 449 632

1,030 5,990 4,260 4,400 3,125 2,290 3,000 5,500

1457 819 807

38,810 23,800 24,420

823

25,030

231.8 232 30 247 −33.2

1,720 (1,700) 3,000 3,050 2,190

2270

68,000

−149.8 143.5

(4,300)

38.2 −23 1825

(2,060) 2,240 (11,400)

136

3390 −0.4

(8,400) 1,800

(5900) 17.3

(176,000) 6,350

55.1c

9,990c

−108.0

3,110

907 732 118

27,430 28,710 8,960

357c 311c 431c

25,800c 25,290c 29,030c

−111.5 419.5 283 1975 1645

2715

Material

1,595 (5,500) 4,470 (9,000)

20,800

623 113 78.3 −52.3

Heat of vaporization,a,b cal/mol

20,740 8,330 7,320 4,420

8,350

Kemp and Giauque, J. Am. Chem. Soc., 59 (1937): 79. Brown and Manov, J. Am. Chem. Soc., 59 (1937): 500. Giauque and Powell, J. Am. Chem. Soc., 61 (1939): 1970. n Overstreet and Giauque, J. Am. Chem. Soc., 59 (1937): 254. o Stephenson and Giauque, J. Chem. Phys., 5 (1937): 149. p Giauque and Stephenson, J. Am. Chem. Soc., 60 (1938): 1389. q Osborne, Stimson, and Ginnings, Bur. Standards J. Research, 23, 197 (1939): 261. r Miles and Menzies, J. Am. Chem. Soc., 58 (1936): 1067. s Long and Kemp, J. Am. Chem. Soc., 58 (1936): 1829. t Giauque and Blue, J. Am. Chem. Soc., 58 (1936): 831. u Ruehrwein and Giauque, J. Am. Chem. Soc., 61 (1939): 2940. k

l

m

TABLE 2-67 Heats of Fusion of Miscellaneous Materials Alloys 30.5 Pb + 69.5 Sn 36.9 Pb + 63.1 Sn 63.7 Pb + 36.3 Sn 77.8 Pb + 22.2 Sn 1 Pb + 9 Sn 24 Pb + 27.3 Sn + 48.7 Bi 25.8 Pb + 14.7 Sn + 52.4 Bi + 7 Cd Silicates Anorthite (CaAl2Si2O8) Orthoclase (KAlSi2O8) Microcline (KAlSi3O8) Wollastonite (CaSiO8) Malacolite (Ca8MgSi4O12) Diopside (CaMgSi2O4) Olivine (Mg2SiO4) Fayalite (Fe2SiO4) Spermaceti Wax (bees’)

740

bp at 1 atm, °C

mp, °C

Heat of fusion, cal/g

183 179 177.5 176.5 236 98.8 75.5

17 15.5 11.6 9.54 28 6.85 8.4

43.9 61.8

100 100 83 100 94 100 130 85 37.0 42.3

2-118

PHYSICAL AnD CHEMICAL DATA

TABLE 2-68 Heats of Fusion of Organic Compounds The values for the hydrocarbons are from the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards, with some from Parks and Huffman, Ind. Eng. Chem., 23, 1138 (1931). The values for the nonhydrocarbon compounds were recalculated from data in International Critical Tables, vol. 5. Hydrocarbon compounds

Formula

mp, °C

Heat of fusion, cal/g

Paraffins Methane Ethane Propane n-Butane 2-Methylpropane n-Pentane 2-Methylbutane 2,2-Dimethylpropane n-Hexane 2-Methylpentane 2,2-Dimethylbutane 2,3-Dimethylbutane n-Heptane 2-Methylhexane 3-Ethylpentane 2,2-Dimethylpentane 2,4-Dimethylpentane 3,3-Dimethylpentane 2,2,3-Trimethylbutane n-Octane 2-Methylheptane 3-Methylpentane 4-Methylheptane 2,2-Dimethylhexane 2,5-Dimethylhexane 3,3-Dimethylhexane 2-Methyl-3-ethylpentane 3-Methyl-3-ethylpentane 2,2,3-Trimethylpentane 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 2,3,4-Trimethylpentane 2,2,3,3-Tetramethylbutane n-Nonane n-Decane n-Undecane n-Dodecane Eicosane Pentacosane Tritriacontane Aromatics Benzene Methylbenzene (Toluene) Ethylbenzene o-Xylene m-Xylene p-Xylene n-Propylbenzene Isopropylbenzene 1-Methyl-2-ethylbenzene

CH4 C2H 6 C3H 8 C4H10 C4H10 C5H12 C5H12 C5H12 C6H14 C6H14 C6H14 C6H14 C7H16 C7H16 C7H16 C7H16 C7H16 C7H16 C7H16 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C9H20 C10H22 C11H24 C12H26 C20H42 C25H52 C33H68

−182.48 −183.23 −187.65 −138.33 −159.60 −129.723 −159.890 −16.6 −95.320 −153.680 −99.73 −128.41 −90.595 −118.270 −118.593 −123.790 −119.230 −134.46 −24.96 −56.798 −109.04 −120.50 −120.955 −121.18 −91.200 −126.10 −114.960 −90.870 −112.27 −107.365 −100.70 −109.210 +100.69 −53.9 −30.0 −25.9 −9.6 +36.4 +53.3 +71.1

14.03 22.712 19.100 19.167 18.668 27.874 17.076 10.786 36.138 17.407 1.607 2.251 33.513 21.158 22.555 13.982 15.968 16.856 5.250 43.169 21.458 23.795 22.692 24.226 26.903 14.9 23.690 22.657 18.061 19.278 3.204 19.392 14.900 41.2 48.3 34.1 51.3 52.0 53.6 54.0

C6H 6 C 7H 8 C8H10 C8H10 C8H10 C8H10 C9H12 C9H12 C9H12

+5.533 −94.991 −94.950 −25.187 −47.872 +13.263 −99.500 −96.028 −80.833

30.100 17.171 20.629 30.614 26.045 38.526 16.97 19.22 21.13

Nonhydrocarbon compounds

Formula

mp, °C

Acetic acid Acetone Acrylic acid Allo-cinnamic acid Aminobenzoic acid (o-) (m-) (p-) Amyl alcohol Anethole Aniline Anthraquinone Apiol Azobenzene Azoxybenzene

C2H4O2 C3H6O C3H4O2 C9H8O2 C7H7NO2 C7H7NO2 C7H7NO2 C5H12O C10H12O C6H5NH2 C14H8O2 C12H14O4 C12H10N2 C12H10N2O

16.7 −95.5 12.3 68 145 179.5 188.5 −78.9 22.5 −6.3 284.8 29.5 67.1 36

46.68 23.42 37.03 27.35 35.48 38.03 36.46 26.65 25.80 27.09 37.48 25.80 28.91 21.62

Benzil Benzoic acid Benzophenone Benzylaniline Bromocamphor Bromochlorbenzene (o-) (m-) (p-) Bromoiodobenzene (o-) (m-) (p-) Bromol hydrate Bromophenol (p-) Bromotoluene (p-)

C14H10O2 C7H8O2 C13H10O C13H13N C10H15BrO C6H4BrCl C6H4BrCl C6H4BrCl C6H4BrI C6H4BrI C6H4BrI C2H3Br3O2 C6H5BrO C7H7Br

95.2 122.45 47.85 32.37 78 −12.6 −21.2 64.6 21 9.3 90.1 46 63.5 28

22.15 33.90 23.53 21.86 41.57 15.41 15.29 23.41 12.18 10.27 16.60 16.90 20.50 20.86

Heat of fusion, cal/g

Hydrocarbon compounds Aromatics—(Cont.) 1-Methyl-3-ethylbenzene 1-Methyl-4-ethylbenzene 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 1,3,5-Trimethylbenzene Naphthalene Camphene Durene Isodurene Prehnitene p-Cymene n-Butyl benzene tert-Butyl benzene β-Methyl naphthalene Diphenyl Hexamethyl benzene Diphenyl methane Anthracene Phenanthrene Tolane Stilbene Dibenzil Triphenyl methane Alkyl cyclohexanes Cyclohexane Methylcyclohexane Alkyl cyclopentanes Cyclopentane Methylcyclopentane Ethylcyclopentane 1,1-Dimethylcyclopentane cis-1,2-Dimethylcyclopentane trans-1,2-Dimethylcyclopentane trans-1,3-Dimethylcyclopentane Monoolefins Ethene (Ethylene) Propene (Propylene) 1-Butene cis-2-Butene trans-2-Butene 2-Methylpropene (isobutene) 1-Pentene cis-2-pentene trans-2-pentene 2-Methyl-1-butene 3-Methyl-1-butene 2-Methyl-2-butene Acetylenes Acetylene 2-Butyne (dimethylacetylene)

mp, °C

Heat of fusion, cal/g

C9H12 C9H12 C9H12 C9H12 C9H12 C10H8 C10H12 C10H14 C10H14 C10H14 C10H14 C10H14 C10H14 C11H10 C12H10 C12H18 C13H12 C14H10 C14H10 C14H10 C14H12 C14H14 C19H16

−95.55 −62.350 −25.375 −43.80 −44.720 +80.0 +51 +79.3 −24.0 −7.7 −68.9 −88.5 −58.1 +34.1 +68.6 +165.5 +25.2 +216.5 +96.3 +60 +124 +51.4 +92.1

15.14 25.29 16.64 24.54 18.97 36.0 57 37.4 23.0 20.0 17.1 19.5 14.9 20.1 28.8 30.4 26.4 38.7 25.0 28.7 40.0 30.7 21.1

C6H12 C7H14

+6.67 −126.58

7.569 16.429

C5H10 C6H12 C7H14 C7H14 C7H14 C7H14 C7H14

−93.80 −142.445 −138.435 −69.73 −53.85 −117.57 −133.680

2.068 19.68 11.10 3.36 3.87 15.68 17.93

C2H4 C3H6 C4H8 C4H8 C4H8 C4H8 C5H10 C5H10 C5H10 C5H10 C5H10 C5H10

−169.15 −185.25 −185.35 −138.91 −105.55 −140.35 −165.27 −151.363 −140.235 −137.560 −168.500 −133.780

28.547 17.054 16.393 31.135 41.564 25.265 16.82 24.239 26.536 26.879 18.009 25.738

C2H2 C4H6

−81.5 −132.23

23.04 40.808

Formula

Formula

mp, °C

Heat of fusion, cal/g

Butyl alcohol (n-) (t-) Butyric acid (n-)

C4H10O C4H10O C4H8O2

−89.2 25.4 −5.7

29.93 21.88 30.04

Capric acid (n-) Caprylic acid (n-) Carbazole Carbon tetrachloride Carvoxime (d-) (l-) (dl-) Cetyl alcohol Chloracetic acid (α-) (β-) Chloral alcoholate hydrate Chloroaniline (p-) Chlorobenzoic acid (o-) (m-) ( p-) Chloronitrobenzene (m-) (p-) Cinnamic acid anhydride Cresol (p-) Crotonic acid (α-) (cis-) Cyanamide Cyclohexanol

C10H20O2 C8H16O2 C12H9N CCl4 C10H15NO C10H15NO C10H15NO C16H34O C2H3ClO2 C2H3ClO2 C4H7Cl3O2 C2H3Cl3O2 C6H6ClN C7H5ClO2 C7H5ClO2 C7H5ClO2 C6H4ClNO2 C6H4ClNO2 C9H8O2 C18H14O3 C7H8O C4H6O2 C4H6O2 CH2N2 C6H12O

31.99 16.3 243 −22.8 71.5 71 91 49.27 61.2 56 9 47.4 71 140.2 154.25 239.7 44.4 83.5 133 48 34.6 72 71.2 44 25.46

38.87 35.40 42.05 41.57 23.29 23.41 24.61 33.80 31.06 35.12 24.03 33.18 37.15 39.30 36.41 49.21 29.38 31.51 36.50 28.14 26.28 25.32 34.90 49.81 4.19

Nonhydrocarbon compounds

(Continued )

LATEnT HEATS

2-119

TABLE 2-68 Heats of Fusion of Organic Compounds (Continued ) Heat of fusion, cal/g

Nonhydrocarbon compounds

Formula

mp, °C

Dibromobenzene (o-) (m-) (p-) Dibromophenol (2, 4-) Dichloroacetic acid Dichlorobenzene (o-) (m-) (p-) Dihydroxybenzene (o-) (m-) (p-) Di-iodobenzene (o-) (m-) (p-) Dimethyl tartrate (dl-) (d-) pyrone Dinitrobenzene (o-) (m-) (p-) Dinitrotoluene (2, 4-) Dioxane Diphenyl amine

C6H4Br2 C6H4Br2 C6H4Br2 C6H4Br2O C2H2Cl2O2 C6H4Cl2 C6H4Cl2 C6H4Cl2 C6H6O2 C6H6O2 C6H6O2 C6H4I2 C6H4I2 C6H4I2 C6H10O6 C6H10O6 C7H8O2 C6H4N2O4 C6H4N2O4 C6H4N2O4 C7H6N2O4 C4H8O2 C12H11N

1.8 −6.9 86 12 −4(?) −16.7 −24.8 53.13 104.3 109.65 172.3 23.4 34.2 129 87 49 132 116.93 89.7 173.5 70.14 11.0 52.98

12.78 13.38 20.55 13.97 14.21 21.02 20.55 29.67 49.40 46.20 58.77 10.15 11.54 16.20 35.12 21.50 56.14 32.25 24.70 39.99 26.40 34.85 25.23

Elaidic acid Ethyl acetate alcohol Ethylene dibromide Ethyl ether

C18H34O2 C4H8O2 C2H6O C2H4Br2 C4H10O

44.4 83.8 −114.4 10.012 −116.3

52.08 28.43 25.76 13.52 23.54

Formic acid

CH2O2

8.40

58.89

Glutaric acid Glycerol Glycol, ethylene

C6H8O4 C3H8O3 C2H6O2

97.5 18.07 −11.5

37.39 47.49 43.26

Hydrazo benzene Hydrocinnamic acid Hydroxyacetanilide

C12H12N2 C9H10O2 C8H9NO2

134 48 91.3

22.89 28.14 33.59

Iodotoluene (p-) Isopropyl alcohol ether

C7H7I C3H8O C6H14O

34 −88.5 −86.8

18.75 21.08 25.79

Lauric acid (n-) Levulinic acid

C12H24O2 C5H8O3

43.22 33

43.72 18.97

Menthol (l-) (α) Methyl alcohol Myristic acid Methyl cinnamate fumarate oxalate phenylpropiolate succinate

C10H20O CH4O C14H28O2 C10H10O2 C6H8O4 C4H6O4 C10H8O2 C6H10O4

43.5 −97.8 53.86 36 102 54.35 18 19.5

18.63 23.7 47.49 26.53 57.93 42.64 22.86 35.72

Formula

mp, °C

Heat of fusion, cal/g

Naphthol (α-) (β-) Naphthylamine (α-) Nitroaniline (o-) (m-) (p-) Nitrobenzene Nitrobenzoic acid (o-) (m-) (p-) Nitronaphthalene Nitrophenol (o-)

C10H8O C10H8O C10H9N C6H6N2O2 C6H6N2O2 C6H6N2O2 C6H5NO2 C7H5NO4 C7H5NO4 C7H5NO4 C10H7NO2 C6H5NO3

95.0 120.6 50 71.2 114.0 147.3 5.85 145.8 141.1 239.2 56.7 45.13

38.94 31.30 22.34 27.88 40.97 36.46 22.52 40.06 27.59 52.80 25.44 26.76

Palmitic acid Paraldehyde Pelargic acid (n-) (β-) Pelargonic acid (n-) (α-) Phenol Phenylacetic acid Phenylhydrazine Propyl ether (n)

C16H32O2 C6H12O3 C9H18O2 C9H18O2 C6H6O C8H8O2 C6H8N2 C6H14O

61.82 10.5 12.35 40.92 76.7 19.6 −126.1

39.18 25.02 39.04 30.63 29.03 25.44 36.31 20.66

Nonhydrocarbon compounds

Quinone

C6H4O2

115.7

40.85

Stearic acid Succinic anhydride Succinonitrile

C18H30O2 C4H4O3 C4H4N2

68.82 119 54.5

47.54 48.74 11.71

Tetrachloroxylene (o-) (p-) Thiophene Thiosinamine Thymol Toluic acid (o-) (m-) (p-) Toluidine (p-) Tribromophenol (2, 4, 6-) Trichloroacetic acid Trinitroglycerol Trinitrotoluene (2, 4, 6-) Tristearin

C8H6Cl4 C8H6Cl4 C4H4S C4H8N2S C10H14O C8H8O2 C8H8O2 C8H8O2 C7H9N C6H3Br3O C2HCl3O2 C3H5N3O9 C7H5N3O6 C57H110O6

86 95 −39.4 77 51.5 103.7 108.75 179.6 43.3 93 57.5 12.3 80.83 70.8, 54.5

21.02 22.10 14.11 33.45 27.47 35.40 27.59 39.90 39.90 13.38 8.60 23.02 22.34 45.63

Undecylic acid (α-) (n-) (β-) (n-) Urethane

C11H22O2 C11H22O2 C3H7NO2

28.25 48.7

32.20 42.91 40.85

Veratrol

C8H10O2

22.5

27.45

Xylene dibromide (o-) (m-) dichloride (o-) (m-) (p-)

C8H8Br2 C8H8Br2 C8H8Cl2 C8H8Cl2 C8H8Cl2

95 77 55 34 100

24.25 21.45 29.03 26.64 32.73

2-120 TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) Cmpd. no.* 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile

Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N

CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0

Mol. wt.

C1 × 1E-07

C2

C3

C4

Tmin , K

ΔHv at Tmin × 1E-07

44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051

3.4088 9.9475 6.127546 5.8564 4.9258 3.8345 1.7059 6.6599 4.3756 4.3052 0.74587 3.1523 7.6926 0.84215 8.7809 5.0007 6.081621 11.374 6.4966 10.523 8.4762 8.2051 11.544 7.6737 5.5242 5.0392 3.9247 3.1988 3.039582 3.8018 3.6238 9.4943 11.344 7.1274 7.5007 3.3774 4.3478 3.8671 8.8262 8.0911 5.0883 4.7563 4.3143 4.17 6.1947 5.1323

0.043317 0.94835 3.683421 0.33055 1.0809 0.033941 -0.52025 2.2443 2.2571 0.095188 0.47571 0.3914 1.4255 0.28333 0.1933 0.65393 0.2724357 1.4864 0.54598 0.87091 0.35251 1.4438 2.2311 0.28923 1.5015 -0.2027 0.28886 0.2896 0.2698591 0.90446 0.8337 0.64824 1.4414 0.0483 0.09616 0.5107 1.3196 1.0672 1.7772 1.2599 0.47166 0.49657 1.0149 0.23488 1.6524 0.32362

0.21502 -0.51011 -6.193052 -0.057073 -1.3684 0.34283 1.0982 -2.9192 -4.5116 0.47381 -0.71131 -0.2289 -1.6901 0.033281 0.30877 -0.27698 0.4430641 -2.3097 -0.42255 -0.45568 0.43853 -1.8053 -2.5186 0.34048 -1.7185 1.2207 0.38616 0.0344 -0.3789853 -0.74555 -0.82274 -0.24961 -1.9412 0.8966 1.1444 -0.17304 -1.5096 -1.2574 -1.926 -1.2911 -0.0078998 -0.13123 -0.99196 0.020947 -2.8505 0.16979

0.23791 0.015094 2.977694 0.083671 0.69723 -0.13415 -0.29832 1.1113 2.5738 -0.26294 0.60517 0.2309 0.72371 0.030551 -0.14162 0.029569 -0.3449689 1.4025 0.2597

149.780 353.150 289.810 200.150 178.450 229.315 192.400 185.450 286.150 189.630 59.150 195.410 235.650 83.780 403.000 278.680 258.270 395.450 260.280 321.350 257.850 275.650 243.950 342.200 265.850 242.430 154.250 179.440 136.950 164.250 134.860 220.000 196.150 183.850 158.450 87.800 134.260 167.620 199.650 185.300 157.460 133.020 147.430 176.800 250.000 161.300

3.23240 6.36890 2.44660 5.14960 3.66050 3.52490 1.62620 3.63950 2.79650 3.89890 0.63247 2.52980 5.10000 0.65440 7.12860 3.49320 5.06340 6.94850 5.33600 7.48950 6.88000 5.24700 6.26740 6.11280 3.28440 4.71870 3.42380 2.75620 2.82540 2.76410 2.86840 7.58750 8.14880 6.36430 6.59780 3.01970 3.10310 2.77200 5.32550 5.94710 4.37960 4.18430 3.20490 3.77230 4.16190 4.57590

-0.3026 0.79682 0.83063 -0.26011 0.6614 -0.70705 -0.35786 0.0114 0.5165115 0.24234 0.39613 0.058188 1.035 -0.5116 -0.78448 0.05181 0.63987 0.62539 0.63659 0.47381 -0.071247 0.027307 0.40891 0.086255 1.6285 -0.18921

Tmax , K 466.000 761.000 591.950 606.000 508.200 545.500 308.300 506.000 615.000 540.000 132.450 405.650 645.600 150.860 824.000 562.050 689.000 751.000 702.300 830.000 720.150 662.000 718.000 773.000 584.150 670.150 503.800 464.000 452.000 425.000 425.120 680.000 676.000 563.100 535.900 419.500 435.500 428.600 575.400 660.500 570.100 554.000 440.000 537.200 615.700 585.400

ΔHv at Tmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96

Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide

CO2 CS2 CO CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S

124-38-9 75-15-0 630-08-0 56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2

44.0095 76.1407 28.0101 153.8227 88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872

2.173 4.0359 0.8585 4.6113 1.9311 3.068 4.6746 3.253 5.3032 2.442 3.93706 3.9033 6.87 13.355 8.0979 7.5255 2.3558 3.6762 5.193 5.5761 6.6898 4.698 3.4216 3.6524 2.7681 6.7798 9.0851 8.7515 12.531 7.9041 6.6985 8.4103 10.603 0.11867 4.7061 6.057225 6.1207 6.4978 5.3065 6.4394 7.0416 4.7631 5.6489 4.8739 5.6495 4.2593 12.931 2.595917 5.947 4.7806

0.382 1.0897 0.4921 0.55241 0.94983 0.8458 0.013055 0.321 1.0366 -0.298 0.14297 0.3867 -0.39158 2.3486 -0.33815 1.3714 -0.29499 0.76666 1.0019 -1.7498 1.0012 0.44894 -0.21723 0.17652 0.44645 1.1402 1.3026 1.3204 0.76281 -1.36 0.76944 0.40556 1.7758 -0.31087 0.098096 1.372193 1.2282 0.77464 0.20288 0.67955 0.96641 1.0048 1.0038 0.9583 1.0359 -0.0038971 1.2215 -1.334101 1.6416 0.39507

-0.4339 -1.6483 -0.326 -0.18725 -1.0615 -0.9001 0.51777 -0.252 -0.79572 0.87 0.55088 0.008595 1.7208 -2.5463 2.3495 -1.5024 0.34496 -0.74793 -1.0159 4.5168 -0.96028 0.070295 1.0245 0.2777 -0.28756 -1.1701 -1.6803 -1.2441 -0.32459 4.0854 -0.79975 0.34553 -1.6849 0.28353 0.20134 -2.053024 -1.1989 -0.67379 0.039962 -0.58058 -0.86362 -1.2457 -0.7936 -0.79374 -0.98747 0.58142 -1.3197 2.366723 -1.7394 -0.028657

0.42213 0.9779 0.2231 0.022973 0.51894 0.453 -0.18852 0.295 0.16746 -0.271 -0.3511 -0.016793 -0.97478 0.74218 -1.7015 0.59731 0.24271 0.35979 0.46332 -2.4034 0.37622 -0.14736 -0.49752 -0.10817 0.21791 0.45855 0.86441 0.38061 0.054808 -2.3871 0.42379 -0.4009 0.38281 0.34543 0.22064 1.161394 0.40137 0.31825 0.12466 0.36746 0.32976 0.67919 0.17013 0.28069 0.39006 -0.23734 0.50585 -0.7871881 0.5831 0.014929

216.580 161.110 68.130 250.330 89.560 172.120 227.950 136.750 209.630 175.430 150.350 155.970 285.390 304.190 307.930 177.140 245.250 182.480 279.690 296.600 242.000 169.670 179.280 138.130 145.590 189.640 285.000 243.510 304.550 280.050 206.890 247.560 229.150 18.730 210.150 282.850 220.600 175.300 248.390 256.150 326.140 176.190 237.490 178.010 192.500 172.710 301.150 223.350 156.850 169.200

1.52020 3.17860 0.65166 3.47600 1.42150 2.28780 4.32240 2.95540 3.65460 2.41470 3.56930 3.36320 6.37340 6.06020 6.57120 5.41880 2.33890 2.81720 3.38860 6.25790 4.84470 3.98460 3.30460 3.37950 2.33840 5.10540 6.02700 5.60450 8.84640 8.29590 5.35240 6.81720 6.07920 0.12605 4.35520 4.06410 4.18700 5.24340 4.77510 5.09850 4.68520 3.62860 3.84750 3.58500 4.13210 4.03570 8.64260 3.35400 3.75450 4.15460

304.210 552.000 132.920 556.350 227.510 417.150 632.350 460.350 536.400 416.250 503.150 489.000 705.850 697.550 704.650 631.000 400.150 459.930 553.800 650.100 653.000 560.400 511.700 507.000 398.000 664.000 674.000 617.700 722.100 688.000 616.600 696.000 619.850 38.350 628.000 650.150 611.000 584.100 683.950 705.000 684.750 523.000 561.600 510.000 560.000 572.000 736.600 496.600 466.700 557.150

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Continued )

2-121

2-122 TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) (Continued ) Cmpd. no.* 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141

Name 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Diisopropyl amine Diisopropyl ether Diisopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid

Formula C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2

CAS

Mol. wt.

C1 × 1E-07

75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5

66.04997 66.04997 52.02339 101.19 102.17476 114.18546 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211

3.663 4.2313 3.3907 2.8258 4.630224 5.2429 4.3872 4.7999 3.6881 3.4422 4.8054 5.5503 5.4479 5.8702 5.8328 2.6377 5.9186 5.3387 10.263 2.919 4.5493 7.0161 7.66109 5.0368 6.9745 7.993218 10.962 12.86 2.1091 6.5831 4.8272 4.275 7.4288 6.8245 8.7212 5.7624 6.0933 5.7997 2.0639 5.6091 8.9207 4.7462 4.4514 4.4151 11.08845

C2 0.93553 0.90591 1.1148 -1.5731 1.265631 0.80535 0.56226 0.30724 0.37958 -0.49774 1.0013 0.7692 0.56826 1.0022 0.99061 -0.072806 0.37731 0.9509 1.504 0.47315 0.81834 0.9938 0.36322 0.37438 0.43414 1.697066 1.5544 0.50351 0.60646 1.1905 0.2372 0.5857 1.6218 1.071 0.79255 0.46881 0.96339 1.0161 0.80153 0.077011 0.83021 0.37327 1.1569 0.51536 0.7029

C3

C4

Tmin , K

ΔHv at Tmin × 1E-07

-0.9806 -0.59583 -1.2957 2.9709 -2.325122 -1.4147 -0.60662 -0.024545 -0.22063 1.8024 -1.0356 -0.56915 -0.29095 -1.0188 -0.9035 0.54324 0.0051489 -0.97007 -2.441 -0.19035 -0.47199 -1.4767 -0.28551 -0.0004344 -0.26069 -1.895364 -1.5358 0.32986 -0.55492 -1.7666 0.32434 -0.332 -2.0278 -1.943 -0.64882 -0.14511 -0.94933 -0.92313 -0.8128 0.66595 -0.88126 0.047488 -1.2336 -0.39281 -0.10529

0.46753 0.074323 0.58214 -1.1073 1.525306 1.0288 0.4202 0.091361 0.21968 -0.97741 0.4668 0.2328 0.15397 0.46949 0.34792 -0.13977 -0.0027682 0.44354 1.388 0.078322 0.047802 0.97462 0.23966 0.0050378 0.15024 0.6664379 0.46286 -0.42184 0.32799 1.0012 -0.19429 0.169 0.906 1.2788 0.28369 0.061942 0.44931 0.33212 0.4179 -0.43437 0.53255 0.045906 0.50875 0.28461 -0.17295

154.560 215.000 136.950 176.850 187.650 204.810 159.950 226.100 240.910 180.960 145.190 239.660 223.160 184.990 188.440 131.650 212.720 160.000 274.180 122.930 174.880 291.670 413.786 284.950 300.030 210.150 263.570 309.580 90.350 159.050 189.600 192.150 178.200 238.450 258.150 175.150 161.840 134.710 104.000 284.290 260.150 195.200 160.650 193.550 155.150

2.67130 2.78200 2.40150 3.76470 3.47860 4.33570 3.75280 4.05570 2.92830 3.29670 3.72820 4.11250 4.36640 4.47370 4.43890 2.54380 5.09300 4.16640 7.17430 2.50210 3.43160 5.27280 6.19680 3.92500 5.84730 4.77500 6.52590 9.59330 1.78790 5.00600 4.16260 3.29550 5.08620 5.40830 6.51870 4.92230 4.84420 4.65290 1.59660 4.62220 6.87400 3.96760 3.19090 3.63270 9.30840

Tmax , K 386.440 445.000 351.255 523.100 500.050 576.000 507.800 543.000 473.200 437.200 500.000 591.150 606.150 596.150 615.000 400.100 649.600 537.300 766.000 402.000 503.040 729.000 777.400 587.000 766.800 550.000 658.000 768.000 305.320 514.000 523.300 456.150 617.150 698.000 655.000 571.000 609.150 569.500 282.340 593.000 720.000 537.000 469.150 508.400 674.600

ΔHv at Tmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191

Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid

C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4

5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2

130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146

6.6828 4.2527 5.6735 4.292 5.033 5.438 5.0124 0.89107 3.7517 2.4749 1.9302 2.9575 5.8307 2.3195 4.4388 0.012504 15.97 4.7135 5.2516 12.916 7.0236 11.119 6.067 6.2857 4.9437 6.7011 4.8235 14.979 5.3802 4.3848 9.0746 7.035 9.591 5.5382 5.8213 4.249938 4.282053 5.9346 6.8856 6.0629 5.9794 0.10127 1.5513 3.4872 3.3907 13.451 2.6092 4.0385 5.6917 7.7143

0.6664 0.42014 0.85864 0.93726 -0.023028 0.60624 0.48381 0.48888 -0.33542 0.18492 -0.2029 0.098296 -0.62844 1.9091 0.82914 1.3038 1.977 -0.27964 0.51283 1.4923 -1.3652 1.3264 0.18619 0.3899 0.35428 0.38694 0.35765 1.89 0.52771 0.34057 0.8926 -0.9575 1.236 0.19854 0.44196 0.52336 0.5862582 0.41114 1.9737 1.1597 0.9424 0.698 -0.80615 2.1553 0.43574 13.36 0.47883 0.82698 1.2441 -1.0139

-0.4545 -0.17341 -1.1249 -1.0593 0.84791

0.20227 0.14204 0.69714 0.54636 -0.44199

-0.1946 -0.44035 1.0497 -0.21197 0.65339 0.28373 1.6751 -5.0003 -0.72757 -2.6954 -2.2318 0.89761 -0.10982 -1.3795 3.987 -1.1057 0.47762 0.17742 0.22149 0.24973 -0.060379 -2.0762 -0.4757 0.063282 -0.75172 3.1431 -1.359 0.47139 0.090968 -0.57323 -0.9710554 0.043753 -2.4886 -0.99686 -1.398 -1.817 1.1788 -2.9128 -0.56984 –23.383 -0.2233 -2.033 -1.0742 2.2898

0.12282 0.31792 -0.40021 0.36038 -0.16704 -0.77554 3.2641 0.33552 1.7098 0.78544 -0.33523 -0.01018 0.39603 -2.2545 0.36023 -0.26967 -0.19455 -0.2353 -0.26228 0.045749 0.71724 0.3242 -0.017037 0.34378 -1.8066 0.717 -0.31556 -0.15346 0.45101 0.8523437 -0.081964 0.99472 0.32547 0.8862 1.447 -0.070978 1.2442 0.36017 10.785 0.12903 1.4769 0.32331 -0.91517

180.000 140.000 204.150 125.260 199.250 145.650 167.550 53.480 230.940 129.950 131.350 155.150 275.700 250.000 196.290 2.200 295.130 229.800 182.570 265.830 239.150 220.000 234.150 238.150 154.120 229.920 192.220 291.310 214.930 177.830 269.250 228.550 223.000 217.350 217.500 133.390 170.050 192.620 141.250 183.650 274.690 13.950 185.150 158.970 259.830 277.560 187.680 227.150 177.950 409.150

5.46390 3.73840 4.45040 3.50010 4.53900 4.41400 4.29170 0.75083 3.69360 2.31740 1.89050 2.69310 6.17220 1.88650 3.27960 0.00966 8.59730 4.69820 4.31810 7.80040 7.64980 7.18220 5.16400 5.08510 4.32080 5.51330 4.15950 8.19340 4.49940 3.75320 6.47830 7.15090 6.46500 4.75590 4.70770 3.75440 3.73310 5.08670 4.44750 4.26690 4.52380 0.09131 1.81940 1.74720 2.79840 0.71043 1.97460 3.55340 3.74360 8.31300

583.000 489.000 567.000 499.150 546.000 500.230 559.950 144.120 560.090 375.310 317.420 420.000 771.000 588.000 490.150 5.200 736.000 620.000 540.200 677.300 632.300 608.300 606.600 611.400 537.400 645.000 547.000 723.000 594.000 507.600 660.200 611.300 585.300 587.610 582.820 504.000 544.000 623.000 516.200 549.000 653.150 33.190 363.150 324.650 456.650 461.150 373.530 605.000 471.850 834.000

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Continued )

2-123

2-124 TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) (Continued ) Cmpd. no.* 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236

Name Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane

Formula C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10

CAS

Mol. wt.

79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5

86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222

C1 × 1E-07 176.7855 1.0194 3.2615 6.8795 4.329 3.0066 6.2689 4.2834 5.8474 4.2709 4.233 8.223 10.165 4.5217 4.897 4.5822 4.4918 6.8872 3.1821 5.1299 4.4696 5.3789 7.7573 9.4404 9.4625 5.1137 4.2603 4.2081 4.8242 3.7592 5.2256 4.9455 4.7691 4.266 8.1495 3.2575 3.8148 2.7567 4.0063 3.0851 5.6613 10.53 5.0351 5.0003 3.9654

C2 16.29674 0.26087 -1.0407 0.012343 0.18771 0.25873 1.6462 0.90615 -0.6042 0.70788 0.95448 0.80923 1.4422 1.0678 1.1838 1.3506 0.32576 1.2703 -0.89979 0.10033 1.1838 0.71218 0.56959 0.8722 0.88768 0.98237 0.34248 0.43515 1.3456 0.64544 0.9427 0.78235 0.98928 0.37791 1.8479 -0.58542 0.38959 -1.6298 -0.17489 -0.29985 0.3132 0.7454 1.1424 0.42203 1.274

C3

C4

Tmin , K

ΔHv at Tmin × 1E-07

–28.8053 -0.14694 1.8695 0.77544 0.33528 0.033435 -2.2795 -0.93138 2.1528 -0.67299 -0.98289 -0.70838 -1.6123 -1.1735 -1.2079 -1.6049 0.1124 -1.2699 2.8579 0.64085 -0.87047 -0.28902 0.7221 -0.33173 -0.39167 -0.90553 -0.088074 -0.24963 -1.5783 -0.46384 -1.0868 -0.56637 -0.98574 0.0037827 -2.1328 1.4307 -0.15805 3.0001 0.94886 1.4733 0.57076 -0.39297 -1.3269 -0.14687 -1.4255

14.522 0.22154 -0.60801 -0.4379 -0.17125 0.087053 1.0975 0.4776 -1.2871 0.43009 0.45719 0.32497 0.75941 0.55525 0.43353 0.71575 -0.067377 0.44562 -1.7826 -0.38359 0.056694 -0.014989 -0.86278 -0.10938 -0.057899 0.34878 0.13072 0.20811 0.61746 0.21809 0.55491 0.22052 0.42695 -0.001928 0.76628 -0.54833 0.15228 -1.1865 -0.44746 -0.89559 -0.46309 0.047214 0.62481 0.11507 0.60708

288.150 90.690 175.470 301.150 175.150 170.450 196.320 179.690 260.750 159.530 113.250 193.000 155.950 135.580 139.390 160.150 157.480 175.300 183.450 187.350 139.050 146.580 299.150 280.150 269.150 130.730 146.620 168.540 182.550 160.000 186.480 167.230 174.150 188.000 189.150 256.150 127.930 180.150 171.640 150.180 224.950 240.000 119.550 176.000 113.540

4.28480 0.87235 3.97480 5.97080 3.83890 2.56480 4.04870 3.09550 5.78260 3.46030 3.43450 6.57690 7.27510 3.46420 3.61390 3.20970 3.94480 4.96500 3.25930 4.58370 3.16280 4.45440 5.13430 6.16980 6.31440 4.10400 3.84130 3.63850 3.24190 2.98760 3.98780 3.90650 3.51240 3.56270 4.98940 3.22260 3.39970 3.74640 3.89410 2.99210 4.46890 8.11060 3.97590 4.30250 2.93300

Tmax , K 662.000 190.564 512.500 718.000 506.550 402.400 536.000 430.050 693.000 490.000 460.400 643.000 577.200 465.000 470.000 492.000 512.740 593.000 463.200 554.500 442.000 572.100 686.000 614.000 617.000 532.700 542.000 526.000 483.000 437.800 535.500 533.000 487.200 497.000 574.600 488.000 464.480 553.400 553.100 469.950 566.000 694.000 497.700 546.490 407.800

ΔHv at Tmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286

2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan

C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F 3N CH3NO2 N 2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S

75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7

74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378

2.2708 4.3172 4.9563 4.2364 5.7015 2.0613 5.3293 4.0052 3.2566 5.093 0.19063 3.8821 0.74905 1.8859 4.7494 2.2724 0.94287 17.161 4.5173 7.888 12.126 7.5429 14.251 5.9054 6.6716 8.7405 17.264 5.7746 6.7138 12.626 7.2468 12.581 11.048 6.6142 5.4859 7.3618 5.367 7.7236 0.9008 1.7289 10.052 5.2373 4.5087 7.3197 7.39 8.8703 5.3818 4.451 3.5027 5.0573

-3.8183 1.5334 0.22568 0.25325 1.0015 0.33885 0.15144 0.19309 0.10042 -0.44584 -0.048268 -1.2495 0.40406 1.0917 0.1535 0.22278 -2.0627 1.7444 -1.1627 1.3126 0.82704 -1.5966 1.418 0.61039 -0.70869 1.5599 2.167 0.16524 1.0769 1.1753 -1.2464 1.3269 2.5722 0.58562 0.26207 0.63204 0.31607 -0.55914 0.4542 0.12106 0.37778 1.0132 0.95886 1.2093 -0.1464 0.90566 0.35111 -0.5483 0.3481 0.45827

6.7137 -1.9 0.45949 0.58114 -0.95589 -0.63279 0.15411 0.20658 0.26926 1.0348 0.11183 3.2285 -0.317 -1.4143 0.49623 0.29352 3.2659 -1.6657 2.3227 -1.3571 -0.42449 4.6489 -0.53849 -0.54533 2.636 -1.7205 -2.6262 0.095968 -1.0124 -0.835 3.6797 -0.69134 -3.7155 -0.40512 0.50642 -0.29459 0.073613 1.8363 -0.4096 0.088716 0.50709 -1.6348 -0.92384 -1.9114 1.4751 -0.67627 0.40264 2.1051 -0.19672 -0.22568

-2.7247 0.83816 -0.31541 -0.4757 0.38421 0.6454 0.066538 -0.010244 -0.0003252 -0.19528 0.25512 -1.8283 0.27343 0.76165 -0.38464 -0.13493 -1.0186 0.43242 -0.89716 0.5034 0.08636 -2.7229 -0.33162 0.30683 -1.6685 0.64325 1.0161 0.10146 0.37075 0.1489 -2.0665 -0.08027 1.7307 0.22144 -0.43873 0.063444 -0.040895 -0.85806 0.3183 0.10749 -0.46599 1.0473 0.39393 1.1591 -0.9208 0.3485 -0.42577 -1.3486 0.22394 0.16393

298.970 132.810 185.650 133.970 160.170 116.340 249.950 164.550 151.150 353.430 24.560 183.630 63.150 66.460 244.600 182.300 109.500 305.040 267.300 219.660 285.550 268.150 238.150 191.910 253.050 223.150 301.310 251.650 216.380 289.650 257.650 241.550 252.850 255.550 171.450 223.950 193.550 462.650 54.360 80.150 283.070 191.590 143.420 239.150 195.560 200.000 196.290 234.180 108.016 160.750

4.65420 2.92920 4.26690 3.73780 4.42340 1.90240 4.79340 3.60720 2.99980 5.09530 0.17706 4.54440 0.60243 1.46720 4.05640 1.66660 1.44210 9.52160 5.47060 5.25710 8.59240 8.24110 8.32860 4.92180 6.54750 5.46000 8.94580 5.17550 4.69860 7.96680 7.67930 7.57060 5.50930 5.20760 4.79270 5.90250 4.67380 6.56310 0.77419 1.63130 7.76350 4.12150 3.47660 5.38130 6.70050 6.48970 4.45330 4.22720 3.22320 4.43430

506.200 417.900 530.600 476.250 565.000 352.500 654.000 497.100 437.000 748.400 44.400 593.000 126.200 234.000 588.150 309.570 180.150 758.000 658.500 594.600 710.700 670.900 649.500 593.100 681.000 598.050 747.000 638.900 568.700 694.260 652.300 629.800 632.700 627.700 566.900 667.300 574.000 828.000 154.580 261.000 708.000 566.100 469.700 639.160 588.100 561.000 561.080 560.950 464.800 584.300

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Continued )

2-125

2-126 TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) (Continued ) Cmpd. no.* 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321

Name Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene

Formula C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O 2S F 6S O 3S C8H6O4 C18H14 C14H30 C4H8O C10H12

CAS 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2

Mol. wt.

C1 × 1E-07

C2

C3

C4

Tmin , K

ΔHv at Tmin × 1E-07

104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228

5.4925 5.1346 5.4839 10.336 6.283 7.3079 18.461 2.8092 2.9209 6.8988 8.502 5.9068 3.3611 4 4.6242 6.4745 3.4054 7.2986 2.5216 5.7631 4.2077 4.4542 7.097812 6.2374 2.3637 8.6409 11.447 2.846 1.3661 0.8509 11.928 13.0705 12.007 4.0907 10.07

0.38608 1.3829 0.98943 1.0678 -0.64878 1.3522 3.6123 0.30398 0.78237 0.6458 1.474 0.44605 -0.27575 1.3936 0.12029 0.93113 -0.29885 1.2428 0.33721 0.70122 0.33823 0.31385 -0.5348227 0.73316 0.32997 1.8893 -0.04418 -0.24905 -1.1465 -7.1061 -0.063031 1.329955 1.445 0.12318 1.994

0.12415 -1.6264 -0.46159 -1.0693 2.4219 -1.6409 -5.1111 0.017572 -0.77319 -0.5384 -1.878 -0.18075 0.66467 -2.9465 0.62187 -0.65971 0.72173 -1.361 -0.18399 -0.15754 0.2503 0.30517 1.770112 -1.3874 0.055931 -2.1943 1.1282 0.62158 1.5442 11.558 0.89651 -1.300762 -1.3846 0.46123 -2.5052

-0.13245 0.67069 -0.064298 0.39121 -1.4972 0.66839 1.9668 0.10232 0.39246 0.3317 0.933 0.13426

197.450 167.450 163.830 372.380 314.060 243.150 404.150 136.870 85.470 146.950 185.258 199.000 165.000 252.450 180.370 178.150 188.360 173.550 87.890 180.250 142.610 159.950 213.150 388.850 186.350 242.540 460.850 197.670 223.150 289.950 700.150 329.350 279.010 164.650 237.380

4.65540 3.49690 3.99170 7.05940 5.77350 4.95580 6.24970 2.44810 2.47870 5.83560 5.61950 5.07850 3.43940 3.09220 4.16430 4.85340 3.46570 5.46050 2.31770 4.44670 3.70860 3.88960 7.23780 4.92650 1.48720 4.92460 8.50610 2.79080 1.62200 4.41460 7.16890 8.42870 7.33360 3.74660 6.02700

1.794 -0.48327 0.17587 -0.080173 0.56435 0.22377 -0.11477 -0.21085 -0.24568 -0.9904166 1.0391 -0.011041 0.81388 -0.67562 -0.020421 -0.15766 -4.483 -0.5152 0.5044183 0.42836 -0.23807 1.0593

Tmax , K 598.000 481.200 519.000 869.000 694.250 653.000 791.000 394.000 369.830 536.800 508.300 636.000 503.600 600.810 561.300 549.730 496.950 638.350 364.850 538.000 517.000 536.600 626.000 683.000 259.000 636.000 838.000 430.750 318.690 490.850 883.600 857.000 693.000 540.150 720.000

ΔHv at Tmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345

Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene

C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10

110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3

88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165

5.2918 3.8116 5.2472 5.4643 4.1283 11.72 4.6139 5.1056 7.0138 7.8955 5.935 6.0778 10.688 1.9497 10.136 8.7274 4.6643 3.649 4.2629 4.3817 5.66 6.493 6.5393 6.6475

0.57615 -0.60048 0.78829 0.76764 -0.34796 1.6004 0.41881 1.6568 1.0377 1.513 1.1967 1.207 0.38045 -8.4859 1.5084 -1.5834 0.50913 0.4 1.0111 0.26434 0.612041 1.0653 0.98813 1.1739

-0.32236 1.6501 -0.47503 -0.62056 1.0118 -1.6689 -0.23744 -1.6244 -1.1841 -1.9061 -1.2686 -1.3449 -0.00074017 17.865 -1.473 5.0913 -0.55117 0.043 -0.48757 0.034522 -0.625697 -1.1205 -0.91617 -1.2812

0.15218 -0.73052 0.098333 0.25935 -0.32712 0.56396 0.20257 0.41985 0.56211 0.85016 0.51652 0.58 0.0003222 –10.196 0.44521 -3.2171 0.45397 -0.045787 0.071549 0.398804 0.48226 0.35023 0.54229

176.990 373.960 234.940 178.180 236.500 267.760 158.450 156.080 247.790 229.330 165.780 172.220 398.400 354.000 247.570 288.450 180.350 173.150 119.360 178.350 273.160 225.300 247.980 286.410

4.49330 3.17800 3.81710 4.40060 4.13030 6.97470 4.05710 3.08740 5.12030 5.22830 4.34440 4.47800 8.39050 8.84860 6.19520 8.90070 3.97880 2.98760 3.21450 3.91430 4.49810 4.68030 4.65030 4.30350

631.950 568.000 579.350 591.750 602.000 675.000 535.150 433.250 664.500 649.100 543.800 573.500 846.000 828.000 639.000 703.900 519.130 454.000 432.000 543.150 647.096 617.000 630.300 616.200

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

The heat of vaporization ΔHv is calculated by 2

ΔHv = C1(1 - Tr)(C2+C3Tr+C4Tr ) where Tr = T/TC, TC is the critical temperature from Table 2-106, ΔHv is in J/kmol, and T is in K. All substances are listed by chemical family in Table 2-6 and by formula. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York NY (2016).

2-127

2-128

PHYSICAL AnD CHEMICAL DATA

SPECIFIC HEATS SPECIFIC HEATS OF PURE COMPOUnDS Unit Conversions For this subsection, the following unit conversions are applicable: °F = 9⁄5°C + 32 and °R = 1.8 K. To convert calories per gram-kelvin to British thermal units (Btu) per pound-degree Rankine, multiply by 1.0.

To convert kilojoules per kilogram-kelvin to British thermal units per pounddegree Rankine, multiply by 0.2388. Additional References Additional data are contained in the subsection “Thermodynamic Properties.” Data on water are also contained in that subsection.

TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds*

Substance Aluminum1 Al AlBr3 AlCl3 AlCl3⋅6H2O AlF3 AlF3⋅3½H2O AlF3⋅3NaF AlI3 Al2O3 Al2O3⋅SiO2 3Al2O3⋅2SiO2 4Al2O3⋅3SiO2 Al2(SO4)3 Al2(SO4)3⋅18H2O Antimony Sb SbBr3 SbCl3 Sb2O3 Sb2O4 Sb2S3 Argon2 A Arsenic As AsCl3 As2O3 As2S3 Barium BaCl2 BaCl2⋅H2O BaCl2⋅2H2O Ba(ClO3)2⋅H2O BaCO3

State

†

Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K)

Range of temperature, K

Uncertainty, %

273–931 931–1273 273–370 370–407 273–465 465–504 288–327 288–326 288–326 273–1273 1273–1373 273–464 464–480 273–1973 273–1573 273–1673 273–1573 273–576 273–575 273–373 288–325

1 5 3 5 3 3 ? ? ? 2 ? 3 5 3 3 2 3 5 3 ? ?

c l c l c l c c c c l c l c c, sillimanite c, disthene c, andalusite c, mullite c c c

4.80 + 0.00322T 7.00 18.74 + 0.01866T 29.5 13.25 + 0.02800T 31.2 76 19.3 50.5 38.63 + 0.04760T - 449200/T 2 142 16.88 + 0.02266T 28.8 22.08 + 0.008971T - 522500/T 2 40.79 + 0.004763T - 992800/T 2 41.81 + 0.005283T - 1211000/T 2 43.96 + 0.001923T - 1086000/T 2 59.65 + 0.0670T 113.2 + 0.0652T 63.5 235

c l c c c c c

5.51 + 0.00178T 7.15 17.2 + 0.0293T 10.3 + 0.0511T 19.1 + 0.0171T 22.6 + 0.0162T 24.2 + 0.0132T

273–903 903–1273 273–370 273–346 273–929 273–1198 273–821

2 5 ? ? ? ? ?

g

4.97

All

0

c l c c

5.17 + 0.00234T 31.9 8.37 + 0.0486T 25.8

273–1168 286–371 273–548 293–373

5 ? ? ?

c c c c c, α c, β c c c

17.0 + 0.00334T 28.2 37.3 51 17.26 + 0.0131T 30.0 34 39.8 21.35 + 0.0141T

273–1198 273–307 273–307 289–320 273–1083 1083–1255 273–297 285–371 273–1323

? ? ? ? 5 15 ? ? 5

BaMoO4 Ba(NO3)2 BaSO4 Beryllium3,4 Be c 4.698 + 0.001555T - 121000/T 2 273–1173 1 BeO c 8.69 + 0.00365T - 313000/T 2 273–1175 5 BeO ⋅ Al2O3 c 25.4 273–373 ? BeSO4 c 20.8 273–373 ? *From Kelley, U.S. Bur. Mines Bull. 371, 1934. For a revision see Kelley, U.S. Bur. Mines Bull. 477, 1948. Data for many elements and compounds are given by Johnson (ed.), WADD-TR-60-56, 1960, for cryogenic temperatures. Tabulated data for gases can be obtained from many of the references cited in the “Thermodynamic Properties” subsection and other tables in this section. Thinh, Duran, et al., Hydrocarbon Process., 50, 98 (January 1971), review previous equation fits and give newer fits for 408 hydrocarbons and related compounds. Later publications include Duran, Thinh, et al., Hydrocarbon Process., 55, 153 (August 1976); Thompson, J. Chem. Eng. Data, 22(4), 431 (1977); and Passut and Danner, Ind. Eng. Chem. Process Des. Dev., 11, 543 (1972); 13, 193 (1974). † The symbols in this column have the following meaning; c, crystal; l, liquid; g, gas; gls, glass.

SPECIFIC HEATS TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )

State†

Substance Bismuth4 Bi Bi2O3 Bi2S3 Boron B B2O3 BN Bromine Br2 Cadmium Cd CdO CdS CdSO4⋅8/3H2O Calcium Ca CaCl2 CaCO3 CaF2 CaMg(CO3)2 CaMoO4 CaO Ca(OH)2 CaO⋅Al2O3⋅2SiO2 CaO⋅MgO⋅2SiO2 CaO⋅SiO2 CaP2O6 CaSO4 CaSO4⋅2H2O CaWO4 Carbon5 C CH4 CO6 CO2 CS2 Cerium Ce CeO2 Ce2(MoO4)3 Ce2(SO4)3 Ce2(SO4)3⋅5H2O Cesium Cs CsBr CsCl CsF CsI Chlorine Cl2 Chromium4 Cr CrCl3 Cr2O3 CrSb CrSb2 Cr2(SO4)3 Cobalt4 Co CoAs2⋅CoS2 CoSb Co2Sn CoS CoSO4⋅7H2O

Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K)

Range of temperature, K

Uncertainty, %

c l c c

5.38 + 0.00260T 7.60 23.27 + 0.01105T 30.4

273–544 544–1273 273–777 284–372

3 3 2 ?

c gls gls c

1.54 + 0.00440T 5.14 + 0.0320T 30.4 1.61 + 0.00400T

273–1174 273–513 513–623 273–1173

5 3 3 5

g

9.00

300–2000

5

c l c c c

5.46 + 0.002466T 7.13 9.65 + 0.00208T 12.9 + 0.00090T 51.3

273–594 594–973 273–2086 273–1273 293

1 5 ? ? ?

c c c c c c c c c c, anorthite gls c, diopside gls c, wollastonite c, pseudowollastonite gls c c c c

5.31 + 0.00333T 6.29 + 0.00140T 16.9 + 0.00386T 19.68 + 0.01189T - 307600/T 2 14.7 + 0.00380T 40.1 33 10.00 + 0.00484T - 108000/T 2 21.4 63.13 + 0.01500T - 1537000/T 2 67.41 + 0.01048T - 1874000/T 2 54.46 + 0.005746T - 1500000/T 2 51.68 + 0.009724T - 1308000/T 2 27.95 + 0.002056T - 745600/T 2 25.48 + 0.004132T - 488100/T 2 23.16 + 0.009672T - 487100/T 2 39.5 18.52 + 0.02197T - 156800/T 2 46.8 27.9

273–673 673–873 273–1055 273–1033 273–1651 299–372 273–297 273–1173 276–373 273–1673 273–973 273–1573 273–973 273–1573 273–1673 273–973 287–371 273–1373 282–373 292–322

2 2 ? 3 ? ? ? 2 ? 1 1 1 1 1 1 1 ? 5 ? ?

c, graphite c, diamond g g g l

2.673 + 0.002617T - 116900/T 2 2.162 + 0.003059T - 130300/T 2 5.34 + 0.0115T 6.60 + 0.00120T 10.34 + 0.00274T - 195500/T 2 18.4

273–1373 273–1313 273–1200 273–2500 273–1200 293

2 3 2 1½ 1½ ?

c c c c c

5.88 + 0.00123T 15.1 96 66.4 131.6

273–908 273–373 273–297 273–373 273–319

? ? ? ? ?

c l g c c c c

1.96 + 0.0182T 8.00 4.97 12.6 + 0.00259T 11.7 + 0.00309T 11.3 + 0.00285T 11.6 + 0.00268T

273–301 302 All 273–909 273–752 273–957 273–894

3 3 0 ? ? ? ? 1½

g

8.28 + 0.00056T

273–2000

c l c c c c c

4.84 + 0.00295T 9.70 23 26.0 + 0.00400T 12.3 + 0.00120T 19.2 + 0.00184T 67.4

273–1823 1823–1923 286–319 273–2263 273–1383 273–949 273–373

5 10 ? ? ? ? ?

c l c c c c c

5.12 + 0.00333T 8.40 32.9 11.7 + 0.00156T 15.83 + 0.00950T 10.6 + 0.00251T 96

273–1763 1763–1873 283–373 273–1464 273–903 273–1373 286–303

5 5 ? ? 2 ? ? (Continued )

2-129

2-130

PHYSICAL AnD CHEMICAL DATA TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )

State†

Substance Copper7 Cu CuAl CuAl2 Cu3Al CuI CuI2 CuO CuO⋅SiO2⋅H2O CuS Cu2S CuS⋅FeS Cu2Sb Cu2Sb Cu2Se Cu3Si CuSO4 CuSO4⋅H2O CuSO4⋅3H2O CuSO4⋅5H2O Fluorine8 F2 Gallium Ga2O3 Ga2(SO4)3 Germanium4 Ge Gold Au AuSb2 Helium9 He Hydrogen10 H H2 HBr HCl HI H2O H2S H2S2O7 Indium In Iodine I2 Iridium Ir Iron4 Fe

FeAs2 Fe3C FeCO3 FeO Fe2O3 Fe3O4 Fe2O3⋅3H2O FeS FeS2 FeSi Fe2SiO4 FeSO4 Fe2(SO4)3 FeSO4⋅4H2O FeSO4⋅7H2O Krypton Kr

Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K)

Range of temperature, K

Uncertainty, %

273–1357 1357–1573 273–733 273–773 273–775 273–675 274–328 273–810 293–323 273–1273 273–376 376–1173 292–321 273–573 273–693 273–383 383–488 273–1135 282 282 282 282

1 3 2 2 2 ? ? 2 ? ? 3 2 ? 2 2 5 5 ? ? ? ? ?

c l c c c c c c c c c, α c, β c c c c, α c, β c c c c c

5.44 + 0.001462T 7.50 9.88 + 0.00500T 16.78 + 0.00366T 19.61 + 0.01054T 12.1 + 0.00286T 20.1 10.87 + 0.003576T - 150600/T 2 29 10.6 + 0.00264T 9.38 + 0.0312T 20.9 24 13.73 + 0.01350T 21.79 + 0.00900T 20.85 20.35 20.3 + 0.00587T 24.1 31.3 49.0 67.2

g

6.50 + 0.00100T

300–3000

5

c c

18.2 + 0.0252T 62.4

273–923 273–373

? ?

273–1336 1336–1573 273–628 628–713

2 5 1 ?

c c l c, α c, βγ

5.61 + 0.00144T 7.00 17.12 + 0.00465T 11.47 + 0.01756T

g

4.97

All

0

g g g g g l g g c l

4.97 6.62 + 0.00081T 6.80 + 0.00084T 6.70 + 0.00084T 6.93 + 0.00083T See Tables 2-72 and 2-136 8.22 + 0.00015T + 0.00000134T 2 7.20 + 0.00360T 27 58

All 273–2500 273–2000 273–2000 273–2000

0 2 2 1½ 2

300–2500 300–600 281 308

? 8 ? ?

g

9.00

300–2000

5

c

5.50 + 0.00148T

273–1873

1

c, α c, β c, γ c, δ l c c c c c c c c, α c, β c c c c c c c

4.13 + 0.00638T 6.12 + 0.00336T 8.40 10.0 8.15 17.8 25.17 + 0.00223T 22.7 12.62 + 0.001492T - 76200/T 2 24.72 + 0.01604T - 423400/T 2 41.17 + 0.01882T - 979500/T 2 47.8 2.03 + 0.0390T 12.05 + 0.00273T 10.7 + 0.01336T 10.54 + 0.00458T 33.57 + 0.01907T - 879700/T 2 22 66.2 63.6 96

273–1041 1041–1179 1179–1674 1674–1803 1803–1873 283–373 273–1173 293–368 273–1173 273–1097 273–1065 286–373 273–411 411–1468 273–773 273–903 273–1161 293–373 273–373 282 291–319

3 3 5 5 5 ? 10 ? 2 2 2 ? 5 3 ? 2 2 ? ? ? ?

g

4.97

c

All

0

SPECIFIC HEATS TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )

State†

Substance Lanthanum La La2O3 La2(MoO4)3 La2(SO4)3 La2(SO4)3⋅9H2O Lead4 Pb Pb3(AsO4)2 PbB2O4 PbB4O7 PbBr2 PbCl2 2PbCl2⋅NH4Cl PbCO3 PbCrO4 PbF2 PbI2 PbMoO4 Pb(NO3)2 PbO PbO2 Pb2P2O7 PbS PbSO4 PbS2O3 PbWO4 Lithium Li LiBr LiBr⋅H2O LiCl LiCl⋅H2O LiF LiI LiI⋅H2O LiI⋅2H2O LiI⋅3H2O LiNO3 Magnesium4 Mg MgAg Mg4Al3 MgAu Mg2Au Mg3Au MgCl2 MgCl2⋅6H2O MgCO3 MgCu2 Mg2Cu MgNi2 MgO MgO⋅Al2O3 MgO⋅SiO2 6MgO⋅MgCl2⋅8B2O3 Mg(OH)2 Mg3Sb2 Mg2Si MgSO4 MgSO4⋅H2O MgSO4⋅6H2O MgSO4⋅7H2O

Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K)

Range of temperature, K

Uncertainty, %

c c c c c

5.91 + 0.00100T 22.6 + 0.00544T 86 66.9 152

273–1009 273–2273 273–307 273–373 273–319

? ? ? ? ?

c l c c c c l c l c c c c c l c c c c c c c c c

5.77 + 0.00202T 6.8 65.5 26.5 41.4 18.13 + 0.00310T 27.4 15.88 + 0.00835T 27.2 53.1 21.1 29.1 16.5 + 0.00412T 18.66 + 0.00293T 32.3 30.4 36.4 10.33 + 0.00318T 12.7 + 0.00780T 48.3 10.63 + 0.00401T 26.4 29 35

273–600 600–1273 286–370 288–371 289–371 273–761 761–860 273–771 771–851 293 286–320 292–323 273–1091 273–648 648–776 292–322 286–320 273–544 273–? 284–371 273–873 293–372 293–373 273–297

2 5 ? ? ? 2 10 2 10 ? ? ? ? 2 20 ? ? 2 ? ? 3 ? ? ?

c g c c c c c c c c c c l

0.68 + 0.0180T 4.97 11.5 + 0.00302T 22.6 11.0 + 0.00339T 23.6 8.20 + 0.00520T 12.5 + 0.00208T 23.6 32.9 43.2 9.17 + 0.0360T 26.8

273–459 All 273–825 278–318 273–887 279–360 273–1117 273–723 277–359 277–345 277–347 273–523 523–575

10 0 ? ? ? ? ? ? ? ? ? 5 5

c l c c c c c c c c c c c c c c, amphibole c, pyroxene gls c, α c, β c c c c c c c

6.20 + 0.00133T - 67800/T 2 7.4 10.58 + 0.00412T 34.4 + 0.0198T 11.3 + 0.00189T 16.2 + 0.00451T 21.2 + 0.00614T 17.3 + 0.00377T 77.1 16.9 14.96 + 0.00776T 15.5 + 0.00652T 15.87 + 0.00692T 10.86 + 0.001197T - 208700/T 2 28 25.60 + 0.004380T - 674200/T 2 23.35 + 0.008062T - 558800/T 2 23.30 + 0.007734T - 542000/T 2 58.7 + 0.408T 107.2 + 0.2876T 18.2 28.2 + 0.00560T 15.4 + 0.00415T 26.7 33 80 89

273–923 923–1048 273–905 273–736 273–1433 273–1073 273–1103 273–991 292–342 290 273–903 273–843 273–903 273–2073 288–319 273–1373 273–773 273–973 273–538 538–623 292–323 273–1234 273–1343 296–372 282 282 291–319

1 10 2 ? ? ? ? ? ? ? 3 ? 2 2 ? 1 1 1 5 5 ? ? ? ? ? ? ? (Continued )

2-131

2-132

PHYSICAL AnD CHEMICAL DATA TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued ) Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K)

Range of temperature, K

Uncertainty, %

c, α c, β c, γ l c c c c c c c c c c

3.76 + 0.00747T 5.06 + 0.00395T 4.80 + 0.00422T 11.0 16.2 + 0.00520T 7.79 + 0.0421T + 0.0000090T 2 7.43 + 0.01038T - 0.00000362T 2 10.33 + 0.0530T - 0.0000257T 2 19.25 + 0.0538T - 0.0000209T 2 1.92 + 0.0471T - 0.0000297T 2 31 10.21 + 0.00656T - 0.00000242T 2 27.5 78

273–1108 1108–1317 1317–1493 1493–1673 273–923 273–773 273–1923 273–1173 273–1773 273–773 291–322 273–1883 293–373 290–319

5 5 5 10 ? ? ? ? ? ? ? ? ? ?

l g g c c c c c, α c, β c c c

6.61 4.97 9.00 11.05 + 0.00370T 15.3 + 0.0103T 25 11.4 + 0.00461T 17.4 + 0.004001T 20.2 11.5 10.9 + 0.00365T 31.0

273–630 All 300–2000 273–798 273–553 285–319 273–563 273–403 403–523 278–371 273–853 273–307

1 0 5 ? ? ? ? 3 3 ? ? ?

c c c

5.69 + 0.00188T - 50300/T 2 15.1 + 0.0121T 19.7 + 0.00315T

273–1773 273–1068 273–729

5 ? ?

g

4.97

All

0

c, α c, β l c c c c c c c c

4.26 + 0.00640T 6.99 + 0.000905T 8.55 11.3 + 0.00215T 9.25 + 0.00640T 15.8 + 0.00329T 10.0 + 0.00312T 20.78 + 0.0102T 33.4 82 11.00 + 0.00433T

g g c c, α c, β c c c g

6.50 + 0.00100T 6.70 + 0.00630T 22.8 9.80 + 0.0368T 5.0 + 0.0340T 17.8 31.8 51.6 8.05 + 0.000233T - 156300/T 2

300–3000 300–800 274–328 273–457 457–523 273–328 273–293 275–328 300–5000

3 1½ ? 5 5 ? ? ? 2

c

5.686 + 0.000875T

273–1877

1

300–5000

1

State†

Substance Manganese Mn

MnCl2 MnCO3 MnO Mn2O3 Mn3O4 MnO2 Mn2O3⋅H2O MnS MnSO4 MnSO4⋅5H2O Mercury11 Hg Hg2 HgCl HgCl2 Hg(CN)2 HgI HgI2 HgO HgS Hg2SO4 Molybdenum Mo MoO3 MoS2 Neon12 Ne Nickel4 Ni NiO NiS Ni2Si NiSi Ni3Sn NiSO4 NiSO4⋅6H2O NiTe Nitrogen13 N2 NH3 NH4Br NH4Cl NH4I NH4NO3 (NH4)2SO4 NO Osmium Os Oxygen14 O2 Palladium Pd Phosphorus P PCl3 P4O10 Platinum4 Pt Potassium K

273–626 626–1725 1725–1903 273–1273 273–597 273–1582 273–1273 273–904 293–373 291–325 273–700

2

2 5 10 ? 3 ? ? 2 ? ? 2

g

8.27 + 0.000258T - 187700/T

c

5.41 + 0.00184T

273–1822

2

c, yellow c, red l l c g

5.50 0.21 + 0.0180T 6.6 28.7 15.72 + 0.1092T 73.6

273–317 273–472 317–373 284–371 273–631 631–1371

5 10 10 ? 2 3

c

5.92 + 0.00116T

273–1873

1

c l

5.24 + 0.00555T 7.7

273–336 336–373

5 5

SPECIFIC HEATS TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )

State†

Substance Potassium—(Cont.) K K2 KAsO3 KBO2 K2B4O7 KBr KCl KClO3 KClO4 2KCl⋅CuCl2⋅2H2O 2KCl⋅PtCl4 2KCl⋅SnCl4 2KCl⋅ZnCl2 2KCN⋅Zn(CN)2 K2CO3 K2CrO4 K2Cr2O7 KF K4Fe(CN)6 K4Fe(CN)6⋅3H2O KH2AsO4 KH2PO4 KHSO4 KMnO4 KNO3 K2O⋅Al2O3⋅3SiO2

K4P2O7 K2SO4 K2S2O3 K2SO4⋅Al2(SO4)3⋅24H2O K2SO4⋅Cr2(SO4)3⋅24H2O K2SO4⋅MgSO4⋅6H2O K2SO4⋅NiSO4⋅6H2O K2SO4⋅ZnSO4⋅6H2O Prometheum Pr Radon Rn Rhenium Re Rhodium Rh Rubidium Rb RbBr RbCl Rb2CO3 RbF RbI Scandium Sc2O3 Sc2(SO4)3 Selenium Se Silicon Si SiC SiCl4 SiO2

Silver4 Ag

g g c c c c c c c c c c c c c c c l c c c c c c c c c l c, orthoclase gls, orthoclase c, microcline gls, microcline c c c c c c c c

Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K) 4.97 9.00 25.3 12.6 + 0.0126T 51.3 11.49 + 0.00360T 10.93 + 0.00376T 25.7 26.3 63 55 54.5 43.4 57.4 29.9 35.9 42.80 + 0.0410T 96.9 10.8 + 0.00284T 80.1 114.5 32 28.3 30 28 6.42 + 0.0530T 28.8 29.5 69.26 + 0.00821T - 2331000/T 2 69.81 + 0.01053 - 2403000/T 2 65.65 + 0.01102T - 1748000/T 2 64.83 + 0.01438T - 1641000/T 2 63.1 33.1 37 352 324 106 107 120

Range of temperature, K

Uncertainty, %

All 300–2000 290–372 273–1220 290–372 273–543 273–1043 289–371 287–318 292–323 286–319 292–323 279–319 277–319 296–372 289–371 273–671 671–757 273–1129 273–319 273–310 289–319 290–320 292–324 287–318 273–401 401–611 611–683 273–1373 273–1373 273–1373 273–1373 290–371 287–371 293–373 292–322 292–324 292–323 289–319 293–317

0 5 ? ? ? 2 2 ? ? ? ? ? ? ? ? ? 5 5 ? ? ? ? ? ? ? 10 5 10 1½ 1½ 1½ 1½ ? ? ? ? ? ? ? ?

c g

4.97

All

0

c

6.30 + 0.00053T

273–2273

?

c

5.40 + 0.00219T

273–1877

2

c l c c c c c

3.27 + 0.0131T 7.85 11.6 + 0.00255T 11.5 + 0.00249T 28.4 11.3 + 0.00256T 11.6 + 0.00263T

273–312 312–373 273–954 273–987 291–320 273–1048 273–913

2 5 ? ? ? ? ?

c c

21.1 62.0

273–373 273–373

? ?

c l

4.53 + 0.00550T 8.35

273–490 490–570

2 3

c c l c, quartz, α c, quartz, β c, cristobalite, α c, cristobalite, β gls

5.74 + 0.000617T - 101000/T 2 8.89 + 0.00291T - 284000/T 2 32.4 10.87 + 0.008712T - 241200/T 2 10.95 + 0.00550T 3.65 + 0.0240T 17.09 + 0.000454T - 897200/T 2 12.80 + 0.00447T - 302000/T 2

273–1174 273–1629 293–373 273–848 848–1873 273–523 523–1973 273–1973

2 2 ? 1 3½ 2½ 2 3½

c l

5.60 + 0.00150T 8.2

273–1234 1234–1573

1 3 (Continued )

2-133

2-134

PHYSICAL AnD CHEMICAL DATA TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )

State†

Substance Silver—(Cont.) Ag3Al Ag2Al AgAl12 AgBr AgCl AgCNO AgI AgNO3 Ag3PO4 Ag2S Ag3Sb Ag2Se Sodium15 Na NaBO2 Na2B4O7 Na2B4O7⋅10H2O NaBr NaCl NaClO3 NaCNO Na2CO3 NaF Na2HPO4⋅7H2O Na2HPO4⋅12H2O NaI NaNO3 Na2O⋅Al2O3⋅3SiO2 NaPO3 Na4P2O7 Na2SO4 Na2S2O3 Na2S2O3⋅5H2O Sodium-potassium alloys15 Strontium SrBr2 SrBr2⋅H2O SrBr2⋅6H2O SrCl2 SrCl2⋅H2O SrCl2⋅2H2O SrCO3 SrI2 SrI2⋅H2O SrI2⋅2H2O SrI2⋅6H2O SrMoO4 Sr(NO3)2 SrSO4 Sulfur16 S S2 S2Cl2 SO2 Tantalum Ta Tellurium Te Thallium Tl

Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K)

Range of temperature, K

Uncertainty, %

273–902 273–903 273–768 273–703 703–836 273–728 728–806 273–353 273–423 273–433 433–482 482–541 293–325 273–448 448–597 273–694 273–406 406–460

2 2 5 6 5 2 5 ? 6 2 5 5 ? 5 5 5 5 5

273–371 371–451 All 273–1239 289–371 292–323 273–543 273–1074 1073–1205 273–528 528–572 273–353 288–371 273–1261 275–307 275–307 273–936 273–583 583–703 273–1373 273–1173 290–319 290–371 289–371 273–307 273–307

1½ 2 0 ? ? ? 2 2 3 3 5 ? ? ? ? ? ? 5 10 1 1 ? ? ? ? ?

c c c c l c l c c, α c, α c, β l c c, α c, β c c, α c, β

22.56 + 0.00570T 16.85 + 0.00450T 58.62 + 0.0575T 8.58 + 0.0141T 14.9 9.60 + 0.00929T 14.05 18.7 8.58 + 0.0141T 18.83 + 0.0160T 25.7 30.2 37.5 18.8 21.8 19.53 + 0.0160T 20.2 20.4

c l g c c c c c l c l c c c c c c c l c, albite gls c c c c c l

5.01 + 0.00536T 7.50 4.97 10.4 + 0.0199T 47.9 147 11.74 + 0.00233T 10.79 + 0.00420T 15.9 9.48 + 0.0468T 31.8 13.1 28.9 10.4 + 0.00289T 86.6 133.4 12.5 + 0.00162T 4.56 + 0.0580T 37.2 63.78 + 0.01171T - 1678000/T 2 61.25 + 0.01768T - 1545000/T 2 22.1 60.7 32.8 34.9 86.2

c c c c c c c c c c c c c c

18.1 + 0.00311T 28.9 82.1 18.2 + 0.00244T 28.7 38.3 21.8 18.6 + 0.00304T 28.5 39.1 84.9 37 38.3 26.2

273–923 277–370 276–327 273–1143 276–365 277–366 281–371 273–783 276–363 275–336 275–333 273–297 290–320 293–369

? ? ? ? ? ? ? ? ? ? ? ? ? ?

c, rhombic c, monoclinic g l g

3.63 + 0.00640T 4.38 + 0.00440T 8.58 + 0.00030T 27.5 7.70 + 0.00530T - 0.00000083T 2

273–368 368–392 300–2500 273–332 300–2500

3 3 5 ? 2½

c

5.91 + 0.00099T

273–1173

2

c

5.19 + 0.00250T

273–600

3

c, α c, β

5.32 + 0.00385T 8.12

273–500 500–576

1 1

SPECIFIC HEATS TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )

State†

Substance Thallium—(Cont.) Tl TlBr TlCl Thorium Th ThO2 Th(SO4)2 Tin4 Sn SnAu SnCl2 SnCl4 SnO SnO2 SnPt SnS SnS2 Titanium Ti TiCl4 TiO2 Tungsten W WO3 Uranium U U3O8 Vanadium V Xenon Xe Zinc4 Zn ZnCl2 ZnO ZnS ZnSb ZnSO4 ZnSO4⋅H2O ZnSO4⋅6H2O ZnSO4⋅7H2O Zirconium ZrO2 ZrO2⋅SiO2 1

Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K)

Range of temperature, K

Uncertainty, %

l c l c l

7.12 12.53 + 0.00100T 16.0 12.56 + 0.00088T 14.2

576–773 273–733 733–800 273–700 700–803

3 10 10 5 10

c c c

6.40 14.6 + 0.00507T 41.2

273–373 273–1273 273–373

? ? ?

c l c c l c c c c c

5.05 + 0.00480T 6.6 11.79 + 0.00233T 16.2 + 0.00926T 38.4 9.40 + 0.00362T 13.94 + 0.00565T - 252000/T 2 11.49 + 0.00190T 12.1 + 0.00165T 20.5 + 0.00400T

273–504 504–1273 273–581 273–520 286–371 273–1273 273–1373 273–1318 273–1153 273–873

2 10 1 ? ? ? ? 1 ? ?

c l c

8.91 + 0.00114T - 433000/T 2 35.7 11.81 + 0.00754T - 41900/T 2

273–713 285–372 273–713

3 ? 3

c c

5.65 + 0.00866 16.0 + 0.00774T

273–2073 273–1550

1 ?

c c

6.64 59.8

273–372 276–314

? ?

c

5.57 + 0.00097T

273–1993

?

g

4.97

All

0

c l c c c c c c c c

5.25 + 0.00270T 7.59 + 0.00055T 15.9 + 0.00800T 11.40 + 0.00145T - 182400/T 2 12.81 + 0.00095T - 194600/T 2 11.5 + 0.00313T 28 34.7 80.8 100.2

273–692 692–1122 273–638 273–1573 273–1173 273–810 293–373 282 282 273–307

1 3 ? 1 5 ? ? ? ? ?

c c

11.62 + 0.01046T - 177700/T 2 26.7

273–1673 297–372

5 ?

See also Table 2-71. Data to 298 K are also given by Scott, Cryogenic Engineering, Van Nostrand, Princeton, N.J., 1959. For liquid and gas data, see Johnson (ed.), WADD-TR-60-56, 1960. Stalder, NACA Tech. Note 4141, 1957 (Fig. 5), gives data from 400 to 2600°R. 4 See also Table 2-71. 5 For data from 400 to 5500°R see Stalder, NACA Tech. Note 4141, 1975 (Fig. 4). 6 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-60-56, 1960. 7 For data from 400 to 2350°R see Stalder, NACA Tech. Note 4141, 1957. 8 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-60-56, 1960. 9 For liquid and gas data, see Johnson (ed.), WADD-TR-60-56, 1960. 10 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-60-56, 1960. 11 See also Table 2-71. Douglas, Ball, et al., Bur. Stand. J. Res., 46 (1951): 334; Busey and Giaque, J. Am. Chem. Soc., 75 (1953): 806; Sheldon, ASME Pap. 49-A-30, 1949. 12 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-56-60, 1960. 13 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-56-60, 1960. 14 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-56-60, 1960. Ozone: For liquid see Brabets and Waterman, J. Chem. Phys., 28 (1958): 1212. 15 For data on liquid Na-K alloys to 1500°F and for liquid Na to 1460°F, see Lubarsky and Kaufman, NACA Rep. 1270, 1956. 16 See also Evans and Wagman, Bur. Stand. J. Res. 49 (1952): 141; Gratch, OTS PB 124957, 1950; Guthrie, Scott et al., J. Am. Chem. Soc., 76 (1954): 1488. 2 3

2-135

2-136

PHYSICAL AnD CHEMICAL DATA

TABLE 2-71 Specific Heat [kJ/(kg·K)] of Selected Elements Temperature, K Symbol

4

6

8

10

20

40

60

80

100

200

250

300

400

600

800

Al Be Bi Cr Co

0.00026 0.00008 0.00054 0.00016 0.00036

0.00050

0.00088

0.214

0.357

0.00541 0.00050 0.00085

0.0089 0.0014 0.0340 0.0021 0.0048

0.0775

0.00220 0.00029 0.00059

0.00140 0.00028 0.01040 0.00081 0.00121

0.0729 0.0107 0.0404

0.092 0.059 0.110

0.102 0.127 0.184

0.481 0.195 0.109 0.190 0.234

0.797 1.109 0.120 0.382 0.376

0.859 1.537 0.121 0.424 0.406

0.902 1.840 0.122 0.450 0.426

0.949 2.191 0.123 0.501 0.451

1.042 2.605 0.142 0.565 0.509

1.134 2.823 0.136 0.611 0.543

Cu Ge Au Ir Fe

0.00011

0.00024

0.00018

0.00047

0.00048 0.00037 0.00126

0.137 0.108 0.084

0.203 0.153 0.100

0.00061

0.00090

0.0076 0.0129 0.0163 0.0021 0.0039

0.059 0.0619 0.0569

0.00038

0.00086 0.00081 0.00255 0.00032 0.00127

0.0276

0.086

0.154

0.254 0.192 0.109 0.090 0.216

0.357 0.286 0.124 0.122 0.384

0.377 0.305 0.127 0.128 0.422

0.386 0.323 0.129 0.131 0.450

0.396 0.343 0.131 0.133 0.491

0.431 0.364 0.136 0.140 0.555

0.448 0.377 0.141 0.146 0.692

Pb Mg Hg Mo Ni

0.00075 0.00034 0.00417 0.00011 0.00054

0.00242 0.00080 0.01420 0.00019 0.00086

0.00747 0.00155 0.01820 0.00032 0.00121

0.01350 0.00172 0.02250 0.00050 0.00178

0.0531 0.0148 0.0515 0.0029 0.0058

0.0944 0.138 0.0895 0.0236 0.0380

0.108 0.336 0.107 0.061 0.103

0.114 0.513 0.116 0.105 0.173

0.118 0.648 0.121 0.140 0.232

0.125 0.929 0.136 0.223 0.383

0.127 0.985 0.141 0.241 0.416

1.129 1.005 0.139 0.248 0.444

0.132 1.082 0.136 0.261 0.490

0.142 1.177 0.135 0.280 0.590

1.263 0.104 0.292 0.530

Pt Ag Sn Zn

0.00019 0.00016 0.00024 0.00011

0.00028 0.00035 0.00127 0.00029

0.00067 0.00093 0.00423 0.00096

0.00112 0.00186 0.00776 0.00250

0.0077 0.0159 0.0400 0.0269

0.0382 0.0778 0.108 0.123

0.069 0.133 0.149 0.205

0.088 0.166 0.173 0.258

0.101 0.187 0.189 0.295

0.127 0.225 0.214 0.366

0.132 0.232 0.220 0.380

0.134 0.236 0.222 0.389

0.136 0.240 0.245 0.404

0.140 0.251 0.257 0.435

0.146 0.264 0.257 0.479

TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)]

2-137

Eqn

Cmpd. no.

100 100 100 100 100 100 100 100 100 100 100 114 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114 114 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide

Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO

CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0

Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101

C1

C2

C3

152.99 10,2300 13,9640 26,0050 13,5600 73,381 –122,020 103,090 55,300 109,750 –214,460 61.289 150,940 134,390 161,440 129,440 162,940 119,780 -5,480 66,950 156,130 –334,997 87,500 100,320 121,770 179,400 121,600 95,588 102,760 135,150 128,860 191,030 55.136 42.152 191,200 533,390 182,050 126,680 112,760 111,850 182,470 232,190 197,890 136,340 194,170 237,700 154,800 -8,304,300 85,600 65.429

598.64 128.7 -320.8 -565.43 -177 60.042 3082.7 -247.8 300 -108.61 9185.1 80925 93.455 -1989.4 260.66 -169.5 -344.94 180.34 647.12 333.33 454.49 3644.21 480 346.89 429.3 -667.11 -9.45 -110.94 -230.08 -311.14 -323.1 -1675 314200 324580 -730.4 -4986.2 -1611 -65.47 -104.7 384.52 -13.912 -804.35 -491.54 -300.4 -532.38 -746.4 -239.75 104370 -122 28723

-0.89481 0.8985 1.1035 0.2837 -15.895 1.0343 0.35246 -106.12 799.4 0.23602 11.043

C4

C5

0.000689 0.027732

0.41616 -2651

0.64781 0.85562

-7.77514

1.0701 0.358 0.41864 0.51796 0.97007 1.015 12.5 280.19 517.35 2.2998 18.908 11.963 -0.64 0.5214 0.72897 2.7063 1.7219 1.0216 1.4286 1.829 0.68616 -433.33 0.5605 -847.39

0.00591102

-0.0001523 0.000032 -0.03874 1413.9 1449.5

0.000046121

-0.02 -0.037454 0.002912

0.000045027

-0.0023017 -0.0012499

0.60052 -0.001452 1959.6

0.000002008

Tmin, K

Cp at Tmin × 1E-05

Tmax, K

Cp at Tmax × 1E-05

149.78 354.15 289.81 200.15 178.45 229.32 192.40 253.00 286.15 189.63 75.00 203.15 298.15 83.78 403.00 278.68 278.68 258.27 395.45 260.28 321.35 257.85 275.65 243.95 342.20 265.90 293.15 154.25 179.44 136.95 165.00 134.86 220.00 196.15 183.85 158.45 87.80 134.26 167.62 298.15 185.30 157.46 133.02 147.43 176.80 267.95 161.30 220.00 161.11 68.15

0.69743 1.47880 1.22130 1.91090 1.16960 0.87150 0.80208 1.06600 1.41150 1.01830 0.53065 0.75753 1.99780 0.45230 2.66490 1.32510 1.33260 1.66360 2.50420 1.53710 3.02180 1.89060 2.19810 1.84940 2.68680 0.77675 1.49600 0.88436 0.78152 1.10340 1.03330 1.12720 1.55900 0.62506 1.34650 1.38480 1.10150 1.13400 1.09860 2.26490 2.04920 1.63650 1.60030 1.14260 1.44700 1.69020 1.33980 0.78265 0.75774 0.59115

294.15 571.00 391.05 412.70 329.44 354.81 250.00 379.50 375.00 400.00 115.00 401.15 484.20 135.00 563.15 353.24 500.00 442.29 450.00 464.15 640.00 478.60 458.15 472.03 533.37 331.90 495.08 311.49 280.15 290.00 350.00 400.00 670.00 670.00 391.00 372.90 380.00 350.00 274.03 399.26 400.00 390.00 370.00 298.15 347.94 436.42 390.74 290.00 552.00 132.00

0.98820 1.75790 1.51590 2.14650 1.32710 0.94685 0.88530 1.58010 1.67800 1.22700 0.71317 4.18470 2.51530 0.67080 3.08230 1.50400 2.04380 1.99540 2.85720 2.21670 4.47000 2.76170 3.07410 2.64060 3.50750 0.75866 2.04670 1.01650 0.78955 1.22790 1.41480 2.22370 5.20450 5.24370 2.57210 2.66210 1.81030 1.50220 1.23220 2.65370 2.93540 1.93590 1.88440 1.37590 1.81880 2.60310 1.65880 1.66030 1.31250 6.47990 (Continued )

2-138

TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)] (Continued ) Eqn 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114 100 100

Cmpd. no. 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

Name Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane

Formula CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2

CAS 56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5

Mol. wt. 153.8227 88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339

C1 -752,700 104,600 63,936 -1,307,500 118,380 124,850 107,900 134,733 69,362 -246,700 -185,150 259,980 61,723 77,461 101,920 -220,600 -40,000 6,110.4 105,850 122,530 125,380 89,952 177,560 218,480 278,620 219,840 4,988,500 417,440 314,570 276,900 149,400 200,560 202,580 270,720 114,880 93,093 133,950 126,340 179,170 98,968 144,560 111,560 184,200 101,330 44,400 238,520 67.155 82,577 263,980

C2

C3

8966.1 -500.6 46.35 15338 -248.915 -166.34 -330.13 -176.332 215.01 3256.8 3148 -1112.3 494.81 111.51 -215.81 3118.3 853 600.94 -60 -403.8 -349.7 -196.63 -179.12 374.14 -197.91 140.41 -52898 -1616.5 -160.93 -371.23

-30.394 2.2851 -0.1623 -53.974 0.68074 0.43209 0.808 0.55966

0.034455

-7.4202 -8.0367 4.9427

0.0060467 0.007254 -0.0054367

0.8103 -9.4216

0.010687

-231.8 -491.44 -726.3 -259.83 187.25 183.97 -24.84 -94.63 -444.74 -62.941 -53.605 149.44 286 243.18 1301 -1038.4 105580 109.85 -1791.1

0.5946 0.9187 1.3377 0.95427

0.68 1.7344 1.143 0.65237 0.76723 0.11851 1.0737 0.9968 216.35 5.3948 0.95561 1.5774

C4

0.063483

-0.0010975

-0.37538 -0.004348

0.2314 0.48191 0.32 0.93009 0.23265 0.30617

-5.5 4.0587 310.21 4.3666

C5

0.008763 -0.0044691 -490.54

0.00023674

Tmin, K

Cp at Tmin × 1E-05

Tmax, K

Cp at Tmax × 1E-05

250.33 89.56 172.12 227.95 136.75 233.15 175.43 150.35 200.00 285.39 304.20 307.93 177.14 245.25 190.00 279.69 296.60 290.00 169.67 179.28 138.13 150.00 189.64 285.00 243.51 304.75 280.00 206.89 247.56 229.15

1.27630 0.78095 0.67106 1.36170 0.97071 1.09560 0.74852 1.20870 1.12360 2.18950 2.32970 2.27400 1.49370 1.04810 0.90168 1.48360 2.13000 1.80380 1.15250 0.99559 0.98884 0.75136 1.71180 3.34740 2.94090 3.55210 3.53690 2.75410 3.33300 2.74660

388.71 145.10 239.12 360.00 298.15 366.48 303.15 319.67 308.85 400.00 400.00 400.00 425.56 253.82 298.15 400.00 434.00 489.75 356.12 322.40 317.38 298.15 431.95 481.65 460.00 543.15 503.15 494.00 512.35 447.15

1.63740 0.80073 0.65739 1.81010 1.04680 1.21920 0.82076 1.35560 1.35770 2.55780 2.52430 2.57940 2.72290 1.05760 1.09610 2.03230 3.30200 3.00420 1.70720 1.35840 1.29530 0.89318 2.43340 4.26180 4.14780 5.90170 5.01740 4.11250 4.82970 4.26290

210.15 282.85 240.00 175.30 248.39 273.15 326.14 176.19 237.49 180.00 192.50 275.00 301.15 223.35 156.92 181.95 154.56 179.60 200.00

1.26950 1.35060 1.05320 2.54500 1.61390 1.60610 1.77110 1.19600 1.26010 0.95176 1.45590 1.52660 2.70330 1.55640 1.46980 1.57030 0.99146 1.02310 0.80424

381.15 410.00 370.10 450.00 400.00 528.75 513.56 330.45 356.59 320.00 361.25 369.52 541.54 328.60 460.00 322.08 359.98 283.65 250.00

1.47430 1.53500 1.17010 3.47040 1.89780 2.55060 2.48290 1.30010 1.38850 1.02650 1.65150 1.66780 3.39080 1.81240 3.32020 1.75790 1.68740 1.13740 0.89118

2-139

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 149 150 151 152

Diisopropyl amine Diisopropyl ether Diisopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorine Fluorobenzene Fluoroethane Fluoromethane

C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 F2 C6H5F C2H5F CH3F

108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 7782-41-4 462-06-6 353-36-6 593-53-3

101.19 102.17476 114.18546 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 37.9968064 96.1023032 48.0595 34.03292

98,434 163,000 179,270 187,790 199,930 88,153 -214,870 129,450 134,500 150,130 155,560 171,580 110,100 147,900 146,420 206,560 131,810 146,950 240,300 195,251 956,860 134,160 49,120 508,210 352,720 44.009 102,640 226,230 121,700 154,040 124,500 56,359 82,434 132,360 178,520 247,390 184,440 35,540 46,848 144,710 80,000 207,670 146,040 106,250 229,250 134,670 76,330 103,680 173,110 -94,585 1,724,400 148,640 65,106 141,790

429.04 -4.5 28.37 -313.41 -191.5 124.16 3787.2 18.5 8.765 -62.38 -145.26 -256.67 -157.47 -106 59.2 325.75 -380.06 -595 419.918 -5559.9 447.67 562.24 -1368.7 807.32 89718 -139.63 -624.8 38.993 -142.29 370.6 603.02 422.45 72.74 -518.35 -4428 -150.2 436.78 205.35 -758.87 223.6 -17.907 458.22 292.15 -404.54 -234.39 400.1 726.3 -697.18 7529.9 -59924 -202.58 103.44 -814.32

0.62 0.5375 1.1023 0.87664 -13.781 0.608 0.81151 0.8851 1.0932 0.5727 0.51853 0.384 0.604

0.016924

1.2035 1.013

-0.00084787

9.6124

3.1015 0.2122 918.77 -0.030341 1.472

–1886 0.0020386

0.80539

0.20992 0.64738 2.3255 40.936 0.37044 -0.18486

-0.0016818 -0.1697

2.8261

-0.003064

0.00026816

1.0493

1.1382 0.59656 -2.6047 3.7615 -139.6 537.85 0.66374 0.67161 2.2673

0.0040957 -0.005289 1.1301

-0.0074083 0

1.6179E-06 -0.0033241

0.000019119

275.00 187.65 204.81 159.95 226.10 240.91 180.96 145.19 239.66 223.16 184.99 188.44 131.65 273.82 90.00 274.16 298.15 174.88 291.67 413.79 284.95 300.03 277.90 263.57 309.58 92.00 159.05 189.60 192.15 178.20 238.45 258.15 285.50 161.84 134.71 104.00 284.29 260.15 250.00 160.65 254.20 155.15 298.15 298.15 204.15 125.26 298.15 145.65 167.55 58.00 53.48 230.94 129.95 131.35

2.16420 1.83990 2.07630 1.65860 2.01450 1.18060 1.19470 1.44950 1.83210 1.80290 1.66100 1.43550 0.98356 1.47670 1.56640 2.95870 1.31810 1.12760 1.52930 3.69010 1.53060 2.68470 2.05370 3.62920 6.22990 0.68554 0.87867 1.60680 1.29190 1.54260 2.12870 2.12030 2.20150 1.61090 1.46780 0.70123 1.71680 1.36660 0.98186 0.83031 1.36840 2.30150 2.82660 1.93350 1.94100 1.14670 1.95620 1.66860 1.38290 0.55414 0.57975 1.37260 0.79084 0.73946

357.05 341.45 410.00 337.45 366.15 300.13 298.15 331.13 392.70 402.94 396.58 360.00 250.00 466.44 380.00 360.00 298.15 310.48 422.15 559.20 374.47 570.00 407.90 433.15 616.93 290.00 390.00 350.21 289.73 409.35 486.55 466.95 428.25 404.95 301.82 252.70 390.41 493.15 329.00 283.85 374.20 510.10 417.15 326.15 386.55 315.25 410.00 320.00 371.05 98.00 56.00 504.08 337.78 285.70

2.51620 2.33750 2.81260 2.07550 2.47340 1.25420 1.37790 2.02240 2.63090 2.68700 2.69890 1.53400 1.03140 1.82000 2.56130 3.23830 1.31810 1.19590 1.69650 4.30070 2.22770 3.89330 2.78460 4.97260 9.31540 1.24440 1.64500 1.87960 1.33000 2.30750 3.04820 3.37940 3.01850 2.67980 1.87670 0.97582 1.82260 2.05980 1.14410 0.86932 1.63670 4.71570 3.37190 2.01530 2.42950 1.20070 2.40370 2.03580 1.92770 0.59663 0.55354 2.15180 1.40050 0.94206 (Continued )

2-140

TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)] (Continued ) Eqn

Cmpd. no.

100 100 100 100 100 100 100 100 114 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114 100 100 100 100 114 100 100 100 100 114 100 100 100 100 100 100 100 100

153 154 155 156 157 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201

Name Formaldehyde Formamide Formic acid Furan Helium-4 Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene

Formula CH2O CH3NO CH2O2 C4H4O He He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8

CAS 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4

Mol. wt. 30.02598 45.04062 46.0257 68.07396 4.0026 4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702

C1 70,077 63,400 78,060 114,370 387,220 410,430 376,970 176,120 61.26 194,570 2,416,800 1,070,000 270,730 265,040 267,950 236,870 46,798 370,350 157,820 172,120 161,980 1,638,600 1,409,400 208,250 235,960 164,640 82,795 303,320 93,000 94,860 79,815 66.653 57,720 47,300 95,398 62,520 64.666 127,540 -32,469 138,790 146,290 65.708 256,040 62,600 61,260 79,791 275,500 92,520 125,630 135,370

C2 -661.79 150.6 71.54 -215.69 -465570 -464890 347.82 242.92 314410 -23.206 -26105 -9470 -399.89 -375.68 -1315.9 -158.01 761.13 231.47 157.44 -183.78 44.116 -17261 -12553 -107.47 -345.94 -200.37 283.4 -1009 326 254.15 50.929 6765.9 9.9 90 -197.52 -223.02 49354 -65.35 1977.1 121.24 -58.59 38883 -2741.4 243.4 270.9 89.49 -1147 37.45 279.75 -133.34

C3

C4

C5

Tmin, K

Cp at Tmin × 1E-05

Tmax, K

Cp at Tmax × 1E-05

5.9749

-0.01813

0.00001983

155.15 292.00 281.45 187.55 2.20 1.80 295.13 229.80 182.57 265.83 239.15 220.00 234.15 238.15 154.12 229.92 200.00 291.31 214.93 177.83 269.25 228.55 223.00 217.35 217.50 133.39 300.00 192.62 200.00 300.00 274.69 13.95 185.15 165.00 259.83 189.79 187.68 270.00 177.95 409.15 288.15 90.69 175.47 359.00 253.40 200.00 196.32 179.69 260.75 159.53

0.55005 1.07380 0.98195 0.99486 0.10866 0.11352 5.30050 2.31940 1.99890 2.50870 2.35900 2.28350 2.35220 2.32420 1.81500 2.42290 1.73870 4.96020 1.91660 1.67500 2.25260 1.98210 2.04940 2.01850 2.05320 1.53540 1.67820 2.14950 1.58200 1.71110 0.97078 0.12622 0.59553 0.62150 0.70291 0.42875 0.67327 1.70310 1.46210 1.88400 1.59150 0.53605 0.71489 1.49980 1.29910 0.97689 1.49300 0.99249 1.98570 1.30350

253.85 493.00 380.00 304.50 4.60 2.10 575.30 426.15 520.00 496.15 448.60 432.90 480.00 490.00 430.00 460.00 372.93 560.01 401.15 460.00 478.85 460.00 412.40 460.00 460.00 404.00 354.35 430.00 344.48 357.67 653.15 32.00 206.45 185.00 298.85 292.67 370.00 427.65 320.00 580.00 434.15 190.00 503.15 538.50 373.40 249.94 353.35 266.82 472.65 314.56

0.72876 1.37650 1.05250 1.16090 0.29652 0.29952 7.68690 2.79640 4.06570 4.00650 3.87660 4.45840 3.23030 3.21630 2.75540 3.31310 2.43190 7.15210 2.20980 2.75340 3.45680 3.51970 3.98500 2.70870 2.76320 2.27060 1.83220 2.76390 2.05300 1.85760 1.31580 1.31220 0.59764 0.63950 0.71049 0.51186 4.91830 2.51140 1.66710 2.09110 1.88370 14.97800 2.46460 1.93670 1.62410 1.02160 1.90840 1.02510 2.57850 1.56620

0.72691 211800 135100 0.57895 1824.6 0.88395 110.03 33.004 1.0601 1.0024 6.5242 0.78982 -0.62882 0.68632 0.88734 0.709 71.721 40.991 0.2062 0.94278 0.8784 3.3885

0.043379 -123.63

0.3883 0.6297 22.493 0.82867 -7.0145 0.3582 -257.95 14.777

2.568

0.63868

-42494

3212.9

-2547.9 -0.19172 -0.0334

0.00011968 0

-0.011994

9.3808E-06

-0.12026 -0.04 0.00070293

0.000071087

-0.002762

478.27

-1623 0.0086913

614.07 -0.035078

0.000032719

2-141

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255

2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal

C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N CH3NO2 N2O NO C19H40 C9H18O

78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6

72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862

108,300 74,200 206,600 149,510 151,600 81,919 177,850 198,390 105,200 102,930 47,726 131,340 50,578 118,600 118,170 155,920 53,271 46,457 27,030 85,383 132,300 161,240 130,200 92,919 183,650 149,770 143,440 191,170 211,170 115,300 255,100 226,650 142,220 251,890 172,370 -925,460 87,680 71,140 144,110 179,850 113,470 76,822 134,580 73,600 29,800 1,034,100 187,740 281,970 101,400 116,270 67,556 –2,979,600 342,570 195,220

146 417.4 -761.14 -247.63 -266.72 181.01 -171.57 -220.35 191.1 129.1 338.4 -63.1 508.59 447.07 447.99 -490 327.92 346.93 413 199.08 200.87 -288.61 -396 324.43 -79.862 -529.82 -154.07 -331.04 -661.97 -263.23 -938.4 15.421 -47.83 -468.32 -1783.9 7894.9 217.1 335.5 -102.09 -264.1 421.6 90.833 184.7 527.5 -138770 -497.6 -12281 -682.11 -135.3 54.373 76602 762.08 378.71

-0.292

0.00151

2.5899 0.91849 0.90847 0.74379 0.76096 0.62516 0.8125

2.1383

-0.061547 -0.9597 0.78179 1.21 0.60769 1.3499 0.7255 0.98445 2.4216 0.60412 2.413 1.0578 0.739 1.2209 14.759 -17.661 -0.9153

-0.0015585

0.0019533

-0.0021383

-0.047909 0.013617 0.002266

0.00005805

0.58113 0.79202

0.011456

7154 1.0691 248 3.8912 0.345 -652.59 0.20481 0.029716

0.00095984

-162.55 -2.2182

1.8879

1.3841 0.0074902

113.25 321.50 155.95 135.58 139.39 298.15 157.48 175.30 200.00 277.25 250.00 146.58 300.00 300.00 300.00 130.73 200.00 200.00 250.00 160.00 186.48 167.23 174.15 298.15 189.15 256.15 127.93 180.15 171.64 150.18 224.95 240.00 119.55 176.00 113.54 298.96 132.81 300.00 133.97 160.17 298.15 249.95 164.55 151.15 353.43 24.56 183.63 63.15 117.00 244.60 182.30 109.50 305.04 267.30

1.23280 2.08390 1.50890 1.32820 1.32070 1.35890 1.69280 1.83150 1.43420 1.86780 1.32330 1.39550 2.03160 2.52720 2.52570 1.24920 1.18860 1.15840 1.30280 1.15660 1.49050 1.34840 0.97934 1.89650 1.90290 1.02630 1.35600 1.63480 1.58080 0.89393 1.66110 2.91280 1.47060 2.07280 0.99613 2.20160 1.05680 1.71790 1.40860 1.57870 1.13470 1.82200 1.54110 1.01520 2.16230 0.36664 1.32420 0.55925 0.74860 1.03820 0.77468 0.62287 5.94090 2.98570

310.00 481.50 404.15 304.31 311.71 305.40 343.31 510.00 299.49 415.87 325.00 320.00 441.15 438.15 440.15 366.48 348.64 338.05 350.00 280.50 373.15 339.80 304.90 350.00 389.15 366.00 310.00 440.00 357.91 298.15 373.45 518.15 333.41 372.00 380.00 460.00 343.15 390.00 312.20 368.69 298.15 438.65 328.20 278.65 491.14 40.00 387.22 112.00 175.50 473.15 200.00 150.00 603.05 465.52

1.70480 2.75180 3.22010 1.59210 1.56730 1.37200 2.06610 2.83940 1.62430 2.64740 1.57710 1.94350 2.74940 3.14480 3.15350 1.86820 1.67600 1.63740 1.71580 1.36380 1.75110 1.53440 1.21950 2.06470 2.44600 1.36680 1.65400 2.36100 1.86410 0.90520 2.41180 5.18640 2.08420 2.46630 2.07250 2.94550 1.45960 2.01990 1.68880 1.90140 1.13470 2.61760 1.99560 1.25070 2.88880 0.69796 1.55360 0.79596 1.01540 1.29490 0.78431 1.99090 8.76630 3.77960 (Continued )

2-142

TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)] (Continued ) Eqn

Cmpd. no.

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114 100 100 100 100 100 100 100 100 100 100 100

256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306

Name Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate

Formula C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2

CAS 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7

Mol. wt. 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512

C1 383,080 224,336 10,483,000 1,510,000 254,490 265,350 253,580 399,430 171,960 224,830 205,260 571,370 1,115,100 300,400 289,980 509,420 240,040 42,642 63,131 175,430 60,046 346,910 102,000 159,080 145,050 201,200 883,630 194,590 193,020 156,100 188,200 213,760 86,200 68,671 103,370 101,720 60,834 145,400 66,230 62.983 158,760 471,710 201,400 55,679 213,660 121,750 83,400 139,530 174,380 114,140 75,700

C2 -1139.8 49.726 -115220 -12600 -298.06 -46.22 -366.3 374.64 383.28 -186.63 44.392 -4849 -9773.8 -426.2 -417.27 -4279.1 -33.198 886.67 199.92 -6152.3 281.16 219.54 389.95 -270.5 28.344 -651.3 -8220.5 -263.86 -176.43 -456.94 -140.84 -324.4 256.6 246.66 527.03 317.61 215.89 252.4 98.275 113630 -635 -4172.1 -450.6 406.13 -702.7 -149.56 384.1 78 -101.8 -343.72 326.1

C3 2.7101 0.9813 476.87 40.7 1.1707 0.79154 1.4881 0.58156 -0.059074 0.95891 0.8956 19.725 34.252 1.1172 1.2218 21.477 0.67889 -0.69315 113.92 0.65632 -0.32545 0.99537 0.6372 2.275 29.125 0.76808 0.5669 2.255 0.63581 0.9472

C4

-0.85381 -0.0386

0.79 1.0905

0.00056246

-0.021532 -0.03454

-0.044462

0.000035028

-0.92382

0.0027963

-0.02989

-0.003163

0.29552

633.21 1.969 14.745 1.7053 -0.50303 1.6605 0.47759

C5

-873.46 -0.014402

0.00000238

Tmin, K

Cp at Tmin × 1E-05

Tmax, K

Cp at Tmax × 1E-05

219.66 285.55 310.00 238.15 191.91 253.05 223.15 301.31 251.65 216.38 289.65 250.00 241.55 252.86 255.55 171.45 240.00 200.00 462.65 54.36 90.00 283.07 191.59 143.42 239.15 200.14 200.00 196.29 234.18 108.02 160.75 197.45 200.00 200.00 372.39 314.06 243.15 404.15 200.00 85.47 146.95 185.26 199.00 165.00 252.45 180.37 274.70 188.36 173.55 87.89 298.15

2.63480 3.18550 3.50590 2.96270 2.40410 3.04340 2.45940 5.65110 2.64670 2.29340 2.93260 2.55500 2.65930 2.64060 2.63140 2.13270 2.71180 1.92250 1.55620 0.53646 0.85350 4.61650 1.64760 1.40760 1.88270 1.61980 1.65410 1.72390 1.82790 1.29390 1.81990 1.86640 1.37520 1.18000 2.99630 2.01470 1.30800 2.47410 0.85885 0.84879 1.07970 1.13280 1.79260 1.09000 1.42090 1.10310 1.88910 1.54220 1.80510 0.92354 1.72930

325.00 528.75 460.00 471.70 475.00 492.95 423.85 589.86 445.15 460.00 512.85 467.10 452.90 500.00 440.65 454.00 472.19 399.35 516.00 142.00 150.00 543.84 375.15 390.00 458.95 389.15 392.20 375.46 375.14 372.00 385.15 399.79 313.33 329.27 500.00 425.00 489.75 557.65 238.65 360.00 400.00 463.00 431.65 322.15 414.32 370.25 404.70 340.00 432.39 298.15 398.15

2.98900 5.24980 4.64940 5.71150 3.77050 4.34910 3.65660 8.22760 3.30870 3.41890 4.63580 4.15660 5.05560 3.66600 3.43350 3.20980 3.75730 2.86190 1.66290 0.90662 1.02220 6.60420 2.02490 2.04980 2.92280 2.92270 3.36360 2.03800 2.06610 1.80920 2.28270 2.35460 1.66600 1.49890 3.66890 2.36700 2.37450 2.86150 0.89683 2.60790 2.19800 2.71460 3.24630 1.34310 2.07560 1.31850 2.38850 1.66050 2.78060 1.08600 2.05540

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345

2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene

C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O2S F6S O3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10

75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3

76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165

138,390 167,330 58,080 45,810 829,380 113,340 186,250 85,743 119,500 258,090 131,270 182,900 353,140 171,730 81,760 123,300 43,326 84,864 140,140 103,350 350,180 111,480 136,050 119,450 178,800 95,275 388,620 40,364 133,530 293,980 -1,360,200 136,300 68,720 -10,320 49,516 276,370 133,860 36,500 -35,500

-117.11 -319.1 445.2 368.33 -7331.5 290.2 247.8 5.7443

345.64 635.09 29.13 -800.47 455.38 -130.1 630.73 91.725 -152.3 159.3 -104.7 368.13 -288 324.54 -128.47 696.7 -1439.5 664.46 514.64 -114.98 10964 -106.17 135 322.8 420.35 -2090.1 7.8754 1017.5 1287.2

0.47059 0.8127

19.203 -0.6051

0.86116 2.8934

0.0013567

-0.0025015

0.6229 0.13243 0.695 1.0022 0.9913 0.83741 -1.3765 3.2187

0.0021734

0.96936 -20.86 0.75175

0.013055

8.125 0.52265 -2.63 -2.599

-0.014116 0.00302 0.002426

9.3701E-06

142.61 159.95 213.15 388.85 186.35 242.54 460.85 197.67 230.15 303.15 700.15 329.35 279.01 164.65 237.38 176.98 375.41 234.94 178.18 236.50 267.76 200.00 156.08 247.79 229.33 165.78 280.00 398.40 354.00 247.57 289.05 259.56 200.00 200.00 178.35 273.16 217.00 247.98 286.41

1.31260 1.37080 1.52970 1.89040 1.30000 1.67490 3.00450 0.86878 1.19500 2.58090 3.73270 3.92070 4.28310 1.07210 1.89860 1.19790 2.80110 1.13720 1.35070 1.41020 3.94000 1.85110 1.15250 1.99870 1.93380 1.82850 2.37910 3.05080 3.15710 3.24930 3.81370 1.59390 0.95720 0.54240 1.24490 0.76150 1.60180 1.73140 1.76970

350.00 340.87 460.75 683.00 253.15 418.31 591.00 350.00 230.15 303.15 795.28 609.15 526.73 339.12 480.77 394.27 426.00 357.31 500.00 300.00 508.62 361.92 276.02 449.27 350.00 520.00 320.00 475.47 475.00 433.42 523.15 389.35 278.25 400.00 363.85 533.15 540.15 417.58 600.00

1.55050 1.52990 2.63210 2.97380 2.04030 2.28160 3.32700 0.87754 1.19500 2.58090 4.06150 5.69770 6.07410 1.35460 3.00690 1.68830 3.12020 1.34550 2.37740 1.51140 5.56190 2.44710 1.32080 2.65260 2.36420 3.90950 2.57570 3.56290 3.77980 4.26240 5.35730 2.08920 1.06280 1.18800 2.02460 0.89394 2.90600 2.22690 3.25200

For the 11 substances: ammonia; 1,2-butanediol; 1,3-butanediol; carbon monoxide; 1,1-difluoroethane; ethane; heptane; hydrogen; hydrogen sulfide; methane; and propane; the liquid heat capacity CpL is calculated with Eq. (2-114): CpL = C12/τ + C2 - 2C1C3τ - C1C4τ2 - C32τ3/3 - C3C4τ4/2 - C42τ5/5, where τ = 1 - Tr , Tr = T/TC, TC is the critical temperature from Table 2-106, CpL is in J/(kmol∙K) and T is in K. For all other compounds, Eqn 100 is used. Eqn 100: CpL = C1 + C2T + C3T 2 + C4T 3 + C5T 4. For benzene, fluorine, and helium, two sets of constants are given for Eqn 100 that cover different temperature ranges, as shown in the table. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016).

2-143

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PHYSICAL AnD CHEMICAL DATA TABLE 2-73 Specific Heats of Organic Solids Recalculated from International Critical Tables, vol. 5, pp. 101–105 Compound

Formula

Acetic acid Acetone Aminobenzoic acid (o-) (m-) (p-) Aniline Anthracene

C2H4O2 C3H6O C7H7NO2 C7H7NO2 C7H7NO2 C6H7N C14H10

Anthraquinone Apiol Azobenzene

C14H8O2 C12H14O4 C12H10N2

Benzene

C6H6

Benzoic acid Benzophenone

C7H6O2 C13H10O

Betol

C17H12O3

Bromoiodobenzene (o-) (m-) (p-) Bromonaphthalene (β-) Bromophenol

C6H4BrI C6H4BrI C6H4BrI C10H7Br C6H5BrO

Camphene Capric acid Caprylic acid Carbon tetrachloride

C10H16 C10H20O2 C8H16O2 CCl4

Cerotic acid Chloral alcoholate hydrate Chloroacetic acid Chlorobenzoic acid (o-) (m-) (p-) Chlorobromobenzene (o-) (m-) (p-) Crotonic acid Cyamelide Cyanamide Cyanuric acid

C27H54O2 C4H7Cl3O2 C2H3Cl3O2 C2H3ClO2 C7H5ClO2 C7H5ClO2 C7H5ClO2 C6H4BrCl C6H4BrCl C6H4BrCl C4H6O2 C3H3N3O3 CH2N2 C3H3N3O3

Dextrin Dextrose

(C6H10O5)x C6H12O6

Dibenzyl Dibromobenzene (o-) (m-) (p-) Dichloroacetic acid Dichlorobenzene (o-) (m-) (p-) Dicyandiamide

C14H14 C6H4Br2 C6H4Br2 C6H4Br2 C2H2Cl2O2 C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4N4

Temperature, °C -200 to +25 -210 to -80 85 to mp 120 to mp 128 to mp

sp ht, cal/(g⋅°C)

50 100 150 0 to 270 10 28

0.330 + 0.00080t 0.540 + 0.0156t 0.254 + 0.00136t 0.253 + 0.00122t 0.287 + 0.00088t 0.741 0.308 0.350 0.382 0.258 + 0.00069t 0.299 0.330

-250 -225 -200 -150 -100 -50 0 20 to mp -150 -100 -50 0 +20 -150 -100 0 +50 -50 to 0 -75 to -15 -40 to 50 41 32

0.0399 0.0908 0.124 0.170 0.227 0.299 0.375 0.287 + 0.00050t 0.115 0.172 0.220 0.275 0.303 0.129 0.167 0.248 0.308 0.143 + 0.00025t 0.143 0.116 + 0.00032t 0.260 0.263

35 8 -2 -240 -200 -160 -120 -80 -40 15 78 32 60 80 to mp 94 to mp 180 to mp -34 -52 -40 38 to 70 40 20 40

0.380 0.695 0.628 0.013 0.081 0.131 0.162 0.182 0.201 0.387 0.509 0.213 0.363 0.228 + 0.00084t 0.232 + 0.00073t 0.242 + 0.00055t 0.192 0.150 0.150 0.520 + 0.00020t 0.263 0.547 0.318

0 to 90 -250 -200 -100 0 20 28 -36 -25 -50 to +50

0.291 + 0.00096t 0.016 0.077 0.160 0.277 0.300 0.363 0.248 0.134 0.139 + 0.00038t 0.406 0.185 0.186 0.219 + 0.0021t 0.456

-48.5 -52 -50 to +53 0 to 204

SPECIFIC HEATS TABLE 2-73 Specific Heats of Organic Solids (Continued ) Recalculated from International Critical Tables, vol. 5, pp. 101–105 Compound

Formula

Dihydroxybenzene (o-) (m-) (p-)

C6H6O2 C6H6O2 C6H6O2

Di-iodobenzene (o-) (m-) (p-) Dimethyl oxalate Dimethylpyrene Dinitrobenzene (o-) (m-) (p-) Diphenyl Diphenylamine Dulcitol

C6H4I2 C6H4I2 C6H4I2 C4H6O4 C7H8O2 C6H4N2O4 C6H4N2O4 C6H4N2O4 C12H10 C12H11N C6H14O6

Erythritol Ethyl alcohol

C4H10O4 C2H6O (crystalline)

(vitreous)

Temperature, °C

sp. ht., cal/(g⋅°C)

-163 to mp -160 to mp -250 -240 -220 -200 -150 to mp -50 to +15 -52 to -42 -50 to +80 10 to 50 50 -160 to mp -160 to mp 119 to mp 40 26 20

0.278 + 0.00098t 0.269 + 0.00118t 0.025 0.038 0.061 0.081 0.268 + 0.00093t 0.109 + 0.00026t 0.100 + 0.00026t 0.101 + 0.00026t 0.212 + 0.0044t 0.368 0.252 + 0.00083t 0.248 + 0.00077t 0.259 + 0.00057t 0.385 0.337 0.282

60 -190 -180 -160 -140 -130 -190 -180 -175 -170 -190 to -40

0.351 0.232 0.248 0.282 0.318 0.376 0.260 0.296 0.380 0.399 0.366 + 0.00110t

Ethylene glycol

C2H6O2

Formic acid

CH2O2

-22 0

0.387 0.430

Glutaric acid Glycerol

C5H8O4 C3H8O3

20 -265 -260 -250 -220 -200 -100 0

0.299 0.009 0.022 0.047 0.085 0.115 0.217 0.330

Hexachloroethane Hexadecane Hydroxyacetanilide

C2Cl6 C16H34 C8H9NO2

Iodobenzene Isopropyl alcohol

C6H5I C3H8O

Lactose Lauric acid Levoglucosane Levulose

C12H22O11 C12H22O11⋅H2O C12H24O2 C6H10O5 C6H12O6

Malonic acid Maltose Mannitol Melamine Myristic acid Naphthalene Naphthol (α-) (β-) Naphthylamine (α-) Nitroaniline (o-) (m-) (p-) Nitrobenzoic acid (o-) (m-) (p-) Nitronaphthalene

41 to mp

25

0.174 0.495 0.249 + 0.00154t

40 -200 to -160

0.191 0.051 + 0.00165t

20 20 -30 to +40 40 20

0.287 0.299 0.430 + 0.000027t 0.607 0.275

C3H4O4 C12H22O11 C6H14O6 C3H6N6 C14H28O2

20 20 0 to 100 40 0 to 35

0.275 0.320 0.313 + 0.00025t 0.351 0.381 + 0.00545t

C10H8 C10H8O C10H8O C10H9N C6H6N2O2 C6H6N2O2 C6H6N2O2 C7H5NO4 C7H5NO4 C7H5NO4 C10H7NO2

-130 to mp 50 to mp 61 to mp 0 to 50 -160 to mp -160 to mp -160 to mp -163 to mp 66 to mp -160 to mp 0 to 55

0.281 + 0.00111t 0.240 + 0.00147t 0.252 + 0.00128t 0.270 + 0.0031t 0.269 + 0.000920t 0.275 + 0.000946t 0.276 + 0.001000t 0.256 + 0.00085t 0.258 + 0.00091t 0.247 + 0.00077t 0.236 + 0.00215t (Continued)

2-145

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PHYSICAL AnD CHEMICAL DATA TABLE 2-73 Specific Heats of Organic Solids (Continued ) Recalculated from International Critical Tables, vol. 5, pp. 101–105 Compound

Formula

Temperature, °C

sp ht, cal/(g⋅°C)

Oxalic acid

C2H2O4 C2H2O4⋅2H2O

-200 to +50 -200 -100 0 +50 100

0.259 + 0.00076t 0.117 0.239 0.338 0.385 0.416

Palmitic acid

C16H32O2

Phenol Phthalic acid Picric acid

C6H6O C8H6O4 C6H3N3O7

Propionic acid Propyl alcohol (n-)

C3H6O2 C3H8O

Pyrotartaric acid

C6H8O4

-180 -140 -100 -50 0 +20 14 to 26 20 -100 0 +50 100 120 -33 -200 -175 -150 -130 20

0.167 0.208 0.251 0.306 0.382 0.430 0.561 0.232 0.165 0.240 0.263 0.297 0.332 0.726 0.170 0.363 0.471 0.497 0.301

Quinhydrone

C12H10O4

Quinone

C6H4O2

-250 -225 -200 -100 0 -250 -225 -200 -150 to mp

0.017 0.061 0.098 0.191 0.256 0.031 0.082 0.113 0.282 + 0.00083t

Salol Stearic acid Succinic acid Sucrose Sugar (cane)

C13H10O3 C18H36O2 C4H6O4 C12H22O11 C12H22O11

32 15 0 to 160 20 22 to 51

0.289 0.399 0.248 + 0.00153t 0.299 0.301

Tartaric acid Tartaric acid

C4H6O6 C4H6O6⋅H2O

Tetrachloroethylene Tetryl

C2Cl4 C7H5N5O8

1 Tetryl + 1 picric acid 1 Tetryl + 2 TNT

C13H8N8O15 C21H15N11O20

Thymol Toluic acid (o-) (m-) (p-) Toluidine (p-)

C10H14O C8H8O2 C8H8O2 C8H8O2 C7H9N

Trichloroacetic acid Trimethyl carbinol Trinitrotoluene

C2HCl3O2 C4H10O C7H5N3O6

Trinitroxylene

C8H7N3O6

Triphenylmethane

C19H16

36 -150 -100 -50 0 +50 -40 to 0 -100 -50 0 +100 -100 to +100 -100 0 +50 0 to 49 54 to mp 54 to mp 130 to mp 0 20 40 solid -4 -100 -50 0 +100 -185 to +23 20 to 50 0 to 91

0.287 0.112 0.170 0.231 0.308 0.366 0.198 + 0.00018t 0.182 0.199 0.212 0.236 0.253 + 0.00072t 0.172 0.280 0.325 0.315 + 0.0031t 0.277 + 0.00120t 0.239 + 0.00195t 0.271 + 0.00106t 0.337 0.387 0.440 0.459 0.559 0.170 0.253 0.311 0.385 0.241 0.423 0.189 + 0.0027t

Urea

CH4N2O

20

0.320

TABLE 2-74 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to a Polynomial Cp [J/(kmol∙K)] Cmpd. no. 1 7 8 14 16 27 29 31 34 37 38 43 59 60 61 64 67 81 88 95 97 98 99 112 120 125 126 134 145 151 156 157 182 183 190 194 197 217 221 231 236 237 238 243 246 247 248 251

Name Acetaldehyde Acetylene Acrolein Argon Benzene Bromoethane 1,2-Butadiene Butane 1-Butanol cis-2-Butene trans-2-Butene 1-Butyne m-Cresol o-Cresol p-Cresol Cyclobutane Cyclohexanone 1,1-Dibromoethane 1,1-Dichloroethane Diethyl ether 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Dimethyl ether 1,4-Dioxane Ethane Ethanol Ethylcyclopentane Ethyl mercaptan Fluoroethane Furan Helium-4 Hydrazine Hydrogen Isopropyl amine Methanol Methyl acetylene Methylcyclopentane Methylethyl ether Methyl mercaptan 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene alpha-Methyl styrene Naphthalene Neon Nitroethane Nitromethane

Formula C2H4O C2H2 C3H4O Ar C6H6 C2H5Br C4H6 C4H10 C4H10O C4H8 C4H8 C4H6 C7H8O C7H8O C7H8O C4H8 C6H10O C2H4Br2 C2H4Cl2 C4H10O C2H4F2 C2H4F2 CH2F2 C2H6O C4H8O2 C2H6 C2H6O C7H14 C2H6S C2H5F C4H4O He H4N2 H2 C3H9N CH4O C3H4 C6H12 C3H8O CH4S C4H10 C4H10O C4H8 C9H10 C10H8 Ne C2H5NO2 CH3NO2

CAS 75-07-0 74-86-2 107-02-8 7440-37-1 71-43-2 74-96-4 590-19-2 106-97-8 71-36-3 590-18-1 624-64-6 107-00-6 108-39-4 95-48-7 106-44-5 287-23-0 108-94-1 557-91-5 75-34-3 60-29-7 75-37-6 624-72-6 75-10-5 115-10-6 123-91-1 74-84-0 64-17-5 1640-89-7 75-08-1 353-36-6 110-00-9 7440-59-7 302-01-2 1333-74-0 75-31-0 67-56-1 74-99-7 96-37-7 540-67-0 74-93-1 75-28-5 75-65-0 115-11-7 98-83-9 91-20-3 7440-01-9 79-24-3 75-52-5

Mol. wt. 44.05256 26.03728 56.06326 39.948 78.11184 108.965 54.09044 58.1222 74.1216 56.10632 56.10632 54.09044 108.13782 108.13782 108.13782 56.10632 98.143 187.86116 98.95916 74.1216 66.04997 66.04997 52.02339 46.06844 88.10512 30.069 46.06844 98.18606 62.13404 48.0595 68.07396 4.0026 32.04516 2.01588 59.11026 32.04186 40.06386 84.15948 60.09502 48.10746 58.1222 74.1216 56.10632 118.1757 128.17052 20.1797 75.0666 61.04002

C1 29705 30800 30702 20786 35978 27112 27400 17330 25300 39760 20908 25300 29002 16192 29090 31863 32182 20560 19560 26040 29736 27581 33851 25940 28345 31742 32585 34710 23014 30358 40860 20786 32998 64979 23590 30270 30810 35465 23337 31520 21380 17080 24970 37735 29120 20786 33055 38782

C2

C3

127.43 -53.08 80.95

-0.21793 0.384 0.191

-101.69 117.99 177.6 458.16 371.2 108.8 324.73 183.2 158.79 469.81 166 37.226 116.87 285.2 249.01 388 72.364 169.88 -20.966 178.46 88.3 26.567 87.4 304.96 271.36 62.839 -160.3

0.939

-5.2147 -788.17 310.42 84.64 35.8 147.38 309.03 60.1 271.2 381.7 211.8 112.94 82.88 89.54 -48.39

C4

C5

-0.816 -0.461 -0.411 0.635 -0.479 0.616 0.23616 0.547 -0.332 -0.22187 -0.268 0.228 -0.1581 0.17584 -0.186 0.446 0.12927 0.05 -0.084 -0.4427 0.1067 0.87 0.21379 5.8287 -0.274 -0.188 0.27 0.242 -0.285 -0.092 -0.199 0.846 0.964 0.238 0.413

-0.018459

2.164E-05

Tmin, K 50 50 50 100 50 100 50 50 50 50 50 50 50 50 50 50 50 100 100 50 50 50 50 50 50 50 50 50 50 50 100 100 50 50 50 50 50 50 50 50 50 50 50 50 50 100 50 50

Cp at Tmin 3.553E+04 2.911E+04 3.523E+04 2.079E+04 3.324E+04 3.891E+04 3.628E+04 3.820E+04 4.271E+04 4.520E+04 3.612E+04 3.446E+04 3.853E+04 3.849E+04 3.893E+04 3.431E+04 3.939E+04 4.576E+04 4.224E+04 4.477E+04 3.392E+04 3.568E+04 3.324E+04 3.440E+04 3.388E+04 3.339E+04 3.708E+04 4.975E+04 3.548E+04 3.377E+04 3.353E+04 2.079E+04 3.327E+04 3.797E+04 3.843E+04 3.403E+04 3.328E+04 4.344E+04 3.808E+04 3.453E+04 3.471E+04 3.567E+04 3.556E+04 4.550E+04 3.567E+04 2.079E+04 3.813E+04 3.740E+04

Tmax, K

Cp at Tmax

200 200 200 1500 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 1500 200 250 200 200 200 200 200 200 200 200 200 200 200 1500 200 200

4.647E+04 3.554E+04 5.453E+04 2.079E+04 5.320E+04 5.071E+04 6.292E+04 7.632E+04 8.110E+04 6.152E+04 6.941E+04 6.194E+04 8.616E+04 9.099E+04 8.693E+04 4.875E+04 7.744E+04 6.432E+04 6.049E+04 9.292E+04 5.333E+04 5.523E+04 3.669E+04 5.419E+04 6.385E+04 4.223E+04 5.207E+04 9.234E+04 5.958E+04 4.719E+04 4.360E+04 2.079E+04 4.051E+04 2.834E+04 7.471E+04 3.968E+04 4.877E+04 7.462E+04 7.374E+04 4.354E+04 7.194E+04 8.546E+04 6.733E+04 9.416E+04 8.426E+04 2.079E+04 6.048E+04 4.562E+04

2-147

(Continued)

2-148 TABLE 2-74 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to a Polynomial Cp [J/(kmol∙K)] (Continued ) Cmpd. no.

Name

253 289 290 294 295 296 304 310 320 321 322 324 331

Nitric oxide 2-Pentyne Phenanthrene Propadiene Propane 1-Propanol Propylbenzene Quinone Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene Thiophene 1,2,4-Trimethylbenzene

Formula NO C5H8 C14H10 C3H4 C3H8 C3H8O C9H12 C6H4O2 C4H8O C10H12 C4H8S C4H4S C9H12

CAS 10102-43-9 627-21-4 85-01-8 463-49-0 74-98-6 71-23-8 103-65-1 106-51-4 109-99-9 119-64-2 110-01-0 110-02-1 95-63-6

Mol. wt. 30.0061 68.11702 178.2292 40.06386 44.09562 60.09502 120.19158 108.09476 72.10572 132.20228 88.17132 84.13956 120.19158

C1 34980 24330 27700 31690 26675 28800 22880 29668 36970 28560 41195 36765 35652

C2 -35.32 335.7 210 17.1 147.04 257 538.46 129.07 -12.28 225.1 -88.3 -112.82 323.89

C3 0.07729 -0.37 1.24 0.282 -0.35 -0.546 0.53105 0.444 0.616 0.942 0.862 0.305

C4

C5

Tmin, K

-5.7357E-05

1.4526E-08

100 50 50 50 50 50 50 50 50 50 50 50 50

Cp at Tmin 3.216E+04 4.019E+04 4.130E+04 3.325E+04 3.403E+04 4.078E+04 4.844E+04 3.745E+04 3.747E+04 4.136E+04 3.914E+04 3.328E+04 5.261E+04

Tmax, K

Cp at Tmax

1500 200 200 200 200 200 200 200 200 200 200 200 200

3.586E+04 7.667E+04 1.193E+05 4.639E+04 5.608E+04 6.620E+04 1.087E+05 7.672E+04 5.227E+04 9.822E+04 6.122E+04 4.868E+04 1.126E+05

Constants in this table can be used in the following equation to calculate the ideal gas heat capacity C0p. C0p = C1 + C2T + C3T 2 + C4T 3 + C5T 4 where C 0p is in J/(kmol∙K) and T is in K. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties AIChE New York NY (2016)”.

TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)] Cmpd. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride

Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4

CAS

Mol. wt.

75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5

44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 153.8227

C1 × 1E-05

C2 × 1E-05

0.48251 1.06650 0.34200 1.29400 0.40200 1.36750 0.87998 1.66350 0.57040 1.63200 0.44346 0.84650 0.36921 0.31793 0.57019 0.91830 0.60590 1.37030 0.56303 1.09720 0.28958 0.09390 0.33427 0.48980 0.76370 2.93770 See Table 2-155 1.95810 1.70190 0.55238 1.73380 0.68950 2.32750 0.77594 2.64550 0.76820 2.26350 1.00990 4.48980 0.84115 3.14280 0.95210 2.88680 0.99192 2.96330 1.07590 4.21050 0.30113 0.08009 0.72100 2.06400 0.52310 0.89110 0.36241 0.69248 0.66964 1.09950 0.50950 1.70500 0.80154 1.62420 1.04780 2.54900 1.06600 2.57500 0.74540 2.59070 0.90878 2.55080 0.64257 2.06180 0.65121 1.43250 0.74296 1.34760 1.16840 3.76900 1.13800 4.45400 0.92478 2.77950 0.92367 2.51660 0.66492 1.07260 0.89240 1.56750 1.48800 1.35220 0.82142 1.32340 0.29370 0.34540 0.30100 0.33380 0.29108 0.08773 0.37582 0.70540

C3 × 1E-03

C4 × 1E-05

1.99290 1.07500 1.26200 0.80153 1.60700 1.63980 0.67805 0.76747 1.64750 0.91248 3.01200 2.03600 1.60510

0.78851 0.64000 0.70030 0.76076 0.96800 0.49487 0.33430 0.38554 1.04460 -0.44070 0.07580 0.22560 2.17000

1.32570 0.76425 1.51200 1.79250 0.74786 1.31100 1.95390 0.70207 1.55830 1.90410 0.75140 1.65040 0.81205 1.74540 0.83737 1.53240 0.84149 1.87760 1.96700 1.60730 1.89300 1.67680 0.85796 0.87025 1.95600 1.55070 1.68370 1.61090 0.79390 0.90190 1.14600 0.84021 1.42800 0.89600 3.08510 0.51210

-37.41700 0.72545 1.75160 2.23820 -0.67585 2.83950 2.57430 1.63850 2.21160 4.17850 0.10780 1.68700 0.67540 0.44781 0.68373 1.33700 1.05750 1.87500 1.95100 1.73200 1.85200 1.33240 0.89648 0.89116 2.81800 3.04970 1.59740 1.56410 0.74240 1.09840 -678.00000 0.67932 0.26400 0.28930 0.08455 0.48500

C5

Tmin, K

Cp at Tmin × 1E-05

912.78 502 569.7 2310.1 731.5 761.47 3036.6 2375.4 751.49 1178.4 1484 882 751.2

298.15 100 50 298.15 200 298.15 298.15 298.15 250 298.15 50 100 300

0.54732 0.34481 0.40200 1.10440 0.60487 0.52233 0.44032 0.71326 0.69837 0.64356 0.28958 0.33427 1.13020

1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200

1.29930 1.49970 1.57560 2.69700 1.88200 1.11990 0.75868 1.56240 1.74240 1.37940 0.34956 0.66465 3.02260

41.232 2445.7 697.9 835.9 896 627.4 850.06 2002.6 719.16 828.81 314.6 765.3 2809 793.32 2441.1 685.6 2476.1 833 860.5 712.4 832.13 757.06 2477.2 2463.4 811.2 708.86 758.68 739.2 -2458.4 2566 6.98 2313.7 588 374.7 1538.2 236.1

298.15 298.15 200 200 298 300 298.15 300 300 200 100 200 298.15 298.15 298.15 200 298.15 298.15 298.15 298.15 298.15 250 298.15 298.15 298.15 200 200 200 298.15 298.15 298.15 298.15 50 100 60 100

1.27450 0.82616 0.76894 0.81258 1.09070 1.80010 1.11980 1.55010 1.41560 1.14810 0.30901 0.76789 0.63800 0.42454 0.79668 0.57563 0.98586 1.26670 1.26790 1.07860 1.12570 0.75708 0.80241 0.87766 1.52810 1.26590 0.97140 0.97633 0.81441 1.02830 1.15330 0.97246 0.29370 0.31003 0.29108 0.47299

1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500.1 1500.15 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 5000 1500 1500 1500

3.25010 2.41800 2.67390 2.97120 2.68100 4.93110 3.28800 4.34450 3.29570 4.55570 0.37938 2.46280 1.54570 0.90758 1.92080 1.95550 2.66050 3.02890 3.03110 2.85090 2.87300 2.28980 2.27180 2.28360 3.67240 4.84350 3.10080 2.96150 1.92210 2.67780 2.59050 2.28510 0.63346 0.61475 0.35208 1.06620

Tmax, K

Cp at Tmax × 1E-05

2-149

(Continued)

2-150

TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)] (Continued ) Cmpd. no. 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

Name Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Diisopropyl amine Diisopropyl ether Diisopropyl ketone

Formula CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O

CAS

Mol. wt.

C1 × 1E-05

C2 × 1E-05

C3 × 1E-03

75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0

88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19 102.17476 114.18546

0.92004 0.29142 0.80110 0.52590 0.39420 0.36220 0.64710 0.61809 0.90974 0.79880 0.92021 1.08100 0.45894 0.50835 0.43200 0.90430 0.85860 0.58171 0.41600 0.48074 0.33800 0.54305 1.94250 1.67200 0.24457 1.69840 1.71010 1.93100 1.50450 0.30290 0.66622 0.74906 0.39100 1.61220 0.70000 0.69480 0.69780 0.63412 0.65271 0.36280 0.71450 0.78658 1.20800 0.91020 0.99953 0.91273 0.55477 0.57793 0.37540 1.13840 1.09300 1.08690

0.16446 0.09176 2.31000 1.40200 0.65730 0.69810 1.79800 1.80230 2.13210 2.85300 2.11060 3.79320 0.41286 1.64870 3.73500 2.57710 2.57770 3.17170 3.01400 2.51590 1.68940 3.99620 5.14030 5.35300 6.54600 5.39200 5.20890 5.48150 4.37940 0.09750 0.81703 1.27250 0.64800 4.47770 2.07460 2.08040 2.07800 0.83862 1.12540 0.68040 1.73440 1.74290 3.06600 2.67400 1.70380 2.41000 1.23610 0.89811 0.53510 2.57470 3.68300 4.05400

1.07640 0.94900 2.15700 2.03700 0.92800 1.80500 1.67600 1.54380 0.76324 1.47650 0.76622 1.75050 1.38120 0.82849 1.19200 0.78820 0.84895 1.54350 1.46170 1.58030 1.61350 1.35750 1.89780 1.61410 1.08990 1.56800 1.72650 1.60850 1.32910 2.51500 0.76285 1.98100 1.19400 1.68310 1.36640 1.36320 1.36350 0.76898 1.73760 1.25600 1.52400 1.71570 2.08900 1.71900 0.87072 1.66860 0.83501 0.84727 0.86687 0.73840 1.60570 1.78020

C4 × 1E-05 -5083.80000 0.10030 2.04600 0.99820 0.49300 0.44470 1.23300 1.18930 0.93355 2.04200 0.95073 3.00270 0.33023 0.86658 1.63500 1.30680 0.77780 2.12730 1.80950 1.74540 1.17680 2.56230 4.17520 3.78200 4.86420 3.93800 3.59350 3.74000 2.55570 -0.02750 0.40941 0.94370 0.42000 2.91800 1.59830 1.59400 1.59650 0.44030 0.87800 0.42750 1.22300 1.26270 2.34300 1.79260 1.07460 1.65200 -0.40972 0.43249 0.22998 1.62000 2.34200 2.97860

C5 2.3486 425 897.6 861.18 399.6 844.27 755.78 685.93 2474.5 664.7 2464.6 794.8 559.94 2472.4 530.1 1952.2 2401.5 701.62 668.8 718.37 722.8 618.54 859.95 742 424 720.5 782.92 754.75 632.01 368 2488.3 845.2 501 781.6 620.16 619.2 619.37 2533.2 795.45 548 674.2 765.1 891 794.94 2471.3 771.08 1033.4 2424.2 2437.2 2143 699 791.6

Tmin, K

Cp at Tmin × 1E-05

298 50 200 298.15 100 298.15 298.15 200 298.15 200 298.15 200 273.15 298.15 100 200 298.15 150 100 150 100 300 298.15 200 298.15 298.15 298.15 200 298 100 298.15 200 100 200 200 200 200 298.15 200 100 150 200 298.15 200 298.15 200 298.15 298.15 298.15 300 298.15 300

0.61055 0.29142 0.82193 0.62879 0.40484 0.41193 0.84674 0.67679 1.24780 0.91584 1.25080 1.14800 0.54968 0.70636 0.43657 0.96478 1.14170 0.59782 0.41650 0.49182 0.33813 1.26440 2.37630 1.79670 2.52320 2.43540 2.23040 2.04340 2.19380 0.30195 0.79599 0.76345 0.39288 1.68410 0.82450 0.81978 0.82283 0.76395 0.67221 0.36369 0.72683 0.82172 1.41970 0.95017 1.16950 0.95673 0.67988 0.67730 0.42969 1.59950 1.56690 1.51020

Tmax, K 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500.1 1500 1500 1500 1500 1500 1500 1500 1500 1500

Cp at Tmax × 1E-05 1.04650 0.37930 2.53270 1.55080 1.00630 0.90655 2.09750 2.10230 3.21580 3.21630 3.21320 4.18080 0.81268 2.32330 3.65160 3.82510 3.47740 3.21320 2.92980 2.56190 1.72130 3.72360 6.04070 6.09320 6.10990 6.21860 5.87450 6.46130 5.27940 0.34251 1.56840 1.70410 0.95987 5.21450 2.51610 2.51610 2.51750 1.56330 1.57430 0.95430 2.16090 2.18940 3.46740 3.05190 2.92630 2.87240 1.54560 1.55140 0.94201 4.19410 4.05350 4.30930

103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157

1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4

C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He

534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7

90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026

1.15560 1.01130 0.65340 0.55650 0.77720 1.07760 1.10390 1.09910 0.78430 0.57431 0.72200 0.85438 1.39600 0.61453 0.60370 0.69490 1.14025 0.68444 1.09850 1.21140 2.12950 3.24810 0.44256 0.49200 0.99810 0.59400 0.78440 1.09440 1.04550 1.11500 1.10590 0.93177 0.33380 0.72860 0.63012 0.34300 0.33460 0.53700 1.57770 1.63400 1.09530 1.24000 0.60436 0.93700 1.13200 0.96993 0.29122 0.73393 0.49090 0.35193 0.33503 0.38220 0.33810 0.43673 See Table 2-155

1.83050 3.23930 1.61790 1.63840 4.03200 4.67180 4.64450 4.64010 1.43640 0.94494 1.78300 4.57720 4.78000 1.74380 1.37470 1.52400 5.36801 1.98020 4.34120 2.61270 6.63300 11.09000 0.84737 1.45770 2.09310 1.61800 3.39900 4.17940 2.31480 3.39100 4.63060 2.79330 0.94790 1.84360 1.45840 1.42700 1.21160 1.88600 4.40170 4.51190 3.00320 3.20000 0.87524 2.82900 2.94000 1.08780 0.10132 2.37390 0.88880 0.65344 0.49394 0.93000 0.75930 1.28390

0.95919 1.56110 1.78370 1.73410 1.54400 1.65400 1.69430 1.66790 1.58360 0.89551 1.53200 1.51810 2.19000 1.34180 1.64100 1.65140 2.08860 0.82793 1.62220 0.78956 1.71550 1.63600 0.87224 1.66280 2.02260 1.81200 1.55900 0.88375 0.71000 1.67050 1.66280 0.78650 1.59600 1.68800 1.67300 1.63800 1.60840 1.20700 1.74940 1.75320 1.79880 1.96700 0.78662 1.64800 1.82700 0.70467 1.45300 2.30860 0.83107 1.13330 1.92800 1.84500 1.19250 0.74699

0.99605 2.15010 1.02420 1.08990 2.50800 3.33970 3.39490 3.37360 0.87100 0.65065 1.31000 2.97400 3.97050 1.01020 0.79880 1.06580 4.13440 0.90830 3.64550 1.69030 4.51610 7.45000 0.67130 0.93900 1.80300 1.07800 2.42600 -1.60900 1.47100 2.51800 3.29900 1.64590 0.55100 1.19900 0.97296 1.03700 0.82410 0.86400 3.23780 3.10320 2.13110 2.34600 0.62622 2.15500 2.05500 0.55556 0.09410 2.45890 0.54120 0.15240 0.29728 0.69000 0.31800 0.47541

2826.3 689.3 821.4 793.04 649.95 792.5 798.35 781.97 730.65 2467.4 762 641.01 900.6 592.09 743.5 722.2 809.837 2447.1 743.62 2394.4 777.5 726.27 2430.4 744.7 928.05 820 702 1183.1 2061.6 733.6 781.1 2303.3 740.8 767.3 773.65 744.7 737.3 496 792.34 809.75 817.35 896 –2190 724.7 852 2089.7 662.91 906.45 2446 5316.2 965.04 850 550 2500.6

298.15 298.15 200 200 200 200 200 200 200 298.15 200 200 300 200 200 200 298.15 298.15 300 300 200 200 298.15 273.15 200 200 200 300 300 298 200 298.15 60 300 300 150 50 100 298.15 298.15 298.15 298.15 298.15 300 298.15 298.15 50 200 298.15 100 298.15 150 50 298.15

1.27770 1.46380 0.67211 0.58115 0.93628 1.15350 1.17770 1.18200 0.81551 0.65866 0.75937 1.05500 1.74810 0.70950 0.62976 0.73547 1.67000 0.92284 1.72980 1.59000 2.24420 3.52350 0.52652 0.61172 1.01260 0.61390 0.89121 1.45980 1.51020 1.55830 1.18750 1.33350 0.33380 0.91775 0.77997 0.34798 0.33460 0.54118 2.02790 2.03600 1.36200 1.44790 0.73021 1.33770 1.35380 1.18910 0.29122 0.75730 0.59646 0.35193 0.35440 0.38326 0.33810 0.65450

1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200.15 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200 1200 1200 1500 1200 1500 1500 1500 1500 1500 6000 1500 1500 1500 1500

3.06780 3.66690 1.91480 1.85850 4.03530 4.95430 4.92430 4.92750 1.95230 1.65840 2.25960 4.59830 4.47400 2.09440 1.69490 1.92550 4.97220 2.81860 4.51430 4.24840 7.43250 12.21100 1.45610 1.65760 2.65940 1.85280 3.61470 4.25400 3.63300 3.62130 4.91840 4.14000 1.09870 2.20160 1.80950 1.51780 1.32970 2.14850 5.12010 4.87440 3.22890 3.42340 1.66280 3.05690 3.45350 2.21700 0.38122 2.50800 1.49880 1.05710 0.71121 1.12030 0.99328 1.79520

2-151

(Continued)

2-152

TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)] (Continued ) Cmpd. no. 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209

Name Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide

Formula C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S

CAS

Mol. wt.

C1 × 1E-05

629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5

240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214

2.78780 1.30930 1.20150 1.31350 1.22150 1.41060 1.27680 1.25070 1.18510 1.44200 1.07120 2.62830 1.18400 1.04400 1.16220 1.06250 1.26150 1.09400 1.12370 1.04340 0.93760 1.26620 0.91290 1.03600 0.41729 0.27617 0.29120 0.29157 0.30125 0.29134 0.33288 0.74694 0.79534 0.49522 0.72510 0.33298 0.39252 0.61160 0.55500 0.51734 0.12060 0.41000 0.93960 0.67100 0.74600 1.84580 0.92139 0.87026 0.81924 0.79060 0.82051 1.07850

C2 × 1E-05 9.52470 3.53810 4.00100 2.33170 3.99100 2.88580 3.38100 2.14800 3.63620 4.16030 3.02580 8.97330 3.07260 3.52300 2.07080 3.52100 3.59640 1.80700 2.93600 3.07490 3.01500 3.72940 2.55770 3.00900 0.54686 0.09560 0.09530 0.09048 0.31710 0.09325 0.26086 2.43560 1.44250 1.87180 2.08900 0.79933 0.87900 2.02900 1.78200 0.68157 2.37660 1.05780 2.55900 2.22200 3.26500 1.74300 3.33710 2.55560 2.60380 1.65600 3.08690 2.73880

C3 × 1E-03

C4 × 1E-05

C5

Tmin, K

Cp at Tmin × 1E-05

Tmax, K

Cp at Tmax × 1E-05

1.69350 1.52500 1.67660 0.67567 1.58000 0.80394 1.38310 0.69120 1.73590 1.66030 1.52730 1.69120 1.70770 1.69460 0.68661 1.58350 1.84450 0.68900 1.40100 1.74590 1.90570 1.65740 1.52900 2.11600 0.81130 2.46600 2.14200 2.09380 1.61020 2.90500 0.91340 1.71500 0.81831 1.29580 1.85160 2.08690 1.91650 1.76830 1.26000 0.80525 1.05430 1.70800 0.82500 1.42100 1.54500 1.22000 1.83610 1.77570 1.75930 1.69260 1.38640 1.58850

6.66510 2.23950 2.74000 1.82400 2.83500 1.49680 1.88800 1.61900 2.50480 2.65720 2.09750 6.26400 2.11740 2.36900 1.53550 2.46200 2.59400 1.47400 1.60100 2.07280 1.98600 2.30800 1.73700 2.10600 0.41755 0.03760 0.01570 -0.00107 0.21790 0.00195 -0.17979 1.84840 0.95493 1.48520 1.64830 0.41602 0.53654 1.33020 0.85300 0.51402 1.81860 0.68360 1.36000 1.19400 1.92300 -56.11000 2.46440 1.76360 1.71950 1.21670 1.78860 1.90670

744.57 740.37 756.4 1846 717.7 2456.1 650.3 1759.3 785.73 759.39 689.62 744.41 790.64 761.6 1932.5 715.75 819.17 1772 650.5 793.53 817 757.8 683 902.4 2639.2 567.6 1400 120 626 1326 949.4 757.75 2499.9 569.96 798.43 991.96 896.7 835.5 562 2463.8 418.8 735 3000 614.7 666.7 31.2 757.83 807.82 800.93 788.4 613.87 749.6

200 298.15 200 300 298.15 298.15 200 150 298.15 200 200 200 298.15 200 298.15 298.15 298.15 200 150 298 300 200 200 300 298.15 250 50 50 100 50 100 298.15 298.15 300 298.15 50 273.15 300 298 298.15 298.15 150 300 150 200 300 298.15 200 200 298.15 300 273.15

3.00340 1.70230 1.28280 1.84970 1.75720 1.79590 1.39680 1.26880 1.54340 1.51910 1.17210 2.83120 1.48160 1.11170 1.61070 1.53110 1.58290 1.18150 1.14430 1.33010 1.19090 1.33400 1.00040 1.22150 0.48803 0.28426 0.29120 0.29137 0.30137 0.29134 0.33288 1.04270 0.97640 0.97903 0.94749 0.33298 0.42513 0.76980 0.84891 0.60784 0.99083 0.41364 1.25860 0.69311 0.85462 1.27930 1.31350 0.90596 0.85589 0.96319 1.33000 1.31730

1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1200.1 1500 1500 1500 1500 1500 1200.1 1500 1200 1500 1500 1500 1500 1500 1500 1500.15 1200 1200

10.41600 4.27590 4.42830 4.29410 4.53460 4.59900 4.13860 3.84460 4.08360 4.78310 3.59850 9.81820 3.66440 3.86200 3.76360 3.97260 4.06720 3.32070 3.58740 3.48190 3.18890 4.24830 3.03710 3.18940 1.05830 0.32248 0.34786 0.34063 0.55224 0.32243 0.51432 2.53830 2.45580 2.14970 2.20570 0.88904 1.05330 2.22090 2.07540 1.33000 2.16630 1.23880 3.35690 2.50280 3.37920 3.22620 3.48560 2.89230 2.87090 2.15020 3.19940 3.16870

210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263

3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane

C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F 3N CH3NO2 N 2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38

598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3

68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432

0.82740 0.89400 0.59895 0.92270 0.79590 0.92279 0.92279 0.78439 0.69411 0.64220 0.72830 0.79188 0.78400 0.75083 0.50600 0.72840 1.22700 0.47400 0.89232 1.59140 0.99247 0.43697 0.86400 1.74830 0.90300 0.94326 0.76394 0.90658 0.73226 0.77650 0.92151 0.93775 0.46149 1.00010 0.98059 0.60865 0.89232 See Table 2-155 0.64084 0.29105 0.33284 0.47876 0.29338 See Table 2-155 3.10620 1.71190 1.51750 0.12660 1.54000 1.81180 1.53520 1.76460 1.62890 2.95020

2.13770 2.91000 1.16360 4.11500 2.59600 2.67090 2.67090 2.50070 3.02090 3.07110 1.03070 1.31660 2.10320 1.95770 1.21900 3.17130 2.19500 1.22600 2.47650 1.76400 2.72750 0.50387 1.81100 4.92880 3.80100 3.59650 1.68020 1.71370 1.36060 2.44200 2.39430 2.61780 1.27810 2.65370 3.08940 1.59650 2.67720

1.75500 1.57000 1.56500 1.65040 0.62130 0.68784 0.68784 0.81937 1.69030 1.63870 1.54290 0.87136 1.54880 1.64240 1.63700 1.35200 0.84200 2.18800 1.69600 1.20760 2.00300 0.80924 0.75430 1.73840 1.60200 1.35330 0.82654 0.80201 0.84872 1.71400 1.69360 1.72910 1.45650 0.77176 1.64560 1.61900 0.76122

1.51490 2.07300 0.81581 2.90060 2.28800 1.98470 1.98470 1.30010 2.12090 2.12980 0.78110 0.86597 1.18550 1.19490 0.89400 1.89480 1.19100 0.85983 1.55980 -407.40000 1.89740 0.42223 0.80000 3.58970 2.45300 2.05690 1.02850 1.04240 0.88667 1.81800 1.48960 1.62360 0.79115 1.11620 2.09850 0.93783 1.02010

782 678.3 690.39 779.48 1698.6 1732.4 1732.4 2416.4 781.56 750.25 668.94 2468 693 749.19 743 585.14 2460 1008.2 791.4 10.503 849.64 2192.4 2160 788.01 691.6 599.92 2483.1 2489.7 2499.8 716 797.79 783.23 643.23 2405.2 732.6 739.55 2435.5

200 298 200 200 300 300 300 298.15 200 200 200 298.15 200 273.16 250 300 298.15 298.15 200 300 273 298.15 298.15 298.15 200 300 298.15 298.15 298.15 300 298 298.15 200 298.15 298.15 300 298.15

0.86459 1.34610 0.63795 0.99530 1.53020 1.50990 1.50990 1.09680 0.74637 0.70833 0.77172 0.92283 0.83967 0.90040 0.58880 1.32000 1.47550 0.51946 0.92804 1.12910 1.13770 0.50277 1.16210 2.25670 1.01920 1.56000 0.96745 1.13730 0.88184 1.12420 1.12510 1.17280 0.51411 1.40620 1.35330 0.77480 1.32040

1500 1200 1500 1500 1200 1200 1200 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500.15 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1200 1200 1500 1500 1500 1500 1500 1500

2.52550 3.07660 1.55930 4.31800 4.13590 4.14670 4.14670 3.54830 3.14960 3.15490 1.58930 2.29440 2.48160 2.31780 1.51090 3.19870 3.65320 1.35950 2.86960 2.99910 2.99520 1.06940 2.86370 5.71770 3.96170 3.74090 2.66680 2.85290 2.28420 2.52760 2.63910 2.99040 1.52530 3.86080 3.47810 1.88710 3.73860

1.16310 0.08615 0.49837 0.78357 0.32360

0.80970 1.70160 0.70930 0.82960 1.12380

0.59591 0.00103 0.23264 0.37215 0.21770

2425.6 909.79 372.91 2433.8 479.4

298.15 50 100 298.15 100

0.79235 0.29105 0.34036 0.57242 0.29475

1500 1500 1500 1500 1500

1.92450 0.34838 0.80919 1.32860 0.58278

10.57500 4.50580 4.91500 6.01100 4.93600 3.59270 4.68440 5.04400 3.97080 10.03400

0.76791 1.71000 1.64480 1.08150 1.57800 0.81841 1.72880 1.61820 1.89280 0.77107

-4.56610 3.36580 3.47000 4.59460 3.58800 2.17920 3.23040 3.38570 3.21360 -4.30120

912.03 807.38 749.6 418.2 721.11 2550.1 783.67 755.48 855.52 916.73

200 298.15 200 298.15 298.15 298.15 298.15 200 298.15 200

3.35330 2.15310 1.62570 2.29530 2.20920 2.26250 2.00140 1.86580 1.96930 3.18000

1500 1500 1500 1500 1500 1500 1500 1500 1500 1500

11.61300 5.42420 5.54070 5.52670 5.66060 5.85550 5.27760 5.90820 4.79240 11.01600

2-153

(Continued)

2-154 TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)] (Continued ) Cmpd. no. 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305

Name Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene

Formula C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6

CAS

Mol. wt.

C1 × 1E-05

C2 × 1E-05

C3 × 1E-03

124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1

128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974

1.59550 1.35540 1.40820 1.38050 1.58030 1.39010 1.49520 1.35990 1.59810 1.23070 0.56777 0.29103 0.33483 2.46790 1.06000 0.88050 2.83600 0.90600 1.08530 0.90053 0.96896 0.82523 1.13270 1.09740 0.75300 0.82096 1.27200 0.43400 0.59683 0.73640 0.48308 0.59474 0.61900 0.73145 1.05630 0.71306 0.69590 0.52525 1.79940 0.76078 1.13460 0.43852

3.14670 4.43100 4.34360 4.45900 3.23480 3.80600 4.41030 4.16050 4.60630 3.49420 1.11940 0.10040 0.29577 8.42120 2.85000 3.01100 1.08000 3.06200 3.07470 2.70850 2.49070 2.59430 2.94700 3.29590 2.09050 1.46770 3.56890 2.44500 2.55330 2.54400 0.73665 1.26610 2.02130 2.03130 4.33970 1.16890 1.77780 1.46630 1.75300 2.10490 2.80980 1.50600

0.85788 1.63560 1.46620 1.57510 0.79814 1.37170 0.80211 1.73170 1.62950 1.52800 0.62070 2.52650 1.52170 1.68650 1.93000 1.65020 2.10700 1.60540 1.86720 1.65920 1.41770 1.72910 1.74180 1.67610 1.53070 0.84463 0.75021 1.15200 1.23970 1.08520 0.78152 0.84431 1.62930 1.93750 1.60980 0.92731 1.70980 1.54760 1.19600 1.72560 0.79504 1.39880

C4 × 1E-05 1.47130 3.05400 2.76870 3.20160 1.78820 2.25730 -2.09580 2.86750 3.03010 2.46170 -0.38079 0.09356 0.27151 5.85370 2.01000 1.89200 -3.56000 2.11500 2.22710 1.80120 1.30100 1.76800 2.09870 1.94860 1.37800 0.96258 1.32990 1.51200 1.55190 0.80800 0.48698 0.86165 1.29560 1.48150 3.18100 1.02100 1.26540 0.93033 -4.12000 1.39360 1.23760 0.74754

C5

Tmin, K

Cp at Tmin × 1E-05

Tmax, K

Cp at Tmax × 1E-05

2679.4 746.4 659.38 718.8 2434.3 660.96 981.95 784.47 756.28 694.81 676.72 1153.8 680.35 743.6 879.23 747.6 283 717.97 825.4 743.96 646.7 778.7 795.78 757.67 672.8 2452.3 2409.4 507 576.78 573 2480 2482.7 727.4 843.37 729.66 2512.8 763.78 674.15 108.2 789.03 2449.5 616.46

298.15 200 298.15 298.15 298.15 150 200 298.15 200 200 298.15 50 100 200 298.15 200 298.15 298.15 298.15 200 200 298.15 298 200 200 298.15 298.15 100 298.15 298.15 298.15 298.15 298.15 298.15 300 298.15 298.15 298.15 298.15 200 298.15 130

1.92770 1.45290 2.06520 1.98320 2.02310 1.41620 1.57750 1.77230 1.68810 1.34480 0.79711 0.29103 0.33489 2.65860 1.25200 0.94039 1.38240 1.30440 1.35390 0.95908 1.05360 1.08560 1.42020 1.15470 0.82759 0.98524 1.86940 0.44014 1.10540 1.07450 0.59127 0.73665 0.85428 0.89664 1.63920 0.80337 0.89382 0.73244 1.35940 0.79326 1.52430 0.44363

1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1000.15 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500

4.91940 4.97640 5.04110 5.09650 5.20600 4.65470 4.90670 4.68070 5.35490 4.16040 1.56180 0.36533 0.59282 9.22090 3.24590 3.29270 3.29520 3.41330 3.47010 3.07970 3.03580 2.88970 3.49940 3.69560 2.47540 2.50600 5.06820 2.60450 2.83900 2.67370 1.33810 2.05600 2.24580 2.27600 4.65270 2.11890 2.12480 1.72030 3.20240 2.43530 4.16280 1.68170

306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345

Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene

C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O 2S F 6S O 3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10

110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3

88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165

0.87100 0.73815 0.74740 2.01140 0.80992 0.36810 0.89300 0.71806 0.33375 0.35256 0.33408 1.00130 2.07190 2.30820 0.54850 1.05550 0.65341 1.13520 0.48694 0.58140 0.66554 2.14960 1.27660 0.71070 1.05200 1.22100 1.13900 0.98200 2.03670 2.15400 1.95290 1.85900 0.53600 0.55978 0.42364 0.84894 0.33363 0.75680 0.85210 0.75120

2.44700 1.95290 1.95230 0.80820 1.57510 0.71245 2.15030 2.26690 0.25864 1.22700 0.49677 2.61780 6.26680 7.86780 1.84910 3.21010 1.71150 5.63310 1.23760 2.86300 1.12570 7.30450 2.55590 1.50510 3.79000 2.68650 5.28600 5.40200 1.81810 2.44320 6.09980 5.86900 2.11900 1.21410 0.87350 1.14710 0.26790 3.39240 3.29540 3.39700

1.92540 1.59540 1.63100 1.86560 0.74707 0.65201 0.77200 1.27390 0.93280 0.67938 0.87322 0.87239 2.40440 1.68230 0.83310 0.78248 0.77705 1.62110 0.71271 1.44060 1.54540 1.66950 0.80937 0.79662 1.48140 0.82886 1.59400 1.53100 1.20890 1.11260 1.70870 1.57180 1.19800 1.61020 1.64920 1.38000 2.61050 1.49600 1.49440 1.49280

1.88800 1.23560 1.21120 -2.44040 0.60196 0.46721 0.99900 1.73420 0.10880 0.78407 0.28563 1.28310 6.34500 5.44860 0.89089 1.43950 0.91824 3.38290 0.47248 1.89800 0.97196 4.99980 1.48290 0.84537 2.33100 1.42030 3.35100 3.49300 0.79777 0.58651 4.13020 4.32600 1.14700 0.89079 0.65560 0.90000 0.08896 2.24700 2.11500 2.24700

821.3 730.5 750.92 279.98 2344.9 286.03 2442 537.65 423.7 351.27 393.74 3521.5 967.71 743.1 2458.5 2433 2432.6 681.9 2484.2 650.43 717.04 741.02 2231.7 2187.6 667.3 2443 677.94 639.9 1060.8 950.59 775.4 722.7 510 710.4 739.07 644.61 1169 675.9 675.8 675.1

298.15 200 200 298.15 298.15 100 100 300 100 100 100 298.15 298.15 200 298.15 298.15 298.15 200 298.15 200 298.15 200 200 200 200 298.15 200 200 298.15 298.15 200 298.15 100 200 200 298.15 100 200 200 200

1.10220 0.78247 0.78483 1.02180 1.07700 0.41815 0.89310 1.33700 0.33538 0.38719 0.34081 1.26040 2.47630 2.48640 0.76617 1.52510 0.90956 1.30690 0.72827 0.70157 0.84963 2.31560 1.32780 0.74387 1.18320 1.54310 1.31390 1.21940 2.10540 2.27260 2.05940 2.66140 0.54044 0.59670 0.44572 1.07540 0.33363 0.87588 0.96428 0.87096

1500 1500 1500 1000.15 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 2273.15 1500 1500 1500

2.74840 2.32870 2.32160 2.11750 2.49790 1.05370 3.24160 2.58230 0.56950 1.53970 0.79673 3.59670 6.69470 8.62250 2.55380 4.53700 2.56890 5.57840 1.81130 3.00290 1.64330 8.02510 4.20460 2.43220 4.19830 4.18780 5.37690 5.37540 3.75850 4.35600 6.83420 6.78340 2.37500 1.55900 1.14230 1.85950 0.52760 3.59200 3.59650 3.59230

Constants in this table can be used in the following equation to calculate the ideal gas heat capacity C0p. C0p = C1 + C2[C3/T/sinh(C3/T)]2 + C4[C5/T/cosh(C5/T)]2 where C0p is in J/(kmol∙K) and T is in K. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.

2-155

2-156

PHYSICAL AnD CHEMICAL DATA

TABLE 2-76 Cp/Cv: Ratios of Specific Heats of Gases at 1 atm Pressure*

Compound

Formula

Acetaldehyde Acetic acid Acetylene

C2H4O C2H4O2 C2H2

Air

Ammonia Argon

NH3 Ar

Temperature, °C

Ratio of specific heats, (γ) = Cp /Cv

30 136 15 -71 925 17 -78 -118 15 15 -180 0–100

1.14 1.15 1.26 1.31 1.36 1.403 1.408 1.415 1.320 1.670 1.715 1.67

Benzene Bromine

C6H6 Br2

90 20–350

1.10 1.32

Carbon dioxide

CO2

disulfide monoxide

CS2 CO

1.299 1.37 1.21 1.402 1.433 1.355 1.15 1.256 1.315

Chlorine Chloroform Cyanogen Cyclohexane

Cl2 CHCl3 (CN)2 C6H12

15 -75 100 15 -180 15 100 15 80

Dichlorodifluormethane

CCl2F2

25

1.139

Ethane

C2H6

Ethyl alcohol ether

C2H6O C4H10O

Ethylene

C2H4

100 15 -82 90 35 80 100 15 -91

1.157 1.200 1.28 1.13 1.08 1.086 1.201 1.253 1.345

Helium Hexane (n-) Hydrogen

He C6H14 H2

-180 80 15 -76 -181 20 15 100 65 140 210

1.667 1.066 1.407 1.441 1.607 1.42 1.41 1.40 1.31 1.28 1.24

bromide chloride

HBr HCl

cyanide

HCN

Compound

Formula

Hydrogen (Cont.) iodide sulfide

HI H 2S

Iodine Isobutane

I2 C4H10

Krypton

Kr

Mercury Methane

Hg CH4

Methyl acetate alcohol ether Methylal

C3H6O2 CH4O C2H6O C3H8O2

Neon Nitric oxide

Ne NO

Nitrogen

N2

Nitrous oxide

N2O

Oxygen

O2

Pentane (n-) Phosphorus Potassium

C5H12 P K

Sodium Sulfur dioxide

Na SO2

Xenon

Xe

Temperature, °C

Ratio of specific heats, (γ) = Cp /Cv

20–100 15 -45 -57

1.40 1.332 1.350 1.356

185 15

1.30 1.110

19

1.672

360 600 300 15 -80 -115 15 77 6–30 13 40

1.67 1.113 1.196 1.310 1.339 1.347 1.14 1.237 1.11 1.06 1.09

19 15 -45 -80 15 -181 100 15 -30 -70

1.667 1.400 1.39 1.38 1.402 1.433 1.28 1.303 1.31 1.34

15 -76 -181

1.398 1.405 1.439

86 300 850

1.071 1.17 1.77

750–920 15

1.68 1.290

19

1.678

*For compounds that appear in Tables 2-109 to 2-122, values are from E. W. Lemmon, M. O. McLinden, and D. G. Friend, “Thermophysical Properties of Fluid Systems” in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds. P. J. Linstrom and W. G. Mallard, June 2005, National Institute of Standards and Technology, Gaithersburg, Md. (http://webbook.nist.gov). Values for other compounds are from International Critical Tables, vol. 5, pp. 80–82.

SPECIFIC HEATS OF AQUEOUS SOLUTIOnS

TABLE 2-79 Ethyl Alcohol

Additional References Most of the tables below are from International Critical Tables, vol. 5, pp. 115–116, 122–125. Specific heats for other compounds in aqueous solution can also be found in the same reference. TABLE 2-77 Acetic Acid (at 38çC) Mole % acetic acid Cal/(g⋅°C)

0 1.0

6.98 0.911

30.9 0.73

54.5 0.631

100 0.535

Specific heat, cal/(g⋅°C) Mole % C2H5OH

3°C

23°C

41°C

4.16 11.5 37.0 61.0 100.0

1.05 1.02 0.805 0.67 0.54

1.02 1.03 0.86 0.727 0.577

1.02 1.03 0.875 0.748 0.621

TABLE 2-80

TABLE 2-78 Ammonia

Glycerol Specific heat, cal/(g⋅°C)

Specific heat, cal/(g⋅°C) Mole % NH3

2.4°C

20.6°C

41°C

61°C

0 10.5 20.9 31.2 41.4

1.01 0.98 0.96 0.956 0.985

1.0 0.995 0.99 1.0

0.995 1.06 1.03

1.0 1.02

Mole % C3H5(OH)3

15°C

32°C

2.12 4.66 11.5 22.7 43.9 100.0

0.961 0.929 0.851 0.765 0.67 0.555

0.960 0.924 0.841 0.758 0.672 0.576

SPECIFIC HEATS TABLE 2-81 Hydrochloric Acid

TABLE 2-86 Potassium Hydroxide (at 19çC)

Specific heat, cal/(g⋅°C) Mole % HCl 0.0 9.09 16.7 20.0 25.9

2-157

0°C

10°C

20°C

40°C

60°C

1.00 0.72 0.61 0.58 0.55

0.72 0.605 0.575

0.74 0.631 0.591

0.75 0.645 0.615

0.78 0.67 0.638 0.61

TABLE 2-82 Methyl Alcohol Specific heat, cal/(g⋅°C) Mole % CH3OH

5°C

20°C

40°C

5.88 12.3 27.3 45.8 69.6 100

1.02 0.975 0.877 0.776 0.681 0.576

1.0 0.982 0.917 0.811 0.708 0.60

0.995 0.98 0.92 0.83 0.726 0.617

Specific heat at 20°C, cal/(g⋅°C)

0 10 20 30 40 50 60 70 80 90

1.000 0.900 0.810 0.730 0.675 0.650 0.640 0.615 0.575 0.515

0 1.0

0.497 0.975

1.64 0.93

4.76 0.814

9.09 0.75

TABLE 2-87 normal Propyl Alcohol Specific heat, cal/(g⋅°C) Mole % C3H7OH

5°C

20°C

40°C

1.55 5.03 11.4 23.1 41.2 73.0 100.0

1.03 1.07 1.035 0.877 0.75 0.612 0.534

1.02 1.06 1.032 0.90 0.78 0.645 0.57

1.01 1.03 0.99 0.91 0.815 0.708 0.621

TABLE 2-88 Sodium Carbonate* Temperature, °C

% Na2CO3 by weight 0.000 1.498 2.000 2.901 4.000 5.000 6.000 8.000 10.000 13.790 13.840 20.000 25.000

TABLE 2-83 nitric Acid % HNO3 by Weight

Mole % KOH Cal/(g⋅°C)

17.6

30.0

76.6

98.0

0.9992 0.9807

0.9986

1.0098

1.0084

0.9786 0.9597 0.9594 0.9428

0.9761 0.9392

0.9183 0.9086 0.8924

0.9452 0.8881 0.8631

0.8936 0.8615

0.8911

*J. Chem. Soc. 3062–3079 (1931).

TABLE 2-89 Sodium Chloride Specific heat, cal/(g⋅°C) TABLE 2-84 Phosphoric Acid*

Mole % NaCl

%H2PO4

Cp at 21.3°C cal/(g⋅°C)

%H3PO4

Cp at 21.3°C cal/(g⋅°C)

2.50 3.80 5.33 8.81 10.27 14.39 16.23 19.99 22.10 24.56 25.98 28.15 29.96 32.09 33.95 36.26 38.10 40.10 42.08 44.11 46.22 48.16 49.79

0.9903 0.9970 0.9669 0.9389 0.9293 0.8958 0.8796 0.8489 0.8300 0.8125 0.8004 0.7856 0.7735 0.7590 0.7432 0.7270 0.7160 0.7024 0.6877 0.6748 0.6607 0.6475 0.6370

50.00 52.19 53.72 56.04 58.06 60.23 62.10 64.14 66.13 68.14 69.97 69.50 71.88 73.71 75.79 77.69 79.54 80.00 82.00 84.00 85.98 88.01 89.72

0.6350 0.6220 0.6113 0.5972 0.5831 0.5704 0.5603 0.5460 0.5349 0.5242 0.5157 0.5160 0.5046 0.4940 0.4847 0.4786 0.4680 0.4686 0.4593 0.4500 0.4419 0.4359 0.4206

*Z. Physik. Chem., A167, 42 (1933).

TABLE 2-85 Potassium Chloride Specific heat, cal/(g⋅°C) Mole % KCl

6°C

20°C

33°C

40°C

0.99 3.85 5.66 7.41

0.945 0.828 0.77

0.947 0.831 0.775 0.727

0.947 0.835 0.778

0.947 0.837 0.775

0.249 0.99 2.44 9.09

6°C

20°C

33°C

57°C

0.96 0.91 0.805

0.99 0.97 0.915 0.81

0.97 0.915 0.81

0.923 0.82

TABLE 2-90 Sodium Hydroxide (at 20çC) Mole % NaOH Cal/(g . °C)

0 1.0

0.5 0.985

1.0 0.97

9.09 0.835

16.7 0.80

28.6 0.784

37.5 0.782

TABLE 2-91 Sulfuric Acid* %H2SO4

Cp at 20°C, cal/(g⋅°C)

%H2SO4

Cp at 20°C, cal/(g⋅°C)

0.34 0.68 1.34 2.65 3.50 5.16 9.82 15.36 21.40 22.27 23.22 24.25 25.39 26.63 28.00 29.52 30.34 31.20 33.11

0.9968 0.9937 0.9877 0.9762 0.9688 0.9549 0.9177 0.8767 0.8339 0.8275 0.8205 0.8127 0.8041 0.7945 0.7837 0.7717 0.7647 0.7579 0.7422

35.25 37.69 40.49 43.75 47.57 52.13 57.65 64.47 73.13 77.91 81.33 82.49 84.48 85.48 89.36 91.81 94.82 97.44 100.00

0.7238 .7023 .6770 .6476 .6153 .5801 .5420 .5012 .4628 .4518 .4481 .4467 .4408 .4346 .4016 .3787 .3554 .3404 .3352

*Vinal and Craig, Bur. Standards J. Research, 24, 475 (1940).

2-158

PHYSICAL AnD CHEMICAL DATA

SPECIFIC HEATS OF MISCELLAnEOUS MATERIALS TABLE 2-92 Specific Heats of Miscellaneous Liquids and Solids Material Alumina Alundum Asbestos Asphalt Bakelite Brickwork Carbon (gas retort) (see under Graphite) Cellulose Cement, Portland Clinker Charcoal (wood) Chrome brick Clay Coal tar oils Coal tars Coke Concrete Cryolite Diamond Fireclay brick Fluorspar Gasoline Glass (crown) ( flint) (pyrex) (silicate) wool Granite Graphite Gypsum Kerosene Limestone Litharge Magnesia Magnesite brick Marble Porcelain, fired Berlin Porcelain, green Berlin Porcelain, fired earthenware Porcelain, green earthenware

Specific heat, cal/(g⋅°C) 0.2 (100°C); 0.274 (1500°C) 0.186 (100°C) 0.25 0.22 0.3 to 0.4 About 0.2 0.168 (26 to 76°C) 0.314 (40 to 892°C) 0.387 (56 to 1450°C) 0.204 0.32 0.186 0.242 0.17 0.224 0.26 to 0.37 0.34 (15 to 90°C) 0.35 (40°C); 0.45 (200°C) 0.265 (21 to 400°C) 0.359 (21 to 800°C) 0.403 (21 to 1300°C) 0.156 (70 to 312°F); 0.219 (72 to 1472°F) 0.253 (16 to 55°C) 0.147 0.198 (100°C); 0.298 (1500°C) 0.21 (30°C) 0.53 0.16 to 0.20 0.117 0.20 0.188 to 0.204 (0 to 100°C) 0.24 to 0.26 (0 to 700°C) 0.157 0.20 (20 to 100°C) 0.165 (26 to 76°C); 0.390 (56 to 1450°C) 0.259 (16 to 46°C) 0.47 0.217 0.055 0.234 (100°C); 0.188 (1500°C) 0.222 (100°C); 0.195 (1500°C) 0.21 (18°C) 0.189 (60°C) 0.185 (60°C) 0.186 (60°C) 0.181 (60°C)

TABLE 2-92 Specific Heats of Miscellaneous Liquids and Solids (Continued ) Material

Specific heat, cal/(g⋅°C)

Pyrex glass Pyrites (copper) Pyrites (iron) Pyroxylin plastics Quartz Rubber (vulcanized) Sand Silica Silica brick Silicon carbide brick Silk Steel Stone Stoneware (common) Turpentine Wood (Oak) Woods, miscellaneous Wool Zirconium oxide

0.20 0.131 (30°C) 0.136 (30°C) 0.34 to 0.38 0.17 (0°C); 0.28 (350°C) 0.415 0.191 0.316 0.202 (100°C); 0.195 (1500°C) 0.202 (100°C) 0.33 0.12 about 0.2 0.188 (60°C) 0.42 (18°C) 0.570 0.45 to 0.65 0.325 0.11 (100°C); 0.179 (1500°C)

TABLE 2-93 Oils (Animal, Vegetable, Mineral Oils)

Cp[cal/(g⋅°C)] = A / d 415 + B(t - 15) where d = density, g/cm3. °F = 9⁄5°C + 32; to convert calories per gram-degree Celsius to British thermal units per pound-degree Fahrenheit, multiply by 1.0; to convert grams per cubic centimeter to pounds per cubic foot, multiply by 62.43. Oils

A

Castor Citron Fatty drying nondrying semidrying oils (except castor) Naphthene base Olive Paraffin base Petroleum oils

0.500 0.440 0.450 0.445 0.450 0.405 0.425 0.415

B 0.0007 (0.438 at 54°C) 0.0007 0.0007 0.0007 0.0007 0.0009 (0.47 at 7°C) 0.0009 0.0009

PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS Unit Conversions °F = 9⁄5°C + 32; to convert kilocalories per gram-mole to British thermal units per pound-mole, multiply by 1.799 × 10-3.

PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS

2-159

TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds* The values given in the following table for the heats and free energies of formation of inorganic compounds are derived from (a) Bichowsky and Rossini, “Thermochemistry of the Chemical Substances,” Reinhold, New York, 1936; (b) Latimer, “Oxidation States of the Elements and Their Potentials in Aqueous Solution,” Prentice-Hall, New York, 1938; (c) the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards; and (d) the tables of Selected Values of Chemical Thermodynamic Properties of the National Bureau of Standards. The reader is referred to the preceding books and tables for additional details as to methods of calculation, standard states, and so on.

State†

Compound Aluminum Al AlBr3 Al4C3 AlCl3 AlF3 AlI3 AlN Al(NH4)(SO4)2 Al(NH4)(SO4)2⋅12H2O Al(NO3)3⋅6H2O Al(NO3)3⋅9H2O Al2O3 Al(OH)3 Al2O3⋅SiO2 Al2O3⋅SiO2 Al2O3⋅SiO2 3Al2O3⋅2SiO2 Al2S3 Al2(SO4)3 Al2(SO4)3⋅6H2O Al2(SO4)3⋅18H2O Antimony Sb SbBr3 SbCl3 SbCl5 SbF3 SbI3 Sb2O3 Sb2O4 Sb2O5 Sb2S3 Arsenic As AsBr3 AsCl3 AsF3 AsH3 AsI3 As2O3 As2O5 As2S3 Barium Ba BaBr2 BaCl2 Ba(ClO3)2 Ba(ClO4)2 Ba(CN)2 Ba(CNO)2 BaCN2 BaCO3 BaCrO4 BaF2 BaH2 Ba(HCO3)2 BaI2

c c aq c c aq, 600 c aq c aq c c c c c c, corundum c c, sillimanite c, disthene c, andalusite c, mullite c c aq c c

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol 0.00 -123.4 -209.5 -30.8 -163.8 -243.9 -329 -360.8 -72.8 -163.4 -57.7 -561.19 -1419.36 -680.89 -897.59 -399.09 -304.8 -648.7 -642.4 -642.0 -1874 -121.6 -820.99 -893.9 -1268.15 -2120

c c c l c c c, I, orthorhombic c, II, octahedral c c c, black

0.00 -59.9 -91.3 -104.8 -216.6 -22.8 -165.4 -166.6 -213.0 -230.0 -38.2

c c l l g c c c c amorphous

0.00 -45.9 -80.2 -223.76 43.6 -13.6 -154.1 -217.9 -20 -34.76

c c aq, 400 c aq, 300 c aq, 1600 c aq, 800 c c aq c c, witherite c c aq, 1600 c aq c aq, 400

0.00 -180.38 -185.67 -205.25 -207.92 -176.6 -170.0 -210.2

*For footnotes see end of table.

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol 0.00 -189.2 -29.0 -209.5 -312.6 -152.5 -50.4 -486.17 -1179.26 -526.32 -376.87 -272.9

-739.53 -759.3 -1103.39 0.00 -77.8

-146.0 -186.6 -196.1 -36.9 0.00 -70.5 -212.27 37.7 -134.8 -183.9 -20 0.00 -183.0 -196.5 -134.4 -155.3

-63.6 -284.2 -342.2 -287.9 -284.6 -40.8 -459 -144.6 -155.17

BaMoO4 Ba3N2 Ba(NO2)2 Ba(NO3)2 BaO Ba(OH)2 BaO⋅SiO2 Ba3(PO4)2 BaPtCl6 BaS BaSO3 BaSO4 BaWO4 Beryllium Be BeBr2 BeCl2 BeI2 Be3N2 BeO Be(OH)2 BeS BeSO4 Bismuth Bi BiCl3 BiI3 BiO Bi2O3 Bi(OH)3 Bi2S3 Bi2(SO4)3 Boron B BBr3 BCl3 BF3 B2H6 BN B2O3 B(OH)3 B2S3 Bromine Br2

-180.7

BrCl Cadmium Cd CdBr2

-271.4

CdCl2

-48 -212.1

-265.3 -31.5 -414.4 -158.52

State†

Compound Barium (Cont.) Ba(IO3)2

Cd(CN)2 CdCO3 CdI2 Cd3N2 Cd(NO3)2

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol

c aq c c c aq c aq, 600 c c aq, 400 c c c c c c c

-264.5 -237.50 -370 -90.7 -184.5 -179.05 -236.99 -227.74 -133.0 -225.9 -237.76 -363 -992 -284.9 -111.2 -282.5 -340.2 -402

c c aq c aq c aq c c c c c aq

0.00 -79.4 -142 -112.6 -163.9 -39.4 -112 -134.5 -145.3 -215.6 -56.1 -281

c c aq c aq c c c c c

0.00 -90.5 -101.6 -24 -27 -49.5 -137.1 -171.1 -43.9 -607.1

c l g g g g c c gls c c

0.00 -52.7 -44.6 -94.5 -265.2 7.5 -32.1 -302.0 -297.6 -260.0 -56.6

l g g c c aq, 400 c aq, 400 c c c aq, 400 c aq, 400

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol

-198.35

-150.75 -189.94

-209.02

-313.4 0.00 -127.9 -141.4 -103.4 -122.4 -138.3

-254.8

0.00 7.47 3.06 0.00 -75.8 -76.6 -92.149 -96.44 36.2 -178.2 -48.40 -47.46 39.8 -115.67

0.00 -76.4

-43.2 -117.9 -39.1 0.00 -50.9 -90.8 -261.0 19.9 -27.2 -282.9 -280.3 -229.4 0.00 0.931 -0.63 0.00 -70.7 -67.6 -81.889 -81.2 -163.2 -43.22 -71.05 (Continued)

2-160

PHYSICAL AnD CHEMICAL DATA

TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )

State†

Compound Cadmium (Cont.) CdO Cd(OH)2 CdS CdSO4 Calcium Ca CaBr2 CaC2 CaCl2 CaCN2 Ca(CN)2 CaCO3 CaCO3⋅MgCO3 CaC2O4 Ca(C2H3O2)2 CaF2 CaH2 CaI2 Ca3N2 Ca(NO3)2 Ca(NO3)2⋅2H2O Ca(NO3)2⋅3H2O Ca(NO3)2⋅4H2O CaO Ca(OH)2 CaO⋅SiO2 CaS CaSO4 CaSO4⋅½H2O CaSO4⋅2H2O CaWO4 Carbon C CO CO2 Cerium Ce CeN Cesium Cs CsBr CsCl Cs2CO3 CsF CsH CsHCO3 CsI CsNH2 CsNO3 Cs2O CsOH Cs2S Cs2SO4

c c c c aq, 400 c c aq, 400 c c aq c c aq c, calcite c, aragonite c c c aq c aq c c aq, 400 c c aq, 400 c c c c c aq, 800 c, II, wollastonite c, I, pseudowollastonite c c, insoluble form c, soluble form α c, soluble form β c c c

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol -62.35 -135.0 -34.5 -222.23 -232.635 0.00 -162.20 -187.19 -14.8 -190.6 -209.15 -85 -43.3 -289.5 -289.54 -558.8 -332.2 -356.3 -364.1 -290.2 -286.5 -46 -128.49 -156.63 -103.2 -224.05 -228.29 -367.95 -439.05 -509.43 -151.7 -235.58 -239.2 -377.9 -376.6 -114.3 -338.73 -336.58 -335.52 -376.13 -479.33 -387

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol -55.28 -113.7 -33.6 -194.65 0.00 -181.86 -16.0 -179.8 -195.36 -54.0 -270.8 -270.57

-311.3 -264.1 -35.7 -157.37 -88.2 -177.38 -293.57 -351.58 -409.32 -144.3 -213.9 -207.9 -357.5 -356.6 -113.1 -311.9 -309.8 -308.8 -425.47

c, graphite c, diamond g g

0.00 0.453 -26.416 -94.052

0.00 0.685 -32.808 -94.260

c c

0.00 -78.2

0.00 -70.8

c c aq, 500 c aq, 400 c c aq, 400 c c aq, 2000 c aq, 400 c c aq, 400 c c aq, 200 c c aq

0.00 -97.64 -91.39 -106.31 -102.01 -271.88 -131.67 -140.48 -12 -230.6 -226.6 -83.91 -75.74 -28.2 -121.14 -111.54 -82.1 -100.2 -117.0 -87 -344.86 -340.12

0.00 -94.86

Chlorine Cl2 ClF ClO ClO2 ClO3 Cl2O Cl2O7 Chromium Cr CrBr3 Cr3C2 Cr4C CrCl2 CrF2 CrF3 CrI2 CrO3 Cr2O3 Cr2(SO4)3 Cobalt Co CoBr2 Co3C CoCl2 CoCO3 CoF2 CoI2 Co(NO3)2 CoO Co3O4 Co(OH)2 Co(OH)3 CoS Co2S3 CoSO4 Columbium Cb Cb2O5 Copper Cu CuBr CuBr2 CuCl CuCl2 CuClO4 Cu(ClO3)2 Cu(ClO4)2 CuI CuI2

-101.61

Cu3N Cu(NO3)2

-135.98 -7.30

CuO Cu2O Cu(OH)2 CuS Cu2S CuSO4

-210.56 -82.61 -96.53 -107.87 -316.66

State†

Compound

Cu2SO4 Erbium Er Er(OH)3 Fluorine F2 F2O

g g g g g g g c aq c c c aq c c c aq c c aq

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol 0.00 -25.7 33 24.7 37 18.20 63 0.00 -21.008 -16.378 -103.1

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol 0.00 29.5 22.40 0.00 -122.7 -21.20 -16.74 -93.8 -102.1

-152 -231 -63.7 -64.1 -139.3 -268.8

-249.3 -626.3

c c aq c c aq, 400 c aq c aq c aq c c c c c c c aq, 400

0.00 -55.0 -73.61 9.49 -76.9 -95.58 -172.39 -172.98 -24.2 -43.15 -102.8 -114.9 -57.5 -196.5 -131.5 -177.0 -22.3 -40.0 -216.6

c c

0.00 -462.96

0.00

0.00 -26.7 -34.0 -42.4 -31.4 -48.83 -64.7 -28.3

0.00 -23.8

c c c aq c c aq, 400 aq aq, 400 aq c c aq c c aq, 200 c c c c c c aq, 800 c aq

0.00 -61.96 7.08 -66.6 -75.46 -155.36 -144.2 -37.4 -65.3 -108.9 -142.0 -19.8 -188.9

-17.8 -4.8 -11.9 17.78 -73.1 -83.6 -38.5 -43.00 -108.9 -11.6 -18.97 -184.7 -200.78 -179.6

-33.25 -24.13 1.34 15.4 -5.5 -16.66 -8.76 -36.6 -31.9 -38.13 -85.5 -11.69 -20.56 -158.3 -160.19 -152.0

c c

0.00 -326.8

0.00

g g

0.00 5.5

0.00 9.7

PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS

2-161

TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )

State†

Compound Gallium Ga GaBr3 GaCl3 GaN Ga2O Ga2O3 Germanium Ge Ge3N4 GeO2 Gold Au AuBr AuBr3 AuCl AuCl3 AuI Au2O3 Au(OH)3 Hafnium Hf HfO2 Hydrogen H3AsO3 H3AsO4 HBr HBrO HBrO3 HCl HCN HClO HClO3 HClO4 HC2H3O2 H2C2O4 HCOOH H2CO3 HF HI HIO HIO3 HN3 HNO3 HNO3⋅H2O HNO3⋅3H2O H2O H2O2 H3PO2 H3PO3 H3PO4 H2S H2S2 H2SO3 H2SO4 H2Se

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol

c c c c c c

0.00 -92.4 -125.4 -26.2 -84.3 -259.9

0.00

c c c

0.00 -15.7 -128.6

0.00

c c c aq c c aq c c c

0.00 -3.4 -14.5 -11.0 -8.3 -28.3 -32.96 0.2 11.0 -100.6

0.00

c c

0.00 -271.1

0.00 -258.2

aq c aq g aq, 400 aq aq g aq, 400 g aq, 100 aq, 400 aq aq, 660 l aq, 400 c aq, 300 l aq, 200 aq g aq, 200 g aq, 400 aq c aq g g l aq, 400 l l g l l aq, 200 c aq c aq c aq, 400 g aq, 2000 l aq, 200 l aq, 400 g aq

-175.6 -214.9 -214.8 -8.66 -28.80 -25.4 -11.51 -22.063 -39.85 31.1 24.2 -28.18 -23.4 -31.4 -116.2 -116.74 -196.7 -194.6 -97.8 -98.0 -167.19 -64.2 -75.75 6.27 -13.47 -38 -56.77 -54.8 70.3 -31.99 -41.35 -49.210 -112.91 -252.15 -57.7979 -68.3174 -45.16 -45.80 -145.5 -145.6 -232.2 -232.2 -306.2 -309.32 -4.77 -9.38 -3.6 -146.88 -193.69 -212.03 20.5 18.1

-153.04

Hydrogen (Cont.) H2SeO3 H2SeO4

24.47

H2SiO3 H4SiO4 H2Te H2TeO3 H2TeO4 Indium In InBr3 InCl3 InI3

4.21 -0.76 18.71

-183.93 -12.72 -24.58 -19.90 5.00 -22.778 -31.330 27.94 26.55 -19.11 -0.25 -10.70 -93.56 -96.8 -165.64 -82.7 -85.1 -149.0 -64.7 0.365 -12.35 -23.33 -32.25 78.50 -17.57 -19.05 -78.36 -193.70 -54.6351 -56.6899 -28.23 -31.47 -120.0 -204.0 -270.0 -7.85 -128.54 17.0 18.4

State†

Compound

InN In2O3 Iodine I2 IBr ICl ICl3 I 2 O5 Iridium Ir IrCl IrCl2 IrCl3 IrF6 IrO2 Iron Fe FeBr2 FeBr3 Fe3C Fe(CO)5 FeCO3 FeCl2 FeCl3 FeF2 FeI2 FeI3 Fe4N Fe(NO3)2 Fe(NO3)3 FeO Fe2O3 Fe3O4 Fe(OH)2 Fe(OH)3 FeO⋅SiO2 Fe2P FeSi FeS FeS2 FeSO4 Fe2(SO4)3 FeTiO3 Lanthanum La LaCl3 La3H8 LaN La2O3 LaS2 La2S3 La2(SO4)3

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol

c aq c aq, 400 c c g c aq aq

-126.5 -122.4 -130.23 -143.4 -267.8 -340.6 36.9 -145.0 -145.0 -165.6

c c aq c aq c aq c c

0.00 -97.2 -112.9 -128.5 -145.6 -56.5 -67.2 -4.8 -222.47

c g g g c c

0.00 14.88 10.05 4.20 -21.8 -42.5

0.00 4.63 1.24 -1.32 -6.05

c c c c l c

0.00 -20.5 -40.6 -60.5 -130 -40.14

0.00 -16.9 -32.0 -46.5

c, α c aq, 540 aq c l c, siderite c aq c aq, 2000 aq, 1200 c aq aq c aq aq, 800 c c c c c c c c c c, pyrites c, marcasite c aq, 400 aq, 400 c, ilmenite

0.00 -57.15 -78.7 -95.5 5.69 -187.6 -172.4 -81.9 -100.0 -96.4 -128.5 -177.2 -24.2 -47.7 -49.7 -2.55 -118.9 -156.5 -64.62 -198.5 -266.9 -135.9 -197.3 -273.5 -13 -19.0 -22.64 -38.62 -33.0 -221.3 -236.2 -653.3 -295.51

0.00

c c aq c c c c c aq

0.00 -253.1 -284.7 -160 -72.0 -539 -148.3 -351.4 -972

-101.36 -247.9 33.1 -115.7

0.00 -97.2 -117.5 -60.5

-69.47 -76.26 4.24 -154.8 -72.6 -83.0 -96.5 -151.7 -45 -39.5 0.862 -72.8 -81.3 -59.38 -179.1 -242.3 -115.7 -166.3

-23.23 -35.93 -195.5 -196.4 -533.4 -277.06 0.00

-64.6

(Continued)

2-162

PHYSICAL AnD CHEMICAL DATA

TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )

Compound Lead Pb PbBr2 PbCO3 Pb(C2H3O2)2 PbC2O4 PbCl2 PbF2 PbI2 Pb(NO3)2 PbO PbO2 Pb3O4 Pb(OH)2 PbS PbSO4 Lithium Li LiBr LiBrO3 Li2C2 LiCN LiCNO LiC2H3O2 Li2CO3 LiCl LiClO3 LiClO4 LiF LiH LiHCO3 LiI LiIO3 Li3N LiNO3 Li2O Li2O2 LiOH LiOH⋅H2O Li2O⋅SiO2 Li2Se Li2SO4 Li2SO4⋅H2O Magnesium Mg Mg(AsO4)2 MgBr2 Mg(CN)2 MgCN2 Mg(C2H3O2)2 MgCO3 MgCl2

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol

c c aq c, cerussite c aq, 400 c c aq c c c aq, 400 c, red c, yellow c c c c c

0.00 -66.24 -56.4 -167.6 -232.6 -234.2 -205.3 -85.68 -82.5 -159.5 -41.77 -106.88 -99.46 -51.72 -50.86 -65.0 -172.4 -123.0 -22.38 -218.5

0.00 -62.06 -54.97 -150.0

c c aq, 400 aq c aq aq aq c aq, 1900 c aq, 278 aq aq c aq, 400 c aq, 2000 c aq, 400 aq c c aq, 400 c c aq c aq, 400 c gls c aq c aq, 400 c

0.00 -83.75 -95.40 -77.9 -13.0 -31.4 -101.2 -183.9 -289.7 -293.1 -97.63 -106.45 -87.5 -106.3 -145.57 -144.85 -22.9 -231.1 -65.07 -80.09 -121.3 -47.45 -115.350 -115.88 -142.3 -151.9 -159 -116.58 -121.47 -188.92 -374 -84.9 -95.5 -340.23 -347.02 -411.57

c c aq c aq, 400 aq c aq c c aq, 400

0.00 -731.3 -749 -123.9 -167.33 -39.7 -61 -344.6 -261.7 -153.220 -189.76

State†

-184.40 -75.04 -68.47 -148.1 -41.47 -58.3 -45.53 -43.88 -52.0 -142.2 -102.2 -21.98 -192.9 0.00 -95.28 -65.70 -31.35 -94.12 -160.00 -269.8 -267.58 -102.03 -70.95 -81.4

Compound Magnesium (Cont.) MgCl2⋅H2O MgCl2⋅2H2O MgCl2⋅4H2O MgCl2⋅6H2O MgF2 MgI2 MgMoO4 Mg3N2 Mg(NO3)2 Mg(NO3)2⋅2H2O Mg(NO3)2⋅6H2O MgO MgO⋅SiO2 Mg(OH)2 MgS MgSO4 MgTe MgWO4 Manganese Mn MnBr2 Mn3C Mn(C2H3O2)2 MnCO3 MnC2O4 MnCl2 MnF2 MnI2

-136.40 -210.98 -83.03 -102.95 -37.33 -96.95 -138.0 -106.44 -108.29

-105.64 -314.66 -375.07 0.00

Mn5N2 Mn(NO3)2 Mn(NO3)2.6H2O MnO MnO2 Mn2O3 Mn3O4 MnO.SiO2 Mn(OH)2 Mn(OH)3 Mn3(PO4)2 MnSe MnS MnSO4 Mn2(SO4)3 Mercury Hg HgBr HgBr2

-630.14

Hg(C2H3O2)2

-156.94 -29.08

HgCl2

-286.38 -241.7 -143.77

HgCl Hg2Cl2 Hg(CN)2 HgC2O4

State†

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol

c c c c c c aq, 400 c c c aq, 400 c c c c c, ppt. c, brucite c aq c aq, 400 c c

-230.970 -305.810 -453.820 -597.240 -263.8 -86.8 -136.79 -329.9 -115.2 -188.770 -209.927 -336.625 -624.48 -143.84 -347.5 -221.90 -223.9 -84.2 -108 -304.94 -325.4 -25 -345.2

c, α c aq c c aq c c c aq, 400 aq, 1200 c aq c c aq, 400 c c c c c c c c c c c, green c aq, 400 c aq

0.00 -91 -106 1.1 -270.3 -282.7 -211 -240.9 -112.0 -128.9 -206.1 -49.8 -76.2 -57.77 -134.9 -148.0 -557.07 -92.04 -124.58 -229.5 -331.65 -301.3 -163.4 -221 -736 -26.3 -47.0 -254.18 -265.2 -635 -657

l g c aq c aq c aq g c c aq, 1110 c

0.00 23 -40.68 -38.4 -196.3 -192.5 -53.4 -50.3 19 -63.13 62.8 66.25 -159.3

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol -205.93 -267.20 -387.98 -505.45 -132.45 -100.8 -140.66 -160.28 -496.03 -136.17 -326.7 -200.17 -193.3 -277.7 -283.88

0.00 -97.8 1.26 -227.2 -192.5 -102.2 -180.0 -73.3 -46.49 -101.1 -441.2 -86.77 -111.49 -209.9 -306.22 -282.1 -143.1 -190 -27.5 -48.0 -228.41

0.00 18 -38.8 -9.74 -139.2 -42.2 -23.25 14

PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS

2-163

TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued ) Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol

g c, red g c aq aq c, red c, yellow ppt. c c, black c c

57.1 -25.3 33 -28.88 -56.8 -58.5 -21.6 -20.8 -21.6 -10.7 -166.6 -177.34

52.25 -24.0 23 -26.53 -13.09 -15.65 -13.94

c c c c c c c

0.00 4.36 -8.3 -130 -180.39 -56.27 -61.48

c c aq c aq aq c aq, 400 c aq c aq c aq, 200 c c c c c aq, 200

0.00 -53.4 -72.6 9.2 -249.6 230.9 -75.0 -94.34 -157.5 -171.6 -22.4 -42.0 -101.5 -113.5 -58.4 -129.8 -163.2 -20.4 -216 -231.3

g g g aq, 200 c aq c aq, 400 c aq c aq aq c aq c aq, 400 c aq c aq c aq c aq c aq, 500

0.00 -27 -10.96 -19.27 -64.57 -60.27 -148.1 -148.58 -0.7 3.6 -17.8 -12.3 -223.4 -266.3 -260.6 -75.23 -71.20 -69.4 -63.2 -276.9 -271.3 -111.6 -110.2 -48.43 -44.97 -87.40 -80.89

State†

Compound Mercury (Cont.) HgH HgI2 HgI Hg2I2 Hg(NO3)2 Hg2(NO3)2 HgO Hg2O HgS HgSO4 Hg2SO4 Molybdenum Mo Mo2C Mo2N MoO2 MoO3 MoS2 MoS3 Nickel Ni NiBr2 Ni3C Ni(C2H3O2)2 Ni(CN)2 NiCl2 NiF2 NiI2 Ni(NO3)2 NiO Ni(OH)2 Ni(OH)3 NiS NiSO4 Nitrogen N2 NF3 NH3 NH4Br NH4C2H3O2 NH4CN NH4CNS (NH4)2CO3 (NH4)2C2O4 NH4Cl NH4ClO4 (NH4)2CrO4 NH4F NH4I NH4NO3

-12.80 -8.80 -149.12 0.00 2.91 -118.0 -162.01 -54.19 -57.38 0.00 -60.7 8.88 -190.1 66.3 -74.19 -142.9 -36.2 -64.0 -51.7 -105.6

-187.6

Nitrogen (Cont.) NH4OH (NH4)2S (NH4)2SO4 N2H4 N2H4⋅H2O N2H4⋅H2SO4 N2O NO NO2 N2O4 N2O5 NOBr NOCl Osmium Os OsO4 Oxygen O2 O3 Palladium Pd PdO Phosphorus P P P2 P4 PBr3 PBr5 PCl3 PCl5 PH3 PI3 P2O5 POCl3 Platinum Pt PtBr4

0.00 -3.903 -43.54 -108.26 20.4 4.4 -164.1 -196.2 -48.59 -21.1

PtCl2 PtCl4 PtI4 Pt(OH)2 PtS PtS2 Potassium K K3AsO3 K3AsO4 KH2AsO4 KBr KBrO3 KC2H3O2 KCl

-209.3 -84.7 -31.3

State†

Compound

KClO3 KClO4 KCN

aq aq, 400 c aq, 400 l l c g g g g c l g

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol -87.59 -55.21 -281.74 -279.33 12.06 -57.96 -232.2 19.55 21.600 7.96 2.23 -10.0 11.6 12.8

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol

-14.50 -215.06 -214.02

24.82 20.719 12.26 23.41 19.26 16.1

c c g

0.00 -93.6 -80.1

0.00 -70.9 -68.1

g g

0.00 33.88

0.00 38.86

c c

0.00 -20.40

0.00

0.00 -4.22 150.35 33.82 13.2 -45 -60.6 -70.0 -76.8 -91.0 2.21 -10.9 -360.0 -138.4

0.00 -1.80 141.88 24.60 5.89

c, white (“yellow”) c, red (“violet”) g g g l c g l g g c c g c c aq c c aq c c c c c aq aq c c aq, 400 c aq, 1667 c aq, 400 c aq, 400 c aq, 400 c aq, 400 c aq, 400

0.00 -40.6 -50.7 -34 -62.6 -82.3 -18 -87.5 -20.18 -26.64 0.00 -323.0 -390.3 -271.2 -94.06 -89.19 -81.58 -71.68 -173.80 -177.38 -104.348 -100.164 -93.5 -81.34 -103.8 -101.14 -28.1 -25.3

-65.2 -63.3 -73.2 -1.45 -127.2 0.00

-67.9 -18.55 -24.28 0.00 -355.7 -236.7 -90.8 -92.0 -60.30 -156.73 -97.76 -98.76 -69.30 -72.86 -28.08 (Continued)

2-164

PHYSICAL AnD CHEMICAL DATA

TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )

State†

Compound Potassium (Cont.) KCNO KCNS K2CO3 K2C2O4 K2CrO4 K2Cr2O7 KF K3Fe(CN)6 K4Fe(CN)6 KH KHCO3 KI KIO3 KIO4 KMnO4 K2MoO4 KNH2 KNO2 KNO3 K2O K2O⋅Al2O3⋅SiO2 K2O⋅Al2O3⋅SiO2 KOH K3PO3 K3PO4 KH2PO4 K2PtCl4 K2PtCl6 K2Se K2SeO4 K2S K2SO3 K2SO4 K2SO4⋅Al2(SO4)3 K2SO4⋅Al2(SO4)3· 24H2O K2S2O6 Rhenium Re ReF6 Rhodium Rh RhO Rh2O Rh2O3

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol

c aq c aq, 400 c aq, 400 c aq, 400 c aq, 400 c aq, 400 c aq, 180 c aq c aq c c aq, 2000 c aq, 500 c aq, 400 aq c aq, 400 aq, 880 c aq c aq, 400 c c, leucite gls c, adularia c, microcline gls c aq, 400 aq aq c c aq c aq, 9400 c aq aq c aq, 400 c aq c aq, 400 c

-99.6 -94.5 -47.0 -41.07 -274.01 -280.90 -319.9 -315.5 -333.4 -328.2 -488.5 -472.1 -134.50 -138.36 -48.4 -34.5 -131.8 -119.9 -10 -229.8 -224.85 -78.88 -73.95 -121.69 -115.18 -98.1 -192.9 -182.5 -364.2 -28.25 -86.0 -118.08 -109.79 -86.2 -1379.6 -1368.2 -1784.5 -1784.5 -1747 -102.02 -114.96 -397.5 -478.7 -362.7 -254.7 -242.6 -299.5 -286.1 -74.4 -83.4 -267.1 -121.5 -110.75 -267.7 -269.7 -342.65 -336.48 -1178.38

c c

-2895.44 -418.62

-2455.68

c g

0.00 -274

0.00

c c c c

0.00 -21.7 -22.7 -68.3

0.00

-90.85

Rubidium Rb RbBr

-44.08 -264.04

RbCN Rb2CO3

-293.1

RbCl

-306.3 RbF -440.9 -133.13

RbHCO3 RbI

-5.3 -207.71 -77.37 -79.76 -101.87 -99.68 -169.1 -168.0 -342.9 -75.9 -94.29 -93.68

-105.0 -443.3 -326.1 -226.5 -263.6 -99.10 -240.0 -111.44 -251.3 -314.62 -310.96 -1068.48

State†

Compound

RbNH2 RbNO3 Rb2O Rb2O2 RbOH Ruthenium Ru RuS2 Selenium Se Se2Cl2 SeF6 SeO2 Silicon Si SiBr4 SiC SiCl4 SiF4 SiH4 SiI4 Si3N4 SiO2

Silver Ag AgBr Ag2C2 AgC2H3O2 AgCN Ag2CO3 Ag2C2O4 AgCl AgF AgI AgIO3 AgNO2 AgNO3 Ag2O

c c g aq, 500 aq c aq, 220 c g aq, ∞ c aq, 400 c aq, 2000 c g aq, 400 c c aq, 400 c c c aq, 200 c c c, I, hexagonal c, II, red, monoclinic l g c

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol 0.00 -95.82 -45.0 -90.54 -25.9 -273.22 -282.61 -105.06 -53.6 -101.06 -133.23 -139.31 -230.01 -225.59 -81.04 -31.2 -74.57 -27.74 -119.22 -110.52 -82.9 -107 -101.3 -115.8

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol 0.00 -52.50 -93.38 -263.78 -98.48 -57.9 -100.13 -134.5 -209.07 -40.5 -81.13 -95.05

-106.39

0.00 -46.99

0.00 -44.11

0.00 0.2

0.00

-22.06 -246 -56.33

-13.73 -222

0.00 -93.0 -28 -150.0 -142.5 -370 -14.8 -29.8 -179.25 -202.62

0.00

c l c l g g g c c c, cristobalite, 1600° form c, cristobalite, 1100° form c, quartz c, tridymite

-203.35 -203.23

c c c c aq c c c c c aq, 400 c c c aq c aq, 6500 c

0.00 -23.90 84.5 -95.9 -91.7 33.8 -119.5 -158.7 -30.11 -48.7 -53.1 -15.14 -42.02 -11.6 -2.9 -29.4 -24.02 -6.95

-27.4 -133.9 -133.0 -360 -9.4 -154.74

-202.46 -190.4 0.00 -23.02 -70.86 38.70 -103.0 -25.98 -47.26 -16.17 -24.08 3.76 9.99 -7.66 -7.81 -2.23

PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS

2-165

TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )

State†

Compound Silver (Cont.) Ag2S Ag2SO4 Sodium Na Na3AsO3 Na3AsO4 NaBr NaBrO NaBrO3 NaC2H3O2 NaCN NaCNO NaCNS Na2CO3 NaCO2NH2 Na2C2O4 NaCl NaClO3 NaClO4 Na2CrO4 Na2Cr2O7 NaF NaH NaHCO3 NaI NaIO3 Na2MoO4 NaNO2 NaNO3 Na2O Na2O2 Na2O⋅SiO2 Na2O⋅Al2O3⋅3SiO2 Na2O⋅Al2O3⋅4SiO2 NaOH Na3PO3 Na3PO4 Na2PtCl4 Na2PtCl6 Na2Se Na2SeO4 Na2S Na2SO3 Na2SO4

c c aq c aq, 500 c aq, 500 c aq, 400 aq aq, 400 c aq, 400 c aq, 200 c aq c aq, 400 c aq, 1000 c c aq, 600 c aq, 400 c aq, 400 c aq, 476 c aq, 800 aq, 1200 c aq, 400 c c aq c aq, ∞ aq, 400 c aq c aq c aq, 400 c c c c, natrolite c c aq, 400 aq, 1000 c aq, 400 aq c aq c aq, 440 c aq, 800 c aq, 400 c aq, 800 c aq, 1100

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol

-5.5 -170.1 -165.8

-7.6 -146.8 -139.22

0.00 -314.61 -366 -381.97 -86.72 -86.33 -78.9 -68.89 -170.45 -175.450 -22.47 -22.29 -96.3 -91.7 -39.94 -38.23 -269.46 -275.13 -142.17 -313.8 -309.92 -98.321 -97.324 -83.59 -78.42 -101.12 -97.66 -319.8 -323.0 -465.9 -135.94 -135.711 -14 -226.0 -222.1 -69.28 -71.10 -112.300 -364 -358.7 -86.6 -83.1 -111.71 -106.880 -99.45 -119.2 -383.91 -1180 -1366 -101.96 -112.193 -389.1 -457 -471.9 -237.2 -272.1 -280.9 -59.1 -78.1 -254 -261.5 -89.8 -105.17 -261.2 -264.1 -330.50 -330.82

0.00 -341.17 -87.17 -57.59 -152.31 -23.24 -86.00 -39.24 -249.55 -251.36 -283.42 -91.894 -93.92

Sodium (Cont.) Na2SO4⋅10H2O Na2WO4 Strontium Sr SrBr2 Sr(C2H3O2)2 Sr(CN)2 SrCO3 SrCl2 SrF2 Sr(HCO3)2 SrI2 Sr3N2 Sr(NO3)2 SrO SrO⋅SiO2 SrO2 Sr2O Sr(OH)2 Sr3(PO4)2

-62.84

SrS

-73.29

SrSO4

-296.58 -431.18 -129.0 -128.29 -9.30 -202.66 -202.87

SrWO4 Sulfur S

-74.92 -94.84 -333.18 -71.04 -87.62 -88.84 -90.06 -105.0 -361.49 -90.60 -100.18 -428.74 -216.78

-89.42 -230.30 -101.76 -240.14 -241.58 -302.38 -301.28

State†

Compound

S2 S6 S8 S2Br2 SCl4 S2Cl2 S2Cl4 SF6 SO SO2 SO3

SO2Cl2 Tantalum Ta TaN Ta2O5 Tellurium Te TeBr4 TeCl4 TeF6 TeO2 Thallium Tl TlBr TlCl

c c aq c c aq, 400 c aq aq c c aq, 400 c aq c aq, 400 c c aq, 400 c gls c c c aq, 800 c aq c aq c aq, 400 c

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol

-1033.85 -391 -381.5

-870.52

0.00 -171.0 -187.24 -358.0 -364.4 -59.5 -290.9 -197.84 -209.20 -289.0 -459.1 -136.1 -156.70 -91.4 -233.2 -228.73 -140.8 -364 -153.3 -153.6 -228.7 -239.4 -980 -985 -113.1 -120.4 -345.3 -345.0 -393 0.00 -0.071 0.257

-345.18 0.00 -182.36 -311.80 -54.50 -271.9 -195.86 -413.76 -157.87 -76.5 -185.70 -133.7 -139.0 -208.27 -881.54 -109.78 -309.30

c, rhombic c, monoclinic l, λ l, λµ equilibrium g g g g l l l l g g g g l c, α c, β c, γ g l

0.00 0.023 0.072 0.071 43.57 19.36 13.97 12.770

53.25 31.02 27.78 27.090 -4 -13.7 -14.2 -24.1 -262 19.02 -70.94 -94.39 -103.03 -105.09 -105.92 -109.34 -82.04 -89.80

-237 12.75 -71.68 -88.59 -88.28 -88.22 -88.34 -88.98 -74.06 -75.06

c c c

0.00 -51.2 -486.0

0.00 -45.11 -453.7

c c c g c

0.00 -49.3 -77.4 -315 -77.56

0.00 -57.4 -292 -64.66

c c aq c aq

0.00 -41.5 -28.0 -49.37 -38.4

0.00 -39.43 -32.34 -44.46 -39.09

-5.90

(Continued)

2-166

PHYSICAL AnD CHEMICAL DATA

TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )

Compound Thallium (Cont.) TlCl3 TlF TlI TlNO3 Tl2O Tl2O3 TlOH Tl2S Tl2SO4 Thorium Th ThBr4 ThC2 ThCl4 ThI4 Th3N4 ThO2 Th(OH)4 Th(SO4)2 Tin Sn SnBr2 SnBr4 SnCl2 SnCl4 SnI2 SnO SnO2 Sn(OH)2 Sn(OH)4 SnS Titanium Ti TiC TiCl4 TiN TiO2 †

State†

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol

c aq aq c aq c aq c c c aq c c aq, 800

-82.4 -91.0 -77.6 -31.1 -12.7 -58.2 -48.4 -43.18 -120 -57.44 -53.9 -22 -222.8 -214.1

c c aq c c aq aq c c c, “soluble” c aq

0.00 -281.5 -352.0 -45.1 -335 -392 -292.0 -309.0 -291.6 -336.1 -632 -668.1

c, II, tetragonal c, III, “gray,” cubic c aq c aq c aq l aq c aq c c c c c

0.00 0.6 -61.4 -60.0 -94.8 -110.6 -83.6 -81.7 -127.3 -157.6 -38.9 -33.3 -67.7 -138.1 -136.2 -268.9 -18.61

c c l c c, III, rutil amorphous

0.00 -110 -181.4 -80.0 -225.0 -214.1

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol

-44.25 -73.46 -31.3 -20.09 -36.32 -34.01 -45.54 -45.35 -197.79 -191.62 0.00 -295.31 -322.32 -246.33 -282.3 -280.1 -549.2 0.00 1.1 -55.43 -97.66 -68.94 -110.4 -124.67 -30.95 -60.75 -123.6 -115.95 -226.00 0.00 -109.2 -165.5 -73.17 -211.9 -201.4

Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol

Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol

c c c c

0.00 -130.5 -195.7 -84

0.00 -118.3 -177.3

c c c c c c c c c

0.00 -29 -213 -251 -274 -256.6 -756.8 -291.6 -845.1

0.00

c c l l c c c c c

0.00 -147 -187 -165 -41.43 -195 -296 -342 -373

c c c aq, 400 c aq, 400 c c c aq, 400 aq c aq aq, 400 c, hexagonal c c, rhombic c, wurtzite c aq, 400

0.00 -3.6 -77.0 -93.6 -259.4 -269.4 17.06 -192.9 -99.9 -115.44 -192.9 -50.50 -61.6 -134.9 -83.36 -282.6 -153.66 -45.3 -233.4 -252.12

c c c c c, monoclinic c c

0.00 -29.8 -268.9 -82.5 -258.5 -411.0 -337

State†

Compound Tungsten W WO2 WO3 WS2 Uranium U UC2 UCl3 UCl4 U3N4 UO2 UO2(NO3)2⋅6H2O UO3 U3O8 Vanadium V VCl2 VCl3 VCl4 VN V2O2 V2O3 V2O4 V2O5 Zinc Zn ZnSb ZnBr2 Zn(C2H3O2)2 Zn(CN)2 ZnCO3 ZnCl2 ZnF2 ZnI2 Zn(NO3)2 ZnO ZnO⋅SiO2 Zn(OH)2 ZnS ZnSO4 Zirconium Zr ZrC ZrCl4 ZrN ZrO2 Zr(OH)4 ZrO(OH)2

-249.6 -242.2 -617.8

0.00

-35.08 -277 -316 -342 0.00 -3.88 -72.9 -214.4 -173.5 -88.8 -166.6 -49.93 -87.7 -76.19 -44.2 -211.28 0.00 -34.6 -75.9 -244.6 -307.6

The physical state is indicated as follows: c, crystal (solid); l, liquid; g, gas; gls, glass or solid supercooled liquid; aq, in aqueous solution. A number following the symbol aq applies only to the values of the heats of formation (not to those of free energies of formation); and indicates the number of moles of water per mole of solute; when no number is given, the solution is understood to be dilute. For the free energy of formation of a substance in aqueous solution, the concentration is always that of the hypothetical solution of unit molality. ‡ The increment in heat content, ΔH, is the reaction of forming the given substance from its elements in their standard states. When ΔH is negative, heat is evolved in the process, and, when positive, heat is absorbed. § The heat of solution in water of a given solid, liquid, or gaseous compound is given by the difference in the value for the heat of formation of the given compound in the solid, liquid, or gaseous state and its heat of formation in aqueous solution. The following two examples serve as an illustration of the procedure: (1) For NaCl(c) and NaCl(aq, 400H2O), the values of ΔH( formation) are, respectively, -98.321 and -97.324 kcal/mol. Subtraction of the first value from the second gives ΔH = 0.998 kcal/mol for the reaction of dissolving crystalline sodium chloride in 400 mol of water. When this process occurs at a constant pressure of 1 atm, 0.998 kg-cal of energy are absorbed. (2) For HCl(g) and HCl(aq, 400H2O), the values for ΔH( formation) are, respectively, -22.06 and -39.85 kcal/mol. Subtraction of the first from the second gives ΔH = -17.79 kcal/mol for the reaction of dissolving gaseous hydrogen chloride in 400 mol of water. At a constant pressure of 1 atm, 17.79 kcal of energy are evolved in this process. ∙The increment in the free energy, ΔF, is the reaction of forming the given substance in its standard state from its elements in their standard states. The standard states are: for a gas, fugacity (approximately equal to the pressure) of 1 atm; for a pure liquid or solid, the substance at a pressure of 1 atm; for a substance in aqueous solution, the hypothetical solution of unit molality, which has all the properties of the infinitely dilute solution except the property of concentration. ¶ The free energy of solution of a given substance from its normal standard state as a solid, liquid, or gas to the hypothetical one molal state in aqueous solution may be calculated in a manner similar to that described in footnote § for calculating the heat of solution.

TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K Cmpd. no.

2-167

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide

Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO

CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0

Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101

Ideal gas enthalpy of formation, J/kmol × 1E-07 -17.1 -23.83 -43.28 -57.55 -21.57 6.467 22.82 -8.18 -35.591 17.97 0 -4.5898 -6.79 0 -10.09 8.288 11.15 -29.41 21.57 5.68 -9.025 -11.5 9.33 17.849 3.091 10.5018 -6.36 -3.77 16.23 10.924 -12.579 -44.58 -43.32 -27.51 -29.29 -0.05 -0.74 -1.1 -48.56 -1.314 -8.78 -9.66 16.52 -20.62 -47.58 3.342 -39.351 11.69 -11.053

Ideal gas Gibbs energy of formation, J/kmol × 1E-07 -13.78 -15.96 -37.45 -47.6 -15.13 8.241 21.068 -5.68 -30.6 18.92 0 -1.64 2.27 0 -0.211 12.96 14.76 -21.42 25.8 17.3 -0.254 3.37 16.3 27.63 0.314 13.8532 -2.574 -2.7037 19.86 14.972 -1.67 -30.44 -29.18 -15.07 -16.7 7.041 6.536 6.32 -31.26 14.54 1.139 0.512 20.225 -11.48 -36 10.57 -39.437 6.68 -13.715

Ideal gas entropy, J/(kmol∙K) × 1E-05

Standard net enthalpy of combustion, J/kmol × 1E-09

2.6384 2.722 2.825 3.899 2.954 2.438 2.0081 2.97 3.15 2.77267 1.94452 1.9266 3.61 1.54845 3.641 2.693 3.369 3.69 3.21 4.4 3.713 4.39 3.607 3.9367 2.4535 3.24386 2.873 2.421 2.93 2.7889 3.0991 4.065 4.065 3.618 3.566 3.074 3.012 2.965 4.425 4.3949 3.752 3.667 2.9039 3.418 3.601 3.337 2.13677 2.379 1.97556

-1.1046 -1.0741 -0.7866 -1.675 -1.659 -1.18118 -1.257 -1.5468 -1.32717 -1.71238 0 -0.31683 -3.6072 0 -3.39877 -3.136 -3.4474 -3.0951 -3.524 -6.2876 -3.56 -4.83 -4.06 -6.248 0 -3.01917 -1.301 -0.7185 -2.4617 -2.409 -2.65732 -2.2678 -2.2824 -2.454 -2.446 -2.5408 -2.5339 -2.53 -3.28 -5.5644 -2.9554 -2.949 -2.4647 -2.301 -2.008 -2.4146 -1.0769 -0.283 (Continued)

2-168

TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K (Continued ) Cmpd. no. 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98

Name Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane

Formula CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2

CAS 56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6

Mol. wt. 153.8227 88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997

Ideal gas enthalpy of formation, J/kmol × 1E-07

Ideal gas Gibbs energy of formation, J/kmol × 1E-07

-9.581 -92.21 0 5.109 -11.23 -10.29 -8.57 -13.32 -14.477 -13.23 -12.857 -12.535 0.4 30.894 2.85 -12.33 -28.62 -22.61 -0.46 -7.703 3.23 5.33 -9.602 -33.17 -24.946 -59.43 -39.85 -12.47 -21.09 4.1 0 -4.08 -3.89

-5.354 -87.76 0 9.829 -6.045 -7.01 -6.209 -5.251 -6.136 -4.019 -3.543 -3.166 13.79 29.76 11.22 3.191 -10.95 -9.028 10.77 3.885 11.05 10.44 4.886 -6.349 3.318 -30.5 -10.02 12.27 6.165 25.16 0 -1.181 -1.054

-33.34 2.57 3.02 2.25 -12.941 -12.979 -9.552 -15.08 -16.28 -40.847 -7.142 -25.21 -8.356 -49.7 -44.77

-8.827 7.79 8.29 7.67 -7.259 -7.3945 -6.896 -6.52 -8.018 -22.574 7.308 -12.21 1.774 -43.9485 -39.19

Ideal gas entropy, J/(kmol∙K) × 1E-05

Standard net enthalpy of combustion, J/kmol × 1E-09

3.0991 2.62 2.23079 3.1403 2.758 2.956 2.341 3.155 3.0594 3.5604 3.5259 3.5075 3.86 2.4117 2.64396 2.97276 3.277 3.3426 3.10518 2.929 2.91267 2.37378 3.646 5.672 5.457 5.99 5.971 5.433 6.116 5.263 1.4486 3.276 3.297 2.92964 5.014 3.4353 3.4185 3.3674 3.0501 3.0828 2.7018 3.448 3.548 4.29 3.522 3.423 3.681 2.824 2.88194

-0.2653 0.5286 0 -2.976 -1.279 -0.38 -0.6705 -1.864 -1.863 -3.52783 -3.528 -3.52256 -4.951 -1.096 -2.5678 -3.656 -3.4639 -3.299 -3.532 -3.0709 -2.9393 -1.9593 -3.968 -5.958 -6.29422 -5.72 -6.116 -6.1809 -6.6161 -6.1037 -0.24625 -1.16 -1.1769 -4.94691 -2.825 -2.826 -2.802 -1.1104 -1.105 -0.51388 -1.72 -1.707 -2.4105 -2.8003 -2.5035 -2.9607 -0.773662 -0.823

99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

Difluoromethane Diisopropyl amine Diisopropyl ether Diisopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene

CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F

75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6

52.02339 101.19 102.17476 114.18546 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032

-45.23 -14.38 -31.92 -31.14 -38.97 -38.42 14.57 -1.845 -17.68 -18.1 -17.2172 -17.9996 -2.42 -18.41 -19.17 -19.41 -60.5 -9.47 -3.724 -15.046 -62.742 -31.58 5.2 -11.6 -29.072 -45.646 -8.382 -23.495 -44.45 -4.715 2.992 -32.6 -53.78 -48.55 -17.15 -12.69 5.251 -1.73 -39.22 12.3428 -5.263 -38.83 -55.95 -33.37 -28.58 -28.61 -4.63 -46.36 -27.22 -59.15 0 -11.6566

-42.4747 6.42 -12.48 -12.37 -23.8 -20.11 18.49 6.839 -0.3125 3.52293 4.12124 3.44761 1.516 -11.28 -8.84 0.5717 -46.7749 -1.925 0.7302 -8.1441 -41.97 -18.16 17.5 11.96 4.981 11.57 -3.192 -16.785 -32.8 3.616 13.073 -19.05 -35.9 -31.22 3.955 4.48 6.844 10.3 -30.18 17.7987 -1.323 -30.31 -32.49 -9.042 -12.64 -13.3 -0.4814 -31.93 -11.52 -50.66 0 -6.9036

2.4658 4.12 3.989 4.27 3.726 4.038 2.833 2.7296 3.6592 3.65012 3.7451 3.70912 3.35291 2.667 3.26 4.1455 6.6 2.9953 2.8585 3.0627 4.245 3.0012 4.13 3.2 6.2415 9.3787 2.2912 2.8064 3.597 2.848 3.6063 4.55 4.23 4.417 3.826 3.783 2.192 3.21833 3.04891 2.5062 2.4299 3.282 5.097 5.076 3.8 4.069 2.961 4.025 3.881 4.07 2.02789 3.02629

-0.183031 -3.99 -3.70261 -4.095 -2.394 -2.996 -2.4189 -1.6146 -3.84761 -4.8639 -4.87084 -4.86436 -2.0441 -1.3284 -1.78871 -4.46075 -4.4662 -2.569 -1.7443 -1.6054 -4.41057 -2.1863 -5.8939 -4.0189 -7.51368 -12.3908 -1.42864 -1.235 -2.061 -1.5874 -4.3448 -4.41 -3.21203 -3.284 -4.87051 -4.2839 -1.323 -1.691 -1.0527 -1.481 -1.218 -1.50696 -4.448 -4.943 -3.103 -3.4863 -1.7366 -2.674 -3.12 -1.67471 -2.81451

2-169

(Continued)

2-170

TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K (Continued ) Cmpd. no. 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199

Name Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine

Formula C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N

CAS 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5

Mol. wt.

Ideal gas enthalpy of formation, J/kmol × 1E-07

Ideal gas Gibbs energy of formation, J/kmol × 1E-07

Ideal gas entropy, J/(kmol∙K) × 1E-05

48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571

-26.44 -23.43 -10.86 -19.22 -37.88 -3.48 0 -39.445 -26.48 -18.765 -53.62 -33.68 -35.3 -30.1 -30.0453 -6.289 -14.95 10.3 -37.417 -24.8 -16.694 -51.19 -31.62 -33.46 -27.9826 -27.76 -4.167 10.6 -12.92 12.37 10.5 9.5353 0 -3.629 -9.231 13.5143 -27.33 -2.063 -48.41 -8.38 -77.89 -36.8 -7.452 -20.094 -24 -41.19 18.49 -33.3 -2.297

-21.23 -21.03 -10.26 -14.71 -35.11 0.08225 0 9.083 -8.367 0.8165 -33.4 -12.55 -13.7 -12.25 -11.96 9.482 3.622 22.7 8.216 -9.92 -0.006634 -33.8 -13.39 -15.06 -13.0081 -12.6 8.7 19.9 2.759 21.85 19.9 15.917 0 -5.334 -9.53 12.4725 -27.54 -3.344 -36.21 3.192 -69.29 -28.8 -5.049 -16.232 -13.5 -32.42 19.384 -25.7 3.207

2.644 2.22734 2.19 2.4857 2.487 2.6714 1.26152 8.2023 4.5 4.2798 4.8 4.795 4.66 4.58 4.486 4.252 4.939 4.085 7.8102 4.22 3.8874 4.41 4.402 4.349 4.17856 4.092 3.863 3.76 4.546 3.694 3.72 2.3861 1.30571 1.98591 1.86786 2.01719 1.7367 2.056 3.412 3.124 4.003 3.5 1.8627 2.3988 3.2 3.198 2.4836 3.66 2.433

Standard net enthalpy of combustion, J/kmol × 1E-09 -1.127 -0.5219 -0.5268 -0.5021 -0.2115 -1.9959 0 -10.5618 -4.136 -4.46473 -3.839 -4.285 -4.27 -4.098 -4.09952 -4.3499 -4.7865 -4.2717 -9.95145 -3.524 -3.8551 -3.23 -3.675 -3.67 -3.49 -3.492 -3.7397 -3.64 -4.1762 -3.661 -3.64 -0.5342 -0.24182 -0.06904 -0.0286 -0.62329 0.1524 -0.518 -2.0004 -2.1566 -0.7732 -1.93 -0.80262 -0.6382 -1.71 -1.461 -1.8487 -1.9303 -0.97508

200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250

Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride

C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N

93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2

136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.0019096

-28.79 12.908 -15.37 -49.8 -30.3 -3.53 -4.18 26 -25.81 -10.2 13.8 -45.07 -21.5 -15.48 -33.2 -32.7 -35.26 -10.62 -0.38 0.74 -40.2 -21.64 -23.9 -5.96 -35.24 -26.6 -28.64 -6.24 -25.2 -26.26 -8.96 -2.29 -36 -57.95 -17.455 -27.8 -13.499 -31.24 -1.71 -42.75 -23.82 -8.23 -2.91 11.83 -28.3 -10.8 15.058 0 -10.21 0 -13.2089

-18.1 19.75 -1.405 -34.99 -14.54 6.668 6.045 30.25 -10.17 2.691 20.72 -30.53 -16.61 2.733 -12.9 -12.68 -15.24 3.63 10.38 11.38 -34.83 -11.71 -14.7 1.147 -29.5 -10.7 -13.51 0.0244 -12.18 -13.93 1.4509 -0.98 -25.4 -31.8 -0.5338 -9.321 -2.144 -17.76 5.808 -31.1 -11.1 1.793 1.853 21.73 -11.7 -4.73 22.408 0 -0.6125 0 -9.063

4.14 3.2151 3.4374 3.9 3.869 3.395 3.386 2.78 3.901 4.118 3.189 3.988 2.98277 3.433 3.75 3.853 3.853 3.399 3.264 3.305 3.287 3.0881 3.394 3.332 2.852 3.81 4.129 1.955 3.416 3.699 3.59 2.55 4.01 5.533 3.8089 4.32 2.955 3.263 2.9309 3.596 3.52 3.717 2.565 3.725 3.58 3.08 3.3315 1.46327 3.168 1.91609 2.60773

-3.772 -3.032 -3.23954 -2.622 -3.062 -3.1159 -3.1088 -2.93 -3.12818 -3.5723 -3.046 -2.686 -1.693 -4.25714 -4.058 -4.0574 -4.0318 -3.6741 -3.534 -3.5464 -1.357 -1.9314 -2.268 -2.354 -0.8924 -3.122 -3.4762 -1.06 -2.5311 -2.877 -2.957 -1.1517 -2.54 -5.056 -3.84915 -3.739 -2.64812 -2.4239 -2.5242 -2.078 -2.51739 -2.962 -1.999 -4.8214 -3.11 -1.77431 -4.9809 0 -1.25

2-171

(Continued)

2-172

TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K (Continued ) Cmpd. no. 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299

Name Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde

Formula CH3NO2 N2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O

CAS 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6

Mol. wt. 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914

Ideal gas enthalpy of formation, J/kmol × 1E-07

Ideal gas Gibbs energy of formation, J/kmol × 1E-07

Ideal gas entropy, J/(kmol∙K) × 1E-05

Standard net enthalpy of combustion, J/kmol × 1E-09

-7.47 8.205 9.025 -43.579 -31.09 -22.874 -57.73 -37.79 -39.71 -10.35 -19.08 6.17 -41.512 -29.02 -20.875 -55.6 -35.73 -37.62 -32.16 -33.9 -8.194 -17.01 8.23 -71.95 0 14.2671 -35.311 -22.78 -14.676 -49.13 -29.57 -31.37 -25.92 -25.79 -2.162 -11.3 -10.84 14.44 12.89 20.12 -9.6399 -1.454 -37.14 19.05 -10.468 -25.46 -27.21 4.677 -18.49

-0.6934 10.416 8.657 10.74 -7.136 2.498 -31.7 -10.86 -12.61 11.23 5.28 24.34 9.91 -8 1.6 -32.5 -11.7 -13.43 -11.38 -12.81 10.57 4.457 23.5 -66.24 0 16.3164 7.426 -10.67 -0.8813 -34.7 -14.23 -15.88 -13.83 -13.44 7.837 1.814 1.94408 21.03 19.45 30.219 -3.2637 4.87212 -30.7001 20.08 -2.439 -15.99 -17.52 20.85 -12.37

2.751 2.1985 2.106 8.9866 5.266 5.064 5.59 5.579 5.523 5.041 5.724 4.8699 8.5945 4.896 4.6723 5.2 5.187 5.132 4.962 4.879 4.637 5.331 4.478 3.608 2.05147 2.38823 7.4181 3.777 3.4945 4.02 4.01 3.958 3.786 3.7 3.462 4.05 4.154 3.298 3.3084 3.945 3.1481 3.527 3.995 2.439 2.702 3.226 3.175 4.233 3.065

-0.6432 -0.0820482 -0.0902489 -11.7812 -5.35 -5.68455 -5.061 -5.506 -5.506 -5.5716 -6.006 -5.493 -11.1715 -4.74 -5.07415 -4.448 -4.895 -4.894 -4.6984 -4.711 -4.961 -5.3962 -4.88145 -0.1989 0 -0.142671 -9.34237 -2.91 -3.24494 -2.617 -3.064 -3.058 -2.87956 -2.8804 -3.13037 -3.564 -3.5641 -3.051 -3.0291 -6.8282 -2.921 -3.298 -3.1715 -1.8563 -2.04311 -1.844 -1.834 -5.232 -1.684

300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345

Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene

C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O2S F6S O3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10

79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3

74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.0791128 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165

-45.35 5.155 -46.48 -7.05 0.79 2.023 -40.76 -7.59 -6.75 -42.15 -12.29 -161.494 14.74 -81.6 -29.684 -122.047 -39.572 -66.94 27.66 -33.244 -18.418 2.661 -3.376 -22.56 11.544 5.017 -14.2 -31.177 -9.58 -2.431 -0.95 -1.38 -22.401 -21.845 6.24 4.34 -27.043 -41.9 -31.49 30.46 2.845 -48.116 -24.1818 1.732 1.908 1.803

-35.82 9.688 -32.04 4.17 13.76 6.264 -29.36 -0.218 0.2583 -30.4 -6.92 -157.27 21.39 -70.11 -30.012 -111.653 -37.095 -55.01 42.3 6.599 -7.969 16.71 4.59 2.239 12.67 12.22 -8.097 5.771 11.41 9.899 12.61 11.71 1.394 1.828 26.79 28.44 4.116 -9.177 -22.79 30.6 4.195 -42.5514 -22.8572 11.876 12.2 12.14

2.949 2.877 4.023 3.242 4.0014 2.67 3.678 3.243 3.365 3.52 3.205 2.82651 3.451 4.398 2.481 2.91625 2.5651 4.48 5.263 7.0259 2.9729 3.6964 3.1 3.893 2.784 3.2099 3.371 6.6337 4.054 2.87 3.805 3.961 4.2296 4.2702 4.435 4.607 5.8493 6.363 3.28 2.794 2.7354 3.73966 1.88825 3.5854 3.5383 3.52165

-1.395 -1.80056 -2.672 -2.165 -4.95415 -1.9262 -2.041 -2.3398 -2.3458 -1.6476 -2.658 0.7055 -4.219 -1.3591 0.924 0.1422 -3.19 -9.053 -8.73282 -2.325 -5.3575 -2.76549 -5.0639 -2.4352 -3.734 -0.9685 -8.1229 -4.0405 -2.2449 -4.934 -4.9307 -5.06528 -5.06876 -2.6867 -3.2959 -6.9036 -6.726 -1.95 -2.362 -1.178 -1.544 -4.3318 -4.333 -4.333

The compounds are considered to be formed from the elements in their standard states at 298.15 K and 1 bar. These include C (graphite) and S (rhombic). Enthalpy of combustion is the net value for the compound in its standard state at 298.15 K and 1 bar. Products of combustion are taken to be CO2 (gas), H2O (gas), F2(gas), Cl2 (gas), Br2 (gas), I2 (gas), SO2 (gas), N2 (gas), P4O10 (crystalline), SiO2 (crystobalite), and Al2O3 (crystal, alpha). Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”. 2-173

2-174

PHYSICAL AnD CHEMICAL DATA

TABLE 2-96 Ideal Gas Sensible Enthalpies, hT – h298 (kJ/kmol), of Combustion Products Temperature, K

CO

CO2

H

OH

H2

N

NO

NO2

N2

N2O

O

O2

SO2

H2O

-2858 -1692 -1110 -529 0

-3414 -2079 -1383 -665 0

-2040 -1209 -793 -377 0

-2976 -1756 -1150 -546 0

-2774 -1656 -1091 -522 0

-2040 -1209 -793 -378 0

-2951 -1743 -1142 -543 0

-3495 -2104 -1392 -672 0

-2857 -1692 -1110 -528 0

-3553 -2164 -1438 -692 0

-2186 -1285 -840 -398 0

-2868 -1703 -1118 -533 0

-3736 -2258 -1496 -718 0

-3282 -1948 -1279 -609 0

300 320 340 360 380

54 638 1221 1805 2389

69 823 1594 2382 3184

38 454 870 1285 1701

55 654 1251 1847 2442

53 630 1209 1791 2373

38 454 870 1286 1701

55 652 1248 1845 2442

68 816 1571 2347 3130

54 636 1219 1802 2386

72 854 1654 2470 3302

41 478 913 1346 1777

54 643 1234 1828 2425

74 881 1702 2538 3387

62 735 1410 2088 2769

400 420 440 460 480

2975 3563 4153 4643 5335

4003 4835 5683 6544 7416

2117 2532 2948 3364 3779

3035 3627 4219 4810 5401

2959 3544 4131 4715 5298

2117 2533 2949 3364 3780

3040 3638 4240 4844 5450

3927 4735 5557 6392 7239

2971 3557 4143 4731 5320

4149 5010 5884 6771 7670

2207 2635 3063 3490 3918

3025 3629 4236 4847 5463

4250 5126 6015 6917 7831

3452 4139 4829 5523 6222

500 550 600 650 700

5931 7428 8942 10477 12023

8305 10572 12907 15303 17754

4196 5235 6274 7314 8353

5992 7385 8943 10423 11902

5882 6760 8811 10278 11749

4196 5235 6274 7314 8353

6059 7592 9144 10716 12307

8099 10340 12555 14882 17250

5911 7395 8894 10407 11937

8580 10897 13295 15744 18243

4343 5402 6462 7515 8570

6084 7653 9244 10859 12499

8758 11123 13544 16022 18548

6925 8699 10501 12321 14192

750 800 850 900 950

13592 15177 16781 18401 20031

20260 22806 25398 28030 30689

9392 10431 11471 12510 13550

13391 14880 16384 17888 19412

13223 14702 16186 17676 19175

9329 10431 11471 12510 13550

13919 15548 17195 18858 20537

19671 22136 24641 27179 29749

13481 15046 16624 18223 19834

20791 23383 26014 28681 31381

9620 10671 11718 12767 13812

14158 15835 17531 19241 20965

21117 23721 26369 29023 31714

16082 18002 19954 21938 23954

1000 1100 1200 1300 1400

21690 25035 28430 31868 35343

33397 38884 44473 50148 55896

14589 16667 18746 20824 22903

20935 24024 27160 30342 33569

20680 23719 26797 29918 33082

14589 16667 18746 20824 22903

22229 25653 29120 32626 36164

32344 37605 42946 48351 53808

21463 24760 28109 31503 34936

34110 39647 45274 50976 56740

14860 16950 19039 21126 23212

22703 26212 29761 33344 36957

34428 39914 45464 51069 56718

26000 30191 34506 38942 43493

1500 1600 1700 1800 1900

38850 42385 45945 49526 53126

61705 67569 73480 79431 85419

24982 27060 29139 31217 33296

36839 40151 43502 46889 50310

36290 39541 42835 46169 49541

24982 27060 29139 31218 33296

39729 43319 46929 50557 54201

59309 64846 70414 76007 81624

38405 41904 45429 48978 52548

62557 68420 74320 80254 86216

25296 27381 29464 31547 33630

40599 44266 47958 51673 55413

62404 68123 73870 79642 85436

48151 52908 57758 62693 67706

2000 2100 2200 2300 2400

56744 60376 64021 67683 71324

91439 97488 103562 109660 115779

35375 37453 39532 41610 43689

53762 57243 60752 64285 67841

52951 56397 59876 63387 66928

35375 37454 39534 41614 43695

57859 61530 65212 68904 72606

87259 92911 98577 104257 109947

56137 59742 63361 66995 70640

92203 98212 104240 110284 116344

35713 37796 39878 41962 44045

59175 62961 66769 70600 74453

91250 97081 102929 108792 114669

72790 77941 83153 88421 93741

2500 2600 2700 2800 2900

74985 78673 82369 86074 89786

121917 128073 134246 140433 146636

45768 47846 49925 52004 54082

71419 75017 78633 82267 85918

70498 74096 77720 81369 85043

45777 47860 49945 52033 54124

76316 80034 83759 87491 91229

115648 121357 127075 132799 138530

74296 77963 81639 85323 89015

122417 128501 134596 140701 146814

46130 48216 50303 52391 54481

78328 82224 86141 90079 94036

120559 126462 132376 138302 144238

99108 104520 109973 115464 120990

3000 3500 4000 4500 5000

93504 112185 130989 149895 168890

152852 184109 215622 247354 279283

56161 66554 75947 87340 97733

89584 108119 126939 145991 165246

88740 107555 126874 146660 166876

56218 66769 77532 88614 100111

94973 113768 132671 151662 170730

144267 173020 201859 230756 259692

92715 111306 130027 148850 167763

152935 183636 214453 245348 276299

56574 67079 77675 88386 99222

98013 118165 188705 159572 180749

150184 180057 210145 240427 270893

126549 154768 183552 212764 242313

200 240 260 280 298.15

Converted and usually rounded off from JANAF Thermochemical Tables, NSRDS-NBS-37, 1971 (1141 pp.).

PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS

2-175

TABLE 2-97 Ideal Gas Entropies s°, kJ/(kmol· K), of Combustion Products Temperature, K

CO

CO2

H

OH

H2

N

NO

NO2

N2

N2O

O

O2

SO2

H2O

200 240 260 280 298.15

186.0 191.3 193.7 195.3 197.7

200.0 206.0 208.8 211.5 213.8

106.4 110.1 111.8 113.3 114.7

171.6 177.1 179.5 181.8 183.7

119.4 124.5 126.8 129.2 130.7

145.0 148.7 150.4 151.9 153.3

198.7 204.1 206.6 208.8 210.8

225.9 232.2 235.0 237.7 240.0

180.0 185.2 187.6 189.8 191.6

205.6 211.9 214.8 217.5 220.0

152.2 156.2 158.0 159.7 161.1

193.5 198.7 201.1 203.3 205.1

233.0 239.9 242.8 245.8 248.2

175.5 181.4 184.1 186.6 188.8

300 320 340 360 380

197.8 199.7 201.5 203.2 204.7

214.0 216.5 218.8 221.0 223.2

114.8 116.2 117.4 118.6 119.7

183.9 185.9 187.7 189.4 191.0

130.9 132.8 134.5 136.2 137.7

153.4 154.8 156.0 157.2 158.3

210.9 212.9 214.7 216.4 218.0

240.3 242.7 245.0 247.2 249.3

191.8 193.7 195.5 197.2 198.7

220.2 222.7 225.2 227.5 229.7

161.2 162.6 163.9 165.2 166.3

205.3 207.2 209.0 210.7 212.5

248.5 251.1 253.6 256.0 258.2

189.0 191.2 193.3 195.2 197.1

400 420 440 460 480

206.2 207.7 209.0 210.4 211.6

225.3 227.3 229.3 231.2 233.1

120.8 121.8 122.8 123.7 124.6

192.5 194.0 195.3 196.6 197.9

139.2 140.6 141.9 143.2 144.5

159.4 160.4 161.4 162.3 163.1

219.5 221.0 222.3 223.7 225.0

251.3 253.2 255.1 257.0 258.8

200.2 201.5 202.9 204.2 205.5

231.9 234.0 236.0 238.0 239.9

167.4 168.4 169.4 170.4 171.3

213.8 215.3 216.7 218.0 219.4

260.4 262.5 264.6 266.6 268.5

198.8 200.5 202.0 203.6 205.1

500 550 600 650 700

212.8 215.7 218.3 220.8 223.1

234.9 239.2 243.3 247.1 250.8

125.5 127.5 129.3 131.0 132.5

199.1 201.8 204.4 206.8 209.0

145.7 148.6 151.1 153.4 155.6

164.0 166.0 167.8 169.4 171.0

226.3 229.1 231.9 234.4 236.8

260.6 264.7 268.8 272.6 276.0

206.7 209.4 212.2 214.6 216.9

241.8 246.2 250.4 254.3 258.0

172.2 174.2 176.1 177.7 179.3

220.7 223.7 226.5 229.1 231.5

270.5 274.9 279.2 283.1 286.9

206.5 210.5 213.1 215.9 218.7

750 800 850 900 950

225.2 227.3 229.2 231.1 232.8

255.4 257.5 260.6 263.6 266.5

133.9 135.2 136.4 137.7 138.8

211.1 213.0 214.8 216.5 218.1

157.6 159.5 161.4 163.1 164.7

172.5 173.8 175.1 176.3 177.4

239.0 241.1 243.0 245.0 246.8

279.3 282.5 285.5 288.4 291.3

219.0 221.0 223.0 224.8 226.5

261.5 264.8 268.0 271.1 274.0

180.7 182.1 183.4 184.6 185.7

233.7 235.9 237.9 239.9 241.8

290.4 293.8 297.0 300.1 303.0

221.3 223.8 226.2 228.5 230.6

1000 1100 1200 1300 1400

234.5 237.7 240.7 243.4 246.0

269.3 274.5 279.4 283.9 288.2

139.9 141.9 143.7 145.3 146.9

219.7 222.7 225.4 228.0 230.3

166.2 169.1 171.8 174.3 176.6

178.5 180.4 182.2 183.9 185.4

248.4 251.8 254.8 257.6 260.2

293.9 298.9 303.6 307.9 311.9

228.2 231.3 234.2 236.9 239.5

276.8 282.1 287.0 291.5 295.8

186.8 188.8 190.6 192.3 193.8

243.6 246.9 250.0 252.9 255.6

305.8 311.0 315.8 320.3 324.5

232.7 236.7 240.5 244.0 247.4

1500 1600 1700 1800 1900

248.4 250.7 252.9 254.9 256.8

292.2 296.0 299.6 303.0 306.2

148.3 149.6 150.9 152.1 153.2

232.6 234.7 236.8 238.7 240.6

178.8 180.9 182.9 184.8 186.7

186.9 188.2 189.5 190.7 191.8

262.7 265.0 267.2 269.3 271.3

315.7 319.3 322.7 325.9 328.9

241.9 244.1 246.3 248.3 250.2

299.8 303.6 307.2 310.6 313.8

195.3 196.6 197.9 199.1 200.2

258.1 260.4 262.7 264.8 266.8

328.4 332.1 335.6 338.9 342.0

250.6 253.7 256.6 259.5 262.2

2000 2100 2200 2300 2400

258.7 260.5 262.2 263.8 265.4

309.3 312.2 315.1 317.8 320.4

154.3 155.3 156.3 157.2 158.1

242.3 244.0 245.7 247.2 248.7

188.4 190.1 191.7 193.3 194.8

192.9 193.9 194.8 195.8 196.7

273.1 274.9 276.6 278.3 279.8

331.8 334.5 337.2 339.7 342.1

252.1 253.8 255.5 257.1 258.7

316.9 319.8 322.6 325.3 327.9

201.3 202.3 203.2 204.2 205.0

268.7 270.6 272.4 274.1 275.7

345.0 347.9 350.6 353.2 355.7

264.8 267.3 269.7 272.0 274.3

2500 2600 2700 2800 2900

266.9 268.3 269.7 271.0 272.3

322.9 325.3 327.6 329.9 332.1

158.9 159.7 160.5 161.3 162.0

250.2 251.6 253.0 254.3 255.6

196.2 197.7 199.0 200.3 201.6

197.5 198.3 199.1 199.9 200.6

281.4 282.8 284.2 285.6 286.9

344.5 346.7 348.9 350.9 352.9

260.2 261.6 263.0 264.3 265.6

330.4 332.7 335.0 337.3 339.4

205.9 206.7 207.5 208.3 209.0

277.3 278.8 280.3 281.7 283.1

358.1 360.4 362.6 364.8 366.9

276.5 278.6 380.7 282.7 284.6

3000 3500 4000 4500 5000

273.6 279.4 284.4 288.8 292.8

334.2 343.8 352.2 359.7 366.4

162.7 165.9 168.7 171.1 173.3

256.8 262.5 267.6 272.1 276.1

202.9 208.7 213.8 218.5 222.8

201.3 204.6 207.4 210.1 212.5

288.2 294.0 299.0 303.5 307.5

354.9 363.8 371.5 378.3 384.4

266.9 272.6 277.6 282.1 286.0

341.5 350.9 359.2 366.5 373.0

209.7 212.9 215.8 218.3 220.6

284.4 290.7 296.2 301.1 305.5

368.9 378.1 386.1 393.3 399.7

286.5 295.2 302.9 309.8 316.0

Usually rounded off from JANAF Thermochemical Tables, NSRDS-NBS-37, 1971 (1141 pp.). Equilibrium constants can be calculated by combining Δhf° values from Table 2-95, hT - h298 from Table 2-96, and s° values from the above, using the formula ln kp = -ΔG/(RT), where ΔG = Δhf° + (hT - h298) - T s°.

2-176

PHYSICAL AnD CHEMICAL DATA

HEATS OF SOLUTIOn TABLE 2-98 Heats of Solution of Inorganic Compounds in Water Heat evolved, in kilocalories per gram formula weight, on solution in water at 18°C. Computed from data in Bichowsky and Rossini, Thermochemistry of Chemical Substances, Reinhold, New York, 1936. Substance

Dilution*

Formula

Heat, kcal/mol

Aluminum bromide chloride

aq 600 600 aq aq aq aq aq aq aq aq ∞ aq 600 aq ∞ aq ∞ 800 aq aq aq aq aq

AlBr3 AlCl3 AlCl3⋅6H2O AlF3 AlF3⋅½H2O AlF3⋅3½H2O AlI3 Al2(SO4)3 Al2(SO4)3⋅6H2O Al2(SO4)3⋅18H2O NH4Br NH4Cl (NH4)2CrO4 (NH4)2Cr2O7 NH4I NH4NO3 NH4BO3⋅H2O (NH4)2SO4 NH4HSO4 (NH4)2SO3 (NH4)2SO3⋅H2O SbF3 SbI3 H3AsO4

+85.3 +77.9 +13.2 +31 +19.0 -1.7 +89.0 +126 +56.2 +6.7 -4.45 -3.82 -5.82 -12.9 -3.56 -6.47 -9.0 -2.75 +0.56 -1.2 -4.13 -1.7 -0.8 -0.4

∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ aq aq aq ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ aq aq aq aq aq aq aq aq aq

Ba(BrO3)2⋅H2O BaBr2 BaBr2⋅H2O BaBr2⋅2H2O Ba(ClO3)2 Ba(ClO3)2⋅H2O BaCl2 BaCl2⋅H2O BaCl2.2H2O Ba(CN)2 Ba(CN)2⋅H2O Ba(CN)2⋅2H2O Ba(IO3)2 Ba(IO3)2⋅H2O BaI2 BaI2⋅H2O BaI2⋅2H2O BaI2⋅2½H2O BaI2⋅7H2O Ba(NO3)2 Ba(ClO4)2 Ba(ClO4)2⋅3H2O BaS BeBr2 BeCl2 BeI2 BeSO4 BeSO4⋅H2O BeSO4⋅2H2O BeSO4⋅4H2O BiI3 H3BO3

-15.9 +5.3 -0.8 -3.87 -6.7 -10.6 +2.4 -2.17 -4.5 +1.5 -2.4 -4.9 -9.1 -11.3 +10.5 +2.7 +0.14 -0.58 -6.61 -10.2 -2.8 -10.5 +7.2 +62.6 +51.1 +72.6 +18.1 +13.5 +7.9 +1.1 +3 -5.4

400 400 400 400 400 400 400 400 400 400 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞

CdBr2 CdBr2⋅4H2O CdCl2 CdCl2⋅H2O CdCl2⋅2½H2O Cd(NO3)2⋅H2O Cd(NO3)2⋅4H2O CdSO4 CdSO4⋅H2O CdSO4⋅2⅔H2O Ca(C2H3O2)2 Ca(C2H3O2)2⋅H2O CaBr2 CaBr2⋅6H2O CaCl2 CaCl2⋅H2O CaCl2⋅2H2O CaCl2⋅4H2O CaCl2⋅6H2O

+0.4 -7.3 +3.1 +0.6 -3.00 +4.17 -5.08 +10.69 +6.05 +2.51 +7.6 +6.5 +24.86 -0.9 +4.9 +12.3 +12.5 +2.4 -4.11

fluoride iodide sulfate Ammonium bromide chloride chromate dichromate iodide nitrate perborate sulfate sulfate, acid sulfite Antimony fluoride iodide Arsenic acid Barium bromate bromide chlorate chloride cyanide iodate iodide

nitrate perchlorate sulfide Beryllium bromide chloride iodide sulfate

Bismuth iodide Boric acid Cadmium bromide chloride nitrate sulfate Calcium acetate bromide chloride

Substance Calcium—(Cont.) formate iodide

Dilution*

Formula

Heat, kcal/mol

400 ∞ ∞ ∞ ∞ ∞ ∞ ∞ aq aq ∞ ∞ ∞ aq

+0.7 +28.0 +1.8 +4.1 +0.7 -3.2 -4.2 -7.99 -0.6 -1 +5.1 +3.6 -0.18 +18.6 +5.3 +2.0 +5.7 +18.4 -1.25 +18.5 +9.8 -2.9 +18.8 +15.0 -1.4 -3.6 +2.4 +0.5 +10.3 -2.6 -10.7 +15.9 +9.3 +3.65 -2.85 +11.6

Cuprous sulfate

aq

Ca(CHO2)2 CaI2 CaI2⋅8H2O Ca(NO3)2 Ca(NO3)2⋅H2O Ca(NO3)2⋅2H2O Ca(NO3)2⋅3H2O Ca(NO3)2⋅4H2O Ca(H2PO4)2⋅H2O CaHPO4⋅2H2O CaSO4 CaSO4⋅½H2O CaSO4⋅2H2O CrCl2 CrCl2⋅3H2O CrCl2⋅4H2O CrI2 CoBr2 CoBr2⋅6H2O CoCl2 CoCl2⋅2H2O CoCl2⋅6H2O CoI2 CoSO4 CoSO4⋅6H2O CoSO4⋅7H2O Cu(C2H3O2)2 Cu(CHO2)2 Cu(NO3)2 Cu(NO3)2⋅3H2O Cu(NO3)2⋅6H2O CuSO4 CuSO4⋅H2O CuSO4⋅3H2O CuSO4⋅5H2O Cu2SO4

Ferric chloride

1000 1000 1000 800 aq 400 400 400 aq 400 400 400 400

FeCl3 FeCl3⋅2½H2O FeCl3⋅6H2O Fe(NO3)3⋅9H2O FeBr2 FeCl2 FeCl2⋅2H2O FeCl2⋅4H2O FeI2 FeSO4 FeSO4⋅H2O FeSO4⋅4H2O FeSO4⋅7H2O

+31.7 +21.0 +5.6 -9.1 +18.0 +17.9 +8.7 +2.7 +23.3 +14.7 +7.35 +1.4 -4.4

400 400 aq aq aq 400 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞

Pb(C2H3O2)2 Pb(C2H3O2)2⋅3H2O PbBr2 PbCl2 Pb(CHO2)2 Pb(NO3)2 LiBr LiBr⋅H2O LiBr⋅2H2O LiBr⋅3H2O LiCl LiCl⋅H2O LiCl⋅2H2O LiCl⋅3H2O LiF LiOH LiOH⋅⅛H2O LiOH⋅H2O LiI LiI⋅½H2O LiI⋅H2O LiI⋅2H2O LiI⋅3H2O LiNO3 LiNO3⋅3H2O

+1.4 -5.9 -10.1 -3.4 -6.9 -7.61 +11.54 +5.30 +2.05 -1.59 +8.66 +4.45 +1.07 -1.98 -0.74 +4.74 +4.39 +9.6 +14.92 +10.08 +6.93 +3.43 -0.17 +0.466 -7.87

nitrate

phosphate, monodibasic sulfate Chromous chloride iodide Cobaltous bromide chloride iodide sulfate Cupric acetate formate nitrate sulfate

nitrate Ferrous bromide chloride iodide sulfate

Lead acetate bromide chloride formate nitrate Lithium bromide

chloride

fluoride hydroxide iodide

nitrate

aq aq aq 400 400 400 aq 400 400 400 aq aq 200 200 200 800

*The numbers represent moles of water used to dissolve 1 g formula weight of substance; ∞ means “infinite dilution”; and aq means “aqueous solution of unspecified dilution.”

HEATS OF SOLUTIOn

2-177

TABLE 2-98 Heats of Solution of Inorganic Compounds in Water (Continued ) Dilution*

Substance Lithium—(Cont.) sulfate Magnesium bromide chloride

iodide nitrate phosphate sulfate

sulfide Manganic nitrate sulfate Manganous acetate bromide chloride formate iodide

sulfate Mercuric acetate bromide chloride nitrate Mercurous nitrate Nickel bromide Nickel chloride

iodide nitrate sulfate Phosphoric acid, orthopyroPotassium acetate aluminum sulfate

Formula

Heat, kcal/mol +6.71 +3.77

∞ ∞

Li2SO4 Li2SO4⋅H2O

∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ aq ∞ ∞ ∞ ∞ ∞ ∞ aq 400 400 400 aq aq aq aq aq aq 400 400 400 aq aq aq aq aq aq aq 400 400 400 aq aq aq aq aq

MgBr2 MgBr2⋅H2O MgBr2⋅6H2O MgCl2 MgCl2⋅2H2O MgCl2⋅4H2O MgCl2⋅6H2O MgI2 Mg(NO3)2⋅6H2O Mg3(PO4)2 MgSO4 MgSO4⋅H2O MgSO4⋅2H2O MgSO4⋅4H2O MgSO4⋅6H2O MgSO4⋅7H2O MgS Mn(NO3)2 Mn(NO3)2⋅3H2O Mn(NO3)2⋅6H2O Mn2(SO4)3 Mn(C2H3O2)2 Mn(C2H3O2)2⋅4H2O MnBr2 MnBr2⋅H2O MnBr2⋅4H2O MnCl2 MnCl2⋅2H2O MnCl2⋅4H2O Mn(CHO2)2 Mn(CHO2)2⋅2H2O MnI2 MnI2⋅H2O MnI2⋅2H2O MnI2⋅4H2O MnI2⋅6H2O MnSO4 MnSO4⋅H2O MnSO4⋅7H2O Hg(C2H3O2)2 HgBr2 HgCl2 Hg(NO3)2⋅½H2O Hg2(NO3)2⋅2H2O

+43.7 +35.9 +19.8 +36.3 +20.8 +10.5 +3.4 +50.2 -3.7 +10.2 +21.1 +14.0 +11.7 +4.9 +0.55 -3.18 +25.8 +12.9 -3.9 -6.2 +22 +12.2 +1.6 +15 +14.4 +16.1 +16.0 +8.2 +1.5 +4.3 -2.9 +26.2 +24.1 +22.7 +19.9 +21.2 +13.8 +11.9 -1.7 -4.0 -2.4 -3.3 -0.7 -11.5

aq aq 800 800 800 800 aq 200 200 200 200 400 400 aq aq ∞ 600 600

NiBr2 NiBr2⋅3H2O NiCl2 NiCl2⋅2H2O NiCl2⋅4H2O NiCl2⋅6H2O NiI2 Ni(NO3)2 Ni(NO3)2⋅6H2O NiSO4 NiSO4⋅7H2O H3PO4 H3PO4⋅½H2O H4P2O7 H4P2O7⋅1½H2O KC2H3O2 KAl(SO4)2 KAl(SO4)2⋅3H2O KAl(SO4)2⋅12H2O KHCO3 KBrO3 KBr K2CO3 K2CO3⋅½H2O K2CO3⋅1½H2O KClO3 KCl K2CrO4 KCr(SO4)2 KCr(SO4)2⋅H2O KCr(SO4)2⋅2H2O KCr(SO4)2⋅6H2O KCr(SO4)2⋅12H2O

+19.0 +0.2 +19.23 +10.4 +4.2 -1.15 +19.4 +11.8 -7.5 +15.1 -4.2 +2.79 -0.1 +25.9 +4.65 +3.55 +48.5 +26.6 -10.1 -5.1 -10.13 -5.13 +6.58 +4.25 -0.43 -10.31 -4.404 -4.9 +55 +42 +33 +7 -9.5

bicarbonate bromate bromide carbonate

2000 ∞ ∞ ∞

chlorate chloride chromate chrome sulfate

∞ ∞ 2185 600

Substance Potassium—(Cont.) cyanide dichromate fluoride hydrosulfide hydroxide

iodate iodide nitrate oxalate perchlorate permanganate phosphate, dihydrogen pyrosulfite sulfate sulfate, acid sulfide sulfite thiocyanate thionate, dithiosulfate Silver acetate nitrate Sodium acetate arsenate bicarbonate borate, tetrabromide carbonate

chlorate chloride chromate cyanide fluoride hydrosulfide Sodium hydroxide

iodide metaphosphate nitrate nitrite perchlorate phosphate di triphosphate di diphosphite, monodipyrophosphate di-

Dilution*

Formula

Heat, kcal/mol

∞ 400 aq aq aq ∞ 800 ∞ aq aq ∞ aq ∞

KCN K2Cr2O7 KF KF⋅2H2O KF⋅4H2O KHS KHS⋅¼H2O KOH KOH⋅¾H2O KOH⋅H2O KOH⋅7H2O KIO3 KI KNO3 K2C2O4 K2C2O4⋅H2O KClO4 KMnO4 KH2PO4 K2S2O5 K2S2O5⋅½H2O K2SO4 KHSO4 K2S K2SO3 K2SO3⋅H2O KCNS K2S2O6 K2S2O3

-3.0 -17.8 +3.96 -1.85 -6.05 +0.86 +1.21 +12.91 +4.27 +3.48 +0.86 -6.93 -5.23 -8.633 -4.6 -7.5 -12.94 -10.4 +4.7 -11.0 -10.22 -6.32 -3.10 -11.0 +1.8 +1.37 -6.08 -13.0 -4.5

aq 200 ∞ ∞ 500 500 1800 900 900 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 800 800 800 200 200 200 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 600 ∞ aq ∞ 1600 1600 1600 1600 1600 1600 600 600 800 800 1600 1600 1200 1200

AgC2H3O2 AgNO3 NaC2H3O2 NaC2H3O2⋅3H2O Na3AsO4 Na3AsO4⋅12H2O NaHCO3 Na2B4O7 Na2B4O7⋅10H2O NaBr NaBr⋅2H2O Na2CO3 Na2CO3⋅H2O Na2CO3⋅7H2O Na2CO3⋅10H2O NaClO3 NaCl Na2CrO4 Na2CrO4⋅4H2O Na2CrO4⋅10H2O NaCN NaCN⋅½H2O NaCN⋅2H2O NaF NaHS NaHS⋅2H2O NaOH NaOH⋅½H2O NaOH⋅⅔H2O NaOH⋅¾H2O NaOH⋅H2O NaI NaI⋅2H2O NaPO3 NaNO3 NaNO2 NaClO4 Na2HPO4 Na3PO4 Na3PO4⋅12H2O Na2HPO4⋅2H2O Na2HPO4⋅7H2O Na2HPO4⋅12H2O NaH2PO3 NaH2PO3⋅2½H2O Na2HPO3 Na2HPO3⋅5H2O Na4P2O7 Na4P2O7⋅10H2O Na2H2P2O7 Na2H2P2O7⋅6H2O

-5.4 -4.4 +4.085 -4.665 +15.6 -12.61 -4.1 +10.0 -16.8 -0.58 -4.57 +5.57 +2.19 -10.81 -16.22 -5.37 -1.164 +2.50 -7.52 -16.0 -0.37 -0.92 -4.41 -0.27 +4.62 -1.49 +10.18 +8.17 +7.08 +6.48 +5.17 +1.57 -3.89 +3.97 -5.05 -3.6 -4.15 +5.21 +13 -15.3 -0.82 -12.04 -23.18 +0.90 -5.29 +9.30 -4.54 +11.9 -11.7 -2.2 -14.0

200 1600 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 400

(Continued)

2-178

PHYSICAL AnD CHEMICAL DATA

TABLE 2-98 Heats of Solution of Inorganic Compounds in Water (Continued )

Substance Sodium—(Cont.) sulfate sulfate, acid sulfide

sulfite thiocyanate thionate, diSodium thiosulfate Stannic bromide Stannous bromide iodide Strontium acetate bromide

Dilution*

Formula

Heat, kcal/mol

∞ ∞ 800 800 ∞ ∞ ∞ ∞ ∞ ∞ ∞ aq aq aq aq aq aq aq ∞ ∞ ∞ ∞ ∞ ∞ ∞

Na2SO4 Na2SO4⋅10H2O NaHSO4 NaHSO4⋅H2O Na2S Na2S⋅4½H2O Na2S⋅5H2O Na2S⋅9H2O Na2SO3 Na2SO3⋅7H2O NaCNS Na2S2O6 Na2S2O6⋅2H2O Na2S2O3 Na2S2O3⋅5H2O SnBr4 SnBr2 SnI2 Sr(C2H3O2)2 Sr(C2H3O2)2⋅½H2O SrBr2 SrBr2⋅H2O SrBr2⋅2H2O SrBr2⋅4H2O SrBr2⋅6H2O

+0.28 -18.74 +1.74 +0.15 +15.2 +0.09 -6.54 -16.65 +2.8 -11.1 -1.83 -5.80 -11.86 +2.0 -11.30 +15.5 -1.6 -5.8 +6.2 +5.9 +16.4 +9.25 +6.5 +0.4 -6.1

Substance

Dilution*

Strontium—(Cont.) chloride

iodide

nitrate sulfate Sulfuric acid, pyroZinc acetate bromide chloride iodide nitrate sulfate

Formula

∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞

SrCl2 SrCl2⋅H2O SrCl2⋅2H2O SrCl2⋅6H2O SrI2 SrI2⋅H2O SrI2⋅2H2O SrI2⋅6H2O Sr(NO3)2 Sr(NO3)2⋅4H2O SrSO4 H2S2O7

+11.54 +6.4 +2.95 -7.1 +20.7 +12.65 +10.4 -4.5 -4.8 -12.4 +0.5 -18.08

400 400 400 400 400 aq 400 400 400 400 400 400

Zn(C2H3O2)2 Zn(C2H3O2)2⋅H2O Zn(C2H3O2)2⋅2H2O ZnBr2 ZnCl2 ZnI2 Zn(NO3)2⋅3H2O Zn(NO3)2⋅6H2O ZnSO4 ZnSO4⋅H2O ZnSO4⋅6H2O ZnSO4⋅7H2O

+9.8 +7.0 +3.9 +15.0 +15.72 +11.6 -5 -6.0 +18.5 +10.0 -0.8 -4.3

note: To convert kilocalories per mole to British thermal units per pound-mole, multiply by 1.799 × 10-3.

TABLE 2-99 Heats of Solution of Organic Compounds in Water (at Infinite Dilution and Approximately Room Temperature) Recalculated and rearranged from International Critical Tables, vol. 5, pp. 148–150. cal/mol = Btu/(lb⋅mol) × 1.799.

Solute Acetic acid (solid), C2H4O2 Acetylacetone, C5H8O2 Acetylurea, C3H6N2O2 Aconitic acid, C6H6O6 Ammonium benzoate, C7H9NO2 picrate succinate (n-) Aniline, hydrochloride, C6H8ClN Barium picrate Benzoic acid, C7H6O2 Camphoric acid, C10H16O4 Citric acid, C6H8O7 Dextrin, C12H20O10 Fumaric acid, C4H4O4 Hexamethylenetetramine, C6H12N4 Hydroxybenzamide (m-), C7H7NO2 (m-), (HCl) (o-), C7H7NO2 (p-) Hydroxybenzoic acid (o-), C7H6O3 (p-), C7H6O3 Hydroxybenzyl alcohol (o-), C7H8O2 Inulin, C36H62O31 Isosuccinic acid, C4H6O4 Itaconic acid, C5H6O4 Lactose, C12H22O11⋅H2O Lead picrate (2H2O) Magnesium picrate (8H2O) Maleic acid, C4H4O4 Malic acid, C4H6O5 Malonic acid, C3H4O4 Mandelic acid, C8H2O3 Mannitol, C6H14O6 Menthol, C10H20O Nicotine dihydrochloride, C10H16Cl2N2 Nitrobenzoic acid (m-), C7H5NO4 (o-), C7H5NO4 (p-), C7H5NO4 Nitrophenol (m-), C6H5NO3 (o-), C6H5NO3 (p-), C6H5NO3

Heat of solution, cal/mol solute* -2,251 -641 -6,812 -4,206 -2,700 -8,700 -3,489 -2,732 -4,708 -6,501 -502 -5,401 268 -5,903 4,780 -4,161 -7,003 -4,340 -5,392 -6,350 -5,781 -3,203 -96 -3,420 -5,922 -3,705 -7,098 -13,193 14,699 -15,894 -4,441 -3,150 -4,493 -3,090 -5,260 0 6,561 -5,593 -5,306 -8,891 -5,210 -6,310 -4,493

Solute Oxalic acid, C2H2O4 (2H2O) Phenol (solid), C6H6O Phthalic acid, C8H6O4 Picric acid, C6H3N3O7 Piperic acid, C12H10O4 Piperonylic acid, C8H6O4 Potassium benzoate citrate tartrate (n-) (0.5 H2O) Pyrogallol, C6H6O3 Pyrotartaric acid Quinone Raffinose, C18H32O16 (5H2O) Resorcinol, C6H6O2 Silver malonate (n-) Sodium citrate (tri-) picrate potassium tartrate (4H2O) succinate (n-) (6H2O) tartrate (n-) (2H2O) Strontium picrate (6H2O) Succinic acid, C4H6O4 Succinimide, C4H5NO2 Sucrose, C12H22O11 Tartaric acid (d-) Thiourea, CH4N2S Urea, CH4N2O acetate formate nitrate oxalate Vanillic acid Vanillin Zinc picrate (8H2O)

Heat, kcal/mol

Heat of solution, cal/mol solute* -2,290 -8,485 -2,605 -4,871 -7,098 -10,492 -9,106 -1,506 2,820 -5,562 -3,705 -5,019 -3,991 -9,703 -3,960 -9,799 5,270 -6,441 -1,817 -12,342 2,390 -10,994 -1,121 -5,882 7,887 -14,412 -6,405 -4,302 -1,319 -3,451 -5,330 -3,609 -8,795 -7,194 -10,803 -17,806 -5,160 -5,210 -11,496 -15,894

*+ denotes heat evolved, and - denotes heat absorbed. The data in the International Critical Tables were calculated by E. Anderson.

THERMAL EXPAnSIOn AnD COMPRESSIBILITY

2-179

THERMAL EXPAnSIOn AnD COMPRESSIBILITY Unit Conversion For this subsection, the following unit conversion is applicable: °F = 9⁄5°C + 32. Additional References Some of the tables given under this subject are reprinted by permission from the Smithsonian Tables. For other data on thermal expansion, see International Critical Tables. The tabular index is in volume 3, and the data are in volume 2.

Thermal Expansion of Gases No tables of coefficients of thermal expansion of gases are given in this edition. The coefficient at constant pressure, 1/u (∂u/∂T)p, for an ideal gas is merely the reciprocal of the absolute temperature. For a real gas or liquid, both it and the coefficient at constant volume 1/p (∂p/∂T)v should be calculated either from the equation of state or from tabulated PVT data. For expansion of liquids and solids, see the following tables.

TABLE 2-100 Linear Expansion of the Solid Elements* C is the true expansion coefficient at the given temperature; M is the mean coefficient between given temperatures; where one temperature is given, the true coefficient at that temperature is indicated; α and β are coefficients in formula lt = l0(1 + αt + βt2); l0 is length at 0°C (unless otherwise indicated, when, if x is the reference temperature, lt = lx[1 + α(t - tx) + β(t - tx)2]; lt is length at t °C). Element

Temp., °C

C × 104

Aluminum Aluminum Antimony Arsenic Bismuth Cadmium Cadmium Carbon, diamond graphite Chromium Cobalt Copper Copper Gold Gold Indium Iodine Iridium Iridium Iron, soft cast wrought steel Lead (99.9)

20 300 20 20 20 0 0 50 50

0.224 0.284 0.136∙ 0.05 0.014∙ 0.54∙ 0.20⊥ 0.012 0.06

20 20 200 20

0.123 0.162 0.170 0.140

40

0.417

20

0.065

40 20 20 20

0.1210 0.118 0.119 0.114

100 280 20

0.291 0.343 0.254

20

0.233

Molybdenum

20

0.053

Nickel

20

0.126

Osmium Palladium

40 20

0.066 0.1173

Platinum

20 20

0.0887 0.0893

40 40 0 40 20 20

0.0850 0.0963 0.439 0.0763 0.1846 0.195

Magnesium Manganese †

Potassium Rhodium Ruthenium Selenium Silicon Silver Sodium Steel, 36.4Ni Tantalum†

20

0.065

Tellurium Thallium Tin

20 40 20 20 27 20‡ 20‡ 20

0.016∙ 0.302 0.214 0.305∙ 0.0444 0.643∙ 0.125⊥ 0.358

†

Tungsten Zinc

Temp. range, °C

M × 104

100 500 20

0.235 0.311 0.080⊥

20 -180, -140 -180, -140

0.103⊥ 0.59∙ 0.117⊥

20,

100

0.068

17, -191,

100 300 100 17

0.166 0.175 0.143 0.132

-190,

17

0.837

α × 104

β × 106

0,

500

0.22

0.009

20, 20,

100 100

0.526∙ 0.214⊥

20, 6, 0,

500 121 625

0.086 0.121 0.161

0.0064 0.0040

0,

520

0.142

0.0022

0.0636 0.0679

0.0032 0.0011

Temp. range, °C

0, 80 1070, 1720 0,

20, 20,

100

0.11

100 200

0.291 0.300

-100, + 20 20, 100 0, 100 -190, 0 0, 100 25, 100 25, 500 0, 100

0.240 0.260 0.228 0.159 0.052 0.049 0.055 0.130

0, 6,

50 21

0.83 0.0876

0, 100 -3, +18 0, 100

0.660 0.0249 0.197

-190, -17 20, 260 20, 340 -78, 0 0, 100 20

0.622 0.031 0.055 0.059 0.0655 0.272⊥

20 100 -100 100 100

0.154⊥ 0.045 0.656∙ 0.639∙ 0.141⊥

0, -140, +20, +20,

0, 0, 0, 100,

750 750 750 240

0.1158 0.1170 0.1118 0.269

0.0053 0.0053 0.0053 0.011

+ 20,

500

0.2480

0.0096

20, 300 -142, 19 19, +305

0.216 0.0515 0.0501

0.0121 0.0057 0.0014

-190, + 20 + 20, +300 500, 1000

0.1308 0.1236 0.1346

0.0166 0.0066 0.0033

-190, 0, -190, 0, 0,

+100 1000 -100 + 80 1000

0.1152 0.1167 0.0875 0.0890 0.0887

0.00517 0.0022 0.00314 0.00121 0.00132

-75, -112

0.0746

-75, 0, 20, 0, 260, 340, 20,

-67 875 500 50 500 500 400

0.0182 0.1827 0.1939 0.72 0.144 0.136 0.0646

0.0009

8,

95

0.2033

0.0263

-105, +502 + 0, 400

0.0428 0.354

0.00058 0.010

0.00479 0.00295

*Smithsonian Tables. For more complete tabulations see Table 142, Smithsonian Physical Tables, 9th ed., 1954; Handbook of Chemistry and Physics, 40th ed., pp. 2239–2245. Chemical Rubber Publishing Co.; Goldsmith, and Waterman, WADC-TR-58-476, 1959; Johnson (ed.), WADD-TR-60-56, 1960, etc. † Molybdenum, 300 to 2500°C; lt = l300[1 + 5.00 × 10-6(t - 300) + 10.5 × 10-10(t - 300)2] Tantalum, 300 to 2800°C; lt = l300[1 + 6.60 × 10-6(t - 300) + 5.2 × 10-10(t - 300)2] Tungsten, 300 to 2700°C; lt = l300[1 + 4.44 × 10-6(t - 300) + 4.5 × 10-10(t - 300)2] Beryllium, 20 to 100°C; 12.3 × 10-6 per °C. Columbium, 0 to 100°C; 7.2 × 10-6 per °C. Tantalum, 20 to 100°C; 6.6 × 10-6 per °C. ‡ These values for zinc were taken from Grüneisen and Goens, Z. Physik., 29:141 (1924).

2-180

PHYSICAL AnD CHEMICAL DATA

TABLE 2-101

Linear Expansion of Miscellaneous Substances*

The coefficient of cubical expansion may be taken as three times the linear coefficient. In the following table, t is the temperature or range of temperature, and C, the coefficient of expansion. t, °C

Substance Amber Bakelite, bleached Brass: Cast Wire Wire 71.5 Cu + 27.7 Zn + 0.3 Sn + 0.5 Pb 71 Cu + 29 Zn Bronze: 3 Cu + 1 Sn 3 Cu + 1 Sn 3 Cu + 1 Sn 86.3 Cu + 9.7 Sn + 4 Zn 97.6 Cu + hard 2.2 Sn + soft 0.2 P Caoutchouc Caoutchouc Celluloid Constantan Duralumin, 94Al

{

Ebonite Fluorspar, CaF2 German silver Gold-platinum, 2 Au + 1 Pt Gold-copper, 2 Au + 1 Cu Glass: Tube Tube Plate Crown (mean) Crown (mean) Flint Jena ther- 16III mometer normal

}

0–30 0–09 20–60

C × 104 0.50 0.61 0.22

0–100 0–100 0–100

0.1875 0.1930 0.1783–0.193

40 0–100

0.1859 0.1906

16.6–100 16.6–350 16.6–957 40 0–80 0–80

0.1844 0.2116 0.1737 0.1782 0.1713 0.1708

16.7–25.3 20–70 4–29 20–100 20–300 25.3–35.4 0–100 0–100 0–100 0–100

0.657–0.686 0.770 1.00 0.1523 0.23 0.25 0.842 0.1950 0.1836 0.1523 0.1552

0–100 0–100 0–100 0–100 50–60 50–60 0–100

0.0833 0.0828 0.0891 0.0897 0.0954 0.0788 0.081

Substance Jena thermometer 59III Jena thermometer 59III Gutta percha Ice Iceland spar: Parallel to axis Perpendicular to axis Lead tin (solder) 2 Pb + 1 Sn Limestone Magnalium Manganin Marble Monel metal Paraffin Paraffin Paraffin Platinum-iridium, 10 Pt + 1 Ir Platinum-silver, 1 Pt + 2 Ag Porcelain Porcelain Bayeux Quartz: Parallel to axis Parallel to axis Perpend. to axis Quartz glass Quartz glass Quartz glass Rock salt Rubber, hard Rubber, hard Speculum metal Steel, 0.14 C, 34.5 Ni

t, °C 0–100 −191–+16 20 −20–−1

C × 104

Substance

0.058 0.424 1.983 0.51

Topas: Parallel to lesser horizontal axis Parallel to greater horizontal axis Parallel to vertical axis Tourmaline: Parallel to longitudinal axis Parallel to horizontal axis Type metal Vulcanite Wedgwood ware Wood: Parallel to fiber: Ash Beech Chestnut Elm Mahogany Maple Oak Pine Walnut Across the fiber: Beech Chestnut Elm Mahogany Maple Oak Pine Walnut Wax white Wax white Wax white Wax white

0–80 0–80

0.2631 0.0544

0–100 25–100 12–39 15–100 25–100 25–600 0–16 16–38 38–49

0.2508 0.09 0.238 0.181 0.117 0.14 0.16 1.0662 1.3030 4.7707

40

0.0884

0–100 20–790 1000–1400

0.1523 0.0413 0.0553

0–80 −190 to + 16 0–80 –190 to + 16 16 to 500 16 to 1000 40 0 –160 0–100 25–100 25–600

0.0797 0.0521 0.1337 −0.0026 0.0057 0.0058 0.4040 0.691 0.300 0.1933 0.037 0.136

t, °C

C × 104

0−100

0.0832

0−100 0−100

0.0836 0.0472

0−100

0.0937

0−100 16.6−254 0−18 0−100

0.0773 0.1952 0.6360 0.0890

0−100 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34

0.0951 0.0257 0.0649 0.0565 0.0361 0.0638 0.0492 0.0541 0.0658

2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 10−26 26−31 31−43 43−57

0.614 0.325 0.443 0.404 0.484 0.544 0.341 0.484 2.300 3.120 4.860 15.227

*Smithsonian Tables. For a more complete tabulation see Tables 143, 144. Smithsonian Physical Tables. 9th ed., 1954, also reprinted in American Institute of Physics Handbook, McGraw-Hill, New York, 1957; Handbook of Chemistry and Physics, 40th ed., pp. 2239–2245, Chemical Rubber Publishing Co. For data on many solids prior to 1926, see Gruneisen, Handbuch der Physik, vol. 10, pp. 1–52, 1926, translation available as N.A.S.A. RE 2-18-59W, 1959. For eight plastic solids below 300 K, see Scott, Cryogenic Engineering, p. 331, Van Nostrand, Princeton, NJ, 1959. For 11 other materials to 300 K, see Scott, loc. cit., p. 333. For quartz and silica, see Cook, Brit. J. Appl. Phys., 7, 285 (1956).

THERMAL EXPAnSIOn AnD COMPRESSIBILITY TABLE 2-102

Volume Expansion of Liquids*

TABLE 2-103

If V0 is the volume at 0°, then at t° the expansion formula is Vt = V0(1 + αt + βt2 + γ t3). The table gives values of α, β, and γ, and of C, the true coefficient of volume expansion at 20° for some liquids and solutions. The temperature range of the observation is ∆t. Values for the coefficient of volume expansion of liquids can be derived from the tables of specific volumes of the saturated liquid given as a function of temperature later in this section. C = (dV/dt)/V0 Liquid

Range

α × 103

β × 106

γ × 108

C × 103 at 20°

Acetic acid 16−107 1.0630 0.12636 1.0876 1.071 Acetone 0−54 1.3240 3.8090 −0.87983 1.487 Alcohol: Amyl −15–80 0.9001 0.6573 1.18458 0.902 Ethyl, 30% by volume 18−39 0.2928 10.790 −11.87 Ethyl, 50% by volume 0−39 0.7450 1.85 0.730 Ethyl, 99.3% by volume 27−46 1.012 2.20 1.12 Ethyl, 500 atm pressure 0−40 0.866 Ethyl, 3000 atm pressure 0−40 0.524 Methyl 0−61 1.1342 1.3635 0.8741 1.199 Benzene 11−81 1.17626 1.27776 0.80648 1.237 Bromine 0−59 1.06218 1.87714 −0.30854 1.132 Calcium chloride: 5.8% solution 18−25 0.07878 4.2742 0.250 40.9% solution 17−24 0.42383 0.8571 0.458 Carbon disulfide −34–60 1.13980 1.37065 1.91225 1.218 500 atm pressure 0−50 0.940 3000 atm pressure 0−50 0.581 Carbon tetrachloride 0−76 1.18384 0.89881 1.35135 1.236 Chloroform 0−63 1.10715 4.66473 −1.74328 1.273 Ether −15–38 1.51324 2.35918 4.00512 1.656 Glycerin 0.4853 0.4895 0.505 Hydrochloric acid, 33.2% solution 0−33 0.4460 0.215 0.455 Mercury 0−100 0.18182 0.0078 0.18186 Olive oil 0.6821 1.1405 −0.539 0.721 Pentane 0−33 1.4646 3.09319 1.6084 1.608 Potassium chloride, 24.3% solution 16−25 0.2695 2.080 0.353 Phenol 36−157 0.8340 0.10732 0.4446 1.090 Petroleum, 0.8467 density 24−120 0.8994 1.396 0.955 Sodium chloride, 20.6% solution 0−29 0.3640 1.237 0.414 Sodium sulfate, 24% solution 11−40 0.3599 1.258 0.410 Sulfuric acid: 10.9% solution 0−30 0.2835 2.580 0.387 100.0% 0−30 0.5758 −0.432 0.558 Turpentine −9−106 0.9003 1.9595 −0.44998 0.973 Water 0−33 −0.06427 8.5053 −6.7900 0.207 *Smithsonian Tables, Table 269. For a detailed discussion of mercury data, see Cook, Brit. J. Appl. Phys., 7, 285 (1956). For data on nitrogen and argon, see Johnson (ed.), WADD-TR-60-56, 1960. Bromoform1 7.7 − 50°C. Vt = 0.34204[1 + 0.00090411(t − 7.7) + 0.0000006766(t − 7.7)2] 0.34204 is the specific volume of bromoform at 7.7°C. Glycerin2 −62 to 0°C. Vt = V0(1 + 4.83 × 10−4t − 0.49 × 10−6t2) 0 − 80°C. Vt = V0(1 + 4.83 × 10−4t + 0.49 × 10−6t2) 3 Mercury 0 − 300°C. Vt − V0[1 + 10−8(18,153.8t + 0.7548t2 + 0.001533t2 + 0.00000536t4)] 1 Sherman and Sherman, J. Am. Chem. Soc., 50, 1119 (1928). (An obvious error in their equation has been corrected.) 2 Samsoen, Ann. phys., (10) 9, 91 (1928). 3 Harlow, Phil. Mag., (7) 7, 674 (1929).

2-181

Volume Expansion of Solids*

If v2 and v1 are the volumes at t2 and t1, respectively, then v2 = v1(1 + C∆t), C being the coefficient of cubical expansion and ∆t the temperature interval. Where only a single temperature is stated, C represents the true coefficient of volume expansion at that temperature. Substance

t or ∆t

Antimony 0−100 Beryl 0−100 Bismuth 0−100 Copper† 0−100 Diamond 40 Emerald 40 Galena 0−100 Glass, common tube 0−100 hard 0−100 Jena, borosilicate 59 III 20−100 pure silica 0−80 Gold 0−100 Ice −20 to −1 Iron 0−100 Lead† 0−100 Paraffin 20 Platinum 0−100 Porcelain, Berlin 20 chloride 0−100 nitrate 0−100 sulfate 20 Quartz 0−100 Rock salt 50−60 Rubber 20 Silver 0−100 Sodium 20 Stearic acid 33.8−45.4 Sulfur, native 13.2−50.3 Tin 0−100 Zinc† 0−100 *Smithsonian Tables, Table 268. † See additional data below. Aluminum1 100 − 530°C. V = V0(1 + 2.16 × 10−5t + 0.95 × 10−8t2) 1 Cadmium 130 − 270°C. V = V0(1 + 8.04 × 10−5t + 5.9 × 10−8t2) 1 Copper 110 − 300°C. V = V0(1 + 1.62 × 10−5t + 0.20 × 10−8t2) Colophony2 0 − 34°C. V = V0(1 + 2.21 × 10−4t + 0.31 × 10−6t2) 34 − 150°C. V = V34[1 + 7.40 × 10−4(t − 34) + 5.91 × 10−6(t − 34)2] 1 Lead 100 − 280°C. V = V0(1 + 1.60 × 10−5t + 3.2 × 10−8t2) 2 Shellac 0 − 46°C. V = V0(1 + 2.73 × 10−4t + 0.39 × 10−6t2) 46 − 100°C. V = V46[1 + 13.10 × 10−4(t − 46) + 0.62 × 10−6(t − 46)2] Silica (vitreous)3 0 − 300°C. Vt = V0[1 + 10−8(93.6t + 0.7776t2 − 0.003315t2 + 0.000005244t4) Sugar (cane, amorphous)2 0 − 67°C. Vt = V0(1 + 2.34 × 10−4t + 0.14 × 10−6t2) 67 − 160°C. Vt = V67[1 + 5.02 × 10−4(t − 67) + 0.43 × 10−6(t − 67)2] Zinc1 120 − 360°C. Vt = V0(1 + 8.50 × 10−5t + 3.9 × 10−8t2) 1 2 3

Uffelmann, Phil. Mag., (7) 10, 633 (1930). Samsoen, Ann. phys., (10) 9, 83 (1928). Harlow, Phil. Mag., (7) 7, 674 (1929).

C × 104 0.3167 0.0105 0.3948 0.4998 0.0354 0.0168 0.558 0.276 0.214 0.156 0.0129 0.4411 1.1250 0.3550 0.8399 5.88 0.265 0.0814 1.094 1.967 1.0754 0.3840 1.2120 4.87 0.5831 2.13 8.1 2.23 0.6889 0.8928

2-182

PHYSICAL AnD CHEMICAL DATA

GAS EXPAnSIOn: JOULE-THOMSOn EFFECT Introduction The Joule-Thomson coefficient, (∂T/∂P)H , is the change in gas temperature with pressure during an adiabatic expansion (a throttling process, at constant enthalpy H). The temperature at which the Joule-Thomson coefficient changes sign is called the Joule-Thomson inversion temperature. Joule-Thomson coefficients for substances listed in Table 2-104 are given in tables in the Thermodynamic Properties section.

Unit Conversions To convert the Joule-Thomson coefficient µ, in degrees Celsius per atmosphere to degrees Fahrenheit per atmosphere, multiply by 1.8. Temperature conversion: °F = 9⁄5°C + 32; °R = 9⁄5 K. To convert bars to pounds-force per square inch, multiply by 14.504; to convert bars to kilopascals, multiply by 100.

TABLE 2-104 Additional References Available for the Joule-Thomson Coefficient Temp. range, °C

Pressure range, atm Gas

0–10

10–50

50–200

12, 15, 19 35

15, 19, 35

Ammonia Argon Benzene Butane Carbon dioxide

12, 15, 16 19, 35 28 39 31 26 7, 8, 28 37 17

Air

Carbon monoxide Deuterium Dowtherm A Ethane Ethylene Helium Hydrogen

46 45 1, 38 24, 30

39 31 26 7, 8, 37 17 22, 24, 25 1∗ 46 45

>200

300

Other references 3, 4, 18 2, 3

31

46 48

13

19

29, 42, 47

29, 47

∗See also 14 (generalized chart); 18 (review, to 1919); 20–22; 23 (review, to 1948); 27 (review, to 1905); 32, 36, 41, 50. References: 1. Baehr. Z. Elektrochem., 60, 515 (1956). 2. Beattie, J. Math. Phys., 9, 11 (1930). 3. Beattie, Phys. Rev., 35, 643 (1930). 4. Bradley and Hale, Phys. Rev., 29, 258 (1909). 5. Brown and Dean, Bur. Stand. J. Res., 60, 161 (1958). 6. Budenholzer, Sage, et al., Ind. Eng. Chem., 29, 658 (1937). 7. Burnett, Phys. Rev., 22, 590 (1923). 8. Burnett, Univ. Wisconsin Bull. 9(6), 1926. 9. Charnley, Ph.D. thesis. University of Manchester, 1952. 10. Charnley, Isles, et al., Proc. R. Soc. (London), A217, 133 (1953). 11. Charnley, Rowlinson, et al., Proc. R. Soc. (London), A230, 354 (1955). 12. Dalton, Commun. Phys. Lab. Univ. Leiden, no. 109c, 1909. 13. Deming and Deming, Phys. Rev., 48, 448 (1935). 14. Edmister, Pet. Refiner, 28, 128 (1949). 15. Eucken, Clusius, et al., Z. Tech. Phys., 13, 267 (1932). 16. Eumorfopoulos and Rai, Phil. Mag., 7, 961 (1926). 17. Huang, Lin, et al., Z. Phys., 100, 594 (1936). 18. Hoxton, Phys. Rev., 13, 438 (1919). 19. Ishkin and Kaganev, J. Tech. Phys. U.S.S.R., 26, 2323 (1956). 20. Isles, Ph.D. thesis, Leeds University. 21. Jenkin and Pye, Phil. Trans. R. Soc. (London), A213, 67 (1914); A215, 353 (1915). 22. Johnston, J. Am. Chem. Soc., 68, 2362 (1946). 23. Johnston, Trans. Am. Soc. Mech. Eng., 70, 651 (1948). 24. Johnston, Bezman, et al., J. Am. Chem. Soc., 68, 2367 (1946). 25. Johnston, Swanson, et al., J. Am. Chem. Soc., 68, 2373 (1946). 26. Kennedy, Sage, et al., Ind. Eng. Chem., 28, 718 (1936). 27. Kester, Phys. Rev., 21, 260 (1905). 28. Keyes and Collins, Proc. Nat. Acad. Sci., 18, 328 (1932). 29. Kleinschmidt, Mech. Eng., 45, 165 (1923); 48, 155 (1926). 30. Koeppe, Kältetechnik, 8, 275 (1956). 31. Lindsay and Brown, Ind. Eng. Chem., 27, 817 (1935). 32. Noell, dissertation, Munich, 1914, Forschungsdienst, 184, p. 1, 1916. 33. Palienko, Tr. Inst. Ispol’ z. Gaza, Akad. Nauk Ukr. SSR, no. 4, p. 87, 1956. 34. Pattee and Brown, Ind. Eng. Chem., 26, 511, (1934). 35. Roebuck, Proc. Am. Acad. Arts Sci., 60, 537 (1925); 64, 287 (1930). 36. Roebuck, see 49 below, 37. Roebuck and Murrell, Phys. Rev., 55, 240 (1939). 38. Roebuck and Osterberg, Phys. Rev., 37, 110 (1931); 43, 60 (1933). 39. Roebuck and Osterberg, Phys. Rev., 46, 785 (1934). 40. Roebuck and Osterberg, Phys. Rev., 48, 450 (1935). 41. Roebuck, Murrell, et al., J. Am. Chem. Soc., 64, 400 (1942). 42. Sage, unpublished data, California Institute of Technology, 1959. 43. Sage and Lacy, Ind. Eng. Chem., 27, 1484 (1934). 44. Sage, Kennedy, et al., Ind. Eng. Chem., 28, 601 (1936). 45. Sage, Webster, et al., Ind. Eng. Chem., 29, 658 (1937). 46. Ullock, Gaffert, et al., Trans. Am. Inst. Chem. Eng., 32, 73 (1936). 47. Yang, Ind. Eng. Chem., 45, 786 (1953). 48. Zelmanov, J. Phys. U.S.S.R., 3, 43 (1940). 49. Roebuck, recalculated data. 50. Michels et al., van der Waals laboratory publications. Gunn, Cheuh, and Prausnitz, Cryogenics, 6, 324 (1966), review equations relating the inversion temperatures and pressures. The ability of various equations of state to relate these was also discussed by Miller, Ind. Eng. Chem. Fundam., 9, 585 (1970); and Juris and Wenzel, Am. Inst. Chem. Eng. J., 18, 684 (1972). Perhaps the most detailed review is that of Hendricks, Peller, and Baron. NASA Tech. Note D 6807, 1972.

CRITICAL COnSTAnTS

TABLE 2-105 Approximate Inversion-Curve Locus in Reduced Coordinates (Tr = T/Tc ; Pr = P/Pc)* Pr

0

0.5

1

1.5

2

2.5

3

4

TrL TrU

0.782 4.984

0.800 4.916

0.818 4.847

0.838 4.777

0.859 4.706

0.880 4.633

0.903 4.550

0.953 4.401

Pr

5

6

7

8

9

10

11

11.79

TrL 1.01 1.08 1.16 1.25 1.35 1.50 1.73 2.24 TrU 4.23 4.06 3.88 3.68 3.45 3.18 2.86 2.24 ∗Calculated from the best three-constant equation recommended by Miller, Ind. Eng. Chem. Fundam., 9, 585 (1970). TrL refers to the lower curve, and TrU, to the upper curve.

Additional References For other inorganic substances see Mathews, Chem. Rev., 72 (1972):71–100. For other organics see Kudchaker, Alani, and Zwolinski, Chem. Rev., 68 (1968): 659–735.

TABLE 2-106 Cmpd. no.

2-183

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

Critical Constants and Acentric Factors of Inorganic and Organic Compounds Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Chlorine

Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4 CF4 Cl2

CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5 75-73-0 7782-50-5

Mol. wt.

TC, K

44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 153.8227 88.0043 70.906

466 761 591.95 606 508.2 545.5 308.3 506 615 540 132.45 405.65 645.6 150.86 824 562.05 689 751 702.3 830 720.15 662 718 773 584.15 670.15 503.8 464 452 425 425.12 680 676 563.1 535.9 419.5 435.5 428.6 575.4 660.5 570.1 554 440 537.2 615.7 585.4 304.21 552 132.92 556.35 227.51 417.15

PC, MPa 5.57 6.6 5.786 4 4.701 4.85 6.138 5 5.66 4.66 3.774 11.28 4.25 4.898 5.05 4.895 4.74 4.47 4.215 3.352 4.374 3.11 4.06 3.38 10.3 4.5191 5.565 6.929 4.36 4.32 3.796 5.21 4.02 4.414 4.1885 4.02 4.21 4.1 3.09 2.89 3.97 4.06 4.6 4.41 4.06 3.88 7.383 7.9 3.499 4.56 3.745 7.71

VC, m3/kmol 0.154 0.215 0.177 0.304 0.209 0.193 0.112 0.197 0.208 0.216 0.09147 0.07247 0.337 0.07459 0.346 0.256 0.315 0.344 0.3132 0.5677 0.382 0.442 0.367 0.497 0.135 0.324 0.204 0.152 0.22 0.221 0.255 0.303 0.305 0.273 0.27 0.241 0.234 0.238 0.389 0.497 0.307 0.307 0.208 0.258 0.293 0.291 0.094 0.16 0.0944 0.276 0.143 0.124

ZC 0.221 0.224 0.208 0.241 0.233 0.206 0.268 0.234 0.23 0.224 0.313 0.242 0.267 0.291 0.255 0.268 0.261 0.246 0.226 0.276 0.279 0.25 0.25 0.261 0.286 0.263 0.271 0.273 0.255 0.27 0.274 0.279 0.218 0.258 0.254 0.278 0.272 0.274 0.251 0.262 0.257 0.271 0.262 0.255 0.232 0.232 0.274 0.275 0.299 0.272 0.283 0.276

Acentric factor 0.262493 0.421044 0.466521 0.455328 0.306527 0.341926 0.191185 0.319832 0.538324 0.310664 0 0.252608 0.350169 0 0.5585 0.2103 0.262789 0.602794 0.343214 0.501941 0.363116 0.433236 0.312604 0.402873 0.128997 0.250575 0.205275 0.153426 0.165877 0.195032 0.200164 0.630463 0.704256 0.58828 0.580832 0.184495 0.201877 0.217592 0.439393 0.394149 0.271361 0.25059 0.246976 0.282553 0.675003 0.3601 0.223621 0.110697 0.0481621 0.192552 0.178981 0.0688183 (Continued)

2-184

TABLE 2-106 Cmpd. no. 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

Critical Constants and Acentric Factors of Inorganic and Organic Compounds (Continued ) Name Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Di–isopropyl amine Di–isopropyl ether Di–isopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene

Formula C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6

CAS 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3

Mol. wt. 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19 102.17476 114.18546 90.121 104.14758 54.09044

TC, K

PC, MPa

VC, m3/kmol

632.35 460.35 536.4 416.25 503.15 489 705.85 697.55 704.65 631 400.15 459.93 553.8 650.1 653 560.4 511.7 507 398 664 674 617.7 722.1 688 616.6 696 619.85 38.35 628 650.15 611 584.1 683.95 705 684.75 523 561.6 510 560 572 736.6 496.6 466.7 557.15 386.44 445 351.255 523.1 500.05 576 507.8 543 473.2

4.5191 5.27 5.472 6.68 4.425 4.54 4.56 5.01 5.15 3.209 5.924 4.98 4.08 4.26 4 4.35 4.51 4.8 5.54 3.97 2.6 2.11 2.28 2.308 2.223 2.13 2.37 1.6617 6.03 5.4769 7.17 2.46 4.07 4.07 4.07 5.07 5.37 6.08 4.24 4.24 4.27 3.71 3.64 3.96 4.5198 4.34 5.784 3.2 2.88 3.02 3.773 3.446 4.87

0.308 0.192 0.239 0.141 0.243 0.247 0.312 0.282 0.277 0.434 0.151 0.21 0.308 0.322 0.311 0.291 0.26 0.245 0.162 0.355 0.575 0.617 0.639 0.645 0.584 0.624 0.552 0.060263 0.276 0.2616 0.223 0.487 0.351 0.351 0.351 0.24 0.22 0.185 0.291 0.291 0.349 0.301 0.28 0.318 0.179 0.195 0.123 0.418 0.386 0.416 0.297 0.35 0.221

ZC 0.265 0.264 0.293 0.272 0.257 0.276 0.242 0.244 0.244 0.265 0.269 0.273 0.273 0.254 0.229 0.272 0.276 0.279 0.271 0.255 0.267 0.254 0.243 0.26 0.253 0.23 0.254 0.314 0.319 0.265 0.315 0.247 0.251 0.244 0.251 0.28 0.253 0.265 0.265 0.259 0.243 0.27 0.263 0.272 0.252 0.229 0.244 0.308 0.267 0.262 0.265 0.267 0.274

Acentric factor 0.249857 0.188591 0.221902 0.151 0.215047 0.198553 0.448034 0.43385 0.50721 0.327406 0.275605 0.18474 0.208054 0.369047 0.299006 0.212302 0.194874 0.19611 0.127829 0.264134 0.520066 0.492328 0.813724 0.606986 0.480456 0.587421 0.51783 −0.14486 0.125025 0.206724 0.20945 0.447646 0.27898 0.219189 0.284638 0.233943 0.286595 0.198622 0.252928 0.256391 0.952882 0.303856 0.281065 0.29002 0.275052 0.222428 0.277138 0.388315 0.338683 0.404427 0.32768 0.352222 0.238542

106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal Heptane

2-185

C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O C7H16

124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5

45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026 240.46774 114.18546 100.20194

437.2 500 591.15 606.15 596.15 615 400.1 649.6 537.3 766 402 503.04 729 777.4 587 766.8 550 658 768 305.32 514 523.3 456.15 617.15 698 655 571 609.15 569.5 282.34 593 720 537 469.15 508.4 674.6 583 489 567 499.15 546 500.23 559.95 144.12 560.09 375.31 317.42 420 771 588 490.15 5.2 736 620 540.2

5.34 3.15 2.93843 2.93843 2.93843 5.36 5.37 4.42 2.91 2.78 3.56 5.53 5.65 2.76 5.2081 3.08 3.14 1.82 1.16 4.872 6.137 3.88 5.62 3.609 3.18 3.41 2.95 3.04 3.4 5.041 6.29 8.2 6.85 7.19 4.74 2.778 2.46 3.41 3.32 5.49 3.362 3.37007 3.33 5.1724 4.55051 5.028 5.87511 6.59 7.8 5.81 5.5 0.2275 1.34 3.16 2.74

0.18 0.361 0.45 0.46 0.46 0.252 0.17 0.26199 0.393 0.53 0.258 0.201 0.227 0.529 0.238 0.503 0.402 0.755 1.34 0.1455 0.168 0.286 0.207 0.374 0.489 0.389 0.403 0.43 0.375 0.131 0.264 0.191 0.173 0.140296 0.229 0.528 0.487 0.329 0.369 0.207 0.345 0.339 0.403 0.066547 0.269 0.159 0.113 0.0851 0.163 0.125 0.218 0.0573 1.11 0.434 0.428

0.264 0.274 0.269 0.268 0.273 0.264 0.2744 0.214 0.256 0.231 0.275 0.266 0.212 0.226 0.254 0.243 0.276 0.251 0.243 0.279 0.241 0.255 0.307 0.263 0.268 0.244 0.25 0.258 0.269 0.281 0.337 0.262 0.265 0.25876 0.257 0.262 0.247 0.276 0.26 0.274 0.256 0.275 0.288 0.287 0.263 0.256 0.252 0.161 0.198 0.149 0.294 0.302 0.244 0.266 0.261

0.299885 0.249251 0.232569 0.232443 0.237864 0.205916 0.200221 0.31771 0.296407 0.656848 0.129957 0.194256 0.280551 0.580691 0.279262 0.43889 0.449684 0.576385 0.906878 0.099493 0.643558 0.366409 0.284788 0.30347 0.477055 0.632579 0.401075 0.245525 0.270095 0.0862484 0.472367 0.506776 0.200735 0.197447 0.284736 0.801289 0.494378 0.305629 0.389061 0.187751 0.394373 0.347328 0.269778 0.0530336 0.247183 0.217903 0.194721 0.167887 0.412381 0.312521 0.201538 −0.390032 0.769688 0.405751 0.349469 (Continued)

2-186

TABLE 2-106 Cmpd. no. 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213

Critical Constants and Acentric Factors of Inorganic and Organic Compounds (Continued ) Name Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane

Formula C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14

CAS

Mol. wt.

TC, K

PC, MPa

VC, m3/kmol

111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2

130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606

677.3 632.3 608.3 606.6 611.4 537.4 645 547 723 594 507.6 660.2 611.3 585.3 587.61 582.82 504 544 623 516.2 549 653.15 33.19 363.15 324.65 456.65 461.15 373.53 605 471.85 834 662 190.564 512.5 718 506.55 402.4 536 430.05 693 490 460.4 643 577.2 465 470 492 512.74 593 463.2 554.5 442 572.1

3.043 3.085 3 2.92 2.94 2.92 2.77 3.21 1.4 3.46 3.025 3.308 3.446 3.311 3.287 3.32 3.21 3.53 3.08 3.62 3.53 14.7 1.313 8.552 8.31 5.39 6.48 8.96291 3.7 4.54 6.1 4.79 4.599 8.084 4.98 4.75 5.63 4.25 7.46 3.59 3.83 3.38 3.89 3.93 3.447 3.42 4.38 3.371 3.47 4.2 3.473 4.17 3.48

0.466 0.444 0.447 0.433 0.434 0.402 0.465 0.387 1.04 0.378 0.371 0.408 0.382 0.385 0.378 0.378 0.348 0.331 0.412 0.322 0.331 0.158 0.064147 0.1 0.081 0.139 0.069 0.0985 0.292 0.221 0.279 0.28 0.0986 0.117 0.267 0.228 0.164 0.27 0.154 0.436 0.291 0.306 0.347 0.329 0.292 0.292 0.248 0.329 0.36 0.275 0.34 0.246 0.369

ZC 0.252 0.261 0.265 0.251 0.251 0.263 0.24 0.273 0.243 0.266 0.266 0.246 0.259 0.262 0.254 0.259 0.267 0.258 0.245 0.272 0.256 0.428 0.305 0.283 0.249 0.197 0.117 0.284 0.215 0.256 0.245 0.244 0.286 0.222 0.223 0.257 0.276 0.258 0.321 0.272 0.274 0.27 0.252 0.269 0.26 0.256 0.266 0.26 0.253 0.3 0.256 0.279 0.27

Acentric factor 0.759934 0.562105 0.567733 0.407565 0.418982 0.343194 0.422568 0.377799 0.717404 0.361818 0.301261 0.733019 0.558598 0.553 0.384626 0.380086 0.285121 0.218301 0.368101 0.332699 0.221387 0.314282 −0.215993 0.073409 0.131544 0.409913 0.382283 0.0941677 0.61405 0.275913 0.738273 0.331817 0.0115478 0.565831 0.435111 0.331255 0.211537 0.342296 0.281417 0.420541 0.187439 0.227875 0.589443 0.59002 0.234056 0.28703 0.137046 0.313008 0.3229 0.308085 0.377519 0.225204 0.236055

214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268

1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol

2-187

C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F 3N CH3NO2 N 2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O

590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6

114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228

686 614 617 532.7 542 526 483 437.8 535.5 533 487.2 497 574.6 488 464.48 553.4 553.1 469.95 566 694 497.7 546.49 407.8 506.2 417.9 530.6 476.25 565 352.5 654 497.1 437 748.4 44.4 593 126.2 234 588.15 309.57 180.15 758 658.5 594.6 710.7 670.9 649.5 593.1 681 598.05 747 638.9 568.7 694.26 652.3 629.8

4 3.79 3.79 3.79 4.13 4.13 3.95 4.4 4.15 4.26 6 3.41 3.27 5.48 3.762 3.8 4.021 7.23 3.68 2.54 3.04 3.042 3.64 3.972 4 4.004 3.801 3.97 4.7 3.36 3.286 4.67 4.05 2.653 5.16 3.4 4.4607 6.31 7.245 6.48 1.21 2.68 2.29 2.514 2.527 2.5408 2.428 2.31 2.61 1.27 2.96 2.49 2.779 2.783 2.749

0.374 0.374 0.374 0.319 0.303 0.303 0.289 0.221 0.267 0.254 0.172 0.329 0.369 0.202 0.276 0.31 0.328 0.145 0.323 0.572 0.368 0.38 0.259 0.275 0.239 0.282 0.276 0.307 0.205 0.399 0.329 0.21 0.407 0.0417 0.236 0.08921 0.11875 0.173 0.0974 0.058 1.26 0.543 0.551 0.584 0.576 0.577 0.524 0.571 0.497 1.19 0.488 0.486 0.523 0.509 0.512

0.262 0.278 0.276 0.273 0.278 0.286 0.284 0.267 0.249 0.244 0.255 0.272 0.253 0.273 0.269 0.256 0.28718 0.268 0.253 0.252 0.27 0.254 0.278 0.26 0.275 0.256 0.265 0.259 0.329 0.247 0.262 0.27 0.265 0.3 0.247 0.289 0.272 0.223 0.274 0.251 0.242 0.266 0.255 0.248 0.261 0.271 0.258 0.233 0.261 0.243 0.272 0.256 0.252 0.261 0.269

0.221299 0.68049 0.67904 0.228759 0.23179 0.229606 0.275755 0.231374 0.323369 0.209108 0.255551 0.307786 0.355671 0.300694 0.26555 0.320845 0.24611 0.158174 0.280233 0.791271 0.279149 0.344201 0.183521 0.615203 0.19484 0.346586 0.276999 0.273669 0.131449 0.32297 0.246542 0.241564 0.302034 −0.0395988 0.380324 0.0377215 0.119984 0.348026 0.140894 0.582944 0.852231 0.473309 0.44346 0.778706 0.584074 0.6092 0.436736 0.52604 0.470974 0.811359 0.441993 0.399552 0.773427 0.569694 0.58814 (Continued)

2-188 TABLE 2-106 Cmpd. no. 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308

Critical Constants and Acentric Factors of Inorganic and Organic Compounds (Continued ) Name 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan

Formula C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S

CAS 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9

Mol. wt.

TC, K

128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062

632.7 627.7 566.9 667.3 574 828 154.58 261 708 566.1 469.7 639.16 588.1 561 561.08 560.95 464.8 584.3 598 481.2 519 869 694.25 653 791 394 369.83 536.8 508.3 636 503.6 600.81 561.3 549.73 496.95 638.35 364.85 538 517 536.6

PC, MPa 2.64 2.704 2.663 2.52 2.88 8.2 5.043 5.57 1.48 3.845 3.37 3.63 3.897 3.7 3.694 3.74 3.56 3.536 3.47 4.17 4.03 2.9 6.13 4.06 4.72 5.25 4.248 5.169 4.765 3.12 5.038 4.668 4.26 3.36 4.74 3.2 4.6 4.02 4.75 4.63

VC, m3/kmol 0.497 0.496953 0.464 0.518 0.442 0.227 0.0734 0.089 0.969 0.313 0.313 0.35 0.326 0.326 0.301 0.336 0.2934 0.385 0.359 0.277 0.276 0.554 0.229 0.37 0.421 0.165 0.2 0.219 0.222 0.437 0.204 0.235 0.242 0.345 0.26 0.44 0.185 0.285 0.254 0.254

ZC 0.249 0.257 0.262 0.235 0.267 0.27 0.288 0.228 0.244 0.256 0.27 0.239 0.258 0.259 0.238 0.269 0.27 0.28 0.251 0.289 0.258 0.222 0.243 0.277 0.302 0.264 0.276 0.254 0.25 0.258 0.246 0.22 0.221 0.254 0.298 0.265 0.281 0.256 0.281 0.264

Acentric factor 0.454874 0.440561 0.392149 0.449744 0.42329 0.286278 0.0221798 0.211896 0.68632 0.313152 0.251506 0.706632 0.57483 0.554979 0.343288 0.344846 0.237218 0.26853 0.320705 0.289925 0.175199 0.470716 0.44346 0.412323 0.702495 0.104121 0.152291 0.6209 0.663 0.341975 0.281254 0.579579 0.350057 0.388902 0.279839 0.344391 0.137588 0.308779 0.21381 0.231789

309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345

1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene

C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O 2S F 6S O 3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10

57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3

76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165

626 683 259 636 838 430.75 318.69 490.85 883.6 857 693 540.15 720 631.95 568 579.35 591.75 602 675 535.15 433.25 664.5 649.1 543.8 573.5 846 828 639 703.9 519.13 454 432 543.15 647.096 617 630.3 616.2

6.1 5.96 3.72 3.84 5 7.8841 3.76 8.21 3.486 2.99 1.57 5.19 3.65 5.16 2.87 5.69 4.108 4.48 1.68 3.04 4.07 3.454 3.232 2.57 2.82 3.39 3.04 1.95 2.119 3.958 4.86 5.67 3.06 22.064 3.541 3.732 3.511

0.239 0.291 0.202 0.352 0.33 0.122 0.19852 0.127 0.424 0.731 0.897 0.224 0.408 0.249 0.461 0.219 0.316 0.281 0.826 0.39 0.254 0.414 0.43 0.468 0.455 0.479 0.572 0.685 0.715 0.27 0.205 0.179 0.408 0.0559472 0.375 0.37 0.378

0.28 0.305 0.349 0.256 0.237 0.269 0.282 0.255 0.201 0.307 0.244 0.259 0.249 0.245 0.28 0.259 0.264 0.252 0.247 0.266 0.287 0.259 0.258 0.266 0.269 0.231 0.253 0.252 0.259 0.248 0.264 0.283 0.276 0.229 0.259 0.264 0.259

1.10651 0.494515 0.38584 0.297097 0.743044 0.245381 0.215146 0.42396 0.94695 0.551265 0.643017 0.225354 0.335255 0.199551 0.244953 0.196972 0.264012 0.259135 0.617397 0.316193 0.206243 0.366553 0.37871 0.303455 0.2903 0.862257 0.897249 0.530316 0.623622 0.351307 0.106852 0.100107 0.281543 0.344861 0.326485 0.31013 0.321839

Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.

2-189

2-190

PHYSICAL AnD CHEMICAL DATA

COMPRESSIBILITIES Introduction The compressibility factor Z can be calculated by using the defining equation Z = PV/(RT), where P is pressure, V is molar volume, R is the gas constant, and T is absolute temperature. Values of P, V, and T for substances listed in Table 2-109 are given in tables in the Thermodynamic Properties section. For the units used in these tables, R is 0.008314472 MPadm3/(mol ⋅ K). Values at temperatures and pressures other than those in the tables can be generated for many of the substances in Table 2-109 by

TABLE 2-107

going to http://webbook.nist.gov and selecting NIST Chemistry WebBook, then Thermophysical Properties of Fluid Systems High Accuracy Data. Results can be pasted into a spreadsheet to facilitate calculation of the compressibility factor. Unit Conversions For this subsection, the following unit conversion is applicable: °R = 9⁄5 K. To convert bars to pounds-force per cubic inch, multiply by 14.504. To convert bars to kilopascals, multiply by 100.

Compressibilities of Liquids*

At the constant temperature T, the compressibility β = (1/ V0 )(dV/dP). In general as P increases, β decreases rapidly at first and then slowly; the change of β with T is large at low pressures but very small at pressures above 1000 to 2000 megabars. 1 megabar = 0.987 atm = 106 dynes/cm2 based upon the older usage, 1 bar = 1 dyne/cm2.

Substance

Temp., °C

Pressure, megabars

Compressibility per megabar β × 106

Substance

Temp., °C

Pressure, megabars

Compressibility per megabar β × 106

Substance

Temp., °C

Pressure, megabars

Compressibility per megabar β × 106

Acetone 14 23 111 Ethyl acetate 20 400 75 Methyl alcohol 15 23 103 Acetone 20 500 61 alcohol 14 23 100 alcohol 20 200 95 Acetone 20 1,000 52 alcohol 20 500 63 alcohol 20 400 80 Acetone 40 12,000 9 alcohol 20 1,000 54 alcohol 20 500 65 Amyl alcohol 14 23 88 alcohol 20 12,000 8 alcohol 20 1,000 54 alcohol, iso. 20 200 84 bromide 20 200 100 alcohol 20 12,000 8 alcohol, iso. 20 400 70 bromide 20 400 82 Nitric acid 0 17 32 alcohol, n 20 500 61 bromide 20 500 70 Oils: alcohol, n 20 1,000 46 bromide 20 1,000 54 Almond 15 5 53 alcohol, n 20 12,000 8 bromide 20 12,000 8 Castor 15 5 46 alcohol, n 40 12,000 8 chloride 15 23 151 Linseed 15 5 51 Benzene 17 5 89 chloride 20 500 102 Olive 15 5 55 Benzene 20 200 77 chloride 20 1,000 66 Rapeseed 20 59 Benzene 20 400 67 chloride 20 12,000 8 Phosphorus trichloride 10 250 71 Bromine 20 200 56 ether 25 23 188 trichloride 20 500 63 Bromine 20 400 51 ether 20 500 84 trichloride 20 1,000 47 Butyl alcohol, iso 18 8 97 ether 20 1,000 61 trichloride 20 12,000 8 alcohol, iso 20 200 81 ether 20 12,000 10 Propyl alcohol (n) 20 200 77 alcohol, iso 20 400 64 iodide 20 200 81 alcohol (n) 20 400 67 alcohol, iso 20 500 56 iodide 20 400 69 alcohol (n?) 20 500 65 alcohol, iso 20 1,000 46 iodide 20 500 64 alcohol (n?) 20 1,000 47 alcohol, iso 20 12,000 8 iodide 20 1,000 50 alcohol (n?) 20 12,000 7 Carbon bisulfide 16 21 86 iodide 20 12,000 8 Toluene 20 200 74 bisulfide 20 500 57 Gallium 30 300 3.97 Toluene 20 400 64 bisulfide 20 1,000 48 Glycerol 15 5 22 Turpentine 20 74 bisulfide 20 12,000 6 Hexane 20 200 117 Water 20 13 49 tetrachloride 20 200 86 Hexane 20 400 91 Water 20 200 43 tetrachloride 20 400 73 Kerosene 20 500 55 Water 20 400 41 Chloroform 20 200 83 Kerosene 20 1,000 45 Water 20 500 39 Chloroform 20 400 70 Kerosene 20 12,000 8 Water 40 500 38 Dichloroethylsulfide 32 1,000 34 Mercury 20 300 3.95 Water 40 1,000 33 Dichloroethylsulfide 32 2,000 24 Mercury 22 500 3.97 Water 40 12,000 9 Ethyl acetate 13 23 103 Mercury 22 1,000 3.91 Xylene, meta 20 200 69 acetate 20 200 90 Mercury 22 12,000 2.37 meta 20 400 60 * Smithsonian Tables, Table 106. Scott (Cryogenic Engineering, Van Nostrand, Princeton, N.J., 1959) gives data for liquid nitrogen (p. 283), oxygen (p. 276), and hydrogen (p. 303). For a convenient index to the high-pressure work of Bridgman, see American Institute of Physics Handbook, p. 2-163, McGraw-Hill, New York, 1957.

TABLE 2-108

Compressibilities of Solids

Many data on the compressibility of solids obtained prior to 1926 are contained in Gruneisen, Handbuch der Physik, vol. 10, Springer, Berlin, 1926, pp. 1–52; also available as translation, NASA RE 2-18-59W, 1959. See also Tables 271, 273, 276, 278, and other material in Smithsonian Physical Tables, 9th ed., 1954. For a review of high-pressure work to 1946, see Bridgman, Rev. Mod. Phys., 18, 1 (1946).

THERMODYnAMIC PROPERTIES

2-191

THERMODYnAMIC PROPERTIES Explanation of Tables The following subsection presents thermodynamic properties of a number of fluids. In some cases, transport properties are also included. Property tables generated from the NIST database (Lemmon, E. W., M. O. McLinden, and M. L. Huber, NIST Standard Reference Database 23) are listed in Table 2-109. The number of digits provided in these tables was chosen for uniformity of appearance and formatting and does not represent the uncertainties of the physical quantities: They are the result of calculations from the standard thermophysical property formulations within a fixed format. They were generated using REFPROP software (Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). Megan Friend helped produce these tables initially for Perry’s 8th edition. Because properties for many compounds also can be generated by the user at the NIST website, only more commonly used compounds’ properties are given here. For other compounds, go to http://webbook.nist.gov and select NIST Chemistry WebBook > Thermophysical Properties of Fluid Systems High Accuracy Data. After selecting the desired unit system and temperature and/or pressure increments for which properties are to be generated, the resulting table can be copied into a spreadsheet. Notation cp = isobaric specific heat cv = isochoric specific heat e = specific internal energy h = enthalpy k = thermal conductivity p = pressure s = specific entropy t = temperature T = absolute temperature u = specific internal energy µ = viscosity v = specific volume f = subscript denoting saturated liquid g = subscript denoting saturated vapor Unit Conversions For this subsection, the following unit conversions are applicable: cp, specific heat: To convert kilojoules per kilogram-kelvin to British thermal units (Btu) per pound–degree Fahrenheit, multiply by 0.23885. e, internal energy: To convert kilojoules per kilogram to Btu per pound, multiply by 0.42992.

g, gravity acceleration: To convert meters per second squared to feet per second squared, multiply by 3.2808. h, enthalpy: To convert kilojoules per kilogram to Btu per pound, multiply by 0.42992. k, thermal conductivity: To convert watts per meter-kelvin to Btu–feet per hour–square foot–degree Fahrenheit, multiply by 0.57779. p, pressure: To convert bars to kilopascals, multiply by 100; to convert bars to pounds-force per square inch, multiply by 14.504; and to convert millimeters of mercury to pounds-force per square inch, multiply by 0.01934. s, entropy: To convert kilojoules per kilogram-kelvin to Btu per pound– degree Rankine, multiply by 0.23885. t, temperature: °F = 9⁄ 5°C + 32. T, absolute temperature: °R = 9⁄ 5 K. u, internal energy: To convert kilojoules per kilogram to Btu per pound, multiply by 0.42992. µ, viscosity: To convert pascal-seconds to pound-force–seconds per square foot, multiply by 0.020885; to convert pascal-seconds to cp, multiply by 1000. v, specific volume: To convert cubic meters per kilogram to cubic feet per pound, multiply by 16.018. r, density: To convert kilograms per cubic meter to pounds per cubic foot, multiply by 0.062428. Additional References Bretsznajder, Prediction of Transport and Other Physical Properties of Fluids, Pergamon, New York, 1971. D’Ans and Lax, Handbook for Chemists and Physicists (in German), 3 vols., SpringerVerlag, Berlin. Engineering Data Book, 12th ed., 2004, Natural Gas Processors Suppliers Association, Tulsa, Okla. Ganic, Hartnett, and Rohsenow, Handbook of Heat Transfer, 2nd ed., McGraw-Hill, New York, 1984. Gray, American Institute of Physics Handbook, 3d ed., McGraw-Hill, New York, 1972. Kay and Laby, Tables of Physical and Chemical Constants, Longman, London, various editions and dates. Landolt-Börnstein Tables, many volumes and dates, Springer-Verlag, Berlin. Partington, Advanced Treatise on Physical Chemistry, Longman, London, 1950. Raznjevic, Handbook of Thermodynamic Tables and Charts, McGraw-Hill, New York, 1976 and other editions. Reynolds, Thermodynamic Properties in SI, Department of Mechanical Engineering, Stanford University, 1979. Stephan and Lucas, Viscosity of Dense Fluids, Plenum, New York and London, 1979. Vargaftik, Tables of the Thermophysical Properties of Gases and Liquids, Wiley, New York, 1975. Vargaftik, Filippov, Tarzimanov, and Totskiy, Thermal Conductivity of Liquids and Gases (in Russian), Standartov, Moscow, 1978. Weast, Handbook of Chemistry and Physics, Chemical Rubber Co., Boca Raton, FL, 97th print edition (2016) and online.

2-192

PHYSICAL AnD CHEMICAL DATA

TABLE 2-109

Thermodynamic Properties of Acetone

Temperature K

Pressure MPa

178.50 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 375.00 390.00 405.00 420.00 435.00 450.00 465.00 480.00 495.00 508.10

2.3265E-06 2.8743E-06 1.9454E-05 9.6588E-05 0.00037556 0.0012008 0.0032765 0.0078514 0.016899 0.033259 0.060720 0.10404 0.16891 0.26188 0.39033 0.56235 0.78681 1.0733 1.4324 1.8759 2.4172 3.0725 3.8632 4.6924

178.50 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 375.00 390.00 405.00 420.00 435.00 450.00 465.00 480.00 495.00 508.10

2.3265E-06 2.8743E-06 1.9454E-05 9.6588E-05 0.00037556 0.0012008 0.0032765 0.0078514 0.016899 0.033259 0.060720 0.10404 0.16891 0.26188 0.39033 0.56235 0.78681 1.0733 1.4324 1.8759 2.4172 3.0725 3.8632 4.6924

200.00 250.00 300.00 328.84

0.10000 0.10000 0.10000 0.10000

328.84 350.00 400.00 450.00 500.00 550.00

0.10000 0.10000 0.10000 0.10000 0.10000 0.10000

200.00 250.00 300.00 350.00 400.00 416.48

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

416.48 450.00 500.00 550.00

1.0000 1.0000 1.0000 1.0000

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

0.063601 0.063715 0.064868 0.066048 0.067264 0.068525 0.069840 0.071218 0.072673 0.074217 0.075867 0.077643 0.079569 0.081677 0.084008 0.086616 0.089578 0.093001 0.097051 0.10200 0.10832 0.11706 0.13145 0.21277

0.47366 0.64687 2.3835 4.1282 5.8823 7.6487 9.4311 11.234 13.060 14.915 16.802 18.725 20.687 22.693 24.746 26.852 29.015 31.243 33.546 35.938 38.445 41.117 44.096 49.249

0.47366 0.64687 2.3835 4.1282 5.8823 7.6488 9.4314 11.234 13.062 14.918 16.807 18.733 20.701 22.714 24.779 26.900 29.085 31.343 33.685 36.130 38.707 41.476 44.604 50.247

0.0080825 0.0090488 0.018316 0.026935 0.035003 0.042602 0.049806 0.056674 0.063259 0.069601 0.075739 0.081702 0.087517 0.093209 0.098798 0.10431 0.10975 0.11516 0.12056 0.12599 0.13150 0.13720 0.14341 0.15437

0.082500 0.082598 0.083407 0.084076 0.084758 0.085541 0.086468 0.087553 0.088794 0.090180 0.091697 0.093329 0.095063 0.096886 0.098794 0.10078 0.10286 0.10504 0.10736 0.10986 0.11265 0.11600 0.12077

0.11544 0.11550 0.11604 0.11660 0.11731 0.11825 0.11946 0.12094 0.12270 0.12474 0.12704 0.12962 0.13249 0.13568 0.13924 0.14328 0.14794 0.15350 0.16042 0.16967 0.18350 0.20893 0.28551

1765.7 1757.0 1672.3 1591.8 1514.4 1439.4 1366.3 1294.8 1224.5 1155.2 1086.7 1018.8 951.24 883.84 816.36 748.57 680.21 610.99 540.51 468.19 392.99 312.66 221.66 0

637,900. 520,660. 83,324. 18,065. 4,973.1 1,656.0 642.89 282.74 137.74 72.996 41.482 24.979 15.782 10.377 7.0503 4.9192 3.5050 2.5368 1.8547 1.3611 0.99393 0.71168 0.48154 0.21277

36.689 36.764 37.528 38.314 39.121 39.947 40.790 41.649 42.522 43.406 44.302 45.207 46.119 47.033 47.946 48.849 49.733 50.582 51.376 52.083 52.648 52.968 52.771 49.249

38.173 38.260 39.149 40.059 40.989 41.936 42.897 43.869 44.849 45.834 46.821 47.806 48.784 49.751 50.698 51.615 52.490 53.305 54.033 54.636 55.050 55.154 54.631 50.247

0.21928 0.21801 0.20686 0.19803 0.19103 0.18546 0.18104 0.17754 0.17479 0.17266 0.17102 0.16980 0.16892 0.16831 0.16791 0.16768 0.16754 0.16745 0.16734 0.16711 0.16664 0.16569 0.16367 0.15437

0.050120 0.050280 0.051928 0.053740 0.055800 0.058169 0.060883 0.063945 0.067329 0.070988 0.074863 0.078895 0.083030 0.087227 0.091459 0.095718 0.10001 0.10438 0.10887 0.11357 0.11865 0.12436 0.13126

0.058440 0.058600 0.060265 0.062119 0.064267 0.066795 0.069763 0.073198 0.077094 0.081429 0.086172 0.091302 0.096822 0.10277 0.10927 0.11649 0.12481 0.13483 0.14772 0.16583 0.19480 0.25197 0.42947

172.60 173.29 179.95 186.29 192.29 197.94 203.19 207.99 212.26 215.93 218.90 221.08 222.35 222.60 221.70 219.53 215.94 210.76 203.80 194.82 183.50 169.39 151.36 0

0.065254 0.069389 0.074210 0.077500

2.9626 8.8328 14.913 18.575

2.9691 8.8397 14.921 18.583

0.021248 0.047436 0.069594 0.081247

0.083638 0.086143 0.090180 0.093199

0.11621 0.11902 0.12473 0.12941

45.137 46.843 50.998 55.474 60.316 65.522

47.730 49.643 54.255 59.166 64.436 70.066

0.16988 0.17552 0.18783 0.19939 0.21049 0.22122

0.078579 0.079533 0.085418 0.092823 0.10033 0.10753

0.090892 0.090386 0.094849 0.10175 0.10903 0.11612

220.94 229.44 246.85 262.23 276.40 289.72

2.9486 8.8130 14.885 21.312 28.263 30.714

3.0138 8.8824 14.959 21.392 28.351 30.806

0.021178 0.047357 0.069499 0.089316 0.10788 0.11389

0.083649 0.086152 0.090182 0.095644 0.10213 0.10452

0.11619 0.11896 0.12460 0.13326 0.14605 0.15210

1649.7 1396.0 1162.0 936.35 707.25 627.32

50.387 54.081 59.388 64.832

53.120 57.281 63.156 69.107

0.16747 0.17709 0.18947 0.20081

0.10335 0.10087 0.10402 0.10950

0.13228 0.11921 0.11743 0.12100

212.13 233.76 256.99 275.55

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

JouleThomson K/MPa

Saturated Properties 15.723 15.695 15.416 15.141 14.867 14.593 14.319 14.041 13.760 13.474 13.181 12.880 12.568 12.243 11.904 11.545 11.163 10.753 10.304 9.8043 9.2319 8.5423 7.6072 4.7000 1.5677E-06 1.9207E-06 1.2001E-05 5.5355E-05 0.00020108 0.00060385 0.0015555 0.0035368 0.0072603 0.013699 0.024107 0.040034 0.063362 0.096367 0.14184 0.20329 0.28530 0.39420 0.53918 0.73472 1.0061 1.4051 2.0767 4.7000

−0.43351 −0.43308 −0.42849 −0.42274 −0.41520 −0.40545 −0.39322 −0.37827 −0.36033 −0.33907 −0.31399 −0.28437 −0.24915 −0.20678 −0.15495 −0.090162 −0.0069455 0.10371 0.25760 0.48516 0.85357 1.5474 3.3240 14.310 3845.4 3637.4 2139.7 1312.0 834.10 547.82 370.79 258.27 184.97 136.14 102.93 79.878 63.590 51.884 43.343 37.032 32.325 28.797 26.154 24.184 22.717 21.551 20.240 14.310

Single-Phase Properties 15.325 14.411 13.475 12.903 0.038565 0.035712 0.030709 0.027083 0.024272 0.022008 15.333 14.423 13.491 12.483 11.308 10.852 0.36582 0.31254 0.26538 0.23391

25.930 28.002 32.563 36.923 41.200 45.437 0.065220 0.069336 0.074123 0.080107 0.088431 0.092149 2.7336 3.1996 3.7681 4.2751

1645.6 1391.1 1155.7 1024.0

−0.42678 −0.39768 −0.33922 −0.28685 81.384 58.339 30.192 18.173 12.201 8.8355 −0.42708 −0.39848 −0.34115 −0.24033 −0.042437 0.074613 29.536 20.211 12.984 9.1542

THERMODYnAMIC PROPERTIES

2-193

TABLE 2-109 Thermodynamic Properties of Acetone (Continued ) Temperature K

Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

15.367 14.471 13.560 12.588 11.490 10.123 7.8139 1.7344

0.065073 0.069106 0.073747 0.079439 0.087035 0.098782 0.12798 0.57657

2.8871 8.7271 14.762 21.128 27.958 35.450 44.435 60.563

3.2125 9.0726 15.130 21.525 28.393 35.944 45.075 63.446

15.410 14.528 13.641 12.709 11.683 10.491 8.9733 6.6600

0.064894 0.068831 0.073307 0.078687 0.085592 0.095320 0.11144 0.15015

2.8125 8.6237 14.616 20.916 27.629 34.864 42.815 52.079

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

JouleThomson K/MPa

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

0.020868 0.047011 0.069085 0.088784 0.10711 0.12488 0.14406 0.17943

0.083704 0.086197 0.090197 0.095584 0.10186 0.10898 0.11961 0.12191

0.11609 0.11871 0.12408 0.13214 0.14320 0.16059 0.23343 0.17820

1667.9 1417.7 1189.0 972.15 759.27 538.79 262.33 205.69

−0.42837 −0.40187 −0.34909 −0.25988 −0.10136 0.26123 2.3418 10.650

3.4614 9.3120 15.349 21.703 28.485 35.818 43.930 53.581

0.020488 0.046589 0.068589 0.088163 0.10626 0.12352 0.14060 0.15896

0.083781 0.086264 0.090234 0.095554 0.10166 0.10827 0.11552 0.12442

0.11598 0.11843 0.12351 0.13100 0.14066 0.15332 0.17314 0.22174

1689.9 1443.6 1220.9 1013.1 815.03 622.74 433.48 255.34

−0.42983 −0.40569 −0.35775 −0.27983 −0.15336 0.080235 0.63674 2.7218

Single-Phase Properties (Cont.) 200.00 250.00 300.00 350.00 400.00 450.00 500.00 550.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00 550.00

5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000

250.00 300.00 350.00 400.00 450.00 500.00 550.00

100.00 100.00 100.00 100.00 100.00 100.00 100.00

15.320 14.657 14.023 13.409 12.813 12.234 11.674

0.065276 0.068228 0.071312 0.074574 0.078044 0.081739 0.085664

7.2620 12.852 18.631 24.654 30.941 37.489 44.286

13.790 19.675 25.763 32.112 38.745 45.663 52.852

0.040421 0.061873 0.080632 0.097579 0.11320 0.12777 0.14147

0.088285 0.092127 0.097243 0.10299 0.10892 0.11478 0.12045

0.11631 0.11946 0.12424 0.12980 0.13553 0.14112 0.14639

1791.8 1616.6 1466.4 1337.4 1226.9 1133.0 1053.8

−0.43634 −0.42000 −0.39555 −0.36734 −0.33807 −0.30922 −0.28171

450.00 500.00 550.00

500.00 500.00 500.00

15.616 15.306 15.012

0.064037 0.065335 0.066615

27.237 33.413 39.856

59.256 66.081 73.163

0.097266 0.11164 0.12514

0.11562 0.12123 0.12669

0.13393 0.13909 0.14416

2201.1 2129.8 2067.5

−0.39010 −0.37710 −0.36510

The values in this table were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., and Span, R., “Short Fundamental Equations of State for 20 Industrial Fluids,” J. Chem. Eng. Data, 51(3):785–850, 2006. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties in the equation of state are 0.1% in the saturated liquid density between 280 and 310 K, 0.5% in density in the liquid phase below 380 K, and 1% in density elsewhere, including all states at pressures above 100 MPa. The uncertainties in vapor pressure are 0.5% above 270 K (0.25% between 290 and 390 K), and the uncertainties in heat capacities and speeds of sound are 1%. These uncertainties (in caloric properties and sound speeds) may be higher at pressures above the saturation pressure and at temperatures above 320 K in the liquid phase and at supercritical conditions.

2-194

TABLE 2-110

Thermodynamic Properties of Air

Temperature K

Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

59.75 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

0.005265 0.005546 0.006797 0.008270 0.009994 0.012000 0.014320 0.016988 0.020042 0.023520 0.027461 0.031908 0.036905 0.042498 0.048733 0.055659 0.063326 0.071786 0.081091 0.091294 0.10245 0.11462 0.12785 0.14221 0.15775 0.17453 0.19262 0.21207 0.23295 0.25531 0.27922 0.30475 0.33196 0.36091 0.39166 0.42429 0.45886 0.49543 0.53408 0.57486 0.61786 0.66313 0.71074 0.76077 0.81329 0.86836 0.92606 0.98645 1.0496 1.1156 1.1845 1.2564 1.3314 1.4095 1.4908 1.5753

33.067 33.031 32.888 32.745 32.601 32.457 32.312 32.166 32.020 31.873 31.725 31.576 31.427 31.277 31.126 30.974 30.821 30.668 30.513 30.357 30.200 30.042 29.883 29.722 29.560 29.397 29.232 29.066 28.898 28.729 28.558 28.385 28.210 28.033 27.854 27.673 27.489 27.304 27.115 26.924 26.730 26.533 26.333 26.130 25.923 25.713 25.499 25.281 25.058 24.831 24.598 24.361 24.118 23.868 23.613 23.350

0.030242 0.030275 0.030406 0.030539 0.030674 0.030810 0.030949 0.031089 0.031231 0.031375 0.031521 0.031669 0.031820 0.031972 0.032127 0.032285 0.032445 0.032608 0.032773 0.032941 0.033112 0.033287 0.033464 0.033645 0.033829 0.034017 0.034209 0.034404 0.034604 0.034808 0.035017 0.035230 0.035449 0.035672 0.035901 0.036137 0.036378 0.036625 0.036880 0.037142 0.037411 0.037688 0.037975 0.038270 0.038575 0.038891 0.039217 0.039556 0.039908 0.040273 0.040653 0.041050 0.041464 0.041896 0.042350 0.042826

−1.0619 −1.0481 −0.99308 −0.93803 −0.88298 −0.82792 −0.77286 −0.71777 −0.66267 −0.60755 −0.55239 −0.49720 −0.44196 −0.38669 −0.33135 −0.27597 −0.22051 −0.16499 −0.10939 −0.05371 0.002063 0.057934 0.11391 0.17000 0.22621 0.28255 0.33903 0.39566 0.45245 0.50940 0.56653 0.62386 0.68138 0.73912 0.79709 0.85529 0.91375 0.97248 1.0315 1.0908 1.1505 1.2104 1.2708 1.3315 1.3926 1.4542 1.5162 1.5787 1.6417 1.7053 1.7695 1.8343 1.8997 1.9659 2.0329 2.1007

−1.0617 −1.0480 −0.99287 −0.93778 −0.88267 −0.82755 −0.77241 −0.71725 −0.66205 −0.60681 −0.55152 −0.49619 −0.44079 −0.38533 −0.32979 −0.27417 −0.21846 −0.16265 −0.10673 −0.05070 0.005456 0.061749 0.11819 0.17478 0.23155 0.28849 0.34562 0.40296 0.46051 0.51829 0.57631 0.63459 0.69315 0.75199 0.81115 0.87062 0.93044 0.99063 1.0512 1.1122 1.1736 1.2354 1.2978 1.3606 1.4240 1.4880 1.5525 1.6177 1.6836 1.7502 1.8176 1.8858 1.9549 2.0250 2.0960 2.1682

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

JouleThomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

0.034011 0.033955 0.033731 0.033512 0.033298 0.033089 0.032884 0.032683 0.032486 0.032294 0.032105 0.031920 0.031739 0.031562 0.031388 0.031217 0.031050 0.030886 0.030725 0.030568 0.030413 0.030262 0.030113 0.029968 0.029826 0.029686 0.029550 0.029417 0.029286 0.029158 0.029033 0.028911 0.028792 0.028676 0.028563 0.028453 0.028346 0.028241 0.028140 0.028042 0.027948 0.027856 0.027768 0.027684 0.027603 0.027525 0.027452 0.027383 0.027317 0.027256 0.027200 0.027149 0.027103 0.027062 0.027028 0.027000

0.055064 0.055062 0.055060 0.055062 0.055069 0.055081 0.055098 0.055120 0.055148 0.055181 0.055220 0.055266 0.055317 0.055376 0.055441 0.055514 0.055594 0.055682 0.055779 0.055884 0.055998 0.056122 0.056256 0.056400 0.056556 0.056723 0.056902 0.057094 0.057300 0.057521 0.057757 0.058009 0.058278 0.058566 0.058874 0.059202 0.059553 0.059928 0.060329 0.060757 0.061216 0.061707 0.062232 0.062796 0.063401 0.064052 0.064753 0.065508 0.066323 0.067206 0.068163 0.069205 0.070341 0.071585 0.072951 0.074459

1030.3 1028.3 1020.3 1012.2 1004.0 995.77 987.48 979.13 970.72 962.24 953.70 945.10 936.43 927.70 918.90 910.04 901.11 892.11 883.05 873.91 864.71 855.44 846.09 836.67 827.18 817.61 807.96 798.24 788.44 778.56 768.59 758.55 748.42 738.20 727.90 717.51 707.03 696.46 685.80 675.05 664.20 653.26 642.22 631.08 619.84 608.50 597.06 585.51 573.85 562.09 550.21 538.21 526.10 513.86 501.48 488.97

−0.40785 −0.40743 −0.40565 −0.40375 −0.40173 −0.39958 −0.39729 −0.39485 −0.39227 −0.38952 −0.38660 −0.38352 −0.38024 −0.37677 −0.37310 −0.36922 −0.36511 −0.36076 −0.35616 −0.35130 −0.34616 −0.34074 −0.33500 −0.32894 −0.32254 −0.31577 −0.30862 −0.30107 −0.29308 −0.28464 −0.27572 −0.26628 −0.25629 −0.24573 −0.23455 −0.22270 −0.21016 −0.19686 −0.18275 −0.16779 −0.15189 −0.13501 −0.11705 −0.09794 −0.07758 −0.05588 −0.03271 −0.00795 0.018543 0.046927 0.077386 0.11012 0.14538 0.18342 0.22456 0.26917

171.43 171.02 169.40 167.78 166.16 164.53 162.91 161.28 159.65 158.01 156.37 154.73 153.09 151.44 149.79 148.14 146.49 144.83 143.16 141.50 139.83 138.15 136.48 134.80 133.11 131.42 129.78 128.11 126.44 124.76 123.07 121.38 119.69 118.00 116.30 114.61 112.91 111.21 109.51 107.81 106.11 104.41 102.71 101.01 99.316 97.623 95.933 94.247 92.565 90.888 89.216 87.551 85.893 84.242 82.599 80.965

376.64 371.92 353.83 336.91 321.09 306.27 292.39 279.38 267.17 255.71 244.94 234.81 225.28 216.31 207.85 199.88 192.35 185.23 178.51 172.14 166.11 160.39 154.96 149.80 144.90 140.23 135.78 131.54 127.50 123.63 119.93 116.38 112.98 109.72 106.59 103.58 100.68 97.879 95.179 92.571 90.048 87.605 85.236 82.937 80.703 78.529 76.412 74.347 72.331 70.361 68.432 66.542 64.688 62.867 61.075 59.311

Saturated Properties −0.01536 −0.01513 −0.01422 −0.01333 −0.01245 −0.01158 −0.01073 −0.00989 −0.00906 −0.00824 −0.00744 −0.00664 −0.00586 −0.00508 −0.00432 −0.00357 −0.00282 −0.00209 −0.00136 −0.00064 6.86E-05 0.000772 0.001467 0.002156 0.002838 0.003513 0.004181 0.004844 0.005501 0.006153 0.006799 0.007440 0.008077 0.008708 0.009336 0.009960 0.010579 0.011195 0.011808 0.012418 0.013025 0.013630 0.014232 0.014833 0.015431 0.016029 0.016625 0.017221 0.017816 0.018411 0.019006 0.019602 0.020200 0.020799 0.021400 0.022004

115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 132.63

1.6633 1.7546 1.8495 1.9479 2.0499 2.1557 2.2653 2.3787 2.4960 2.6173 2.7427 2.8721 3.0055 3.1431 3.2845 3.4295 3.5770 3.7228 3.7858

59.75 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101

0.002432 0.002584 0.003274 0.004111 0.005120 0.006325 0.007756 0.009442 0.011416 0.013713 0.016372 0.019431 0.022933 0.026921 0.031443 0.036547 0.042282 0.048702 0.055859 0.063810 0.072611 0.082321 0.093001 0.10471 0.11751 0.13147 0.14665 0.16312 0.18094 0.20018 0.22091 0.24320 0.26712 0.29273 0.32011 0.34934 0.38047 0.41359 0.44878 0.48609 0.52562 0.56742 0.61159

23.080 22.801 22.514 22.217 21.908 21.588 21.253 20.903 20.534 20.144 19.727 19.278 18.788 18.242 17.616 16.863 15.869 14.198 10.448 0.004907 0.005192 0.006475 0.008005 0.009817 0.011948 0.014438 0.017326 0.020659 0.024481 0.028841 0.033789 0.039379 0.045664 0.052702 0.060550 0.069268 0.078918 0.089564 0.10127 0.11410 0.12813 0.14343 0.16006 0.17811 0.19765 0.21875 0.24150 0.26598 0.29228 0.32048 0.35068 0.38298 0.41747 0.45426 0.49345 0.53517 0.57953 0.62667 0.67671 0.72980 0.78609 0.84575

0.043328 0.043857 0.044417 0.045011 0.045645 0.046323 0.047052 0.047841 0.048700 0.049643 0.050691 0.051871 0.053225 0.054818 0.056765 0.059300 0.063015 0.070432 0.095715 203.80 192.59 154.45 124.93 101.86 83.693 69.263 57.715 48.406 40.849 34.673 29.595 25.394 21.899 18.975 16.515 14.437 12.671 11.165 9.8746 8.7639 7.8043 6.9721 6.2475 5.6145 5.0595 4.5715 4.1408 3.7597 3.4214 3.1203 2.8516 2.6111 2.3954 2.2014 2.0265 1.8686 1.7255 1.5957 1.4777 1.3702 1.2721 1.1824

2.1695 2.2392 2.3100 2.3821 2.4554 2.5303 2.6069 2.6854 2.7662 2.8496 2.9363 3.0269 3.1227 3.2253 3.3379 3.4661 3.6243 3.8680 4.4004

2.2415 2.3161 2.3922 2.4697 2.5490 2.6302 2.7135 2.7992 2.8878 2.9796 3.0753 3.1759 3.2827 3.3976 3.5243 3.6695 3.8497 4.1302 4.7627

0.022611 0.023223 0.023840 0.024462 0.025092 0.025731 0.026380 0.027041 0.027717 0.028412 0.029131 0.029880 0.030668 0.031512 0.032436 0.033492 0.034804 0.036863 0.041603

0.026979 0.026965 0.026961 0.026966 0.026982 0.027010 0.027053 0.027113 0.027194 0.027300 0.027438 0.027618 0.027855 0.028171 0.028607 0.029242 0.030266 0.032343

0.076131 0.077996 0.080090 0.082459 0.085163 0.088280 0.091919 0.096227 0.10142 0.10781 0.11589 0.12645 0.14089 0.16186 0.19519 0.25624 0.40151 1.0148

476.31 463.48 450.49 437.29 423.88 410.23 396.30 382.04 367.40 352.31 336.67 320.36 303.21 285.00 265.37 243.75 219.07 189.12 0

4.8774 4.8825 4.9025 4.9225 4.9424 4.9621 4.9817 5.0012 5.0205 5.0397 5.0587 5.0774 5.0960 5.1144 5.1326 5.1505 5.1682 5.1856 5.2028 5.2196 5.2362 5.2525 5.2684 5.2841 5.2994 5.3143 5.3289 5.3431 5.3569 5.3703 5.3832 5.3958 5.4079 5.4195 5.4307 5.4413 5.4514 5.4610 5.4701 5.4785 5.4864 5.4936 5.5002

5.3730 5.3800 5.4081 5.4361 5.4639 5.4915 5.5189 5.5461 5.5731 5.5998 5.6263 5.6525 5.6784 5.7040 5.7292 5.7541 5.7786 5.8027 5.8264 5.8497 5.8726 5.8949 5.9169 5.9383 5.9591 5.9795 5.9993 6.0185 6.0372 6.0552 6.0726 6.0893 6.1054 6.1207 6.1354 6.1492 6.1624 6.1747 6.1862 6.1968 6.2066 6.2154 6.2233

0.096708 0.096323 0.094825 0.093392 0.092020 0.090705 0.089445 0.088235 0.087074 0.085959 0.084887 0.083855 0.082862 0.081906 0.080983 0.080094 0.079235 0.078406 0.077604 0.076828 0.076076 0.075348 0.074643 0.073957 0.073292 0.072645 0.072016 0.071403 0.070806 0.070224 0.069655 0.069099 0.068556 0.068024 0.067503 0.066991 0.066489 0.065995 0.065510 0.065031 0.064560 0.064094 0.063633

0.020805 0.020809 0.020825 0.020843 0.020864 0.020886 0.020911 0.020938 0.020968 0.021000 0.021035 0.021072 0.021113 0.021156 0.021201 0.021250 0.021302 0.021356 0.021414 0.021474 0.021538 0.021605 0.021674 0.021747 0.021822 0.021901 0.021983 0.022068 0.022155 0.022246 0.022340 0.022436 0.022536 0.022638 0.022744 0.022852 0.022964 0.023078 0.023196 0.023317 0.023441 0.023568 0.023698

0.029217 0.029225 0.029261 0.029302 0.029348 0.029399 0.029455 0.029518 0.029587 0.029663 0.029746 0.029836 0.029934 0.030040 0.030155 0.030278 0.030410 0.030552 0.030703 0.030865 0.031037 0.031220 0.031415 0.031621 0.031840 0.032072 0.032317 0.032577 0.032851 0.033141 0.033447 0.033770 0.034111 0.034472 0.034853 0.035256 0.035681 0.036132 0.036610 0.037116 0.037654 0.038225 0.038834

154.83 155.14 156.38 157.60 158.81 159.99 161.16 162.30 163.42 164.53 165.60 166.66 167.69 168.70 169.69 170.65 171.58 172.49 173.37 174.23 175.05 175.85 176.62 177.36 178.07 178.75 179.40 180.02 180.61 181.17 181.69 182.19 182.65 183.08 183.47 183.84 184.17 184.46 184.72 184.95 185.14 185.30 185.42

0.31767 0.37057 0.42848 0.49214 0.56243 0.64047 0.72765 0.82574 0.93703 1.0646 1.2125 1.3865 1.5951 1.8510 2.1752 2.6058 3.2246 4.2808 6.3978 58.283 57.634 55.151 52.832 50.666 48.640 46.742 44.963 43.293 41.724 40.248 38.858 37.548 36.313 35.146 34.043 32.999 32.010 31.072 30.183 29.337 28.534 27.769 27.041 26.346 25.684 25.051 24.447 23.869 23.316 22.786 22.278 21.791 21.324 20.876 20.445 20.031 19.632 19.249 18.879 18.523 18.180 17.848

79.340 77.724 76.119 74.523 72.938 71.363 69.798 68.243 66.700 65.170 63.658 62.176 60.751 59.445 58.409 58.054 59.591 67.802

57.571 55.852 54.152 52.467 50.794 49.130 47.469 45.809 44.141 42.460 40.755 39.013 37.215 35.332 33.316 31.072 28.384 24.467

5.2938 5.3199 5.4244 5.5291 5.6340 5.7391 5.8444 5.9500 6.0559 6.1621 6.2688 6.3759 6.4835 6.5917 6.7005 6.8099 6.9202 7.0312 7.1431 7.2560 7.3700 7.4851 7.6014 7.7192 7.8384 7.9591 8.0817 8.2060 8.3324 8.4610 8.5919 8.7254 8.8616 9.0008 9.1433 9.2893 9.4390 9.5929 9.7513 9.9145 10.083 10.257 10.438

4.2197 4.2382 4.3119 4.3855 4.4590 4.5324 4.6057 4.6788 4.7519 4.8248 4.8976 4.9703 5.0429 5.1154 5.1878 5.2602 5.3325 5.4048 5.4771 5.5494 5.6217 5.6940 5.7664 5.8389 5.9116 5.9844 6.0574 6.1307 6.2043 6.2781 6.3524 6.4272 6.5024 6.5782 6.6547 6.7318 6.8098 6.8887 6.9686 7.0495 7.1317 7.2153 7.3003

2-195

(Continued)

2-196

TABLE 2-110 Thermodynamic Properties of Air (Continued ) Temperature K 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 132.63

Pressure MPa

Density mol/dm3

0.65820 0.70732 0.75903 0.81341 0.87055 0.93052 0.9934 1.0593 1.1282 1.2004 1.2757 1.3545 1.4366 1.5223 1.6115 1.7045 1.8013 1.9020 2.0067 2.1156 2.2287 2.3462 2.4682 2.5949 2.7266 2.8633 3.0055 3.1536 3.3084 3.4712 3.6462 3.7858

0.90895 0.97587 1.0467 1.1217 1.2011 1.2852 1.3742 1.4684 1.5682 1.6740 1.7862 1.9053 2.0318 2.1664 2.3097 2.4625 2.6259 2.8009 2.9889 3.1913 3.4103 3.6481 3.9078 4.1934 4.5101 4.8653 5.2697 5.7405 6.3074 7.0343 8.1273 10.448

Volume dm3/mol 1.1002 1.0247 0.95535 0.89147 0.83254 0.77810 0.72772 0.68102 0.63767 0.59737 0.55985 0.52486 0.49217 0.46160 0.43296 0.40608 0.38082 0.35702 0.33457 0.31335 0.29323 0.27412 0.25590 0.23847 0.22173 0.20554 0.18976 0.17420 0.15854 0.14216 0.12304 0.095715

Sound speed m/s

JouleThomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity mPa⋅s

0.039483 0.040176 0.040918 0.041714 0.042570 0.043492 0.044490 0.045573 0.046751 0.048038 0.049450 0.051005 0.052727 0.054644 0.056790 0.059209 0.061956 0.065102 0.068738 0.072988 0.078015 0.084052 0.091426 0.10063 0.11241 0.12801 0.14959 0.18134 0.23261 0.32992 0.59804

185.51 185.55 185.57 185.54 185.48 185.38 185.24 185.07 184.85 184.60 184.30 183.97 183.59 183.17 182.71 182.21 181.66 181.08 180.45 179.78 179.06 178.31 177.51 176.68 175.81 174.91 173.96 172.98 171.93 170.79 169.40 0

17.528 17.218 16.918 16.628 16.346 16.072 15.805 15.546 15.292 15.044 14.800 14.561 14.324 14.090 13.856 13.623 13.388 13.151 12.909 12.661 12.405 12.137 11.854 11.553 11.229 10.874 10.480 10.033 9.5119 8.8740 7.9854 6.3978

10.626 10.821 11.024 11.237 11.459 11.693 11.939 12.198 12.473 12.764 13.074 13.406 13.762 14.145 14.559 15.008 15.499 16.039 16.635 17.298 18.042 18.884 19.849 20.968 22.288 23.877 25.841 28.367 31.807 37.001 46.996

7.3870 7.4755 7.5659 7.6586 7.7537 7.8514 7.9521 8.0560 8.1634 8.2749 8.3907 8.5114 8.6375 8.7696 8.9086 9.0552 9.2104 9.3755 9.5518 9.7412 9.9456 10.168 10.411 10.681 10.982 11.324 11.720 12.191 12.775 13.553 14.798

0.021087 0.020796 0.021504 0.022817 0.024150 0.025246 0.026091 0.026734 0.027229 0.027619

0.030116 0.029149 0.029830 0.031137 0.032467 0.033562 0.034406 0.035049 0.035544 0.035934

198.24 347.36 446.40 523.89 589.60 648.15 701.76 751.59 798.38 842.62

17.423 2.2510 0.50305 −0.12430 −0.41124 −0.56194 −0.64963 −0.70457 −0.74078 −0.76547

9.4692 26.384 39.944 51.755 62.543 72.680 82.381 91.781 100.97 110.01

7.1068 18.537 27.090 34.176 40.394 46.051 51.325 56.325 61.127 65.783

0.013532 0.017351

0.027868 0.027368

0.061355 0.065680

658.25 582.97

−0.14308 −0.00232

104.97 93.879

88.326 73.903

6.2479 12.289 18.218 24.326 30.698 37.311 44.114 51.065 58.128 65.278

0.060461 0.093372 0.10851 0.11877 0.12677 0.13340 0.13908 0.14405 0.14847 0.15245

0.024739 0.020859 0.021526 0.022830 0.024159 0.025253 0.026096 0.026738 0.027233 0.027622

0.044597 0.029563 0.029954 0.031194 0.032498 0.033582 0.034419 0.035057 0.035550 0.035939

185.23 348.45 448.46 525.96 591.54 649.96 703.44 753.17 799.86 844.02

15.779 2.1789 0.47425 −0.13809 −0.41899 −0.56686 −0.65304 −0.70711 −0.74278 −0.76711

11.965 26.684 40.110 51.868 62.628 72.748 82.438 91.830 101.01 110.05

7.9625 18.672 27.179 34.242 40.446 46.094 51.361 56.357 61.155 65.808

1.2820 12.042

0.012483 0.079244

0.028034 0.021131

0.058181 0.031423

710.56 355.63

−0.21837 1.8817

111.13 28.389

96.436 19.420

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

5.5060 5.5112 5.5156 5.5193 5.5221 5.5240 5.5250 5.5251 5.5241 5.5221 5.5188 5.5143 5.5085 5.5012 5.4924 5.4819 5.4695 5.4550 5.4383 5.4190 5.3969 5.3715 5.3424 5.3089 5.2701 5.2248 5.1713 5.1069 5.0268 4.9209 4.7566 4.4004

6.2302 6.2360 6.2408 6.2444 6.2469 6.2481 6.2480 6.2465 6.2436 6.2391 6.2330 6.2252 6.2156 6.2039 6.1901 6.1740 6.1554 6.1341 6.1097 6.0819 6.0504 6.0147 5.9740 5.9277 5.8746 5.8133 5.7417 5.6563 5.5513 5.4143 5.2053 4.7627

0.063177 0.062726 0.062277 0.061832 0.061389 0.060947 0.060506 0.060065 0.059623 0.059180 0.058735 0.058286 0.057833 0.057375 0.056910 0.056437 0.055955 0.055461 0.054954 0.054432 0.053890 0.053326 0.052735 0.052112 0.051448 0.050732 0.049950 0.049076 0.048067 0.046830 0.045064 0.041603

0.023833 0.023970 0.024112 0.024258 0.024408 0.024563 0.024722 0.024887 0.025058 0.025234 0.025418 0.025608 0.025807 0.026015 0.026232 0.026461 0.026701 0.026956 0.027226 0.027514 0.027823 0.028155 0.028516 0.028910 0.029344 0.029827 0.030371 0.030994 0.031726 0.032619 0.033814

5.6800 9.8544 14.072 18.500 23.201 28.145 33.282 38.568 43.966 49.453

6.4941 12.348 18.231 24.323 30.686 37.293 44.094 51.042 58.104 65.253

0.080463 0.11269 0.12770 0.13794 0.14593 0.15255 0.15823 0.16320 0.16762 0.17160

1.2007 1.5924

1.2383 1.6321

5.5251 9.8022 14.046 18.485 23.190 28.138 33.278 38.565 43.964 49.451 1.0983 9.5710

Single-Phase Properties 100 300 500 700 900 1100 1300 1500 1700 1900 100 106.22

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1 1

108.1 300 500 700 900 1100 1300 1500 1700 1900

1 1 1 1 1 1 1 1 1 1

100 300

5 5

0.12283 0.040103 0.024046 0.017175 0.013359 0.010931 0.009249 0.008016 0.007073 0.006329 26.593 25.232 1.3836 0.40205 0.23974 0.17119 0.13319 0.10902 0.092279 0.079999 0.070604 0.063185 27.222 2.0232

8.1414 24.936 41.586 58.223 74.855 91.486 108.12 124.75 141.38 158.00 0.037604 0.039632 0.72278 2.4873 4.1711 5.8415 7.5079 9.1727 10.837 12.500 14.163 15.827 0.036735 0.49426

500 700 900 1100 1300 1500 1700 1900

5 5 5 5 5 5 5 5

1.1814 0.84321 0.65711 0.53874 0.45667 0.39636 0.35015 0.31361

0.84642 1.1859 1.5218 1.8562 2.1898 2.5229 2.8559 3.1887

13.935 18.417 23.146 28.107 33.256 38.550 43.954 49.445

18.167 24.347 30.755 37.388 44.205 51.165 58.234 65.389

0.094907 0.10529 0.11334 0.11999 0.12568 0.13066 0.13509 0.13907

0.021621 0.022885 0.024197 0.025282 0.026119 0.026757 0.027249 0.027636

0.030478 0.031434 0.032632 0.033664 0.034473 0.035095 0.035577 0.035958

458.30 535.45 600.34 658.10 711.01 760.23 806.49 850.28

0.36370 −0.19118 −0.44905 −0.58606 −0.66646 −0.71716 −0.75073 −0.77366

40.969 52.433 63.045 73.076 82.707 92.057 101.21 110.22

27.606 34.545 40.682 46.287 51.523 56.497 61.278 65.917

100 300 500 700 900 1100 1300 1500 1700 1900

10 10 10 10 10 10 10 10 10 10

27.863 4.0370 2.3157 1.6542 1.2922 1.0618 0.90165 0.78374 0.69321 0.62149

0.035889 0.24771 0.43183 0.60452 0.77388 0.94184 1.1091 1.2759 1.4426 1.6090

0.99444 9.2885 13.802 18.336 23.092 28.070 33.231 38.532 43.943 49.438

1.3533 11.766 18.120 24.382 30.831 37.489 44.321 51.292 58.368 65.528

0.011382 0.072612 0.088894 0.099422 0.10752 0.11420 0.11990 0.12489 0.12932 0.13330

0.028284 0.021441 0.021733 0.022952 0.024243 0.025317 0.026146 0.026780 0.027268 0.027653

0.055716 0.033664 0.031078 0.031710 0.032786 0.033760 0.034537 0.035139 0.035608 0.035981

763.47 369.50 471.81 547.83 611.64 668.47 720.60 769.17 814.87 858.18

−0.27969 1.5212 0.25100 −0.24405 −0.47890 −0.60517 −0.67990 −0.72730 −0.75881 −0.78039

117.77 31.116 42.260 53.257 63.641 73.538 83.082 92.372 101.48 110.45

105.78 20.637 28.194 34.944 40.985 46.531 51.728 56.673 61.432 66.054

100 300 500 700 900 1100 1300 1500 1700 1900

100 100 100 100 100 100 100 100 100 100

33.161 21.138 15.089 11.803 9.7481 8.3307 7.2877 6.4847 5.8456 5.3239

0.030156 0.047309 0.066273 0.084722 0.10258 0.12004 0.13722 0.15421 0.17107 0.18783

0.24746 7.0356 12.371 17.367 22.408 27.580 32.880 38.287 43.779 49.340

3.2631 11.767 18.999 25.840 32.667 39.584 46.602 53.708 60.886 68.123

0.001378 0.049067 0.067619 0.079134 0.087711 0.09465 0.10051 0.10559 0.11009 0.11411

0.031980 0.023981 0.023117 0.023855 0.024903 0.025831 0.026565 0.027131 0.027569 0.027915

0.048218 0.038366 0.034686 0.034011 0.034331 0.034845 0.035323 0.035723 0.036049 0.036317

1192.4 818.47 772.41 790.14 821.78 857.40 894.00 930.40 966.13 1001.0

−0.47290 −0.49747 −0.55640 −0.62591 −0.67702 −0.71435 −0.74281 −0.76506 −0.78264 −0.79653

179.20 86.312 71.549 73.572 79.057 85.797 93.151 100.84 108.75 116.78

252.46 53.642 42.159 43.339 46.948 51.158 55.511 59.875 64.208 68.504

300 500 700 900 1100 1300 1500 1700 1900

500 500 500 500 500 500 500 500 500

34.106 29.826 26.714 24.283 22.305 20.651 19.243 18.027 16.963

0.029320 0.033528 0.037433 0.041180 0.044833 0.048423 0.051966 0.055473 0.058952

6.2145 11.583 16.768 22.008 27.358 32.814 38.354 43.961 49.623

20.875 28.348 35.484 42.598 49.775 57.025 64.337 71.698 79.098

0.033155 0.052311 0.064323 0.073261 0.080460 0.086515 0.091746 0.096353 0.10047

0.028875 0.026614 0.026496 0.026991 0.027539 0.028000 0.02836 0.02864 0.02886

0.039265 0.036111 0.035494 0.035702 0.036073 0.036415 0.036693 0.036911 0.037085

1678.8 1573.6 1514.8 1482.8 1468.3 1465.1 1469.3 1478.5 1491.1

−0.57656 −0.65015 −0.67879 −0.68796 −0.69130 −0.69354 −0.69594 −0.69875 −0.70188

208.23 178.50 161.67 151.95 146.88 144.95 145.84 148.48 152.39

181.12 120.62 97.470 86.531 81.387 79.411 79.312 80.393 82.251

300 500 700 900 1100 1300 1500 1700 1900

1000 1000 1000 1000 1000 1000 1000 1000 1000

40.130 36.567 33.895 31.736 29.916 28.338 26.946 25.701 24.577

0.024919 0.027347 0.029503 0.031510 0.033427 0.035288 0.037111 0.038909 0.040688

6.8286 12.271 17.554 22.890 28.327 33.857 39.461 45.123 50.830

31.747 39.618 47.057 54.399 61.754 69.145 76.573 84.032 91.519

0.024761 0.044944 0.057468 0.066695 0.074073 0.080246 0.085561 0.090229 0.094392

0.032271 0.029334 0.028754 0.028917 0.029215 0.029476 0.029675 0.029821 0.029928

0.041510 0.037843 0.036801 0.036702 0.036858 0.037051 0.037224 0.037369 0.037491

2208.5 2104.7 2033.9 1984.7 1951.3 1929.3 1915.7 1908.3 1905.8

−0.50493 −0.57316 −0.60504 −0.61882 −0.62560 −0.62968 −0.63251 −0.63465 −0.63632

274.96 247.30 230.60 219.72 212.46 207.70 204.81 203.41 203.25

337.76 219.41 174.51 149.43 133.76 123.58 116.94 112.74 110.27

This table was generated for a standard three-component dry air containing mole fractions 0.7812 nitrogen, 0.2096 oxygen, and 0.0092 argon. The values in this table were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., Jacobsen, R. T, Penoncello, S. G., and Friend, D. G., “Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen from 60 to 2000 K at Pressures to 2000 MPa,” J. Phys. Chem. Ref. Data 29(3):331–385, 2000. The source for viscosity and thermal conductivity is Lemmon, E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004. Properties at the freezing point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. In the range from the solidification point to 873 K at pressures to 70 MPa, the estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated speed of sound values is 0.2% and that for calculated heat capacities is 1%. At temperatures above 873 K and 70 MPa, the estimated uncertainty of calculated density values is 0.5%, increasing to 1.0% at 2000 K and 2000 MPa. For viscosity, the uncertainty is 1% in the dilute gas. The uncertainty is around 2% between 270 and 300 K and increases to 5% outside of this region. There are very few measurements between 130 and 270 K for air to validate this claim, and the uncertainties may be even higher in this supercritical region. For thermal conductivity, the uncertainty for the dilute gas is 2% with increasing uncertainties near the triple points. The uncertainties range from 3% between 140 and 300 K to 5% at the triple point and at high temperatures. The uncertainties above 100 MPa are not known due to a lack of experimental data. 2-197

2-198 FIG. 2-3 Pressure-enthalpy diagram for dry air. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of E. W. Lemmon, R. T. Jacobsen,, S. G. Penoncello, and D. G. Friend.

THERMODYnAMIC PROPERTIES TABLE 2-111

Air

Other tables include Stewart, R. B., S. G. Penoncello, et al., University of Idaho CATS report, 85-5, 1985 (0.1-700 bar, 85-750 K), and Lemmon, E. W., Jacobsen, R. T., Penoncello, S. G., and Friend, D. G., Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen from 60 to 2000 K at Pressures to 2000 MPa, J. Phys. Chem. Ref. Data, 29(3): 331-385, 2000. Tables including reactions with hydrocarbons include Gordon, S., NASA Techn. Paper 1907, 4 vols., 1982. See also Gupta, R. N., K-P. Lee, et al., NASA RP 1232, 1990 (89 pp.) and RP 1260, 1991 (75 pp.). Analytic expressions for high temperatures were given by Matsuzaki, R., Jap. J. Appl. Phys., 21, 7 (1982): 1009-1013 and Japanese National Aerospace Laboratory report NAL TR 671, 1981 (45 pp.). Functions from 1500 to 15,000 K were tabulated by Hilsenrath, J. and M. Klein, AEDC-TR-65-58 = AD 612 301, 1965 (333 pp.). Tables from 10000 to 10,000,000 K were authored by Gilmore, F. R., Lockheed rept. 3-27-67-1, vol 1., 1967 (340 pp.), also published as Radiative Properties of Air, IFI/Plenum, New York, 1969 (648 pp.). Saturation and superheat tables and a chart to 7000 psia, 660°R appear in Stewart, R. B., R. T. Jacobsen, et al., Thermodynamic Properties of Refrigerants, ASHRAE, Atlanta, Ga, 1986 (521 pp.). For specific heat, thermal conductivity, and viscosity see Thermophysical Properties of Refrigerants, ASHRAE, 1993. Air, Moist For other data in this handbook, please see Figure 2-2 and the psychrometric tables, figures and descriptions in Section 12. An ASHRAE publication, Thermodynamic Properties of Dry Air and Water and S. I. Psychrometric Charts, 1983 (360 pp.), extensively reviews moist air properties. Gandiduson, P., Chem. Eng., Oct. 29, 1984 gives on page 118 a nomograph from 50 to 120°F, while equations in SI units were given by Nelson, B., Chem. Eng. Progr. 76, 5 (May 1980): 83–85. Liley, P. E., 2000 Solved Problems in M.E. Thermodynamics, McGraw-Hill, New York, 1989, gives four simple equations with which most calculations can be made. Devres, Y.O., Appl. Energy 48 (1994): 1–18 gives equations with which three known properties can be used to determine four others. Klappert, M. T. and G. F. Schilling, Rand RM-4244-PR = AD 604 856, 1984 (40 pp.) gives tables from 100 to 270 K, while programs from −60 to 2°F are given by Sando, F. A., ASHRAE Trans., 96, 2 (1990): 299–308. Viscosity references include Kestin, J. and J. H. Whitelaw, Int. J. Ht. Mass Transf. 7, 11 (1964): 1245–1255; Studnokov, E. L., Inz.-Fiz. Zhur. 19, 2 (1970): 338–340; Hochramer, D. and F. Munczak, Setzb. Ost. Acad. Wiss II 175, 10 (1966): 540–550. For thermal conductivity see, for instance, Mason, E. A. and L. Monchick, Humidity and Moisture Control in Science and Industry, Reinhold, New York, 1965 (257–272).

2-199

2-200 TABLE 2-112 Thermodynamic Properties of Ammonia Temperature K

Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

0.00000 0.32333 1.0480 1.7825 2.5265 3.2793 4.0403 4.8093 5.5862 6.3712 7.1651 7.9691 8.7850 9.6153 10.463 11.333 12.232 13.169 14.158 15.224 16.424 17.969 20.640

0.00014154 0.32353 1.0484 1.7833 2.5279 3.2818 4.0445 4.8160 5.5963 6.3861 7.1866 7.9993 8.8265 9.6714 10.538 11.432 12.361 13.335 14.373 15.503 16.790 18.478 21.499

23.661 23.770 24.006 24.233 24.450 24.655 24.846 25.021 25.179 25.317 25.435 25.528 25.595 25.632 25.634 25.595 25.505 25.350 25.107 24.734 24.144 23.047 20.640

25.279 25.424 25.737 26.038 26.325 26.596 26.847 27.077 27.281 27.459 27.606 27.720 27.796 27.830 27.816 27.746 27.606 27.381 27.042 26.539 25.768 24.386 21.499

Entropy kJ/(mol⋅K)

Sound speed m/s

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

0.00000 0.0016351 0.0051707 0.0085874 0.011894 0.015098 0.018205 0.021222 0.024154 0.027010 0.029797 0.032525 0.035203 0.037843 0.040458 0.043065 0.045682 0.048339 0.051075 0.053961 0.057149 0.061223 0.068559

0.049972 0.049837 0.049521 0.049207 0.048906 0.048613 0.048327 0.048047 0.047774 0.047511 0.047266 0.047044 0.046856 0.046715 0.046636 0.046642 0.046767 0.047064 0.047619 0.048589 0.050319 0.054109

0.071565 0.071988 0.072971 0.073950 0.074883 0.075764 0.076608 0.077448 0.078328 0.079296 0.080412 0.081747 0.083390 0.085465 0.088145 0.091701 0.096576 0.10357 0.11435 0.13314 0.17550 0.38707

2124.2 2080.2 1992.7 1913.7 1839.2 1766.9 1695.6 1624.5 1553.1 1481.0 1407.8 1333.2 1256.7 1177.9 1096.5 1011.8 923.38 830.62 732.78 628.75 515.88 384.58 0

0.12931 0.12714 0.12273 0.11884 0.11536 0.11224 0.10942 0.10684 0.10447 0.10227 0.10021 0.098259 0.096395 0.094589 0.092817 0.091046 0.089242 0.087355 0.085316 0.083003 0.080169 0.075992 0.068559

0.026510 0.026650 0.027053 0.027583 0.028245 0.029043 0.029978 0.031050 0.032253 0.033581 0.035028 0.036584 0.038244 0.040004 0.041868 0.043844 0.045954 0.048233 0.050744 0.053589 0.056957 0.061281

0.035130 0.035345 0.035961 0.036783 0.037836 0.039142 0.040728 0.042623 0.044859 0.047476 0.050530 0.054099 0.058302 0.063320 0.069443 0.077150 0.087280 0.10141 0.12286 0.16000 0.24170 0.59477

354.12 357.91 365.94 373.38 380.19 386.30 391.66 396.20 399.86 402.59 404.30 404.95 404.45 402.70 399.61 395.05 388.86 380.83 370.69 357.96 341.67 318.22 0

Therm. Joule-Thomson cond. K/MPa mW/(m⋅K)

Viscosity µPa⋅s

Saturated Properties 195.50 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.00 390.00 400.00 405.40

0.0060912 0.0086509 0.017739 0.033790 0.060407 0.10223 0.16494 0.25531 0.38107 0.55092 0.77436 1.0617 1.4240 1.8728 2.4205 3.0802 3.8660 4.7929 5.8778 7.1402 8.6045 10.305 11.339

43.035 42.754 42.111 41.442 40.748 40.032 39.293 38.533 37.748 36.939 36.101 35.230 34.320 33.363 32.350 31.264 30.087 28.788 27.321 25.606 23.465 20.232 13.212

195.50 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.00 390.00 400.00 405.40

0.0060912 0.0086509 0.017739 0.033790 0.060407 0.10223 0.16494 0.25531 0.38107 0.55092 0.77436 1.0617 1.4240 1.8728 2.4205 3.0802 3.8660 4.7929 5.8778 7.1402 8.6045 10.305 11.339

0.0037635 0.0052305 0.010249 0.018721 0.032214 0.052667 0.082417 0.12421 0.18126 0.25729 0.35664 0.48448 0.64702 0.85202 1.1094 1.4325 1.8399 2.3598 3.0375 3.9558 5.2979 7.6973 13.212

0.023237 0.023389 0.023747 0.024130 0.024541 0.024980 0.025450 0.025952 0.026491 0.027072 0.027700 0.028385 0.029138 0.029973 0.030912 0.031986 0.033237 0.034737 0.036602 0.039054 0.042616 0.049426 0.075690 265.71 191.19 97.573 53.415 31.043 18.987 12.133 8.0506 5.5168 3.8867 2.8040 2.0641 1.5455 1.1737 0.90139 0.69810 0.54350 0.42377 0.32922 0.25279 0.18875 0.12992 0.075690

−0.23362 −0.22917 −0.21883 −0.20813 −0.19712 −0.18561 −0.17327 −0.15963 −0.14414 −0.12612 −0.10470 −0.078790 −0.046923 −0.0070718 0.043673 0.10967 0.19774 0.31928 0.49497 0.76738 1.2455 2.3557 5.0513 171.13 152.55 120.01 96.215 78.430 64.852 54.280 45.905 39.175 33.701 29.207 25.489 22.391 19.794 17.599 15.728 14.112 12.690 11.400 10.172 8.9038 7.3513 5.0513

818.99 803.14 768.02 733.17 698.80 665.09 632.16 600.07 568.85 538.50 508.99 480.25 452.23 424.83 397.96 371.51 345.32 319.25 293.07 266.57 239.65 216.00 19.636 19.684 19.860 20.132 20.503 20.978 21.560 22.258 23.079 24.034 25.138 26.408 27.872 29.568 31.559 33.945 36.900 40.752 46.149 54.556 70.114 113.54

559.57 507.28 414.98 346.68 294.94 254.85 223.08 197.34 176.06 158.12 142.74 129.33 117.49 106.91 97.325 88.555 80.430 72.796 65.493 58.315 50.877 41.802 6.8396 6.9515 7.2115 7.4846 7.7679 8.0587 8.3552 8.6558 8.9595 9.2664 9.5771 9.8938 10.220 10.561 10.927 11.330 11.792 12.346 13.053 14.025 15.527 18.529

Single-Phase Properties 200.00 239.56 239.56 300.00 400.00 500.00 600.00 700.00 200.00 298.05 298.05 300.00 400.00 500.00 600.00 700.00 200.00 300.00 362.03 362.03 400.00 500.00 600.00 700.00 200.00 300.00 398.32 398.32 400.00 500.00 600.00 700.00 300.00 400.00 500.00 600.00 700.00 300.00 400.00 500.00 600.00 700.00 300.00 400.00 500.00 600.00 700.00

0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 100.00 100.00 100.00 100.00 100.00 500.00 500.00 500.00 500.00 500.00 1000.0 1000.0 1000.0 1000.0 1000.0

42.756 40.064 0.051595 0.040502 0.030171 0.024091 0.020060 0.017188 42.774 35.403 0.45697 0.45215 0.31157 0.24426 0.20197 0.17248 42.852 35.450 28.505 2.4828 1.8706 1.3046 1.0412 0.87563 42.947 35.714 20.945 7.1390 6.5455 2.8656 2.1650 1.7835 38.995 33.105 27.067 21.518 17.303 45.670 42.416 39.515 36.909 34.550 49.944 47.551 45.362 43.378 41.556

0.023388 0.024960 19.382 24.690 33.144 41.509 49.849 58.179 0.023379 0.028246 2.1883 2.2117 3.2095 4.0940 4.9513 5.7977 0.023336 0.028209 0.035081 0.40277 0.53459 0.76650 0.96040 1.1420 0.023284 0.028000 0.047744 0.14008 0.15278 0.34897 0.46190 0.56069 0.025644 0.030207 0.036945 0.046473 0.057794 0.021896 0.023576 0.025307 0.027094 0.028943 0.020022 0.021030 0.022045 0.023053 0.024064

0.32270 3.2461 24.646 26.378 29.297 32.514 36.096 40.068 0.31651 7.8111 25.512 25.592 29.019 32.359 35.994 39.994 0.28942 7.8852 13.365 25.309 27.540 31.630 35.527 39.662 0.25644 7.7848 17.655 23.303 23.801 30.616 34.920 39.241 6.5830 13.432 20.212 26.825 33.074 4.7114 10.633 16.367 22.007 27.680 4.1818 9.8612 15.432 20.911 26.418

0.32504 3.2486 26.584 28.847 32.612 36.665 41.081 45.885 0.33989 7.8393 27.700 27.804 32.229 36.453 40.945 45.792 0.40611 8.0263 13.540 27.323 30.213 35.462 40.329 45.373 0.48928 8.0648 18.132 24.704 25.329 34.106 39.539 44.848 9.1474 16.453 23.907 31.472 38.854 15.660 22.421 29.021 35.554 42.152 24.204 30.891 37.477 43.964 50.481

0.0016320 0.014960 0.11237 0.12080 0.13162 0.14065 0.14869 0.15609 0.0016010 0.031996 0.098633 0.098979 0.11177 0.12119 0.12937 0.13684 0.0014649 0.032243 0.048887 0.086956 0.094581 0.10634 0.11521 0.12298 0.0012980 0.031903 0.060394 0.076892 0.078458 0.098525 0.10844 0.11663 0.027511 0.048523 0.065147 0.078942 0.090326 0.018023 0.037482 0.052215 0.064127 0.074295 0.011750 0.030984 0.045686 0.057514 0.067559

0.049842 0.048626 0.029005 0.028021 0.030417 0.033897 0.037731 0.041678 0.049890 0.047085 0.036271 0.035866 0.031641 0.034312 0.037928 0.041791 0.050097 0.047090 0.047152 0.048722 0.038466 0.036193 0.038798 0.042289 0.050342 0.047164 0.053149 0.060447 0.057611 0.038603 0.039862 0.042896 0.048894 0.046636 0.045999 0.046723 0.048331 0.052877 0.051527 0.050431 0.050614 0.051816 0.055176 0.054864 0.053323 0.052940 0.053649

0.071983 0.075726 0.039079 0.036849 0.038883 0.042280 0.046083 0.050015 0.071938 0.081465 0.053356 0.052493 0.041627 0.043338 0.046628 0.050341 0.071739 0.080899 0.10538 0.10501 0.061581 0.048779 0.049210 0.051836 0.071495 0.079960 0.30653 0.46915 0.30552 0.057806 0.052806 0.053796 0.072740 0.073557 0.075495 0.075193 0.072317 0.067831 0.066802 0.065418 0.065476 0.066615 0.065784 0.066677 0.065150 0.064819 0.065697

2080.3 1770.0 386.05 434.39 497.93 550.96 597.69 640.16 2081.5 1347.9 404.91 407.16 488.94 546.79 595.60 639.15 2086.8 1361.2 811.17 378.95 441.81 528.14 586.79 635.17 2093.5 1394.2 409.04 323.12 336.28 505.64 577.38 631.50 1774.7 1378.2 1081.8 918.11 861.52 2597.1 2353.2 2176.9 2044.6 1943.8 3230.2 2997.6 2842.8 2728.6 2639.0

−0.22921 −0.18613 65.377 27.493 10.681 5.5276 3.2702 2.0841 −0.22959 −0.084271 26.163 25.620 10.494 5.4884 3.2544 2.0746 −0.23126 −0.089577 0.34968 12.419 9.6373 5.2830 3.1693 2.0254 −0.23328 −0.10159 2.0704 7.6606 7.7633 4.9335 3.0278 1.9491 −0.19551 −0.11309 0.049919 0.23722 0.32753 −0.25055 −0.25064 −0.25260 −0.24722 −0.23682 −0.25989 −0.25431 −0.26084 −0.26235 −0.25820

803.24 666.56 20.955 25.100 37.215 53.119 68.607 78.312 804.23 485.81 26.145 26.308 38.087 53.750 69.123 78.751 808.60 487.57 313.94 41.693 45.730 57.294 71.791 80.941 814.02 496.50 218.73 101.04 95.455 63.922 76.053 84.235 622.86 431.98 305.65 234.79 196.04 989.00 804.05 674.00 582.63 511.57 1324.0 1138.9 996.49 887.73 797.25

507.47 256.42 8.0459 10.161 13.971 17.863 21.682 25.391 509.28 131.82 9.8313 9.9115 13.927 17.877 21.717 25.434 517.30 132.49 71.291 12.475 14.036 18.073 21.941 25.662 527.29 136.36 43.632 17.793 17.230 18.722 22.393 26.035 193.71 96.237 60.386 46.188 41.237 376.31 188.46 120.77 91.251 77.538 554.62 274.91 174.11 129.02 107.14

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Tillner-Roth, R., Harms-Watzenberg, F., and Baehr, H. D., “Eine neue Fundamentalgleichung fuer Ammoniak,” DKV-Tagungsbericht, 20:167–181, 1993. The source for viscosity is Fenghour, A., Wakeham, W. A., Vesovic, V., Watson, J. T. R., Millat, J., and Vogel, E., “The Viscosity of Ammonia,” J. Phys. Chem. Ref. Data 24:1649–1667, 1995. The source for thermal conductivity is Tufeu, R., Ivanov, D. Y., Garrabos, Y., and Le Neindre, B., “Thermal Conductivity of Ammonia in a Large Temperature and Pressure Range Including the Critical Region,” Ber. Bunsenges. Phys. Chem. 88:422–427, 1984. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties of the equation of state are 0.2% in density, 2% in heat capacity, and 2% in the speed of sound, except in the critical region. The uncertainty in vapor pressure is 0.2%. The uncertainty varies from 0.5% for the viscosity of the dilute gas phase at moderate temperatures to about 5% for the viscosity at high pressures and temperatures. The uncertainty in thermal conductivity is 2%.

2-201

2-202 TABLE 2-113 Temperature K

Thermodynamic Properties of Carbon Dioxide Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

180.63 176.15 169.67 163.28 156.98 150.75 144.58 138.47 132.40 126.35 120.31 114.25 108.17 102.03 95.810 89.546 83.558 80.593

256.70 242.01 222.19 204.23 187.88 172.96 159.30 146.74 135.14 124.40 114.40 105.02 96.174 87.731 79.548 71.409 62.936 53.107

11.014 11.301 11.745 12.221 12.736 13.297 13.917 14.610 15.396 16.306 17.381 18.687 20.325 22.468 25.424 29.821 37.215 53.689

10.951 11.135 11.409 11.689 11.976 12.272 12.579 12.902 13.245 13.614 14.017 14.469 14.987 15.601 16.361 17.357 18.792 21.306

Saturated Properties 216.59 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 304.13

0.51796 0.59913 0.73509 0.89291 1.0747 1.2825 1.5185 1.7850 2.0843 2.4188 2.7909 3.2033 3.6589 4.1607 4.7123 5.3177 5.9822 6.7131 7.3773

26.777 26.497 26.078 25.646 25.201 24.742 24.264 23.767 23.246 22.697 22.114 21.491 20.817 20.077 19.247 18.284 17.100 15.434 10.625

0.037345 0.037740 0.038347 0.038992 0.039680 0.040418 0.041213 0.042075 0.043018 0.044059 0.045219 0.046531 0.048037 0.049808 0.051957 0.054693 0.058480 0.064793 0.094118

3.5030 3.7943 4.2235 4.6554 5.0908 5.5303 5.9749 6.4256 6.8836 7.3505 7.8282 8.3190 8.8266 9.3560 9.9154 10.519 11.197 12.036 13.928

3.5223 3.8169 4.2517 4.6902 5.1334 5.5821 6.0375 6.5007 6.9733 7.4571 7.9544 8.4681 9.0024 9.5633 10.160 10.810 11.547 12.471 14.622

0.022943 0.024279 0.026209 0.028110 0.029986 0.031840 0.033678 0.035505 0.037326 0.039148 0.040979 0.042829 0.044711 0.046643 0.048657 0.050805 0.053196 0.056151 0.063094

0.042895 0.042682 0.042383 0.042103 0.041843 0.041605 0.041393 0.041212 0.041079 0.041029 0.041109 0.041351 0.041750 0.042270 0.042900 0.043734 0.045175 0.049288

0.085960 0.086338 0.087024 0.087886 0.088954 0.090263 0.091866 0.093831 0.096251 0.099258 0.10306 0.10798 0.11457 0.12385 0.13790 0.16176 0.21098 0.38279

975.85 951.21 915.16 879.09 842.88 806.38 769.44 731.78 693.01 652.58 610.07 565.46 519.14 471.54 422.75 371.95 315.91 245.67 0

−0.14430 −0.13180 −0.11104 −0.086994 −0.059053 −0.026454 0.011808 0.057087 0.11121 0.17663 0.25672 0.35639 0.48324 0.64959 0.87650 1.2037 1.7218 2.7258 5.8665

216.59 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 304.13

0.51796 0.59913 0.73509 0.89291 1.0747 1.2825 1.5185 1.7850 2.0843 2.4188 2.7909 3.2033 3.6589 4.1607 4.7123 5.3177 5.9822 6.7131 7.3773

0.31268 0.35941 0.43766 0.52878 0.63442 0.75654 0.89743 1.0599 1.2472 1.4637 1.7149 2.0080 2.3535 2.7663 3.2702 3.9074 4.7654 6.1028 10.625

3.1982 2.7824 2.2849 1.8912 1.5762 1.3218 1.1143 0.94353 0.80180 0.68320 0.58314 0.49800 0.42490 0.36150 0.30579 0.25593 0.20985 0.16386 0.094118

17.286 17.329 17.387 17.438 17.481 17.515 17.538 17.550 17.549 17.532 17.498 17.441 17.359 17.241 17.078 16.848 16.509 15.935 13.928

18.943 18.996 19.067 19.127 19.175 19.210 19.230 19.234 19.220 19.185 19.125 19.037 18.913 18.746 18.519 18.209 17.764 17.035 14.622

0.094138 0.093276 0.092055 0.090878 0.089736 0.088622 0.087526 0.086439 0.085352 0.084254 0.083133 0.081972 0.080750 0.079437 0.077987 0.076319 0.074270 0.071364 0.063094

0.027691 0.028120 0.028782 0.029488 0.030241 0.031042 0.031899 0.032827 0.033844 0.034955 0.036164 0.037482 0.038949 0.040628 0.042629 0.045155 0.048677 0.054908

0.039992 0.040943 0.042489 0.044244 0.046248 0.048555 0.051242 0.054421 0.058244 0.062912 0.068721 0.076168 0.086123 0.10020 0.12177 0.15906 0.23904 0.52463

222.78 223.15 223.49 223.57 223.40 222.96 222.24 221.22 219.87 218.19 216.15 213.75 210.96 207.72 203.94 199.45 193.84 185.33 0

26.174 25.084 23.617 22.288 21.077 19.969 18.950 18.005 17.117 16.277 15.476 14.704 13.947 13.185 12.387 11.509 10.459 9.0093 5.8665

Single-Phase Properties 250.00 450.00 650.00 850.00 1050.0

0.10000 0.10000 0.10000 0.10000 0.10000

0.048542 0.026758 0.018506 0.014148 0.011452

250.00 450.00 650.00 850.00 1050.0

1.0000 1.0000 1.0000 1.0000 1.0000

0.53250 0.27038 0.18527 0.14131 0.11430

250.00 287.43

5.0000 5.0000

287.43 450.00 650.00 850.00 1050.0

5.0000 5.0000 5.0000 5.0000 5.0000

250.00 450.00 650.00 850.00 1050.0

10.000 10.000 10.000 10.000 10.000

18.448 24.664 32.199 40.636 49.704

20.509 28.401 37.602 47.705 58.436

0.11415 0.13712 0.15397 0.16750 0.17883

0.026766 0.034775 0.040192 0.043944 0.046573

0.035428 0.043148 0.048529 0.052271 0.054895

247.79 324.41 385.01 437.11 483.65

17.399 4.0212 1.6551 0.78058 0.34646

12.950 29.346 45.466 60.295 73.843

12.565 21.901 29.873 36.707 42.692

1.8779 3.6985 5.3976 7.0767 8.7487

18.023 24.546 32.133 40.591 49.671

19.901 28.244 37.530 47.668 58.419

0.093263 0.11771 0.13473 0.14830 0.15965

0.029361 0.034954 0.040239 0.043965 0.046585

0.042504 0.043866 0.048779 0.052397 0.054970

235.08 322.89 385.36 438.06 484.84

17.606 3.9880 1.6311 0.76632 0.33777

13.584 29.620 45.651 60.435 73.956

12.691 21.954 29.907 36.732 42.712

0.041563 0.053196

6.2824 10.202

6.4902 10.468

0.034925 0.049681

0.041321 0.043268

0.090937 0.14775

762.21 398.39

142.22 92.760

153.15 75.598

0.28090 0.70647 1.0755 1.4237 1.7650

16.977 24.000 31.842 40.395 49.524

18.381 27.533 37.219 47.513 58.349

0.077209 0.10313 0.12091 0.13469 0.14613

0.043774 0.035769 0.040445 0.044055 0.046637

0.13705 0.047478 0.049898 0.052945 0.055297

201.86 317.50 387.59 442.64 490.31

11.974 3.8034 1.5263 0.70611 0.30129

27.323 31.164 46.589 61.117 74.494

16.808 22.429 30.157 36.899 42.836

24.459 2.9910 1.8632 1.3930 1.1205

0.040885 0.33433 0.53671 0.71790 0.89248

6.0862 23.276 31.482 40.155 49.347

6.4950 26.619 36.849 47.334 58.271

0.034120 0.095787 0.11461 0.12866 0.14021

0.041488 0.036785 0.040693 0.044164 0.046701

0.087624 0.052935 0.051293 0.053603 0.055685

804.05 314.60 391.91 449.04 497.48

−0.034849 3.4705 1.3965 0.63635 0.25964

147.52 33.917 48.005 62.093 75.242

162.47 23.679 30.687 37.224 43.066

24.060 18.798 3.5600 1.4155 0.92982 0.70241 0.56658

20.601 37.372 54.037 70.683 87.321

0.015208 1.0195

250.00 450.00 650.00 850.00 1050.0

100.00 100.00 100.00 100.00 100.00

28.075 19.246 13.677 10.636 8.7929

0.035619 0.051959 0.073117 0.094022 0.11373

4.3002 16.560 27.132 37.076 46.995

7.8621 21.756 34.444 46.478 58.368

0.026023 0.067062 0.090445 0.10660 0.11916

0.043569 0.040841 0.043108 0.045620 0.047676

0.073521 0.066107 0.061252 0.059534 0.059512

1227.6 753.30 646.36 646.61 668.90

−0.27302 −0.11128 −0.054084 −0.13292 −0.21482

206.28 106.65 86.093 87.259 94.022

287.05 83.996 58.868 54.445 55.058

450.00 650.00 850.00 1050.0

500.00 500.00 500.00 500.00

28.922 25.661 23.144 21.126

0.034576 0.038969 0.043208 0.047334

13.014 23.302 33.551 43.903

30.302 42.786 55.155 67.570

0.050604 0.073576 0.090166 0.10328

0.047702 0.048419 0.049676 0.050818

0.063434 0.061885 0.061912 0.062247

1576.4 1404.7 1320.1 1278.7

−0.38514 −0.40369 −0.41098 −0.41674

239.59 197.25 177.31 168.50

303.64 191.14 145.07 123.33

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Span, R., and Wagner, W., “A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa,” J. Phys. Chem. Ref. Data 25(6):1509–1596, 1996. The source for viscosity is Fenghour, A., Wakeham, W. A., and Vesovic, V., “The Viscosity of Carbon Dioxide,” J. Phys. Chem. Ref. Data 27:31–44, 1998. The source for thermal conductivity is Vesovic, V., Wakeham, W. A., Olchowy, G. A., Sengers, J. V., Watson, J. T. R., and Millat, J., “The Transport Properties of Carbon Dioxide,” J. Phys. Chem. Ref. Data 19:763–808, 1990. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. At pressures up to 30 MPa and temperatures up to 523 K, the estimated uncertainty ranges from 0.03% to 0.05% in density, 0.03% (in the vapor) to 1% in the speed of sound (0.5% in the liquid), and 0.15% (in the vapor) to 1.5% (in the liquid) in heat capacity. Special interest has been focused on the description of the critical region and the extrapolation behavior of the formulation (to the limits of chemical stability). The uncertainty in viscosity ranges from 0.3% in the dilute gas near room temperature to 5% at the highest pressures. The uncertainty in thermal conductivity is less than 5%.

2-203

2-204

TABLE 2-114 Thermodynamic Properties of Carbon Monoxide Temperature K

Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

30.330 30.064 29.773 29.478 29.180 28.878 28.573 28.262 27.947 27.626 27.300 26.967 26.627 26.280 25.924 25.559 25.184 24.798 24.399 23.987 23.560 23.114 22.649 22.161 21.646 21.099 20.513 19.878 19.179 18.390 17.464 16.288 10.850

0.032971 0.033262 0.033588 0.033924 0.034270 0.034628 0.034999 0.035383 0.035782 0.036197 0.036630 0.037082 0.037556 0.038052 0.038574 0.039125 0.039708 0.040326 0.040985 0.041689 0.042446 0.043263 0.044151 0.045124 0.046197 0.047395 0.048749 0.050307 0.052141 0.054377 0.057259 0.061393 0.092166

−0.81158 −0.70065 −0.58046 −0.46058 −0.34088 −0.22127 −0.10165 0.018099 0.13806 0.25835 0.37906 0.50030 0.62218 0.74482 0.86835 0.99289 1.1186 1.2457 1.3742 1.5045 1.6368 1.7713 1.9085 2.0487 2.1925 2.3405 2.4938 2.6536 2.8221 3.0024 3.2010 3.4328 4.2912

−0.81106 −0.69995 −0.57950 −0.45927 −0.33915 −0.21900 −0.098716 0.021834 0.14277 0.26421 0.38629 0.50915 0.63291 0.75773 0.88377 1.0112 1.1402 1.2710 1.4039 1.5390 1.6768 1.8175 1.9616 2.1097 2.2624 2.4205 2.5853 2.7583 2.9420 3.1403 3.3608 3.6210 4.6137

−0.010820 −0.0092140 −0.0075210 −0.0058785 −0.0042823 −0.0027285 −0.0012138 0.00026503 0.0017110 0.0031269 0.0045153 0.0058787 0.0072195 0.0085399 0.0098422 0.011129 0.012402 0.013663 0.014916 0.016162 0.017404 0.018646 0.019891 0.021142 0.022406 0.023688 0.024996 0.026343 0.027744 0.029230 0.030854 0.032745 0.040039

5.1252 5.1600 5.1971 5.2334 5.2688 5.3031 5.3363 5.3682 5.3988 5.4280 5.4556 5.4816 5.5058 5.5280 5.5482 5.5661 5.5816 5.5945 5.6044 5.6112 5.6145 5.6138 5.6088

5.6859 5.7343 5.7859 5.8361 5.8849 5.9320 5.9775 6.0210 6.0625 6.1019 6.1388 6.1733 6.2050 6.2338 6.2595 6.2819 6.3007 6.3157 6.3265 6.3327 6.3339 6.3295 6.3191

0.084499 0.082704 0.080887 0.079194 0.077613 0.076131 0.074739 0.073426 0.072185 0.071007 0.069885 0.068813 0.067785 0.066796 0.065840 0.064912 0.064007 0.063120 0.062248 0.061385 0.060526 0.059665 0.058797

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

0.035351 0.034805 0.034248 0.033724 0.033232 0.032768 0.032329 0.031915 0.031522 0.031150 0.030798 0.030463 0.030146 0.029846 0.029562 0.029294 0.029043 0.028809 0.028592 0.028395 0.028218 0.028066 0.027941 0.027850 0.027800 0.027803 0.027874 0.028038 0.028333 0.028826 0.029646 0.031097

0.060430 0.060226 0.060064 0.059961 0.059917 0.059930 0.060002 0.060132 0.060324 0.060578 0.060899 0.061291 0.061760 0.062314 0.062962 0.063716 0.064590 0.065604 0.066781 0.068153 0.069759 0.071656 0.073916 0.076648 0.080005 0.084225 0.089692 0.097070 0.10762 0.12411 0.15392 0.22603

998.20 980.50 961.22 941.89 922.49 903.01 883.44 863.76 843.95 824.00 803.89 783.60 763.12 742.41 721.45 700.22 678.68 656.78 634.50 611.77 588.54 564.73 540.25 515.01 488.86 461.63 433.11 403.00 370.88 336.15 297.82 254.03 0

−0.36906 −0.36553 −0.36074 −0.35489 −0.34794 −0.33981 −0.33041 −0.31966 −0.30742 −0.29356 −0.27794 −0.26034 −0.24056 −0.21834 −0.19335 −0.16523 −0.13353 −0.097704 −0.057078 −0.010824 0.042104 0.10304 0.17371 0.25641 0.35427 0.47167 0.61495 0.79382 1.0239 1.3325 1.7728 2.4703 6.1475

180.28 175.49 170.45 165.55 160.76 156.06 151.45 146.89 142.40 137.96 133.57 129.23 124.94 120.69 116.51 112.38 108.31 104.30 100.36 96.482 92.679 88.948 85.290 81.702 78.180 74.716 71.296 67.896 64.476 60.972 57.261 53.107

274.18 252.15 232.14 215.32 201.01 188.69 177.96 168.52 160.13 152.60 145.77 139.52 133.75 128.38 123.34 118.57 114.02 109.66 105.45 101.35 97.342 93.404 89.510 85.641 81.774 77.888 73.954 69.940 65.797 61.448 56.748 51.348

0.021089 0.021155 0.021238 0.021333 0.021441 0.021563 0.021699 0.021850 0.022017 0.022199 0.022397 0.022611 0.022842 0.023089 0.023352 0.023633 0.023931 0.024248 0.024586 0.024945 0.025329 0.025741 0.026186

0.029785 0.029947 0.030153 0.030394 0.030672 0.030993 0.031360 0.031777 0.032250 0.032783 0.033383 0.034057 0.034813 0.035661 0.036615 0.037690 0.038906 0.040288 0.041869 0.043694 0.045820 0.048326 0.051322

167.25 169.22 171.27 173.22 175.07 176.80 178.42 179.92 181.29 182.54 183.66 184.65 185.51 186.22 186.80 187.23 187.52 187.67 187.66 187.51 187.20 186.73 186.11

40.804 38.426 36.126 34.080 32.250 30.604 29.116 27.763 26.527 25.392 24.345 23.377 22.477 21.638 20.853 20.118 19.426 18.773 18.154 17.565 17.001 16.458 15.930

Cv kJ/(mol⋅K)

Saturated Properties 68.160 70.000 72.000 74.000 76.000 78.000 80.000 82.000 84.000 86.000 88.000 90.000 92.000 94.000 96.000 98.000 100.00 102.00 104.00 106.00 108.00 110.00 112.00 114.00 116.00 118.00 120.00 122.00 124.00 126.00 128.00 130.00 132.86

0.015537 0.021053 0.028718 0.038447 0.050599 0.065559 0.083738 0.10556 0.13148 0.16196 0.19748 0.23852 0.28559 0.33919 0.39983 0.46805 0.54438 0.62934 0.72348 0.82736 0.94154 1.0666 1.2031 1.3517 1.5130 1.6877 1.8765 2.0802 2.2997 2.5360 2.7904 3.0647 3.4982

68.160 70.000 72.000 74.000 76.000 78.000 80.000 82.000 84.000 86.000 88.000 90.000 92.000 94.000 96.000 98.000 100.00 102.00 104.00 106.00 108.00 110.00 112.00

0.015537 0.021053 0.028718 0.038447 0.050599 0.065559 0.083738 0.10556 0.13148 0.16196 0.19748 0.23852 0.28559 0.33919 0.39983 0.46805 0.54438 0.62934 0.72348 0.82736 0.94154 1.0666 1.2031

0.027707 0.036656 0.048780 0.063796 0.082130 0.10424 0.13059 0.16171 0.19810 0.24036 0.28906 0.34486 0.40845 0.48058 0.56209 0.65388 0.75700 0.87260 1.0020 1.1468 1.3088 1.4903 1.6938

36.091 27.281 20.500 15.675 12.176 9.5935 7.6573 6.1841 5.0478 4.1605 3.4595 2.8997 2.4483 2.0808 1.7791 1.5293 1.3210 1.1460 0.99799 0.87198 0.76404 0.67102 0.59039

6.6865 6.8845 7.1009 7.3188 7.5382 7.7592 7.9820 8.2067 8.4335 8.6627 8.8944 9.1291 9.3672 9.6091 9.8555 10.107 10.366 10.632 10.909 11.198 11.502 11.828 12.181

4.6366 4.7768 4.9329 5.0934 5.2589 5.4300 5.6076 5.7922 5.9847 6.1860 6.3968 6.6182 6.8512 7.0969 7.3566 7.6317 7.9239 8.2350 8.5675 8.9238 9.3073 9.7221 10.173

114.00 116.00 118.00 120.00 122.00 124.00 126.00 128.00 130.00 132.86

1.3517 1.5130 1.6877 1.8765 2.0802 2.2997 2.5360 2.7904 3.0647 3.4982

100.00 200.00 300.00 400.00 500.00

0.10000 0.10000 0.10000 0.10000 0.10000

100.00 108.96

1.0000 1.0000

108.96 200.00 300.00 400.00 500.00

1.0000 1.0000 1.0000 1.0000 1.0000

100.00 200.00 300.00 400.00 500.00

5.0000 5.0000 5.0000 5.0000 5.0000

1.9228 2.1815 2.4754 2.8123 3.2027 3.6629 4.2194 4.9212 5.8832 10.850

0.52008 0.45841 0.40397 0.35558 0.31224 0.27301 0.23700 0.20320 0.16998 0.092166

5.5986 5.5827 5.5598 5.5286 5.4872 5.4324 5.3595 5.2594 5.1113 4.2912

6.3016 6.2762 6.2416 6.1959 6.1367 6.0602 5.9605 5.8264 5.6322 4.6137

0.057914 0.057008 0.056070 0.055084 0.054034 0.052892 0.051613 0.050117 0.048216 0.040039

5.7653 7.8674 9.9522 12.045 14.169

6.5785 9.5259 12.446 15.371 18.328

0.080014 0.10048 0.11231 0.12073 0.12733

0.039586 0.042829

1.1047 1.7009

1.1443 1.7437

0.71782 1.6200 2.4867 3.3334 4.1732

5.6147 7.7647 9.8936 12.005 14.140

25.864 3.4130 2.0232 1.4824 1.1786

0.038663 0.29299 0.49426 0.67458 0.84845

0.026671 0.027203 0.027794 0.028462 0.029229 0.030133 0.031233 0.032636 0.034579

0.054966 0.059493 0.065263 0.072864 0.083320 0.098585 0.12291 0.16759 0.27599

185.33 184.38 183.27 181.99 180.52 178.84 176.93 174.68 171.86 0

15.411 14.894 14.372 13.833 13.265 12.648 11.956 11.140 10.100 6.1475

12.569 13.005 13.507 14.101 14.826 15.747 16.981 18.777 21.845

10.667 11.213 11.821 12.509 13.301 14.234 15.373 16.840 18.936

0.021118 0.020812 0.020833 0.021028 0.021479

0.030153 0.029239 0.029191 0.029364 0.029807

201.29 288.05 353.12 407.29 454.00

17.820 5.3111 2.5186 1.2653 0.56244

10.075 19.227 26.605 33.106 39.272

6.9147 12.897 17.731 21.870 25.540

0.012262 0.017998

0.029062 0.028142

0.064114 0.070627

685.44 577.22

−0.14414 0.070176

112.87 90.884

6.3325 9.3847 12.380 15.338 18.313

0.060114 0.080819 0.092976 0.10149 0.10812

0.025522 0.020996 0.020895 0.021064 0.021505

0.046966 0.030510 0.029646 0.029598 0.029948

186.99 286.20 354.42 409.43 456.39

16.739 5.1924 2.4256 1.2088 0.52786

11.655 19.474 26.760 33.222 39.364

0.99666 7.2656 9.6364 11.834 14.015

1.1900 8.7305 12.108 15.207 18.258

0.011154 0.064994 0.078767 0.087691 0.094498

0.029263 0.021878 0.021174 0.021224 0.021618

0.060925 0.038000 0.031673 0.030585 0.030535

737.92 285.27 362.95 420.15 467.56

−0.21740 4.3757 2.0288 0.98413 0.39254

152.30 22.190 27.812 33.871 39.837

112.19 15.094 18.716 22.588 26.139

Single-Phase Properties 0.12298 0.060293 0.040104 0.030062 0.024045 25.261 23.349 1.3931 0.61727 0.40214 0.29999 0.23962

8.1315 16.586 24.935 33.265 41.588

113.83 95.450 9.5017 13.192 17.918 22.024 25.676

100.00 200.00 300.00 400.00 500.00

10.000 10.000 10.000 10.000 10.000

26.482 7.4298 4.0263 2.9079 2.3052

0.037761 0.13459 0.24837 0.34389 0.43381

0.88669 6.5960 9.3290 11.634 13.870

1.2643 7.9419 11.813 15.073 18.208

0.0099878 0.056188 0.072068 0.081462 0.088461

0.029539 0.022832 0.021511 0.021420 0.021755

0.058409 0.048831 0.034036 0.031689 0.031188

792.04 307.84 379.01 435.68 482.48

−0.27800 2.8854 1.5731 0.74980 0.25486

200.46 34.772 30.972 35.414 40.797

110.33 19.114 19.862 23.298 26.682

100.00 200.00 300.00 400.00 500.00

50.000 50.000 50.000 50.000 50.000

29.422 20.591 14.766 11.439 9.3865

0.033988 0.048566 0.067725 0.087418 0.10654

0.39153 4.5424 7.7949 10.518 13.024

2.0910 6.9707 11.181 14.889 18.350

0.0040257 0.038097 0.055259 0.065951 0.073681

0.031398 0.025036 0.023212 0.022620 0.022659

0.052094 0.045541 0.039083 0.035519 0.033937

1066.8 706.01 609.73 604.51 622.30

−0.43831 −0.28689 −0.21242 −0.27153 −0.36911

567.46 256.88 139.18 94.476 76.899

99.463 50.929 34.086 31.319 32.167

31.474 24.888 20.200 16.970 14.662

0.031772 0.040181 0.049505 0.058928 0.068206

0.095937 3.9022 7.0625 9.8487 12.449

3.2732 7.9203 12.013 15.741 19.269

−0.00053857 0.031951 0.048608 0.059353 0.067230

0.033037 0.026437 0.024358 0.023555 0.023434

0.050530 0.043352 0.038799 0.036051 0.034683

1282.4 987.69 866.60 822.33 808.91

−0.47725 −0.50923 −0.54516 −0.59581 −0.64123

100.00 200.00 300.00 400.00 500.00

100.00 100.00 100.00 100.00 100.00

1005.7 536.84 331.69 229.18 173.58

90.560 73.380 54.648 45.748 42.504

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., and Span, R., “Short Fundamental Equations of State for 20 Industrial Fluids,” J. Chem. Eng. Data, 51(3):785–850, 2006. The source for viscosity and thermal conductivity is Version 9.08 of the NIST14 database. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The equation of state is valid from the triple point to 500 K with pressures to 100 MPa. At higher pressures, the deviations from the equation increase rapidly, and it is not recommended to use the equation above 100 MPa. The uncertainties in the equation are 0.3% in density (approaching 1% near the critical point), 0.2% in vapor pressure, and 2% in heat capacities. For viscosity, estimated uncertainty is 2%. For thermal conductivity, estimated uncertainty, except near the critical region, is 4–6%. 2-205

2-206

PHYSICAL AnD CHEMICAL DATA

FIG. 2-4

Temperature-entropy diagram for carbon monoxide. Pressure P, in atmospheres; density r, in grams per cubic centimeter; enthalpy H, in joules per gram. (From J.G. Hust and R.B. Stewart, NBS Tech. Note 202, 1963.)

TABLE 2-115

Thermodynamic Properties of Ethanol

Temperature K

Pressure MPa

250.00 265.00 280.00 295.00 310.00 325.00 340.00 355.00 370.00 385.00 400.00 415.00 430.00 445.00 460.00 475.00 490.00 505.00 513.90

0.00027007 0.00089527 0.0025823 0.0066146 0.015298 0.032394 0.063544 0.11663 0.20205 0.33279 0.52446 0.79509 1.1649 1.6559 2.2916 3.0963 4.0954 5.3159 6.1480

250.00 265.00 280.00 295.00 310.00 325.00 340.00 355.00 370.00 385.00 400.00 415.00 430.00 445.00 460.00 475.00 490.00 505.00 513.90

0.00027007 0.00089527 0.0025823 0.0066146 0.015298 0.032394 0.063544 0.11663 0.20205 0.33279 0.52446 0.79509 1.1649 1.6559 2.2916 3.0963 4.0954 5.3159 6.1480

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

6.9274 8.3792 9.9424 11.630 13.445 15.385 17.444 19.615 21.892 24.268 26.740 29.307 31.970 34.737 37.629 40.684 44.002 47.926 53.880

6.9275 8.3793 9.9426 11.631 13.446 15.387 17.448 19.622 21.905 24.290 26.775 29.362 32.054 34.862 37.810 40.943 44.374 48.480 54.906

0.037330 0.042968 0.048704 0.054574 0.060574 0.066684 0.072875 0.079123 0.085403 0.091699 0.098000 0.10430 0.11061 0.11695 0.12335 0.12991 0.13684 0.14485 0.15723

49.039 49.932 50.851 51.792 52.749 53.717 54.684 55.640 56.573 57.469 58.312 59.087 59.774 60.348 60.777 61.004 60.916 60.144 53.880

51.116 52.134 53.174 54.234 55.307 56.383 57.450 58.494 59.500 60.451 61.329 62.115 62.785 63.312 63.654 63.747 63.453 62.328 54.906

0.21409 0.20808 0.20310 0.19899 0.19561 0.19282 0.19053 0.18862 0.18701 0.18562 0.18438 0.18322 0.18208 0.18088 0.17954 0.17792 0.17578 0.17228 0.15723

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

0.076657 0.083798 0.091653 0.099433 0.10670 0.11322 0.11893 0.12381 0.12792 0.13130 0.13405 0.13625 0.13798 0.13934 0.14041 0.14134 0.14234 0.14382

0.093612 0.10028 0.10829 0.11678 0.12524 0.13340 0.14115 0.14847 0.15543 0.16215 0.16883 0.17576 0.18341 0.19262 0.20504 0.22469 0.26508 0.41790

1325.0 1260.8 1202.8 1149.2 1098.1 1048.0 997.94 947.31 895.56 842.31 787.16 729.67 669.25 605.07 535.80 459.19 371.03 264.74 0

−0.44553 −0.41423 −0.37872 −0.34323 −0.30910 −0.27615 −0.24356 −0.21011 −0.17428 −0.13410 −0.086812 −0.028333 0.047976 0.15384 0.31228 0.57597 1.0976 2.5369 8.6373

178.12 173.58 169.56 165.87 162.38 159.01 155.69 152.39 149.09 145.78 142.47 139.18 135.93 132.78 129.85 127.41 126.33 129.43

3140.9 2182.0 1564.4 1152.5 869.40 669.49 524.87 417.88 337.04 274.76 225.91 186.93 155.35 129.37 107.62 88.972 72.213 55.104

0.058885 0.060795 0.062753 0.064753 0.066816 0.068988 0.071336 0.073932 0.076838 0.080106 0.083774 0.087876 0.092450 0.097544 0.10323 0.10966 0.11709 0.12644

0.067215 0.069146 0.071149 0.073238 0.075464 0.077921 0.080736 0.084059 0.088058 0.092930 0.098936 0.10646 0.11610 0.12898 0.14727 0.17612 0.23200 0.42053

226.86 233.03 238.89 244.41 249.49 254.02 257.88 260.92 263.02 264.03 263.82 262.27 259.21 254.44 247.61 238.10 224.59 203.70 0

Cv kJ/(mol⋅K)

Saturated Properties 17.911 17.642 17.376 17.106 16.828 16.537 16.231 15.905 15.557 15.181 14.774 14.331 13.843 13.298 12.676 11.941 11.007 9.5842 5.9910 0.00012998 0.00040670 0.0011115 0.0027080 0.0059814 0.012150 0.022975 0.040873 0.069039 0.11160 0.17385 0.26261 0.38683 0.55876 0.79629 1.1286 1.6143 2.4339 5.9910

0.055831 0.056681 0.057551 0.058460 0.059426 0.060469 0.061610 0.062872 0.064281 0.065871 0.067684 0.069779 0.072241 0.075202 0.078889 0.083745 0.090848 0.10434 0.16692 7693.7 2458.8 899.69 369.28 167.18 82.305 43.525 24.466 14.485 8.9606 5.7521 3.8080 2.5851 1.7897 1.2558 0.88602 0.61945 0.41086 0.16692

149.30 111.11 87.283 71.858 61.180 53.164 46.697 41.226 36.486 32.353 28.756 25.644 22.967 20.681 18.747 17.136 15.831 14.728 8.6373

14.936 15.737 16.612 17.566 18.602 19.731 20.969 22.341 23.886 25.659 27.741 30.251 33.369 37.377 42.735 50.248 61.578 82.512

7.2715 7.7433 8.2114 8.6756 9.1353 9.5902 10.040 10.486 10.929 11.372 11.820 12.283 12.774 13.318 13.961 14.786 15.982 18.148 (Continued)

2-207

2-208 TABLE 2-115 Thermodynamic Properties of Ethanol (Continued ) Temperature K

Pressure MPa

Entropy kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

164.74 153.26

1047.2 443.11

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

17.016 15.993

0.058768 0.062527

12.219 19.033

12.225 19.040

0.056554 0.077475

0.10193 0.12261

0.11962 0.14658

1132.5 960.72

−0.33179 −0.21908

55.390 59.207 67.925 77.796

58.222 62.477 72.058 82.775

0.18909 0.20043 0.22176 0.24127

0.073221 0.080640 0.092910 0.10403

0.083127 0.089997 0.10162 0.11252

260.21 279.09 312.39 341.55

42.587 28.685 11.830 5.6356

0.058707 0.067589 0.071181

12.202 26.715 30.866

12.261 26.783 30.938

0.056497 0.097937 0.10802

0.10191 0.13400 0.13732

0.11954 0.16857 0.18015

1137.9 791.85 694.41

3.0216 3.9114 4.8846

59.504 67.014 77.311

62.526 70.925 82.195

0.18255 0.20078 0.22131

0.090516 0.096953 0.10581

0.11184 0.11008 0.11605

260.65 300.64 337.33

24.014 12.007 5.6301

0.058443 0.066842 0.097846 0.099875

12.129 26.516 46.419 46.876

12.421 26.851 46.908 47.375

0.056249 0.097435 0.14179 0.14272

0.10185 0.13359 0.14311 0.14340

0.11922 0.16658 0.32410 0.35152

1161.4 829.44 308.88 292.31

−0.33665 −0.11211 1.7596 2.0063

2.1809 1.1372

0.45852 0.87939

60.445 74.966

62.737 79.363

0.17336 0.20395

0.12389 0.11419

0.34099 0.13659

209.80 314.06

15.000 5.6703

75.676 61.725

17.454 18.972

17.203 15.147 11.521 2.8001

0.058131 0.066020 0.086800 0.35713

12.041 26.293 44.752 71.266

12.623 26.953 45.620 74.837

0.055950 0.096860 0.13830 0.19172

0.10179 0.13313 0.14031 0.12599

0.11885 0.16456 0.22204 0.18744

1189.5 872.36 464.50 273.66

−0.34096 −0.13414 0.60618 5.6926

170.07 149.80 130.15 84.190

1111.8 252.40 80.680 23.411

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Single-Phase Properties 300.00 351.05

0.10000 0.10000

351.05 400.00 500.00 600.00

0.10000 0.10000 0.10000 0.10000

300.00 400.00 423.85

1.0000 1.0000 1.0000

423.85 500.00 600.00

1.0000 1.0000 1.0000

300.00 400.00 500.00 501.39

5.0000 5.0000 5.0000 5.0000

501.39 600.00

5.0000 5.0000

300.00 400.00 500.00 600.00

10.000 10.000 10.000 10.000

0.035314 0.030577 0.024191 0.020086 17.034 14.795 14.049 0.33095 0.25567 0.20473 17.111 14.961 10.220 10.013

28.317 32.704 41.338 49.786

−0.33273 −0.089821 0.013963

21.965 26.374 37.865 52.622 165.24 142.87 137.25 32.003 39.539 53.583 167.43 146.07 127.42 128.00

10.369 11.853 14.768 17.543 1053.2 227.32 167.52 12.568 14.859 17.678 1079.6 238.82 61.882 59.510

300.00 400.00 500.00 600.00

100.00 100.00 100.00 100.00

18.389 17.030 15.408 13.601

0.054380 0.058722 0.064899 0.073523

10.984 24.075 39.356 55.055

16.422 29.947 45.846 62.407

0.051802 0.090466 0.12589 0.15608

0.10149 0.12901 0.13221 0.12575

0.11571 0.15081 0.16433 0.16553

1558.1 1348.2 1166.1 1015.1

−0.37198 −0.25352 −0.17199 −0.082822

207.54 195.29 188.35 187.31

1611.3 435.09 192.15 109.49

300.00 400.00 500.00 600.00

200.00 200.00 200.00 200.00

19.244 18.138 16.878 15.505

0.051963 0.055134 0.059250 0.064494

10.349 22.905 37.295 51.902

20.742 33.931 49.145 64.801

0.048505 0.086238 0.12014 0.14869

0.10196 0.12678 0.12868 0.12066

0.11495 0.14539 0.15623 0.15566

1830.4 1660.3 1525.6 1422.7

−0.37578 −0.28090 −0.22946 −0.19099

238.67 228.57 224.49 226.40

2085.4 591.02 269.30 148.43

The values in these tables were generated from the NIST REFPROP software (Lemmon, E.W., McLinden, M.O., and Huber, M.L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Dillon, H.E., and Penoncello, S.G., “A Fundamental Equation for Calculation of the Thermodynamic Properties of Ethanol,” Int. J. Thermophys., 25(2):321–335, 2004. The source for viscosity is Kiselev, S. B., Ely, J. F., Abdulagatov, I. M., and Huber, M. L., “Generalized SAFT-DFT/DMT Model for the Thermodynamic, Interfacial, and Transport Properties of Associating Fluids: Application for n-Alkanols,” Ind. Eng. Chem. Res., 44:6916–6927, 2005. The source for thermal conductivity is unpublished, 2004; however, the fit uses functional form found in Marsh, K., Perkins, R., and Ramires, M.L.V., “Measurement and Correlation of the Thermal Conductivity of Propane from 86 to 600 K at Pressures to 70 MPa,” J. Chem. Eng. Data, 47(4):932–940, 2002. Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties in the equation of state are 0.2% in density, 3% in heat capacities, 1% in speed of sound, and 0.5% in vapor pressure and saturation densities. The estimated uncertainty in the liquid phase along the saturation boundary is approximately 3%, increasing to 10% at pressures to 100 MPa, and is estimated at 10% in the vapor phase. The estimated uncertainty in the liquid phase is approximately 5% and is estimated as 10% in the vapor phase.

THERMODYnAMIC PROPERTIES

FIG. 2-5

Enthalpy-concentration diagram for aqueous ethyl alcohol. Reference states: Enthalpies of liquid water and ethyl alcohol at 0°C are zero. Note: In order to interpolate equilibrium compositions, a vertical may be erected from any liquid composition on the boiling line and its intersection with the auxiliary line determined. A horizontal from this intersection will establish the equilibrium vapor composition on the dew line. (F. Bosnjakovic, Technische Thermodynamik, T. Steinkopff, Leipzig, 1935.)

2-209

2-210 TABLE 2-116

Thermodynamic Properties of normal Hydrogen

Temperature K

Pressure MPa

13.957 14.000 15.000 16.000 17.000 18.000 19.000 20.000 21.000 22.000 23.000 24.000 25.000 26.000 27.000 28.000 29.000 30.000 31.000 32.000 33.190 13.957 14.000 15.000 16.000 17.000 18.000 19.000 20.000 21.000 22.000 23.000 24.000 25.000 26.000 27.000 28.000 29.000 30.000 31.000 32.000 33.190

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

0.0077031 0.0078936 0.013436 0.021534 0.032848 0.048078 0.067960 0.093249 0.12472 0.16314 0.20932 0.26406 0.32818 0.40250 0.48788 0.58524 0.69554 0.81989 0.95964 1.1168 1.3301

38.148 38.129 37.701 37.261 36.802 36.321 35.812 35.274 34.702 34.092 33.439 32.738 31.979 31.152 30.242 29.225 28.067 26.706 25.017 22.637 14.940

0.026214 0.026226 0.026524 0.026838 0.027172 0.027533 0.027923 0.028350 0.028817 0.029333 0.029905 0.030546 0.031271 0.032101 0.033067 0.034217 0.035629 0.037444 0.039973 0.044175 0.066934

−0.10434 −0.10367 −0.088896 −0.074446 −0.059414 −0.043440 −0.026375 −0.0081516 0.011274 0.031947 0.053929 0.077308 0.10222 0.12884 0.15744 0.18843 0.22245 0.26061 0.30524 0.36302 0.53004

−0.10414 −0.10346 −0.088539 −0.073868 −0.058521 −0.042116 −0.024477 −0.0055080 0.014868 0.036732 0.060188 0.085375 0.11248 0.14176 0.17357 0.20846 0.24723 0.29132 0.34360 0.41236 0.61907

−0.0059480 −0.0059000 −0.0048799 −0.0039471 −0.0030355 −0.0021219 −0.0011983 −0.00026211 0.00068790 0.0016528 0.0026344 0.0036357 0.0046610 0.0057167 0.0068122 0.0079614 0.0091865 0.010527 0.012063 0.014035 0.020012

0.0077031 0.0078936 0.013436 0.021534 0.032848 0.048078 0.067960 0.093249 0.12472 0.16314 0.20932 0.26406 0.32818 0.40250 0.48788 0.58524 0.69554 0.81989 0.95964 1.1168 1.3301

0.067540 0.069018 0.11050 0.16764 0.24349 0.34126 0.46437 0.61652 0.80187 1.0251 1.2919 1.6089 1.9848 2.4307 2.9618 3.6003 4.3810 5.3643 6.6763 8.6823 14.940

14.806 14.489 9.0494 5.9651 4.1069 2.9303 2.1535 1.6220 1.2471 0.97549 0.77406 0.62153 0.50383 0.41141 0.33763 0.27775 0.22826 0.18642 0.14978 0.11518 0.066934

0.68715 0.68764 0.69864 0.70899 0.71875 0.72783 0.73614 0.74359 0.75005 0.75541 0.75951 0.76218 0.76318 0.76224 0.75895 0.75276 0.74277 0.72747 0.70374 0.66274 0.53004

0.80120 0.80201 0.82024 0.83745 0.85365 0.86871 0.88249 0.89484 0.90558 0.91455 0.92154 0.92630 0.92853 0.92783 0.92368 0.91531 0.90154 0.88031 0.84748 0.79136 0.61907

0.058918 0.058777 0.055705 0.053010 0.050622 0.048480 0.046537 0.044755 0.043103 0.041554 0.040085 0.038674 0.037303 0.035950 0.034594 0.033206 0.031749 0.030160 0.028317 0.025879 0.020012

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

0.011064 0.010957 0.0096961 0.0096482 0.010003 0.010462 0.010915 0.011323 0.011677 0.011978 0.012235 0.012457 0.012655 0.012840 0.013025 0.013224 0.013460 0.013764 0.014198 0.014926

0.015654 0.015547 0.014420 0.014709 0.015557 0.016642 0.017842 0.019120 0.020476 0.021935 0.023539 0.025351 0.027465 0.030024 0.033265 0.037610 0.043909 0.054194 0.074872 0.14185

1361.1 1359.6 1318.5 1271.6 1226.6 1185.5 1147.3 1110.7 1074.7 1038.2 1000.5 960.99 919.10 874.29 826.00 773.58 716.22 652.73 581.16 497.24 0

−1.4137 −1.4230 −1.5204 −1.4695 −1.3623 −1.2409 −1.1194 −1.0003 −0.88232 −0.76268 −0.63795 −0.50414 −0.35648 −0.18882 0.0073109 0.24446 0.54283 0.93827 1.5038 2.4292 5.3208

76.293 76.650 84.106 90.079 94.784 98.405 101.10 103.01 104.24 104.87 104.98 104.60 103.79 102.53 100.83 98.654 95.935 92.547 88.221 82.176

25.463 25.310 22.215 19.784 17.815 16.182 14.799 13.607 12.565 11.641 10.811 10.057 9.3625 8.7151 8.1034 7.5160 6.9409 6.3620 5.7518 5.0391

0.013157 0.013129 0.012872 0.012907 0.012992 0.013083 0.013178 0.013280 0.013392 0.013514 0.013650 0.013802 0.013973 0.014167 0.014392 0.014655 0.014971 0.015358 0.015854 0.016535

0.021964 0.021944 0.021898 0.022199 0.022618 0.023121 0.023724 0.024449 0.025329 0.026401 0.027724 0.029376 0.031482 0.034234 0.037960 0.043253 0.051322 0.065054 0.093486 0.18606

304.61 305.17 316.15 325.05 333.00 340.22 346.75 352.59 357.75 362.25 366.11 369.34 371.95 373.96 375.38 376.19 376.39 375.97 374.91 373.31 0

Cv kJ/(mol⋅K)

Saturated Properties

31.943 31.808 28.572 25.724 23.407 21.522 19.961 18.642 17.507 16.513 15.629 14.829 14.091 13.396 12.726 12.061 11.374 10.624 9.7362 8.5059 5.3208

10.375 10.431 11.624 12.681 13.681 14.669 15.675 16.716 17.806 18.956 20.180 21.493 22.916 24.477 26.218 28.202 30.535 33.407 37.226 43.200

0.66345 0.66695 0.74268 0.81064 0.87421 0.93555 0.99611 1.0569 1.1186 1.1819 1.2472 1.3151 1.3863 1.4619 1.5433 1.6331 1.7362 1.8628 2.0375 2.3378

Single-Phase Properties 25.000 100.00 175.00 250.00 325.00 400.00

0.10000 0.10000 0.10000 0.10000 0.10000 0.10000

25.000 31.268

1.0000 1.0000

31.268 100.00 175.00 250.00 325.00 400.00

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

25.000 100.00 175.00 250.00 325.00 400.00

5.0000 5.0000 5.0000 5.0000 5.0000 5.0000

0.50823 0.12030 0.068680 0.048077 0.036986 0.030054

1.9676 8.3127 14.560 20.800 27.037 33.273

0.81207 1.7949 3.0224 4.4642 5.9947 7.5545

1.0088 2.6261 4.4785 6.5442 8.6984 10.882

0.049309 0.079163 0.092882 0.10269 0.11022 0.11626

0.012734 0.014263 0.018150 0.020003 0.020681 0.020865

0.022519 0.022637 0.026480 0.028323 0.028998 0.029180

403.66 808.92 1026.9 1209.1 1371.7 1519.7

12.894 1.4058 0.13575 −0.22980 −0.38965 −0.47650

20.761 68.334 117.11 160.59 197.72 234.06

1.3142 4.1896 6.1845 7.9025 9.4561 10.892

0.030538 0.040861

0.089693 0.31894

0.12023 0.35980

0.0041410 0.012531

0.012580 0.014353

0.025394 0.084709

985.14 560.14

−0.51115 1.7031

106.80 86.829

9.9923 5.5759

0.14049 0.83027 1.4653 2.0926 2.7176 3.3418

0.69511 1.7679 3.0101 4.4576 5.9910 7.5525

0.83559 2.5982 4.4754 6.5501 8.7086 10.894

0.027747 0.059751 0.073667 0.083515 0.091062 0.097113

0.016014 0.014331 0.018190 0.020028 0.020699 0.020878

0.10713 0.023244 0.026659 0.028401 0.029039 0.029204

374.52 817.03 1035.8 1217.3 1379.1 1526.4

9.4548 1.3036 0.11718 −0.23428 −0.39039 −0.47605

38.524 70.413 118.31 161.46 198.43 234.65

2.0997 4.2550 6.2213 7.9283 9.4759 10.908

35.661 5.9683 3.3132 2.3268 1.7990 1.4680

0.028042 0.16755 0.30183 0.42978 0.55587 0.68120

0.046611 1.6549 2.9582 4.4292 5.9750 7.5440

0.18682 2.4927 4.4673 6.5781 8.7543 10.950

0.0021443 0.045314 0.059998 0.070022 0.077631 0.083710

0.012376 0.014583 0.018352 0.020136 0.020776 0.020937

0.020610 0.025613 0.027370 0.028723 0.029211 0.029304

1223.4 865.94 1077.3 1254.0 1412.0 1556.2

−0.90198 0.86369 0.032971 −0.25678 −0.39563 −0.47537

119.36 80.395 123.58 165.19 201.36 237.09

13.101 4.5875 6.3871 8.0420 9.5631 10.979

32.746 24.474 7.1182 1.2044 0.68243 0.47788 0.36797 0.29924

25.000 100.00 175.00 250.00 325.00 400.00

10.000 10.000 10.000 10.000 10.000 10.000

37.930 11.417 6.3697 4.5028 3.5006 2.8687

0.026364 0.087588 0.15699 0.22209 0.28567 0.34859

0.020221 1.5346 2.9000 4.3966 5.9563 7.5339

0.28386 2.4105 4.4699 6.6175 8.8130 11.020

0.00059913 0.038585 0.053931 0.064133 0.071811 0.077921

0.012222 0.014838 0.018532 0.020260 0.020867 0.021006

0.018499 0.027423 0.028063 0.029065 0.029402 0.029419

1402.1 955.43 1133.3 1300.6 1453.0 1593.1

−1.0762 0.39679 −0.068718 −0.28786 −0.40519 −0.47687

131.12 94.196 130.39 169.92 205.05 240.15

16.625 5.1692 6.6199 8.1898 9.6733 11.067

100.00 175.00 250.00 325.00 400.00

50.000 50.000 50.000 50.000 50.000

31.993 22.700 17.524 14.304 12.107

0.031257 0.044053 0.057066 0.069911 0.082595

1.1768 2.6415 4.2297 5.8539 7.4773

2.7397 4.8442 7.0830 9.3494 11.607

0.023964 0.039587 0.050225 0.058153 0.064404

0.016349 0.019545 0.020999 0.021434 0.021458

0.026254 0.029321 0.030163 0.030202 0.029985

1710.1 1632.6 1690.7 1784.8 1887.2

−0.57213 −0.46415 −0.46214 −0.48443 −0.51016

192.47 189.52 211.67 237.63 267.11

10.534 9.1377 9.7772 10.827 11.965

33.019 27.257 23.228 20.261

0.030286 0.036688 0.043051 0.049356

2.5589 4.1604 5.8083 7.4555

5.5875 7.8292 10.113 12.391

0.033643 0.044291 0.052281 0.058588

0.020316 0.021603 0.021923 0.021864

0.029140 0.030346 0.030469 0.030246

2128.4 2125.4 2170.6 2235.8

−0.52750 −0.50698 −0.51215 −0.52481

282.17 303.19 327.83 356.83

13.079 12.218 12.546 13.289

175.00 250.00 325.00 400.00

100.00 100.00 100.00 100.00

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Younglove, B. A., “Thermophysical Properties of Fluids. I. Argon, Ethylene, Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen,” J. Phys. Chem. Ref. Data, Suppl. 1, 11: 1–11, 1982. The source for viscosity is McCarty, R. D., and Weber, L. A., “Thermophysical Properties of Parahydrogen from the Freezing Liquid Line to 5000 R for Pressures to 10,000 psia,” N.B.S. Tech. Note 617, 1972. The source for thermal conductivity is McCarty, R. D., and Weber, L. A., “Thermophysical Properties of Parahydrogen from the Freezing Liquid Line to 5000 R for Pressures to 10,000 psia,” N.B.S. Tech. Note 617, 1972. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties in density are 0.1% in the liquid phase, 0.25% in the vapor phase, and 0.2% in the supercritical region. The uncertainty in heat capacity is 3%, and the uncertainty in speed of sound is 2% in the liquid phase and 1% elsewhere. The uncertainty in viscosity ranges from 4% to 15%. The uncertainty in thermal conductivity below 100 K is estimated to be 3% below 150 atm and up to 10% below 700 atm. For temperatures around 100 K at low densities, the uncertainty is about 1%. Above 100 K, the uncertainty is estimated to be on the order of 10%.

2-211

2-212 TABLE 2-117 T, K 273 300 350 400 450

Saturated Hydrogen Peroxide*

P, bar

vf , m3/kg

vg , m3/kg

hf , kJ/kg

hg, kJ/kg

sf , kJ/(kg⋅K)

sg , kJ/(kg⋅K)

cpf , kJ/(kg⋅K)

µf , 10−4 Pa⋅s

kf , W/(m⋅K)

0.0004 0.0031 0.0564 0.4521 2.143

0.00068 0.00069 0.00072 0.00076 0.00081

1672 235 15.1 2.12 0.487

−5577 −5510 −5376 −5238 −5091

−4027 −3995 −3933 −3878 −3820

2.990 3.224 3.631 4.032 4.346

8.662 8.269 7.758 7.440 7.172

1.45 1.48 1.54 1.61 1.68

18.0 11.3 4.3 2.2 1.3

0.483 0.481 0.474 0.464 0.453

1.75 1.82 1.90

500 550 600 650 700

7.126 18.56 40.75 79.27 141.7

0.00088 0.00095 0.00107 0.00125 0.00171

0.155 0.0605 0.0268 0.0125 0.0048

−4945 −4794 −4635 −4463 −4195

−3777 −3745 −3731 −3746 −3860

4.656 4.941 5.209 5.485 5.682

6.992 6.846 6.720 6.582 6.339

708.5c

155.3

0.00284

0.0028

−4012

−4012

5.732

5.732

0.89 0.65 0.50

0.443 0.431 0.416

*Values reproduced or converted from a tabulation by Tsykalo and Tabachnikov in V. A. Rabinovich (ed.), Thermophysical Properties of Gases and Liquids, Standartov, Moscow, 1968; NBS-NSF transl. TT 69-55091, 1970. The reader may be reminded that very pure hydrogen peroxide is very difficult to obtain owing to its decomposition or instability. c = critical point. The FMC Corp., Philadelphia, PA tech. bull. 67, 1969 (100 pp.) contains an enthalpy-pressure diagram to 3000 psia, 1100 K.

TABLE 2-118 Temperature K

Thermodynamic Properties of Hydrogen Sulfide Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

0.034345 0.034479 0.035082 0.035717 0.036390 0.037107 0.037875 0.038702 0.039599 0.040580 0.041662 0.042868 0.044230 0.045791 0.047618 0.049818 0.052573 0.056256 0.061837 0.074429 0.098135

−1.7210 −1.5628 −0.87841 −0.19759 0.48138 1.1602 1.8406 2.5245 3.2135 3.9100 4.6161 5.3348 6.0696 6.8248 7.6068 8.4246 9.2932 10.241 11.335 12.903 14.470

−1.7202 −1.5619 −0.87664 −0.19446 0.48661 1.1686 1.8534 2.5434 3.2408 3.9481 4.6685 5.4053 6.1629 6.9469 7.7650 8.6283 9.5548 10.578 11.779 13.538 15.353

16.328 16.382 16.611 16.832 17.043 17.244 17.431 17.604 17.761 17.899 18.016 18.108 18.171 18.199 18.183 18.109 17.957 17.684 17.192 16.046 14.470

17.876 17.947 18.250 18.541 18.818 19.079 19.320 19.539 19.735 19.902 20.039 20.139 20.198 20.207 20.156 20.027 19.793 19.403 18.736 17.266 15.353

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

−0.34039 −0.33923 −0.33253 −0.32287 −0.30988 −0.29305 −0.27174 −0.24509 −0.21197 −0.17084 −0.11959 −0.055218 0.026636 0.13260 0.27324 0.46655 0.74618 1.1841 1.9714 3.9324 6.3885

254.24 251.74 240.93 230.26 219.81 209.52 199.43 189.56 179.91 170.48 161.26 152.24 143.40 134.71 126.16 117.71 109.36 101.19 93.864 92.754

439.13 428.67 385.68 346.75 311.74 280.37 252.29 227.14 204.60 184.32 166.02 149.44 134.32 120.43 107.58 95.533 84.050 72.784 61.060 46.102

Saturated Properties 187.70 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 373.10

0.023259 0.027106 0.050340 0.087474 0.14366 0.22485 0.33767 0.48934 0.68751 0.94022 1.2558 1.6429 2.1103 2.6672 3.3233 4.0889 4.9755 5.9969 7.1713 8.5294 8.9987

29.116 29.003 28.505 27.998 27.480 26.949 26.403 25.838 25.253 24.642 24.002 23.327 22.609 21.838 21.000 20.073 19.021 17.776 16.172 13.436 10.190

187.70 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 373.10

0.023259 0.027106 0.050340 0.087474 0.14366 0.22485 0.33767 0.48934 0.68751 0.94022 1.2558 1.6429 2.1103 2.6672 3.3233 4.0889 4.9755 5.9969 7.1713 8.5294 8.9987

0.015024 0.017314 0.030704 0.051165 0.080932 0.12253 0.17879 0.25286 0.34834 0.46937 0.62086 0.80887 1.0411 1.3280 1.6843 2.1323 2.7096 3.4881 4.6442 6.9933 10.190

66.559 57.758 32.569 19.545 12.356 8.1613 5.5933 3.9547 2.8707 2.1305 1.6107 1.2363 0.96050 0.75300 0.59373 0.46898 0.36906 0.28669 0.21532 0.14299 0.098135

−0.0085877 −0.0077504 −0.0042394 −0.00091743 0.0022415 0.0052596 0.0081564 0.010949 0.013654 0.016285 0.018857 0.021385 0.023885 0.026373 0.028873 0.031414 0.034044 0.036848 0.040035 0.044599 0.049374

0.044390 0.044124 0.043042 0.042067 0.041188 0.040393 0.039677 0.039030 0.038449 0.037930 0.037470 0.037070 0.036732 0.036462 0.036273 0.036191 0.036265 0.036600 0.037471 0.040079

0.068835 0.068707 0.068273 0.068029 0.067975 0.068115 0.068461 0.069032 0.069859 0.070989 0.072490 0.074466 0.077082 0.080603 0.085498 0.092666 0.10410 0.12534 0.17963 0.63367

1437.8 1425.8 1373.4 1321.0 1268.4 1215.6 1162.3 1108.5 1053.9 998.54 942.08 884.34 825.04 763.84 700.23 633.51 562.59 485.59 398.86 292.76 0

0.095815 0.094930 0.091395 0.088301 0.085567 0.083129 0.080933 0.078934 0.077092 0.075375 0.073752 0.072193 0.070669 0.069149 0.067594 0.065956 0.064157 0.062064 0.059360 0.054674 0.049374

0.025347 0.025386 0.025586 0.025837 0.026142 0.026502 0.026917 0.027388 0.027914 0.028496 0.029136 0.029838 0.030608 0.031458 0.032407 0.033485 0.034746 0.036293 0.038364 0.041755

0.034000 0.034078 0.034487 0.035021 0.035698 0.036537 0.037563 0.038807 0.040312 0.042139 0.044378 0.047166 0.050723 0.055410 0.061879 0.071400 0.086837 0.11617 0.19265 0.80649

245.84 247.20 252.82 257.96 262.58 266.64 270.10 272.91 275.05 276.47 277.15 277.05 276.12 274.34 271.64 268.00 263.35 257.65 250.84 242.80 0

55.730 53.868 46.796 41.090 36.435 32.601 29.412 26.737 24.476 22.550 20.897 19.466 18.212 17.097 16.081 15.116 14.142 13.053 11.629 9.0701 6.3885

10.628 10.775 11.429 12.107 12.816 13.566 14.365 15.227 16.166 17.202 18.360 19.675 21.197 22.997 25.187 27.946 31.600 36.820 45.513 70.939

8.0025 8.1053 8.5566 9.0159 9.4844 9.9634 10.455 10.961 11.485 12.031 12.604 13.213 13.867 14.582 15.380 16.300 17.405 18.833 20.940 25.604 (Continued)

2-213

2-214

TABLE 2-118

Thermodynamic Properties of Hydrogen Sulfide (Continued )

Temperature K

Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

28.506 27.865

0.035080 0.035888

−0.87902 −0.021243

−0.87551 −0.017654

16.888 19.164 21.830 24.642 27.626 30.789

18.615 21.640 25.146 28.794 32.611 36.607

0.035053 0.040795

−0.89011 4.0550

−0.85506 4.0958

2.0080 2.2968 3.2255 4.0993 4.9547 5.8015

17.925 18.775 21.626 24.507 27.525 30.710

19.933 21.072 24.852 28.606 32.480 36.511

0.034935 0.043749 0.052654

−0.93837 5.9433 9.3164

−0.76369 6.1620 9.5797

0.36675 0.55412 0.77288 0.96476 1.1466

17.952 20.549 23.863 27.065 30.353

19.786 23.319 27.728 31.889 36.086

Cp kJ/(mol⋅K)

Sound speed m/s

0.043042 0.041830

0.068269 0.067997

1373.6 1307.4

0.087559 0.099486 0.10956 0.11770 0.12465 0.13081

0.025911 0.025979 0.027268 0.028923 0.030708 0.032534

0.035183 0.034563 0.035693 0.037297 0.039059 0.040873

259.21 309.73 356.35 396.06 431.20 463.05

39.791 16.968 8.9467 5.5432 3.7250 2.6185

−0.0042980 0.016821

0.043058 0.037830

0.068210 0.071266

1377.6 986.97

−0.33351 −0.16116

0.075033 0.079019 0.089907 0.098281 0.10534 0.11155

0.028623 0.027626 0.027708 0.029100 0.030799 0.032589

0.042564 0.039427 0.037234 0.038036 0.039492 0.041157

276.67 296.60 351.09 393.73 430.30 462.94

22.188 17.369 9.0111 5.5366 3.7023 2.5947

−0.0045411 0.023458 0.034113

0.043127 0.036740 0.036269

0.067957 0.075047 0.10449

1394.7 855.61 560.70

0.064108 0.073747 0.083609 0.091196 0.097665

0.034782 0.030043 0.029940 0.031216 0.032838

0.087361 0.048271 0.041996 0.041590 0.042472

263.22 325.86 384.33 427.30 463.26

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

Single-Phase Properties 200.00 212.60

0.10000 0.10000

212.60 300.00 400.00 500.00 600.00 700.00

0.10000 0.10000 0.10000 0.10000 0.10000 0.10000

200.00 272.07

1.0000 1.0000

272.07 300.00 400.00 500.00 600.00 700.00

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

200.00 300.00 340.26

5.0000 5.0000 5.0000

340.26 400.00 500.00 600.00 700.00

5.0000 5.0000 5.0000 5.0000 5.0000

0.057900 0.040389 0.030157 0.024088 0.020059 0.017187 28.528 24.513 0.49800 0.43539 0.31003 0.24394 0.20183 0.17237 28.625 22.858 18.992 2.7266 1.8047 1.2939 1.0365 0.87211

17.271 24.759 33.160 41.515 49.853 58.182

−0.0042425 −0.000082766

−0.33258 −0.31984

−0.33745 −0.017492 0.75500 14.116 9.1749 5.4471 3.5816 2.4840

240.95 227.54 12.288 17.999 24.990 32.218 39.592 47.091 241.31 168.56 17.430 19.015 25.609 32.691 39.980 47.423 242.90 146.15 109.14

385.79 337.30 9.1366 12.954 17.172 21.094 24.714 28.082 387.91 180.39 12.147 13.337 17.465 21.319 24.893 28.227 397.26 139.57 83.760

31.710 29.786 35.063 41.773 48.924

17.437 19.070 22.459 25.773 28.935

200.00 300.00 400.00 500.00 600.00 700.00

10.000 10.000 10.000 10.000 10.000 10.000

28.741 23.238 5.0473 2.8037 2.1399 1.7663

0.034793 0.043033 0.19812 0.35667 0.46730 0.56617

−0.99643 5.7496 18.370 22.959 26.466 29.903

−0.64850 6.1800 20.351 26.526 31.139 35.564

−0.0048367 0.022795 0.062081 0.076030 0.084452 0.091275

0.043212 0.036779 0.034651 0.031080 0.031755 0.033155

0.067668 0.072377 0.10189 0.048875 0.044597 0.044212

1415.5 902.78 291.29 375.68 426.01 465.45

−0.34197 −0.077399 8.2243 5.1487 3.3812 2.3347

244.82 150.49 44.719 38.963 44.210 50.878

408.90 148.08 23.639 24.438 27.165 30.013

300.00 400.00 500.00 600.00 700.00

75.000 75.000 75.000 75.000 75.000

26.050 21.973 17.947 14.519 11.974

0.038388 0.045510 0.055720 0.068874 0.083511

4.3332 9.9713 15.404 20.474 25.148

7.2123 13.384 19.583 25.640 31.412

0.017506 0.035260 0.049092 0.060142 0.069045

0.037754 0.035381 0.034762 0.034994 0.035721

0.061705 0.061962 0.061649 0.059227 0.056291

1276.9 983.51 786.35 688.11 654.55

−0.33612 −0.18247 0.057516 0.27314 0.36585

187.18 134.39 103.90 87.712 82.684

232.59 124.22 81.074 62.531 54.563

27.794 24.751 21.937 19.449 17.335

0.035979 0.040403 0.045585 0.051416 0.057687

3.5100 8.6429 13.539 18.248 22.811

8.9069 14.703 20.377 25.960 31.464

0.013888 0.030575 0.043238 0.053420 0.061906

0.038777 0.036402 0.035779 0.036044 0.036804

0.058983 0.057226 0.056273 0.055409 0.054711

1538.4 1302.6 1132.1 1019.1 949.06

−0.40376 −0.37006 −0.31802 −0.26874 −0.23292

214.24 165.64 135.75 118.38 110.03

311.25 174.85 119.57 93.323 79.581

300.00 400.00 500.00 600.00 700.00

150.00 150.00 150.00 150.00 150.00

The values in these tables were generated from the NIST REFPROP software (Lemmon, E.W., McLinden, M.O., and Huber, M.L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., and Span, R., “Short Fundamental Equations of State for 20 Industrial Fluids,” J. Chem. Eng. Data 51(3): 785–850, 2006. The source for viscosity and thermal conductivity is NIST14, Version 9.08. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties in density are 0.1% in the liquid phase below the critical temperature, 0.4% in the vapor phase, 1% at supercritical temperatures up to 500 K, and 2.5% at higher temperatures. Uncertainties will be higher near the critical point, and may be lower than 0.5% between 400 and 500 K. The uncertainty in vapor pressure is 0.25%, and the uncertainty in heat capacities is estimated to be 1%. For viscosity, estimated uncertainty is 2%. For thermal conductivity, estimated uncertainty, except near the critical region, is 4–6%.

THERMODYnAMIC PROPERTIES

FIG. 2-6

Enthalpy-concentration diagram for aqueous hydrogen chloride at 1 atm. Reference states: enthalpy of liquid water at 0°C is zero; enthalpy of pure saturated HCl vapor at 1 atm (–85.03°C) is 8000 kcal/mol. Note: It should be observed that the weight basis includes the vapor, which is particularly important in the two-phase region. Saturation values may be read at the ends of the tie lines [C.C. Van Nuys, Trans. Am. Inst. Chem. Eng 39: 663 (1943)].

2-215

2-216 TABLE 2-119 Temperature K

Thermodynamic Properties of Methane Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

0.035534 0.036554 0.037143 0.037768 0.038431 0.039138 0.039896 0.040714 0.041600 0.042569 0.043636 0.044825 0.046165 0.047702 0.049500 0.051667 0.054394 0.058078 0.063825 0.079902 0.098628

−1.1526 −0.64728 −0.37306 −0.096585 0.18242 0.46425 0.74927 1.0379 1.3307 1.6284 1.9317 2.2418 2.5602 2.8887 3.2304 3.5895 3.9734 4.3965 4.8955 5.7074 6.2136

−1.1522 −0.64602 −0.37097 −0.093257 0.18750 0.47174 0.75999 1.0529 1.3511 1.6557 1.9676 2.2884 2.6199 2.9647 3.3262 3.7098 4.1244 4.5873 5.1420 6.0685 6.6672

−0.011389 −0.0060856 −0.0034096 −0.00083691 0.0016441 0.0040439 0.0063722 0.0086383 0.010851 0.013020 0.015154 0.017264 0.019362 0.021462 0.023584 0.025755 0.028021 0.030467 0.033313 0.038000 0.041109

63.981 23.782 15.116 10.038 6.9171 4.9183 3.5915 2.6825 2.0424 1.5803 1.2393 0.98256 0.78568 0.63206 0.51014 0.41163 0.33038 0.26139 0.19945 0.12816 0.098628

6.8310 7.0469 7.1582 7.2654 7.3680 7.4652 7.5562 7.6403 7.7165 7.7837 7.8406 7.8856 7.9166 7.9306 7.9238 7.8898 7.8184 7.6893 7.4515 6.7850 6.2136

7.5793 7.8644 8.0104 8.1501 8.2825 8.4067 8.5215 8.6257 8.7180 8.7970 8.8608 8.9074 8.9340 8.9369 8.9109 8.8482 8.7357 8.5480 8.2217 7.3641 6.6672

0.084885 0.079019 0.076413 0.074103 0.072036 0.070168 0.068464 0.066891 0.065421 0.064029 0.062694 0.061391 0.060098 0.058789 0.057431 0.055982 0.054371 0.052471 0.049961 0.044819 0.041109

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

0.034776 0.033908 0.033500 0.033115 0.032749 0.032400 0.032069 0.031757 0.031469 0.031206 0.030974 0.030780 0.030631 0.030541 0.030531 0.030634 0.030920 0.031554 0.033085 0.041746

0.054029 0.054681 0.055135 0.055656 0.056253 0.056941 0.057741 0.058684 0.059809 0.061169 0.062840 0.064932 0.067613 0.071156 0.076044 0.083218 0.094816 0.11699 0.17822 1.5082

1538.6 1452.0 1403.9 1354.7 1304.6 1253.5 1201.3 1148.1 1093.6 1037.7 980.17 920.85 859.39 795.43 728.42 657.52 581.27 497.01 398.59 250.31 0

−0.48191 −0.45812 −0.44202 −0.42328 −0.40145 −0.37589 −0.34578 −0.31006 −0.26735 −0.21579 −0.15286 −0.075032 0.022798 0.14836 0.31398 0.54087 0.86918 1.3866 2.3397 5.2488 6.8877

211.24 199.67 193.03 186.18 179.21 172.15 165.04 157.91 150.78 143.65 136.54 129.43 122.32 115.19 108.01 100.73 93.324 85.799 78.733 96.970

204.52 155.78 136.86 121.34 108.39 97.432 88.031 79.868 72.699 66.333 60.620 55.437 50.682 46.266 42.105 38.115 34.196 30.193 25.773 18.982

0.025243 0.025487 0.025652 0.025842 0.026056 0.026295 0.026560 0.026854 0.027182 0.027549 0.027965 0.028439 0.028989 0.029636 0.030412 0.031374 0.032615 0.034338 0.037087 0.045796

0.033851 0.034425 0.034853 0.035378 0.036016 0.036786 0.037714 0.038836 0.040203 0.041885 0.043985 0.046657 0.050144 0.054849 0.061496 0.071527 0.088273 0.12151 0.21701 2.2590

249.13 260.09 265.31 270.01 274.17 277.76 280.76 283.13 284.86 285.93 286.31 285.97 284.88 283.01 280.30 276.66 271.99 266.04 258.03 238.55 0

47.921 37.826 33.883 30.662 28.004 25.790 23.928 22.347 20.993 19.819 18.789 17.870 17.035 16.255 15.500 14.732 13.896 12.892 11.492 8.4951 6.8877

8.8517 10.015 10.669 11.350 12.062 12.811 13.604 14.449 15.355 16.334 17.402 18.581 19.904 21.423 23.225 25.477 28.545 33.392 43.706 119.40

Cv kJ/(mol⋅K)

Saturated Properties 90.694 100.00 105.00 110.00 115.00 120.00 125.00 130.00 135.00 140.00 145.00 150.00 155.00 160.00 165.00 170.00 175.00 180.00 185.00 190.00 190.56

0.011696 0.034376 0.056377 0.088130 0.13221 0.19143 0.26876 0.36732 0.49035 0.64118 0.82322 1.0400 1.2950 1.5921 1.9351 2.3283 2.7765 3.2852 3.8617 4.5186 4.5992

28.142 27.357 26.923 26.478 26.021 25.551 25.065 24.562 24.038 23.491 22.917 22.309 21.661 20.964 20.202 19.355 18.384 17.218 15.668 12.515 10.139

90.694 100.00 105.00 110.00 115.00 120.00 125.00 130.00 135.00 140.00 145.00 150.00 155.00 160.00 165.00 170.00 175.00 180.00 185.00 190.00 190.56

0.011696 0.034376 0.056377 0.088130 0.13221 0.19143 0.26876 0.36732 0.49035 0.64118 0.82322 1.0400 1.2950 1.5921 1.9351 2.3283 2.7765 3.2852 3.8617 4.5186 4.5992

0.015630 0.042048 0.066154 0.099622 0.14457 0.20332 0.27844 0.37278 0.48962 0.63279 0.80691 1.0177 1.2728 1.5821 1.9603 2.4294 3.0268 3.8257 5.0137 7.8027 10.139

3.6388 3.9976 4.1951 4.3964 4.6019 4.8123 5.0285 5.2517 5.4833 5.7254 5.9806 6.2526 6.5462 6.8688 7.2313 7.6515 8.1609 8.8251 9.8238 12.455

Single-Phase Properties −0.64803 −0.012738

−0.64438 −0.0089413

7.2969 9.5570 12.175 15.151 18.673 22.795

8.1908 11.209 14.665 18.475 22.831 27.784

0.036493 0.044610

−0.65829 2.1878

1.0220 1.5537 2.4524 3.3108 4.1567 4.9971

27.586 5.4706 2.1799 1.5333 1.2013 0.99281

100.00 111.51

0.10000 0.10000

111.51 200.00 300.00 400.00 500.00 600.00

0.10000 0.10000 0.10000 0.10000 0.10000 0.10000

100.00 149.14

1.0000 1.0000

149.14 200.00 300.00 400.00 500.00 600.00

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.97852 0.64363 0.40776 0.30205 0.24058 0.20012

100.00 200.00 300.00 400.00 500.00 600.00

5.0000 5.0000 5.0000 5.0000 5.0000 5.0000

100.00 200.00 300.00 400.00 500.00 600.00

10.000 10.000 10.000 10.000 10.000 10.000

27.360 26.341

−0.0060931 −0.000079677

0.054672 0.055828

0.073456 0.093427 0.10741 0.11834 0.12803 0.13705

0.025904 0.025259 0.027479 0.032300 0.038196 0.044179

0.035558 0.033784 0.035869 0.040652 0.046533 0.052509

271.33 369.98 449.74 510.56 561.86 608.04

29.808 9.2893 4.3216 2.2395 1.2245 0.68722

−0.62179 2.2325

−0.0061960 0.016902

0.033950 0.030810

0.054562 0.064535

1459.6 931.21

−0.46060 −0.089695

7.8788 9.3582 12.072 15.083 18.623 22.755

8.9007 10.912 14.524 18.393 22.780 27.752

0.061614 0.073276 0.087922 0.099023 0.10879 0.11784

0.028353 0.025879 0.027621 0.032360 0.038227 0.044198

0.046147 0.036730 0.036721 0.041056 0.046766 0.052659

286.08 357.81 447.04 510.57 562.99 609.73

18.022 9.5001 4.2699 2.2001 1.1998 0.67124

18.368 23.028 35.152 50.558 68.902 89.200

0.036250 0.18279 0.45874 0.65221 0.83240 1.0072

−0.70190 7.8197 11.590 14.779 18.401 22.581

−0.52065 8.7337 13.884 18.040 22.563 27.617

−0.0066393 0.051495 0.072954 0.084897 0.094971 0.10417

0.034116 0.032029 0.028262 0.032614 0.038361 0.044277

0.054117 0.11667 0.041234 0.042903 0.047789 0.053309

1490.0 291.29 439.25 513.11 569.49 618.13

−0.46993 8.9784 3.9428 2.0089 1.0870 0.60013

204.45 40.612 38.480 52.693 70.509 90.498

165.28 10.828 12.194 14.872 17.410 19.768

27.802 16.593 4.6859 3.1002 2.3887 1.9619

0.035969 0.060268 0.21340 0.32256 0.41863 0.50971

−0.75239 5.1551 10.942 14.401 18.132 22.371

−0.39270 5.7578 13.077 17.627 22.318 27.468

−0.0071652 0.034542 0.065137 0.078246 0.088698 0.098073

0.034314 0.030129 0.028995 0.032902 0.038516 0.044371

0.053642 0.085085 0.048165 0.045220 0.049007 0.054070

1525.7 567.92 444.53 522.58 580.99 630.63

−0.47979 1.0266 3.2606 1.7355 0.94125 0.51200

209.07 84.234 44.730 55.941 72.781 92.268

174.83 29.399 13.896 15.766 18.011 20.217

27.403 22.416

8.9395 16.524 24.901 33.243 41.572 49.895

1452.6 1339.7

−0.45829 −0.41705

0.033911 0.033003

0.11186 0.060518 0.040158 0.030082 0.024055 0.020042

0.036549 0.037963

199.74 184.09 11.561 21.941 34.552 50.127 68.564 88.921 200.62 130.66

155.91 117.20 4.4579 7.8096 11.245 14.272 16.976 19.431 157.63 56.297 6.2043 8.0145 11.367 14.357 17.040 19.483

200.00 300.00 400.00 500.00 600.00

100.00 100.00 100.00 100.00 100.00

25.496 21.266 17.881 15.305 13.357

0.039222 0.047024 0.055926 0.065340 0.074869

3.0510 7.0865 11.121 15.405 20.074

6.9732 11.789 16.713 21.939 27.561

0.020596 0.040126 0.054276 0.065922 0.076160

0.032058 0.031823 0.035273 0.040312 0.045724

0.048512 0.048281 0.050523 0.054139 0.058364

1541.0 1267.5 1115.8 1044.8 1018.4

−0.51619 −0.44889 −0.37484 −0.32811 −0.30439

188.05 137.68 120.38 120.87 130.36

80.392 47.835 37.584 33.590 32.111

200.00 300.00 400.00 500.00 600.00

500.00 500.00 500.00 500.00 500.00

33.003 30.786 28.929 27.331 25.934

0.030301 0.032482 0.034567 0.036588 0.038559

2.3322 5.9505 9.7401 13.934 18.612

17.482 22.192 27.024 32.228 37.892

0.0061671 0.025271 0.039152 0.050747 0.061061

0.037832 0.037006 0.039890 0.044407 0.049344

0.047821 0.047114 0.049933 0.054280 0.059017

2664.2 2500.0 2360.3 2250.3 2168.1

−0.53926 −0.55416 −0.52806 −0.49035 −0.45514

429.60 358.93 312.36 285.41 272.14

205.24 106.90 78.768 66.669 60.413

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Setzmann, U., and Wagner, W., “A New Equation of State and Tables of Thermodynamic Properties for Methane Covering the Range from the Melting Line to 625 K at Pressures up to 1000 MPa,” J. Phys. Chem. Ref. Data 20(6):1061–1151, 1991. The source for viscosity is Younglove, B. A., and Ely, J. F., “Thermophysical Properties of Fluids. II. Methane, Ethane, Propane, Isobutane and Normal Butane,” J. Phys. Chem. Ref. Data 16:577–798, 1987. The source for thermal conductivity is Friend, D. G., Ely, J. F., and Ingham, H., “Tables for the Thermophysical Properties of Methane,” NIST Tech. Note 1325, 1989. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties in density are 0.03% for pressures below 12 MPa and temperatures below 350 K and up to 0.07% for pressures less than 50 MPa. For the speed of sound, the uncertainty ranges from 0.03% (in the vapor phase) to 0.3% depending on temperature and pressure. Heat capacities may be generally calculated within an uncertainty of 1%. The uncertainty in viscosity is 2%, except in the critical region which is 5%. The uncertainty in thermal conductivity of the dilute gas between 130 and 625 K is 2.5%. For temperatures below 130 K, the uncertainty is less than 10%. Excluding the dilute gas, the uncertainty is 2% between 110 and 725 K at pressures up to 70 MPa, except near the critical point which has an uncertainty of 5% or greater. For the vapor at lower temperatures and the dense liquid near the triple point, an uncertainty of 10% is possible. 2-217

2-218 TABLE 2-120 Temperature K

Thermodynamic Properties of Methanol Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Saturated Properties 175.61 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 375.00 390.00 405.00 420.00 435.00 450.00 465.00 480.00 495.00 510.00 513.38

1.8635E-07 3.7619E-07 3.2175E-06 1.9841E-05 9.4330E-05 0.00036348 0.0011791 0.0033166 0.0082787 0.018682 0.038692 0.074453 0.13447 0.22992 0.37483 0.58617 0.88399 1.2914 1.8349 2.5433 3.4456 4.5713 5.9794 7.7496 8.2159

175.61 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 375.00 390.00 405.00 420.00 435.00 450.00 465.00 480.00 495.00 510.00 513.38

1.8635E-07 3.7619E-07 3.2175E-06 1.9841E-05 9.4330E-05 0.00036348 0.0011791 0.0033166 0.0082787 0.018682 0.038692 0.074453 0.13447 0.22992 0.37483 0.58617 0.88399 1.2914 1.8349 2.5433 3.4456 4.5713 5.9794 7.7496 8.2159

28.230 28.096 27.629 27.163 26.703 26.250 25.802 25.360 24.922 24.484 24.041 23.590 23.124 22.638 22.123 21.571 20.973 20.315 19.579 18.741 17.759 16.553 14.880 11.689 8.7852 1.2764E-07 2.5140E-07 1.9855E-06 1.1378E-05 5.0556E-05 0.00018304 0.00056065 0.0014959 0.0035581 0.0076845 0.015300 0.028438 0.049870 0.083267 0.13344 0.20674 0.31179 0.46071 0.67055 0.96219 1.3555 1.9102 2.9050 5.1706 8.7852

0.035423 0.035592 0.036194 0.036815 0.037449 0.038096 0.038756 0.039432 0.040125 0.040844 0.041595 0.042390 0.043244 0.044174 0.045203 0.046358 0.047681 0.049226 0.051075 0.053360 0.056310 0.060411 0.067203 0.085547 0.11383 7,834,400. 3,977,700. 503,660. 87,892. 19,780. 5,463.4 1,783.7 668.48 281.05 130.13 65.359 35.164 20.052 12.009 7.4940 4.8370 3.2073 2.1706 1.4913 1.0393 0.73775 0.52352 0.34423 0.19340 0.11383

−12.440 −12.130 −11.067 −10.001 −8.9277 −7.8395 −6.7318 −5.5991 −4.4351 −3.2329 −1.9858 −0.68700 0.66961 2.0901 3.5806 5.1475 6.7983 8.5423 10.392 12.364 14.488 16.820 19.521 23.297 25.917

−12.440 −12.130 −11.067 −10.001 −8.9277 −7.8395 −6.7318 −5.5990 −4.4347 −3.2322 −1.9842 −0.68385 0.67543 2.1003 3.5975 5.1746 6.8404 8.6058 10.485 12.500 14.682 17.096 19.923 23.960 26.852

−0.049524 −0.047781 −0.042108 −0.036846 −0.031908 −0.027226 −0.022750 −0.018434 −0.014239 −0.010129 −0.0060725 −0.0020451 0.0019747 0.0060049 0.010061 0.014159 0.018314 0.022546 0.026879 0.031347 0.036009 0.040977 0.046590 0.054351 0.059911

0.056728 0.056689 0.056604 0.057072 0.057992 0.059275 0.060916 0.062917 0.065250 0.067864 0.070693 0.073674 0.076752 0.079881 0.083033 0.086189 0.089346 0.092514 0.095722 0.099032 0.10257 0.10666 0.11250 0.12653

0.070390 0.070750 0.070897 0.071215 0.072004 0.073141 0.074617 0.076487 0.078803 0.081584 0.084823 0.088505 0.092616 0.097164 0.10219 0.10776 0.11405 0.12133 0.13007 0.14120 0.15679 0.18345 0.25717 1.1088

1625.1 1590.2 1496.4 1425.3 1363.2 1304.6 1248.2 1194.1 1142.6 1093.5 1046.3 1000.2 954.32 907.64 859.31 808.48 754.41 696.47 634.17 567.09 494.36 412.12 308.94 192.83 0

28.219 28.353 28.810 29.259 29.698 30.123 30.534 30.932 31.321 31.703 32.077 32.442 32.789 33.108 33.385 33.601 33.736 33.767 33.687 33.541 33.439 33.258 32.267 29.688 25.917

29.679 29.850 30.430 31.003 31.564 32.109 32.637 33.149 33.648 34.134 34.606 35.060 35.485 35.869 36.194 36.436 36.571 36.570 36.423 36.184 35.981 35.652 34.325 31.187 26.852

0.19032 0.18544 0.17069 0.15841 0.14806 0.13923 0.13164 0.12508 0.11938 0.11442 0.11009 0.10627 0.10287 0.099808 0.096984 0.094317 0.091723 0.089128 0.086505 0.083978 0.081813 0.079634 0.075685 0.068520 0.059911

0.031874 0.032397 0.035224 0.040104 0.047248 0.056324 0.066572 0.077055 0.086920 0.095581 0.10279 0.10860 0.11331 0.11736 0.12125 0.12546 0.13033 0.13587 0.14101 0.14238 0.13589 0.12618 0.12608 0.13259

0.040287 0.040854 0.043954 0.049389 0.057480 0.067973 0.080135 0.093000 0.10564 0.11740 0.12798 0.13749 0.14644 0.15559 0.16605 0.17917 0.19663 0.21986 0.24709 0.26502 0.25879 0.27959 0.42448 1.9096

239.95 242.62 251.06 258.49 265.30 271.89 278.43 284.90 291.19 297.15 302.63 307.47 311.48 314.48 316.20 316.34 314.53 310.36 303.71 295.26 285.25 267.83 247.46 212.65 0

−0.40884 −0.40373 −0.39791 −0.39361 −0.38674 −0.37793 −0.36733 −0.35457 −0.33915 −0.32073 −0.29904 −0.27385 −0.24479 −0.21121 −0.17199 −0.12529 −0.068163 0.0042669 0.10021 0.23444 0.43762 0.79465 1.6506 4.6061 6.7425 1187400. 857090. 293110. 105090. 39363. 15552. 6557.5 2971.8 1449.9 759.96 426.34 254.84 161.53 108.02 75.802 55.467 42.002 32.587 25.532 19.860 15.568 13.904 12.099 9.5115 6.7425

Single-Phase Properties 200.00 300.00 337.30

0.10000 0.10000 0.10000

337.30 400.00 500.00 600.00

0.10000 0.10000 0.10000 0.10000

200.00 300.00 400.00 409.75

1.0000 1.0000 1.0000 1.0000

409.75 500.00 600.00

1.0000 1.0000 1.0000

200.00 300.00 400.00 484.95

5.0000 5.0000 5.0000 5.0000

484.95 500.00 600.00

5.0000 5.0000 5.0000

200.00 300.00 400.00 500.00 600.00

10.000 10.000 10.000 10.000 10.000

27.474 24.486 23.366 0.037626 0.030452 0.024157 0.020089

0.036398 0.040839 0.042798

−10.709 −3.2300 −0.030266

−0.040317 −0.010133 −0.000089518

0.056702 0.067862 0.075163

0.070943 0.081580 0.090451

1471.5 1094.1 977.93

−0.39677 −0.32081 −0.26023

32.613 36.075 40.921 46.476

35.271 39.359 45.060 51.454

0.10457 0.11581 0.12851 0.14014

0.11100 0.044972 0.051823 0.059065

0.14187 0.054208 0.060380 0.067441

309.54 349.19 387.15 420.71

−10.720 −3.2472 6.2298 7.3401

−10.684 −3.2064 6.2770 7.3883

−0.040354 −0.010176 0.016901 0.019645

0.056724 0.067848 0.088257 0.090347

0.070932 0.081541 0.11177 0.11623

1475.1 1100.0 775.46 736.51

33.758 40.335 46.300

36.586 44.303 51.178

0.090904 0.10818 0.12070

0.13203 0.056676 0.061344

0.20333 0.068069 0.070369

313.48 376.08 413.09

38.678 13.330 4.5635

0.036283 0.040592 0.046640 0.062203

−10.752 −3.3039 6.0896 17.655

−10.571 −3.1010 6.3228 17.966

−0.040517 −0.010367 0.016546 0.042725

0.056820 0.067795 0.087676 0.10826

0.070883 0.081377 0.11029 0.19836

1490.9 1125.5 818.58 381.15

−0.39825 −0.32568 −0.11504 0.98684

2.1711 1.7679 1.1389

0.46060 0.56566 0.87808

33.047 35.907 45.247

35.350 38.735 49.638

0.078574 0.085457 0.10553

0.12499 0.098975 0.072927

0.32263 0.17315 0.087489

260.06 301.43 379.21

13.826 12.155 5.1009

27.648 24.779 21.717 15.932 2.6640

0.036169 0.040357 0.046048 0.062765 0.37537

−10.791 −3.3713 5.9321 19.374 43.262

−10.430 −2.9677 6.3925 20.002 47.015

−0.040716 −0.010598 0.016141 0.046226 0.096406

0.056935 0.067746 0.087087 0.10760 0.088868

0.070820 0.081196 0.10880 0.18959 0.12122

1509.9 1155.3 865.91 424.68 343.60

−0.39966 −0.32990 −0.13884 0.83939 5.0965

−7.8460 −0.44914 8.4277 19.458 32.525

−0.043691 −0.013840 0.011565 0.036085 0.059862

0.057827 0.067889 0.082823 0.095694 0.10406

0.068992 0.079818 0.098951 0.12152 0.13787

1772.1 1515.8 1334.7 1164.1 977.50

−0.41976 −0.35799 −0.26099 −0.14407 −0.023905

10.949 19.430 29.089 40.322

−0.022106 0.0022308 0.023726 0.044161

0.070293 0.077541 0.084883 0.092281

0.080627 0.089761 0.10419 0.12017

2316.0 2194.8 2123.2 2074.1

−0.34762 −0.30897 −0.24751 −0.19279

27.491 24.514 21.193 20.772 0.35352 0.25202 0.20501 27.561 24.635 21.441 16.076

26.577 32.839 41.396 49.779

−10.713 −3.2341 −0.034546

0.036376 0.040793 0.047185 0.048143 2.8287 3.9680 4.8778

200.00 300.00 400.00 500.00 600.00

100.00 100.00 100.00 100.00 100.00

28.911 26.630 24.493 22.020 19.139

0.034588 0.037552 0.040827 0.045413 0.052250

−11.305 −4.2043 4.3449 14.917 27.300

300.00 400.00 500.00 600.00

500.00 500.00 500.00 500.00

30.547 29.154 27.670 26.003

0.032736 0.034300 0.036140 0.038457

−5.4195 2.2795 11.020 21.094

202.71 40.941 12.933 4.3382 −0.39705 −0.32177 −0.090229 −0.047179

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is de Reuck, K. M., and Craven, R. J. B., “Methanol, International Thermodynamic Tables of the Fluid State—12,” IUPAC, Blackwell Scientific Publications, London, 1993. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties of the equation of state are generally 0.1% in density and 2% in the speed of sound, except in the critical region and high pressures.

2-219

2-220 TABLE 2-121 Thermodynamic Properties of nitrogen Temperature K

Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

−4.2230 −4.1194 −4.0071 −3.8946 −3.7819 −3.6689 −3.5556 −3.4419 −3.3278 −3.2132 −3.0980 −2.9822 −2.8657 −2.7483 −2.6301 −2.5107 −2.3902 −2.2683 −2.1449 −2.0196 −1.8923 −1.7625 −1.6298 −1.4938 −1.3537 −1.2086 −1.0571 −0.89741 −0.72635 −0.53833 −0.32093 −0.031475 0.51527

−4.2226 −4.1188 −4.0063 −3.8935 −3.7804 −3.6669 −3.5530 −3.4385 −3.3235 −3.2078 −3.0913 −2.9739 −2.8555 −2.7360 −2.6152 −2.4930 −2.3691 −2.2434 −2.1156 −1.9854 −1.8525 −1.7163 −1.5765 −1.4323 −1.2828 −1.1271 −0.96336 −0.78944 −0.60161 −0.39322 −0.14962 0.17937 0.81891

0.067951 0.069569 0.071270 0.072924 0.074535 0.076105 0.077637 0.079133 0.080597 0.082030 0.083436 0.084815 0.086172 0.087507 0.088823 0.090123 0.091408 0.092682 0.093946 0.095204 0.096459 0.097715 0.098977 0.10025 0.10154 0.10285 0.10420 0.10561 0.10710 0.10873 0.11059 0.11310 0.11807

1.2945 1.3299 1.3675 1.4042 1.4400 1.4747 1.5082 1.5404 1.5713 1.6007 1.6284 1.6544 1.6784 1.7005 1.7203 1.7377 1.7525 1.7645 1.7733 1.7788 1.7804 1.7778 1.7703

1.8147 1.8639 1.9160 1.9668 2.0162 2.0639 2.1099 2.1539 2.1957 2.2353 2.2725 2.3070 2.3386 2.3672 2.3925 2.4143 2.4324 2.4463 2.4557 2.4603 2.4595 2.4528 2.4394

0.16355 0.16161 0.15966 0.15786 0.15618 0.15461 0.15314 0.15176 0.15046 0.14923 0.14806 0.14694 0.14587 0.14485 0.14385 0.14289 0.14195 0.14103 0.14012 0.13922 0.13832 0.13742 0.13651

Cp kJ/(mol⋅K)

Sound speed m/s

0.032951 0.032591 0.032207 0.031831 0.031463 0.031106 0.030760 0.030427 0.030105 0.029795 0.029499 0.029215 0.028944 0.028687 0.028444 0.028215 0.028001 0.027804 0.027624 0.027464 0.027327 0.027214 0.027133 0.027088 0.027089 0.027149 0.027290 0.027545 0.027981 0.028755 0.030317 0.034680

0.056033 0.056121 0.056231 0.056360 0.056512 0.056690 0.056899 0.057142 0.057425 0.057752 0.058130 0.058566 0.059068 0.059647 0.060315 0.061088 0.061983 0.063026 0.064246 0.065684 0.067392 0.069443 0.071937 0.075021 0.078914 0.083966 0.090771 0.10044 0.11531 0.14140 0.20028 0.46831

995.28 976.36 956.04 935.83 915.66 895.49 875.28 855.00 834.61 814.07 793.36 772.44 751.28 729.84 708.09 685.99 663.50 640.57 617.14 593.17 568.58 543.30 517.24 490.29 462.32 433.19 402.67 370.43 335.85 297.68 253.32 195.48 0

−0.40419 −0.39833 −0.39135 −0.38364 −0.37508 −0.36560 −0.35506 −0.34334 −0.33029 −0.31574 −0.29951 −0.28135 −0.26099 −0.23813 −0.21237 −0.18326 −0.15025 −0.11264 −0.069613 −0.020100 0.037239 0.10414 0.18288 0.27654 0.38936 0.52741 0.69974 0.92076 1.2154 1.6317 2.2811 3.5308 6.0831

0.021007 0.021059 0.021123 0.021196 0.021278 0.021370 0.021472 0.021585 0.021709 0.021845 0.021994 0.022157 0.022334 0.022528 0.022738 0.022967 0.023217 0.023489 0.023787 0.024113 0.024471 0.024860 0.025284

0.029647 0.029788 0.029969 0.030180 0.030427 0.030712 0.031039 0.031413 0.031839 0.032323 0.032873 0.033496 0.034204 0.035008 0.035925 0.036973 0.038177 0.039568 0.041185 0.043081 0.045326 0.048012 0.051276

161.11 163.20 165.37 167.43 169.39 171.23 172.95 174.55 176.03 177.38 178.60 179.68 180.63 181.43 182.10 182.62 182.99 183.21 183.28 183.18 182.93 182.51 181.93

40.718 38.268 35.907 33.803 31.922 30.231 28.707 27.328 26.074 24.931 23.884 22.923 22.035 21.212 20.446 19.730 19.057 18.421 17.815 17.236 16.676 16.132 15.600

Cv kJ/(mol⋅K)

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

173.24 169.51 165.49 161.47 157.47 153.46 149.47 145.48 141.50 137.55 133.61 129.66 125.72 121.77 117.83 113.89 109.95 106.02 102.08 98.144 94.208 90.272 86.337 82.404 78.472 74.544 70.626 66.728 62.883 59.196 56.121 56.435

311.59 282.07 254.55 230.85 210.32 192.43 176.75 162.94 150.71 139.82 130.07 121.31 113.38 106.18 99.602 93.568 88.004 82.847 78.042 73.543 69.306 65.292 61.464 57.786 54.224 50.740 47.290 43.824 40.270 36.509 32.310 26.935

Saturated Properties 63.151 65.000 67.000 69.000 71.000 73.000 75.000 77.000 79.000 81.000 83.000 85.000 87.000 89.000 91.000 93.000 95.000 97.000 99.000 101.00 103.00 105.00 107.00 109.00 111.00 113.00 115.00 117.00 119.00 121.00 123.00 125.00 126.19

0.012520 0.017404 0.024300 0.033213 0.044527 0.058656 0.076043 0.097152 0.12247 0.15251 0.18780 0.22886 0.27626 0.33055 0.39230 0.46210 0.54052 0.62817 0.72566 0.83358 0.95259 1.0833 1.2264 1.3826 1.5526 1.7371 1.9370 2.1533 2.3869 2.6391 2.9116 3.2069 3.3958

63.151 65.000 67.000 69.000 71.000 73.000 75.000 77.000 79.000 81.000 83.000 85.000 87.000 89.000 91.000 93.000 95.000 97.000 99.000 101.00 103.00 105.00 107.00

0.012520 0.017404 0.024300 0.033213 0.044527 0.058656 0.076043 0.097152 0.12247 0.15251 0.18780 0.22886 0.27626 0.33055 0.39230 0.46210 0.54052 0.62817 0.72566 0.83358 0.95259 1.0833 1.2264

30.957 30.685 30.387 30.085 29.779 29.468 29.153 28.832 28.506 28.175 27.837 27.492 27.139 26.779 26.409 26.030 25.640 25.238 24.822 24.390 23.941 23.471 22.978 22.457 21.902 21.306 20.658 19.943 19.134 18.187 16.997 15.210 11.184 0.024070 0.032594 0.044300 0.059031 0.077273 0.099542 0.12638 0.15838 0.19613 0.24030 0.29157 0.35069 0.41846 0.49576 0.58355 0.68291 0.79504 0.92134 1.0634 1.2231 1.4027 1.6049 1.8331

0.032303 0.032589 0.032909 0.033239 0.033581 0.033935 0.034302 0.034683 0.035080 0.035493 0.035924 0.036375 0.036847 0.037343 0.037865 0.038417 0.039002 0.039623 0.040288 0.041000 0.041769 0.042605 0.043520 0.044530 0.045658 0.046935 0.048407 0.050144 0.052262 0.054985 0.058834 0.065747 0.089414 41.546 30.680 22.573 16.940 12.941 10.046 7.9124 6.3140 5.0986 4.1614 3.4297 2.8515 2.3897 2.0171 1.7137 1.4643 1.2578 1.0854 0.94038 0.81759 0.71291 0.62309 0.54553

5.6209 5.8164 6.0298 6.2457 6.4645 6.6870 6.9138 7.1458 7.3839 7.6295 7.8837 8.1483 8.4251 8.7163 9.0247 9.3533 9.7060 10.087 10.503 10.960 11.467 12.035 12.679

4.3763 4.5123 4.6601 4.8088 4.9585 5.1096 5.2621 5.4164 5.5727 5.7313 5.8924 6.0565 6.2238 6.3948 6.5700 6.7499 6.9353 7.1270 7.3260 7.5334 7.7509 7.9804 8.2245

109.00 111.00 113.00 115.00 117.00 119.00 121.00 123.00 125.00 126.19

1.3826 1.5526 1.7371 1.9370 2.1533 2.3869 2.6391 2.9116 3.2069 3.3958

100.00 600.00 1100.0 1600.0

0.10000 0.10000 0.10000 0.10000

100.00 103.75

1.0000 1.0000

103.75 600.00 1100.0 1600.0

1.0000 1.0000 1.0000 1.0000

100.00 600.00 1100.0 1600.0

5.0000 5.0000 5.0000 5.0000

2.0916 2.3860 2.7240 3.1162 3.5786 4.1370 4.8380 5.7846 7.3244 11.184

0.47811 0.41911 0.36711 0.32091 0.27944 0.24172 0.20670 0.17287 0.13653 0.089414

1.7573 1.7377 1.7102 1.6730 1.6234 1.5572 1.4665 1.3343 1.1039 0.51527

2.4183 2.3884 2.3479 2.2946 2.2251 2.1341 2.0119 1.8376 1.5417 0.81891

0.13557 0.13461 0.13360 0.13253 0.13138 0.13009 0.12860 0.12675 0.12400 0.11807

0.025750 0.026284 0.026924 0.027721 0.028723 0.029997 0.031683 0.034185 0.039278

0.055332 0.060528 0.067435 0.077010 0.091003 0.11312 0.15295 0.24490 0.66512

181.19 180.28 179.15 177.75 176.01 173.87 171.17 167.43 160.26 0

15.075 14.546 13.996 13.409 12.767 12.045 11.203 10.148 8.6030 6.0831

13.419 14.284 15.315 16.580 18.186 20.329 23.424 28.604 41.535

8.4867 8.7716 9.0860 9.4395 9.8474 10.336 10.953 11.813 13.326

9.3806 44.840 70.075 92.344

6.9581 29.577 44.199 56.398

Single-Phase Properties

100.00 600.00 1100.0 1600.0 600.00 1100.0 1600.0 600.00 1100.0 1600.0

10.000 10.000 10.000 10.000 500.00 500.00 500.00 1000.0 1000.0 1000.0

0.12268 0.020037 0.010930 0.0075152 24.658 23.768 1.4754 0.19960 0.10899 0.074993

8.1514 49.908 91.489 133.06 0.040554 0.042073 0.67778 5.0099 9.1755 13.335

2.0396 12.573 24.284 37.272

2.8547 17.564 33.433 50.579

0.15950 0.21217 0.23131 0.24414

0.021049 0.021796 0.024932 0.026815

0.030012 0.030118 0.033248 0.035130

201.64 496.27 660.05 788.94

16.082 0.021483 −0.65654 −0.81543

−2.0907 −1.8441

−2.0501 −1.8020

0.094493 0.096928

0.027546 0.027281

0.064564 0.068113

609.42 559.22

−0.054514 0.060996

100.58 92.738

76.255 67.783

1.7800 12.554 24.277 37.270

2.4577 17.564 33.452 50.605

0.13799 0.19300 0.21216 0.22499

0.024612 0.021812 0.024938 0.026820

0.046272 0.030198 0.033267 0.035138

182.79 498.66 662.07 790.64

16.471 0.0061465 −0.65940 −0.81612

11.671 44.992 70.155 92.399

7.8351 29.626 44.221 56.411

25.436 0.98084 0.53797 0.37146

0.039314 1.0195 1.8588 2.6921

−2.2176 12.469 24.247 37.259

−2.0210 17.567 33.541 50.720

0.093188 0.17948 0.19875 0.21161

0.027713 0.021881 0.024969 0.026839

0.059868 0.030539 0.033350 0.035170

673.24 509.60 671.08 798.18

−0.17096 −0.057679 −0.67112 −0.81886

108.13 45.797 70.555 92.663

84.510 29.882 44.330 56.476

26.188 1.9183 1.0590 0.73435

0.038186 0.52130 0.94433 1.3618

−2.3398 12.368 24.211 37.246

−1.9580 17.581 33.654 50.864

0.091882 0.17355 0.19296 0.20583

0.028004 0.021965 0.025006 0.026863

0.056646 0.030926 0.033447 0.035209

734.22 523.87 682.37 807.57

−0.25658 −0.12928 −0.68394 −0.82170

115.90 46.995 71.130 93.033

93.648 30.284 44.493 56.570

27.434 21.868 18.335

0.036451 0.045729 0.054541

10.778 23.840 37.584

29.003 46.705 64.855

0.13791 0.15935 0.17295

0.026493 0.027586 0.028647

0.035336 0.035848 0.036665

1574.4 1501.4 1506.6

−0.70223 −0.72394 −0.73166

177.40 149.37 147.47

103.10 79.801 79.226

34.270 29.362 25.920

0.029180 0.034057 0.038580

11.714 25.065 38.999

40.894 59.122 77.579

0.13093 0.15303 0.16685

0.029169 0.029373 0.029977

0.036905 0.036577 0.037212

2107.2 1985.1 1942.0

−0.61888 −0.65271 −0.65439

278.97 232.49 214.36

208.00 129.86 110.35

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Span, R., Lemmon, E. W., Jacobsen, R. T., Wagner, W., and Yokozeki, A., “A Reference Quality Thermodynamic Property Formulation for Nitrogen,” J. Phys. Chem. Ref. Data 29(6):1361–1433, 2000. See also Int. J. Thermophys. 14(4):1121–1132, 1998. The source for viscosity is Lemmon, E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004. The source for thermal conductivity is Lemmon, E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainty in density of the equation of state is 0.02% from the triple point up to temperatures of 523 K and pressures up to 12 MPa and from temperatures of 240 to 523 K at pressures less than 30 MPa. In the range from 270 to 350 K at pressures less than 12 MPa, the uncertainty in density is 0.01%. The uncertainty at very high pressures (>1 GPa) is 0.6% in density. The uncertainty in pressure in the critical region is estimated to be 0.02%. In the gaseous and supercritical region, the speed of sound can be calculated with a typical uncertainty of 0.005% to 0.1%. At liquid states and at high pressures, the uncertainty increases to 0.5% to 1.5%. For pressures up to 30 MPa, the estimated uncertainty for heat capacities ranges from 0.3% at gaseous and gaslike supercritical states up to 0.8% at liquid states and at certain gaseous and supercritical states at low temperatures. The uncertainty is 2% for pressures up to 200 MPa and larger at higher pressures. The estimated uncertainties of vapor pressure, saturated-liquid density, and saturated-vapor density are in general 0.02% for each property. The formulation yields a reasonable extrapolation behavior up to the limits of chemical stability of nitrogen. For viscosity, the uncertainty is 0.5% in dilute gas. Away from the dilute gas (pressures greater than 1 MPa and in the liquid), the uncertainties are as low as 1% between 270 and 300 K at pressures less than 100 MPa, and increase outside that range. The uncertainties are around 2% at temperatures of 180 K and higher. Below this and away from the critical region, the uncertainties steadily increase to around 5% at the triple points of the fluids. The uncertainties in the critical region are higher. For thermal conductivity, the uncertainty for the dilute gas is 2% with increasing uncertainties near the triple point. For the nondilute gas, the uncertainty is 2% for temperatures greater than 150 K. The uncertainty is 3% at temperatures less than the critical point and 5% in the critical region, except for states very near the critical point.

2-221

2-222 FIG. 2-7 Pressure-enthalpy diagram for nitrogen. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of Span, R., E. W. Lemmon, R. T. Jacobsen, W. Wagner, and A. Yokozeki, “A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa.,” J. Phys. Chem. Ref. Data 29:1361–1433, 2000.

TABLE 2-122 Thermodynamic Properties of Oxygen Temperature K

Pressure MPa

Density mol/dm3

54.361 55.000 60.000 65.000 70.000 75.000 80.000 85.000 90.000 95.000 100.00 105.00 110.00 115.00 120.00 125.00 130.00 135.00 140.00 145.00 150.00 154.58

0.00014628 0.00017857 0.00072582 0.0023349 0.0062623 0.014547 0.030123 0.056831 0.099350 0.16308 0.25400 0.37853 0.54340 0.75559 1.0223 1.3509 1.7491 2.2250 2.7878 3.4477 4.2186 5.0428

40.816 40.734 40.064 39.367 38.656 37.936 37.203 36.457 35.692 34.905 34.092 33.245 32.360 31.426 30.434 29.367 28.203 26.907 25.415 23.599 21.110 13.630

54.361 55.000 60.000 65.000 70.000 75.000 80.000 85.000 90.000 95.000 100.00 105.00 110.00 115.00 120.00 125.00 130.00 135.00 140.00 145.00 150.00 154.58

0.00014628 0.00017857 0.00072582 0.0023349 0.0062623 0.014547 0.030123 0.056831 0.099350 0.16308 0.25400 0.37853 0.54340 0.75559 1.0223 1.3509 1.7491 2.2250 2.7878 3.4477 4.2186 5.0428

0.00032370 0.00039060 0.0014561 0.0043291 0.010804 0.023509 0.045891 0.082138 0.13710 0.21627 0.32579 0.47267 0.66506 0.91283 1.2284 1.6285 2.1366 2.7893 3.6487 4.8412 6.7170 13.630

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

0.024500 0.024549 0.024960 0.025402 0.025869 0.026360 0.026879 0.027430 0.028017 0.028649 0.029333 0.030079 0.030903 0.031820 0.032858 0.034051 0.035457 0.037165 0.039347 0.042375 0.047372 0.073368

−6.1954 −6.1613 −5.8938 −5.6258 −5.3573 −5.0889 −4.8202 −4.5510 −4.2806 −4.0084 −3.7337 −3.4556 −3.1732 −2.8853 −2.5904 −2.2867 −1.9711 −1.6394 −1.2839 −0.88908 −0.41330 0.66752

−6.1954 −6.1612 −5.8938 −5.6257 −5.3572 −5.0885 −4.8194 −4.5495 −4.2778 −4.0038 −3.7263 −3.4442 −3.1564 −2.8612 −2.5568 −2.2407 −1.9091 −1.5567 −1.1742 −0.74298 −0.21346 1.0375

0.066946 0.067571 0.072225 0.076516 0.080495 0.084199 0.087667 0.090931 0.094023 0.096967 0.099787 0.10250 0.10513 0.10770 0.11022 0.11271 0.11520 0.11773 0.12035 0.12319 0.12654 0.13442

3089.2 2560.2 686.75 230.99 92.556 42.536 21.791 12.175 7.2938 4.6239 3.0695 2.1156 1.5036 1.0955 0.81405 0.61407 0.46803 0.35852 0.27407 0.20656 0.14888 0.073368

1.1195 1.1327 1.2355 1.3377 1.4393 1.5397 1.6377 1.7320 1.8209 1.9031 1.9772 2.0421 2.0966 2.1391 2.1678 2.1801 2.1722 2.1380 2.0670 1.9383 1.6938 0.66752

1.5714 1.5898 1.7339 1.8770 2.0189 2.1584 2.2941 2.4239 2.5455 2.6571 2.7569 2.8430 2.9136 2.9668 3.0000 3.0097 2.9908 2.9357 2.8311 2.6505 2.3219 1.0375

0.20982 0.20850 0.19935 0.19194 0.18587 0.18083 0.17659 0.17297 0.16984 0.16708 0.16462 0.16238 0.16032 0.15838 0.15652 0.15471 0.15289 0.15100 0.14896 0.14659 0.14345 0.13442

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

0.038252 0.037651 0.034835 0.033469 0.032532 0.031745 0.031030 0.030365 0.029745 0.029169 0.028636 0.028146 0.027703 0.027311 0.026976 0.026712 0.026536 0.026485 0.026634 0.027189 0.028982

0.053541 0.053489 0.053548 0.053668 0.053697 0.053719 0.053808 0.054012 0.054361 0.054880 0.055599 0.056557 0.057816 0.059469 0.061666 0.064659 0.068905 0.075327 0.086099 0.10778 0.17484

1123.4 1126.9 1127.4 1101.7 1066.3 1027.5 987.43 946.87 905.90 864.40 822.19 779.06 734.77 689.03 641.52 591.86 539.50 483.69 423.10 355.20 273.80 0

−0.37992 −0.37886 −0.37011 −0.36312 −0.35686 −0.34972 −0.34056 −0.32856 −0.31302 −0.29316 −0.26804 −0.23637 −0.19639 −0.14551 −0.079899 0.0063780 0.12309 0.28750 0.53357 0.93865 1.7389 5.0628

201.92 201.02 193.94 186.82 179.70 172.58 165.44 158.27 151.05 143.81 136.55 129.25 121.92 114.57 107.23 99.912 92.634 85.404 78.217 71.056 64.190

773.62 747.53 578.07 457.94 371.79 308.66 261.22 224.62 195.64 172.12 152.56 135.93 121.52 108.81 97.426 87.086 77.571 68.687 60.223 51.869 42.900

0.021241 0.021297 0.021815 0.022310 0.022565 0.022513 0.022239 0.021896 0.021624 0.021515 0.021605 0.021894 0.022361 0.022978 0.023726 0.024597 0.025604 0.026794 0.028269 0.030276 0.033574

0.029631 0.029698 0.030320 0.030934 0.031294 0.031336 0.031177 0.031019 0.031053 0.031420 0.032204 0.033461 0.035245 0.037647 0.040839 0.045146 0.051204 0.060349 0.075824 0.10781 0.21201

140.32 141.11 147.03 152.65 158.07 163.33 168.36 173.06 177.30 180.99 184.06 186.44 188.14 189.13 189.41 188.96 187.75 185.74 182.82 178.78 172.82 0

Cv kJ/(mol⋅K)

Saturated Properties

507.90 480.26 284.62 156.71 87.254 52.570 35.817 27.728 23.649 21.338 19.753 18.446 17.250 16.118 15.045 14.029 13.062 12.120 11.155 10.071 8.6358 5.0628

4.4204 4.4842 4.9840 5.4863 5.9925 6.5051 7.0277 7.5654 8.1241 8.7113 9.3362 10.010 10.748 11.571 12.509 13.607 14.940 16.641 18.977 22.582 29.666

4.0962 4.1481 4.5528 4.9555 5.3557 5.7533 6.1486 6.5423 6.9355 7.3301 7.7281 8.1324 8.5467 8.9760 9.4273 9.9112 10.445 11.061 11.823 12.881 14.721 (Continued)

2-223

2-224 TABLE 2-122 Thermodynamic Properties of Oxygen (Continued ) Temperature K

Pressure MPa

Cp kJ/(mol⋅K)

Sound speed m/s

0.020885 0.021078 0.022781 0.024672 0.026045

0.029925 0.029435 0.031108 0.032992 0.034363

188.37 329.72 421.27 493.31 555.60

18.479 2.6530 0.75388 0.10517 −0.18735

0.099680 0.11003

0.028683 0.027000

0.055399 0.061476

826.85 645.19

−0.27181 −0.085501

2.9983 8.6563 14.741 21.176 27.929

0.15666 0.18598 0.20149 0.21230 0.22078

0.023665 0.021148 0.022802 0.024682 0.026051

0.040564 0.029887 0.031240 0.033052 0.034395

189.41 329.90 422.68 494.87 557.14

15.124 2.6066 0.73726 0.098376 −0.19062

12.433 26.894 41.288 54.139 66.001

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

0.12316 0.040116 0.024050 0.017177 0.013360

8.1192 24.928 41.579 58.216 74.849

2.0355 6.2338 10.604 15.357 20.438

2.8474 8.7265 14.762 21.179 27.923

0.17297 0.20531 0.22069 0.23147 0.23994

0.029276 0.032774

−3.7444 −2.6131

−3.7151 −2.5803

0.83209 2.4791 4.1649 5.8360 7.5029

2.1662 6.1772 10.576 15.340 20.426

Cv kJ/(mol⋅K)

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity mPa⋅s

9.0852 26.485 41.046 53.966 65.867

7.7121 20.652 30.486 38.653 45.806

Single-Phase Properties 100.00 300.00 500.00 700.00 900.00

0.10000 0.10000 0.10000 0.10000 0.10000

100.00 119.62

1.0000 1.0000

119.62 300.00 500.00 700.00 900.00

1.0000 1.0000 1.0000 1.0000 1.0000

100.00 154.36

5.0000 5.0000

34.497 16.011

0.028988 0.062457

−3.7983 0.35374

−3.6533 0.66602

0.099132 0.13204

0.028935 0.038878

0.054458 3.5718

850.39 163.89

−0.28978 4.2044

140.71 75.954

160.92 29.668

154.36 300.00 500.00 700.00 900.00

5.0000 5.0000 5.0000 5.0000 5.0000

11.160 2.0616 1.1908 0.84728 0.65931

0.089610 0.48505 0.83975 1.1802 1.5167

1.0294 5.9227 10.454 15.264 20.373

1.4774 8.3480 14.653 21.165 27.956

0.13729 0.17177 0.18787 0.19881 0.20734

0.041906 0.021448 0.022894 0.024726 0.026076

4.2513 0.032003 0.031815 0.033309 0.034537

158.85 332.25 429.36 501.98 564.07

6.0016 2.3730 0.66261 0.068114 −0.20519

72.313 28.797 42.362 54.901 66.593

20.574 21.766 31.267 39.261 46.305

34.158 30.512 1.2018 0.40337 0.24010 0.17135 0.13328

137.23 107.79

153.89 98.249 9.3921 20.846 30.630 38.766 45.899

100.00 300.00 500.00 700.00 900.00

10.000 10.000 10.000 10.000 10.000

34.885 4.2056 2.3538 1.6705 1.3010

0.028665 0.23778 0.42484 0.59861 0.76866

−3.8593 5.6024 10.306 15.171 20.307

−3.5726 7.9802 14.554 21.157 27.993

0.098498 0.16499 0.18182 0.19292 0.20150

0.029235 0.021790 0.022999 0.024776 0.026104

0.053516 0.034749 0.032491 0.033613 0.034706

877.07 339.35 438.67 511.24 572.92

−0.30803 2.0332 0.56900 0.030534 −0.22339

144.82 31.466 43.708 55.839 67.321

169.49 23.153 32.074 39.873 46.804

100.00 300.00 500.00 700.00 900.00

25.000 25.000 25.000 25.000 25.000

35.884 10.393 5.6243 3.9923 3.1222

0.027867 0.096215 0.17780 0.25048 0.32028

−4.0109 4.7194 9.8920 14.907 20.117

−3.3142 7.1247 14.337 21.169 28.124

0.096845 0.15490 0.17346 0.18495 0.19369

0.030037 0.022521 0.023256 0.024901 0.026174

0.051627 0.040917 0.034167 0.034397 0.035155

945.24 390.80 472.62 541.32 600.66

−0.34532 1.0167 0.30658 −0.076019 −0.27597

155.97 41.851 47.943 58.651 69.464

194.38 29.605 34.705 41.714 48.271

100.00 300.00 500.00 700.00 900.00

75.000 75.000 75.000 75.000 75.000

38.263 21.603 13.760 10.201 8.1749

0.026135 0.046289 0.072675 0.098029 0.12233

−4.3340 3.1884 8.8798 14.192 19.571

−2.3739 6.6601 14.330 21.544 28.745

0.092788 0.14315 0.16284 0.17498 0.18403

0.031906 0.023601 0.023725 0.025126 0.026293

0.049123 0.041272 0.036534 0.035903 0.036153

1115.1 645.54 619.75 657.04 701.72

−0.39472 −0.18640 −0.20732 −0.31840 −0.40609

184.96 75.261 64.149 68.835 76.863

274.96 53.378 45.084 48.269 53.163

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Schmidt, R., and Wagner, W., “A New Form of the Equation of State for Pure Substances and Its Application to Oxygen,” Fluid Phase Equilibria, 19:175–200, 1985. The source for viscosity and thermal conductivity is Lemmon, E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties of the equation of state are 0.1% in density, 2% in heat capacity, and 1% in the speed of sound, except in the critical region. For viscosity, the uncertainty is 1% in the dilute gas at temperatures above 200 K, and 5% in the dilute gas at lower temperatures. The uncertainty is around 2% between 270 and 300 K, and increases to 5% outside of this region. The uncertainty may be higher in the liquid near the triple point. The uncertainty for the dilute gas is 2% with increasing uncertainties near the triple point. For thermal conductivity, the uncertainties range from 3% between 270 and 300 K to 5% elsewhere. The uncertainties above 100 MPa are not known due to a lack of experimental data.

FIG. 2-8

Pressure-enthalpy diagram for oxygen. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of Schmidt, R., and W. Wagner, “A New Form of the Equation of State for Pure Substances and Its Application to Oxygen,” Fluid Phase Equilibria 19: 175–200, 1985.

2-225

FIG. 2-9

Enthalpy-concentration diagram for oxygen-nitrogen mixture at 1 atm. Reference states: Enthalpies of liquid oxygen and liquid nitrogen at the normal boiling point of nitrogen are zero. (Dodge, B.F. Chemical Engineering Thermodynamics, McGraw-Hill, New York, 1944.) Wilson, G.M., P.M. Silverberg, and M.G. Zellner, AFAPL TDR 64-64 (AD 603151), 1964, p. 314, present extensive vapor-liquid equilibrium data for the three-component system argon-nitrogen-oxygen as well as for binary systems including oxygen-nitrogen. Calculations for this mixture are also available with the NIST REFPROP software.

6

20

10 1.5

9

.2

.05

1.0

.6

.9 .8

.1

.5

.4

4

Ethylene

2

Methane

1.5

.3

.04

.005

.02

.004

.005 .004

.03

.07

.015

.06

.07

.05

.06

Ethane

.4

3

.1 .09 .08

.09 .08

.7 .6

.006

.006

.7

5000 6000

.01 .009 .03 .008 .007

.15

.8

6

.01 .009 .008 .007

.01 .009

.02

.04

.05

.008

.045

.015

–10

–20

09 .00

.003

.04

.06

.9

5 .001

.004

.05.015

.07

.001

.002

.005

.02

.08 .2

.5

4000

.09

1.0

5

3000

.3

.3

2

7

2000

.1

.4

1.5

00.5

.003

.01 .009 .008 .007 .006

.03

.04

.4

.5

.04

.1 .09.03 .08 .07 .02 .06

.5

3 15

8

1500

.2

.6

.004

.015

.15.05

.7

.6 2

Pressure, kPa

900 1000

4

.3

Propane

500

1 .9 .8 .7

3

5

.9 .8

Temperature, °C

30

4

.02

.05

n-Nonane

1

7

400

.3 .1 .09 .08 .07 .2 .06

.4

0

ne

8

.5

1.5

.03

.1 .09 .08 .07 .06

.005

1 .001 .004 .01 8 0 0 .0 .009 .003 .008 6 .000 .007 .006 .002 5 0 .0

.04

cta n-O

300

5

.015

10

n-Heptane

6

10 9

40

1.5

.15

.5 .15 .4

.6

2

.02

.05

.6 .2

.7

7

250

700 800

2

8 50

600

10 .9 .8

3

.2

n-Hexane

10 9

15

60

3

20

.004

.005 .01 .009 .008 .006 .007 .006

.03

.1 .09 .08 .07 .06

.3

.003

.015

.04

.4

.4 1 .9.3 .8 .7

4

4

20

70

200

5

.15

n-Pentane

6 15

80

5 20

.05

.5

.6 1.5.5

6

.06

.2

.6

Isopentane

30

.8 2 .7

–30

–40

–50

.007

.01

n-Butane

20

100 90

150

8 30 7

9 8 7

Isobutane

25

40

150

Propylene

A 101.3 110

–60

–70 FIG. 2-10 K values (K = y/x) in light-hydrocarbon systems. (a) Low-temperature range. (b) High-temperature range. [C.L. DePriester, Chem. Eng. Prog. Symp., Ser. 7, 49: 1 (1953); converted to SI units by D.B. Dadyburjor, Chem. Eng. Prog. 74: 4 (1978).]

2-226

THERMODYnAMIC PROPERTIES

0 25

150 200 250 300

20

FIG. 2-10

n-Nonane

n-Decane

20 30

200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30

20

10

.001

n-Octane

.005

n-Heptane

Methane

5000

40

n-Hexane

3000 3500 4000

50

Isopentane n-Pentane

2500

60

Isobutane n-Butane

2000

70 90 60 80

Propylene Propane

1500

0

10

Ethane

600 700 800 900 1000

0

Ethylene

500

Pressure, kPa

400

11

0

2 3 5 8 4 1.5 10 76 2 9 15 3 1 30 8 5 0 0 1.5 0 0 4 5 0 1 15 .8 7 70 20 4 90 2 .6 6 10 80 1 20 60 40 3 .5 20 9 5 30 1.5 70 0 8 10 .4 15 50 0 4 7 15 8 3 2 .3 15 60 1 .5 6 7 3 1.5 .9 .4 20 40 .8 .2 5 0 6 5 10 .7 9 5 .6 .3 20 4 2 100 10 1 8 15 9 .9 .5 4 30 .1 .2 90 7 3 40 8 1.5 .8 .4 15 .08 .7 6 .15 80 7 3 .6 .06 .3 5 10 6 70 .5 1. .05 2 .1 30 .9 9 5 20 10 .04 5 .4 2 .8 .2 .08 60 9 8 1.5 .7 .03 4 .3 .06 8 3 .15 7 .6 50 15 1.5 .05 7 .5 .02 6 20 .1 3 .04 .2 .1 .9 6 .09 .015 .4 5 40 2 1 .08 .03 .8 9 .15 .07 10 5 .7 .01 15 .3 4 2 .06 1.5 9 .6 .008 7 4 30 .1 .05 .02 8 .5 6 .006 9 .04 .0 .2 1.0 3 .015 .005 7 .08 1 5 .4 10 3 .07 .004 .9 .03 .15 6 9 6 .0 .8 4 .01 .3 8 .009 .003 .05 1 2 .7 20 5 .02 .008 .9 3 7 .1 2 .007 .04 .6 .8 .09 02 .006 .0 6 .2 8 1.5 .7 .0 .015 4 .5 3 .005 .0015 .07 .0 1.5 15 2 .6 5 .4 .15 .06 4 .01 .00 3 .5 .05 1 .02 .009 1.5 4 3 .001 8 .00 .00 .3 .9 1 .1 .04 .9 .8 .4 15 .007 10 .0 9 .0 .25 .006 .8 9 .08 .7 3 .1 2 .002 .03 .3 .7 .07 .09 .005 8 .6 .01 8 .0 .06 .6 7 .009 .004 1.5 .5 .02 .008 .15 .05 2 .5 6 .06 .007 .2 .4 .003 01 .0 .04 .015 .006 .05 5 .4 1.5 .005 1 .1 .15 .3 3 .0 .9 .09 4 .004 .002 .01 .3 .25 .08 .8 .009 .03 .008 .02 .003 .015 .1 .06 .007 3 06 .0 .015 .02

15

Temperature, °C

B 101.3 110

0 –5

(Continued)

TABLE 2-123 Composition of Selected Refrigerant Mixtures* Composition, mass% Mixed Product Name R-32 R-125 R-134a R-143a R-404A R-407C R-410A

Property Table/Figure 2-126, Fig. 2-12 2-127, Fig. 2-13 2-128, Fig. 2-14 2-129 2-130 2-131, Fig. 2-15 2-132

R-32

R-125

R-134a

R-143a

100 100 100

23 50

44 25 50

4 52

100 52

Ozone Depletion Potential (ODP)†

Global Warming Potential (GWP)‡ (100 year)

0 0 0 0 0 0 0

650 3400 1300 4300 3300 1600 2088

*All products listed here are HFCs (hydrofluorocarbons), the primary replacement for hydrochlorofluorocarbons (HCFCs) like R-22. † The ODP of the old CFC refrigerants R-11 and R-12 is 1. ‡ CO2 is the GWP reference: GWP of CO2 = 1.

2-227

2-228 TABLE 2-124 Thermodynamic Properties of R-22, Chlorodifluoromethane Temperature K

Pressure MPa

115.73 120.00 135.00 150.00 165.00 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 369.30

3.7947E-07 9.9588E-07 1.7187E-05 0.00015627 0.00089946 0.0037009 0.011835 0.031218 0.070909 0.14319 0.26329 0.44888 0.71966 1.0970 1.6039 2.2661 3.1130 4.1837 4.9900

115.73 120.00 135.00 150.00 165.00 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 369.30

3.7947E-07 9.9588E-07 1.7187E-05 0.00015627 0.00089946 0.0037009 0.011835 0.031218 0.070909 0.14319 0.26329 0.44888 0.71966 1.0970 1.6039 2.2661 3.1130 4.1837 4.9900

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Saturated Properties 19.907 19.777 19.325 18.873 18.420 17.963 17.500 17.028 16.542 16.036 15.506 14.944 14.341 13.686 12.956 12.114 11.069 9.5229 6.0582 3.9436E-07 9.9813E-07 1.5313E-05 0.00012533 0.00065634 0.0024808 0.0073561 0.018161 0.038991 0.075182 0.13342 0.22208 0.35201 0.53822 0.80363 1.1882 1.7777 2.8529 6.0582

0.050235 0.050564 0.051747 0.052985 0.054289 0.055670 0.057141 0.058726 0.060453 0.062359 0.064493 0.066919 0.069730 0.073070 0.077181 0.082547 0.090340 0.10501 0.16506 2,535,700. 1,001,900. 65,305. 7,979.0 1,523.6 403.09 135.94 55.062 25.647 13.301 7.4950 4.5029 2.8409 1.8580 1.2443 0.84159 0.56253 0.35052 0.16506

2.5595 2.9559 4.3400 5.7179 7.0951 8.4715 9.8483 11.230 12.622 14.034 15.472 16.945 18.462 20.034 21.676 23.418 25.325 27.613 30.901

2.5595 2.9559 4.3400 5.7179 7.0951 8.4717 9.8490 11.232 12.627 14.043 15.489 16.975 18.513 20.114 21.800 23.605 25.606 28.053 31.725

0.0065813 0.0099451 0.020814 0.030493 0.039243 0.047227 0.054574 0.061399 0.067804 0.073877 0.079692 0.085308 0.090782 0.096166 0.10152 0.10696 0.11267 0.11931 0.12907

0.061918 0.061567 0.060123 0.059099 0.058356 0.057679 0.057097 0.056707 0.056579 0.056737 0.057171 0.057856 0.058767 0.059887 0.061218 0.062814 0.064858 0.068488

0.092976 0.092700 0.091960 0.091824 0.091789 0.091751 0.091898 0.092431 0.093482 0.095120 0.097391 0.10037 0.10424 0.10941 0.11688 0.12929 0.15550 0.25950

1410.9 1388.4 1312.3 1239.0 1166.5 1095.0 1024.5 954.55 884.79 814.96 744.97 674.69 603.91 532.11 458.37 381.15 298.16 201.90 0

27.807 27.929 28.373 28.840 29.329 29.836 30.357 30.885 31.411 31.928 32.428 32.900 33.335 33.717 34.021 34.207 34.184 33.661 30.901

28.769 28.927 29.495 30.087 30.699 31.328 31.966 32.603 33.229 33.833 34.401 34.922 35.380 35.755 36.017 36.114 35.935 35.127 31.725

0.23305 0.22637 0.20715 0.19295 0.18230 0.17421 0.16800 0.16317 0.15937 0.15634 0.15386 0.15178 0.14996 0.14830 0.14666 0.14486 0.14261 0.13896 0.12907

0.028465 0.028872 0.030386 0.031990 0.033655 0.035388 0.037218 0.039177 0.041300 0.043615 0.046138 0.048881 0.051851 0.055064 0.058574 0.062516 0.067254 0.074178

0.036779 0.037186 0.038703 0.040316 0.042018 0.043849 0.045881 0.048204 0.050920 0.054144 0.058023 0.062763 0.068713 0.076534 0.087659 0.10579 0.14389 0.29995

119.91 121.91 128.58 134.79 140.59 145.98 150.87 155.15 158.70 161.35 162.96 163.38 162.45 159.98 155.73 149.36 140.39 127.92 0

−0.44463 −0.44526 −0.44448 −0.43872 −0.43084 −0.42063 −0.40608 −0.38505 −0.35555 −0.31561 −0.26263 −0.19248 −0.097827 0.035333 0.23608 0.57205 1.2334 3.0745 10.366 398.80 367.18 269.83 197.57 146.30 110.28 84.902 66.865 53.872 44.348 37.240 31.852 27.725 24.549 22.102 20.201 18.613 16.641 10.366

Single-Phase Properties 150.00 232.06

0.10000 0.10000

232.06 250.00 350.00 450.00 550.00

0.10000 0.10000 0.10000 0.10000 0.10000

150.00 250.00 296.57

1.0000 1.0000 1.0000

296.57 350.00 450.00 550.00

1.0000 1.0000 1.0000 1.0000

150.00 250.00 350.00 450.00 550.00

5.0000 5.0000 5.0000 5.0000 5.0000

5.7167 13.284

5.7220 13.290

0.030484 0.070699

0.059102 0.056618

0.091820 0.094177

1239.3 851.94

−0.43876 −0.33819

31.656 32.442 37.325 43.093 49.620

33.517 34.465 40.211 46.822 54.186

0.15786 0.16180 0.18105 0.19762 0.21238

0.042364 0.043860 0.053191 0.061672 0.068475

0.052366 0.053391 0.061845 0.070141 0.076877

160.06 166.39 196.16 221.08 243.30

49.032 38.154 13.439 6.7638 4.0604

0.052952 0.063648 0.072248

5.7053 14.961 19.669

5.7582 15.024 19.741

0.030408 0.077665 0.094938

0.059134 0.057020 0.059612

0.091780 0.096318 0.10807

1241.8 773.25 548.68

2.0425 2.6523 3.6110 4.5027

33.635 36.754 42.774 49.400

35.677 39.407 46.385 53.903

0.14867 0.16025 0.17776 0.19283

0.054305 0.055369 0.062289 0.068737

0.074523 0.068138 0.072300 0.077971

160.70 184.85 216.22 241.16

25.205 14.183 6.8582 4.0624

18.931 15.837 11.141 1.6422 1.1832

0.052823 0.063142 0.089759 0.60893 0.84520

5.6555 14.822 25.585 41.131 48.377

5.9197 15.138 26.034 44.175 52.603

0.030074 0.077105 0.11341 0.16067 0.17760

0.059277 0.057135 0.064765 0.065284 0.069855

0.091614 0.095206 0.14356 0.087278 0.083655

1253.0 797.37 317.33 194.56 232.93

−0.44109 −0.30700 1.0314 7.0507 3.9600

18.874 16.306 0.053734 0.049441 0.034652 0.026819 0.021901 18.885 15.711 13.841 0.48960 0.37703 0.27693 0.22209

0.052982 0.061325 18.610 20.226 28.859 37.287 45.660

−0.43921 −0.28642 0.00029448

150.00 250.00 350.00 450.00 550.00

10.000 10.000 10.000 10.000 10.000

18.987 15.982 12.008 4.2433 2.5432

0.052667 0.062569 0.083275 0.23566 0.39321

5.5953 14.663 24.782 38.423 47.019

6.1220 15.289 25.615 40.780 50.951

0.029665 0.076450 0.11098 0.14893 0.16944

0.059460 0.057274 0.063647 0.068870 0.071068

0.091420 0.094054 0.11843 0.12461 0.092204

1266.7 825.41 412.24 184.82 229.21

−0.44331 −0.32844 0.39255 5.5220 3.5059

150.00 250.00 350.00 450.00 550.00

30.000 30.000 30.000 30.000 30.000

19.198 16.469 13.518 10.241 7.3810

0.052089 0.060719 0.073976 0.097648 0.13548

5.3741 14.132 23.279 33.086 42.738

6.9367 15.953 25.499 36.016 46.802

0.028113 0.074181 0.10621 0.13259 0.15425

0.060251 0.057799 0.063170 0.069234 0.073417

0.090769 0.091018 0.10053 0.10864 0.10533

1318.0 921.00 603.47 392.35 317.51

−0.45090 −0.38542 −0.13764 0.40072 0.89994

150.00 250.00 350.00 450.00 550.00

60.000 60.000 60.000 60.000 60.000

19.480 17.029 14.650 12.381 10.405

0.051336 0.058724 0.068258 0.080770 0.096108

5.0916 13.533 22.111 31.083 40.152

8.1717 17.056 26.206 35.929 45.919

0.026007 0.071434 0.10216 0.12657 0.14662

0.061560 0.058519 0.063912 0.070220 0.075020

0.089983 0.088686 0.094730 0.099099 0.10030

1384.9 1034.6 764.59 589.21 492.11

−0.45992 −0.42947 −0.31532 −0.17799 −0.055349

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Kamei, A., Beyerlein, S. W., and Jacobsen, R. T., “Application of Nonlinear Regression in the Development of a Wide Range Formulation for HCFC-22,” Int. J. Thermophys. 16:1155–1164, 1995. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties of the equation of state are 0.1% in density, 1% in heat capacity, and 0.3% in the speed of sound, except in the critical region. The uncertainty in vapor pressure is 0.2%.

2-229

2-230 FIG. 2-11 Pressure-enthalpy diagram for Refrigerant 22. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of Kamei, A., S. W. Beyerlein, and R. T. Jacobsen, “Application of Nonlinear Regression in the Development of a Wide Range Formulation for HCFC-22,” Int. J. Thermophysics 16:1155–1164, 1995.

TABLE 2-125

Thermodynamic Properties of R-32, Difluoromethane

Temperature K

Pressure MPa

136.34 140.00 150.00 160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 351.26

4.8000E-05 8.3535E-05 0.00032474 0.0010410 0.0028536 0.0068782 0.014904 0.029545 0.054344 0.093819 0.15345 0.23965 0.35967 0.52157 0.73415 1.0069 1.3501 1.7749 2.2934 2.9194 3.6686 4.5614 5.6311 5.7826

136.34 140.00 150.00 160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 351.26

4.8000E-05 8.3535E-05 0.00032474 0.0010410 0.0028536 0.0068782 0.014904 0.029545 0.054344 0.093819 0.15345 0.23965 0.35967 0.52157 0.73415 1.0069 1.3501 1.7749 2.2934 2.9194 3.6686 4.5614 5.6311 5.7826

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

−0.99220 −0.68946 0.13324 0.95053 1.7640 2.5753 3.3862 4.1983 5.0135 5.8337 6.6608 7.4969 8.3443 9.2056 10.084 10.983 11.908 12.866 13.867 14.930 16.088 17.428 19.453 20.836

−0.99220 −0.68946 0.13325 0.95057 1.7641 2.5756 3.3868 4.1995 5.0158 5.8377 6.6675 7.5077 8.3609 9.2303 10.120 11.034 11.979 12.963 13.998 15.107 16.328 17.760 19.977 21.546

21.981 22.076 22.335 22.593 22.850 23.103 23.350 23.588 23.816 24.032 24.234 24.421 24.590 24.738 24.860 24.952 25.006 25.011 24.950 24.797 24.503 23.943 22.380 20.836

23.115 23.239 23.581 23.921 24.258 24.589 24.910 25.219 25.513 25.788 26.042 26.272 26.474 26.643 26.775 26.862 26.894 26.858 26.735 26.491 26.068 25.316 23.365 21.546

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

−0.0054608 −0.0032696 0.0024067 0.0076815 0.012613 0.017251 0.021635 0.025800 0.029778 0.033594 0.037271 0.040830 0.044291 0.047671 0.050989 0.054264 0.057517 0.060775 0.064076 0.067477 0.071088 0.075179 0.081343 0.085769

0.055447 0.054980 0.053793 0.052740 0.051818 0.051021 0.050345 0.049783 0.049333 0.048988 0.048747 0.048604 0.048559 0.048610 0.048761 0.049019 0.049399 0.049934 0.050685 0.051776 0.053487 0.056594 0.066340

0.082847 0.082588 0.081975 0.081513 0.081215 0.081087 0.081137 0.081373 0.081803 0.082443 0.083313 0.084442 0.085874 0.087676 0.089947 0.092852 0.096659 0.10185 0.10938 0.12140 0.14404 0.20457 1.2085

1414.4 1395.1 1342.3 1289.9 1237.6 1185.7 1133.8 1082.1 1030.4 978.59 926.62 874.35 821.65 768.33 714.18 658.88 602.05 543.11 481.27 415.41 343.84 263.77 163.70 0

−0.33760 −0.33728 −0.33542 −0.33191 −0.32650 −0.31891 −0.30886 −0.29600 −0.27988 −0.25996 −0.23550 −0.20551 −0.16864 −0.12292 −0.065518 0.0079177 0.10428 0.23517 0.42163 0.70602 1.1876 2.1660 5.4955 8.0731

242.91 241.74 237.64 232.45 226.39 219.64 212.37 204.70 196.75 188.62 180.39 172.14 163.92 155.78 147.75 139.86 132.11 124.48 116.94 109.42 101.80 94.166 97.067

0.17135 0.16765 0.15872 0.15125 0.14493 0.13955 0.13492 0.13090 0.12738 0.12428 0.12151 0.11901 0.11674 0.11464 0.11268 0.11079 0.10895 0.10709 0.10516 0.10305 0.10060 0.097403 0.091024 0.085769

0.025987 0.026110 0.026507 0.027014 0.027667 0.028505 0.029560 0.030843 0.032341 0.034016 0.035821 0.037709 0.039648 0.041621 0.043631 0.045693 0.047840 0.050119 0.052598 0.055390 0.058707 0.063103 0.071998

0.034319 0.034451 0.034889 0.035477 0.036272 0.037336 0.038728 0.040483 0.042613 0.045105 0.047943 0.051127 0.054696 0.058741 0.063434 0.069063 0.076110 0.085424 0.098649 0.11948 0.15836 0.26199 1.9028

169.60 171.76 177.47 182.88 187.97 192.69 197.00 200.85 204.20 206.99 209.19 210.73 211.57 211.65 210.90 209.26 206.64 202.95 198.02 191.66 183.49 172.68 154.59 0

Entropy kJ/(mol⋅K)

Saturated Properties 27.473 27.302 26.835 26.364 25.889 25.409 24.921 24.424 23.916 23.394 22.858 22.303 21.726 21.124 20.491 19.820 19.102 18.323 17.460 16.477 15.299 13.740 10.732 8.1501 4.2353E-05 7.1788E-05 0.00026061 0.00078411 0.0020270 0.0046295 0.0095503 0.018112 0.032028 0.053428 0.084890 0.12949 0.19093 0.27370 0.38340 0.52726 0.71503 0.96054 1.2848 1.7233 2.3442 3.3211 5.7166 8.1501

0.036399 0.036627 0.037265 0.037930 0.038626 0.039357 0.040127 0.040944 0.041814 0.042745 0.043749 0.044838 0.046028 0.047340 0.048802 0.050454 0.052350 0.054577 0.057273 0.060691 0.065364 0.072779 0.093180 0.12270 23,611. 13,930. 3,837.2 1,275.3 493.35 216.01 104.71 55.213 31.223 18.717 11.780 7.7224 5.2375 3.6537 2.6083 1.8966 1.3985 1.0411 0.77830 0.58029 0.42658 0.30111 0.17493 0.12270

881.12 769.01 541.12 391.73 291.02 221.02 170.81 133.79 106.00 84.924 68.870 56.605 47.194 39.922 34.246 29.758 26.148 23.187 20.693 18.510 16.477 14.312 10.637 8.0731

6.9492 6.9554 7.0006 7.0875 7.2166 7.3887 7.6049 7.8668 8.1765 8.5374 8.9546 9.4365 9.9965 10.656 11.449 12.431 13.691 15.376 17.748 21.309 27.173 38.601 87.141 (Continued)

2-231

2-232 TABLE 2-125 Temperature K

Thermodynamic Properties of R-32, Difluoromethane (Continued ) Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Single-Phase Properties 0.037263 0.042866

0.13226 5.9359

0.13599 5.9402

0.0024002 0.034057

0.053795 0.048953

0.081971 0.082538

1342.7 972.15

−0.33547 −0.25719

237.67 187.60

0.056727 0.055592 0.040576 0.032244 26.851 23.159 19.836

17.628 17.988 24.645 31.013 0.037243 0.043179 0.050414

24.058 24.191 26.760 29.631 0.12350 6.2265 10.962

25.821 25.989 29.224 32.733 0.16075 6.2697 11.013

0.12392 0.12467 0.13708 0.14749 0.0023417 0.035360 0.054190

0.034234 0.033681 0.035327 0.041082 0.053807 0.048867 0.049012

0.045439 0.044513 0.044188 0.049630 0.081935 0.082690 0.092777

207.30 209.39 241.95 267.64 1345.7 957.47 660.15

82.688 76.114 25.024 12.117 −0.33584 −0.25084 0.0060372

8.5859 8.7199 12.643 18.907 237.89 185.10 140.04

0.52357 0.46100 0.33917

1.9100 2.1692 2.9484

24.951 25.950 29.227

26.861 28.120 32.175

0.11084 0.11518 0.12727

0.045646 0.041298 0.042549

0.068922 0.057916 0.053538

209.31 223.83 259.50

0.037154 0.042923 0.053448 0.078078

0.085198 6.1394 12.637 18.130

0.27097 6.3541 12.905 18.520

0.0020846 0.034970 0.060001 0.077304

0.053863 0.048922 0.049679 0.059015

0.081784 0.082027 0.096911 0.28240

1358.9 978.81 586.17 224.84

0.25071 0.43051

23.524 26.928

24.777 29.080

0.095475 0.10755

0.065786 0.050835

0.39574 0.090625

166.61 218.44

150.00 221.24

0.10000 0.10000

26.836 23.329

221.24 225.00 300.00 375.00 150.00 225.00 279.77

0.10000 0.10000 0.10000 0.10000 1.0000 1.0000 1.0000

279.77 300.00 375.00

1.0000 1.0000 1.0000

150.00 225.00 300.00 344.33

5.0000 5.0000 5.0000 5.0000

344.33 375.00

5.0000 5.0000

26.915 23.298 18.710 12.808 3.9887 2.3228

29.848 23.889 11.929 −0.33741 −0.26135 0.13431 2.9944 13.148 10.800

12.406 13.334 19.059 238.83 187.71 128.72 91.412 48.235 26.239

150.00 225.00 300.00 375.00

10.000 10.000 10.000 10.000

26.993 23.461 19.196 10.448

0.037047 0.042625 0.052094 0.095714

0.038702 6.0369 12.346 21.112

0.40917 6.4632 12.867 22.069

0.0017692 0.034504 0.058997 0.085980

0.053932 0.048996 0.049538 0.057265

0.081608 0.081303 0.092105 0.21222

1375.0 1004.1 639.69 231.14

−0.33924 −0.27287 0.031716 3.5190

239.97 190.81 134.49 77.284

150.00 225.00 300.00 375.00

30.000 30.000 30.000 30.000

27.285 24.030 20.517 16.472

0.036650 0.041614 0.048739 0.060708

−0.13357 5.6813 11.542 17.786

0.96593 6.9297 13.004 19.607

0.00056834 0.032836 0.056105 0.075712

0.054209 0.049307 0.049670 0.052941

0.081027 0.079197 0.083697 0.093069

1436.1 1094.1 789.57 536.98

−0.34524 −0.30661 −0.15824 0.21392

244.02 201.89 152.78 112.94

225.00 300.00 375.00

70.000 70.000 70.000

24.916 22.090 19.309

0.040135 0.045270 0.051788

5.1400 10.583 16.127

7.9495 13.752 19.752

0.030109 0.052355 0.070195

0.049916 0.050281 0.053544

0.076915 0.078370 0.081767

1240.7 986.17 788.81

−0.34341 −0.28333 −0.18583

219.54 179.29 147.00

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Tillner-Roth, R., and Yokozeki, A., “An International Standard Equation of State for Difluoromethane (R-32) for Temperatures from the Triple Point at 136.34 K to 435 K and Pressures up to 70 MPa,” J. Phys. Chem. Ref. Data 26(6):1273–1328, 1997. Validated equations for the viscosity are not currently available for this fluid. The source for thermal conductivity is unpublished; however, the fit uses the functional form found in Marsh, K., Perkins, R., and Ramires, M. L. V., “Measurement and Correlation of the Thermal Conductivity of Propane from 86 to 600 K at Pressures to 70 MPa,” J. Chem. Eng. Data 47(4):932–940, 2002. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. For the equation of state, typical uncertainties are 0.05% for density, 0.02% for the vapor pressure, and 0.5% to 1% for the heat capacity and speed of sound in the liquid phase. In the vapor phase, the uncertainty in the speed of sound is 0.02%. For thermal conductivity, the estimated uncertainty of the correlation is 5%, except for the dilute gas and points approaching critical where the uncertainty rises to 10%.

FIG. 2-12 Pressure-enthalpy diagram for Refrigerant 32. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of Tillner-Roth, R., and A. Yokozeki, “An International Standard Equation of State for Difluoromethane (R-32) for Temperatures from the Triple Point at 136.34 K to 435 K and Pressures up to 70 MPa,” J. Phys. Chem. Ref. Data 26(6): 1273–1328, 1997.

2-233

2-234 TABLE 2-126 Thermodynamic Properties of R-125, Pentafluoroethane Temperature K

Pressure MPa

172.52 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 339.17

0.0029140 0.0056285 0.012328 0.024602 0.045417 0.078505 0.12833 0.20004 0.29934 0.43250 0.60624 0.82782 1.1050 1.4463 1.8610 2.3600 2.9579 3.6179

172.52 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 339.17

0.0029140 0.0056285 0.012328 0.024602 0.045417 0.078505 0.12833 0.20004 0.29934 0.43250 0.60624 0.82782 1.1050 1.4463 1.8610 2.3600 2.9579 3.6179

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

10.457 11.389 12.646 13.919 15.210 16.523 17.858 19.219 20.607 22.025 23.478 24.971 26.511 28.112 29.793 31.595 33.632 37.417

10.457 11.389 12.647 13.921 15.214 16.529 17.869 19.235 20.632 22.063 23.532 25.048 26.619 28.259 29.994 31.869 34.017 38.174

0.058837 0.064124 0.070919 0.077448 0.083750 0.089856 0.095792 0.10158 0.10725 0.11282 0.11830 0.12374 0.12916 0.13461 0.14015 0.14593 0.15231 0.16438

0.081329 0.082012 0.083102 0.084327 0.085644 0.087029 0.088472 0.089971 0.091529 0.093153 0.094843 0.096594 0.098430 0.10043 0.10274 0.10571 0.11043

0.12417 0.12500 0.12647 0.12825 0.13028 0.13254 0.13505 0.13785 0.14102 0.14468 0.14903 0.15440 0.16135 0.17099 0.18593 0.21395 0.29625

932.57 893.63 843.11 793.91 745.67 698.07 650.89 603.92 556.99 510.02 462.91 415.46 367.36 318.17 267.31 213.55 153.34 0

−0.38374 −0.37406 −0.35818 −0.33901 −0.31627 −0.28935 −0.25723 −0.21839 −0.17062 −0.11056 −0.032921 0.070972 0.21606 0.43036 0.77370 1.4029 2.9184 12.361

31.863 32.307 32.913 33.530 34.157 34.788 35.421 36.052 36.678 37.292 37.890 38.460 38.988 39.453 39.828 40.054 39.964 37.417

33.293 33.795 34.477 35.167 35.860 36.552 37.237 37.911 38.568 39.202 39.805 40.363 40.858 41.267 41.554 41.651 41.355 38.174

0.19120 0.18860 0.18582 0.18368 0.18207 0.18087 0.18000 0.17940 0.17900 0.17874 0.17857 0.17844 0.17826 0.17797 0.17744 0.17649 0.17454 0.16438

0.059815 0.061648 0.064126 0.066646 0.069223 0.071864 0.074575 0.077362 0.080230 0.083141 0.086003 0.088869 0.092050 0.095933 0.10077 0.10679 0.11481

0.068285 0.070217 0.072893 0.075712 0.078713 0.081939 0.085437 0.089271 0.093526 0.098283 0.10368 0.11025 0.11918 0.13255 0.15449 0.19725 0.32843

116.43 118.54 121.15 123.47 125.44 127.01 128.11 128.68 128.64 127.93 126.44 124.10 120.81 116.42 110.71 103.29 93.550 0

90.257 77.516 64.018 53.589 45.456 39.066 34.014 29.998 26.787 24.232 22.293 20.938 20.043 19.438 19.016 18.738 18.404 12.361

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

116.02 112.52 107.79 103.06 98.331 93.653 89.019 84.443 79.940 75.520 71.187 66.940 62.772 58.667 54.597 50.534 46.661

1152.4 957.54 768.40 631.00 527.00 445.76 380.67 327.41 283.01 245.39 213.02 184.73 159.60 136.86 115.81 95.602 74.602

Saturated Properties 14.086 13.885 13.613 13.336 13.052 12.762 12.461 12.150 11.824 11.481 11.117 10.724 10.295 9.8162 9.2637 8.5923 7.6744 4.7790 0.0020381 0.0037809 0.0078784 0.015031 0.026661 0.044514 0.070679 0.10763 0.15835 0.22645 0.31661 0.43510 0.59084 0.79742 1.0777 1.4778 2.1269 4.7790

0.070990 0.072020 0.073461 0.074988 0.076615 0.078360 0.080247 0.082305 0.084572 0.087098 0.089954 0.093245 0.097130 0.10187 0.10795 0.11638 0.13030 0.20925 490.65 264.49 126.93 66.529 37.508 22.465 14.148 9.2907 6.3153 4.4159 3.1585 2.2983 1.6925 1.2540 0.92787 0.67670 0.47016 0.20925

5.2349 5.7185 6.3724 7.0353 7.7081 8.3929 9.0929 9.8136 10.563 11.356 12.213 13.169 14.286 15.680 17.586 20.574 26.607

7.4339 7.7624 8.1999 8.6344 9.0657 9.4944 9.9221 10.353 10.791 11.246 11.732 12.266 12.884 13.638 14.635 16.104 18.766

Single-Phase Properties 200.00 224.79

0.10000 0.10000

224.79 300.00 400.00 500.00

0.10000 0.10000 0.10000 0.10000

200.00 286.46

1.0000 1.0000

286.46 300.00 400.00 500.00

1.0000 1.0000 1.0000 1.0000

200.00 300.00 400.00 500.00

5.0000 5.0000 5.0000 5.0000

13.916 17.160

13.924 17.168

0.077436 0.092721

0.084327 0.087714

0.12823 0.13371

794.34 675.42

−0.33920 −0.27468

35.092 41.155 50.746 61.864

36.881 43.613 54.054 66.012

0.18042 0.20616 0.23608 0.26271

0.073155 0.086960 0.10398 0.11764

0.083578 0.095910 0.11252 0.12607

127.60 149.16 172.25 192.24

36.498 13.603 5.6807 3.1093

0.074878 0.095673

13.888 25.960

13.963 26.055

0.077295 0.12724

0.084329 0.097767

0.12805 0.15865

799.42 384.49

−0.34145 0.15862

103.50 64.240

1.8842 2.0720 3.1466 4.0661

38.807 40.159 50.310 61.591

40.691 42.231 53.456 65.657

0.17833 0.18359 0.21585 0.24302

0.090862 0.092286 0.10520 0.11806

0.11564 0.11224 0.11626 0.12764

122.09 129.90 165.47 189.33

20.318 16.539 5.9354 3.1109

13.866 14.732 22.513 31.336

12.653 13.270 17.404 21.014

13.432 10.214 2.1222 1.3333

0.074450 0.097901 0.47120 0.75004

13.768 27.606 47.739 60.288

14.140 28.095 50.095 64.038

0.076686 0.13288 0.19593 0.22710

0.084364 0.099404 0.11164 0.12001

0.12732 0.15790 0.15240 0.13643

820.94 379.39 136.55 180.53

−0.35061 0.16755 6.6581 2.9952

105.29 62.727 27.340 33.551

671.00 155.81 22.244 23.530

13.337 12.619 0.055877 0.040689 0.030228 0.024108 13.355 10.452 0.53072 0.48261 0.31780 0.24593

0.074979 0.079245 17.897 24.576 33.082 41.479

103.09 91.425 8.7263 14.156 22.115 30.917

631.60 412.85 9.6994 13.041 17.070 20.691 638.78 168.19

200.00 300.00 400.00 500.00

10.000 10.000 10.000 10.000

13.522 10.597 5.5436 2.8438

0.073953 0.094369 0.18039 0.35165

13.626 27.096 43.724 58.555

14.366 28.039 45.528 62.072

0.075959 0.13109 0.18103 0.21813

0.084459 0.098728 0.11417 0.12198

0.12655 0.14971 0.19389 0.14925

845.71 441.85 165.42 183.47

−0.36040 −0.0032571 2.8474 2.4316

107.42 67.164 40.583 37.529

712.07 177.37 46.568 29.745

200.00 300.00 400.00 500.00

30.000 30.000 30.000 30.000

13.835 11.489 9.0272 6.8239

0.072281 0.087039 0.11078 0.14654

13.138 25.838 39.705 54.141

15.306 28.449 43.028 58.538

0.073355 0.12645 0.16830 0.20288

0.085197 0.098551 0.11217 0.12339

0.12439 0.13883 0.15193 0.15662

927.73 597.35 391.05 307.14

−0.38765 −0.23171 0.060756 0.34144

115.19 79.855 59.824 53.649

889.29 245.90 112.78 67.694

300.00 400.00 500.00

60.000 60.000 60.000

12.259 10.465 8.9121

0.081575 0.095559 0.11221

24.732 37.854 51.703

29.626 43.587 58.436

0.12196 0.16206 0.19516

0.10001 0.11339 0.12470

0.13426 0.14453 0.15193

735.32 563.68 471.23

−0.32748 −0.23451 −0.15582

93.938 75.022 67.810

338.04 173.26 113.08

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., and Jacobsen, R. T., “A New Functional Form and New Fitting Techniques for Equations of State with Application to Pentafluoroethane (HFC-125),” J. Phys. Chem. Ref. Data 34(1):69–108, 2005. The source for viscosity is Huber, M. L., and Laesecke, A., “Correlation for the Viscosity of Pentafluoroethane (R125) from the Triple Point to 500 K at Pressures up to 60 MPa,” Ind. Eng. Chem. Res., 45(12):4447–4453, 2006. The source for thermal conductivity is Perkins, R., and Huber, M. L., “Measurement and Correlation of the Thermal Conductivity of Pentafluoroethane (R125) from 190 K to 512 K at Pressures to 70 MPa,” J. Chem. Eng. Data 51(3):898–904, 2006. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainty in density is 0.1% at temperatures from the triple point to 400 K at pressures up to 60 MPa, except in the critical region, where an uncertainty of 0.2% in pressure is generally attained. In the limited region between 340 and 400 K and at pressures from 4 to 10 MPa, as well as for all states above 400 K, the uncertainty in density increases to 0.5%. At temperatures below 330 K and pressures below 30 MPa, the uncertainty in density in the liquid phase may be as low as 0.04%. In the vapor and supercritical region, speed of sound data are represented within 0.05% at pressures below 1 MPa. The estimated uncertainty for heat capacities is 0.5%, and the estimated uncertainty for the speed of sound in the liquid phase is 0.5% for T > 250 K. The estimated uncertainties of vapor pressures and saturated liquid densities calculated using the Maxwell criterion are 0.1% for each property, and the estimated uncertainty for saturated vapor densities is 0.2%. The uncertainty in density increases as the critical point is approached, while the accompanying uncertainty in calculated pressures is 0.2%. The viscosity correlation has an estimated uncertainty of 3.0% along the saturation boundary in the liquid phase, and 0.8% in the vapor. For thermal conductivity, the estimated uncertainty of the correlation is 3%, except for the dilute gas and points approaching critical, where the uncertainty rises to 5%.

2-235

2-236 FIG. 2-13

Pressure-enthalpy diagram for Refrigerant 125.

TABLE 2-127

Thermodynamic Properties of R-134a, 1,1,1,2-Tetrafluoroethane

Temperature K

Pressure MPa

169.85 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 374.21

0.00038956 0.00039617 0.0011275 0.0028170 0.0063130 0.012910 0.024433 0.043287 0.072481 0.11561 0.17684 0.26082 0.37271 0.51805 0.70282 0.93340 1.2166 1.5599 1.9715 2.4611 3.0405 3.7278 4.0591

169.85 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 374.21

0.00038956 0.00039617 0.0011275 0.0028170 0.0063130 0.012910 0.024433 0.043287 0.072481 0.11561 0.17684 0.26082 0.37271 0.51805 0.70282 0.93340 1.2166 1.5599 1.9715 2.4611 3.0405 3.7278 4.0591

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

7.2907 7.3088 8.5179 9.7328 10.957 12.194 13.444 14.710 15.992 17.293 18.613 19.956 21.322 22.716 24.141 25.603 27.108 28.667 30.297 32.029 33.932 36.283 38.947

7.2907 7.3088 8.5179 9.7330 10.958 12.195 13.446 14.713 15.997 17.301 18.627 19.976 21.352 22.759 24.201 25.685 27.219 28.816 30.495 32.293 34.289 36.797 39.756

0.042100 0.042207 0.049117 0.055686 0.061966 0.067999 0.073815 0.079441 0.084899 0.090209 0.095389 0.10046 0.10543 0.11032 0.11516 0.11996 0.12475 0.12956 0.13446 0.13952 0.14496 0.15159 0.15938

0.080831 0.080824 0.080732 0.081114 0.081784 0.082633 0.083595 0.084636 0.085734 0.086879 0.088067 0.089298 0.090576 0.091908 0.093303 0.094777 0.096352 0.098067 0.10001 0.10241 0.10601 0.11372

0.12079 0.12079 0.12112 0.12193 0.12303 0.12434 0.12582 0.12746 0.12927 0.13126 0.13348 0.13597 0.13883 0.14216 0.14615 0.15108 0.15740 0.16598 0.17863 0.20012 0.24863 0.52085

32.764 32.772 33.287 33.821 34.371 34.934 35.508 36.090 36.675 37.261 37.844 38.420 38.986 39.538 40.069 40.573 41.038 41.451 41.785 41.994 41.973 41.323 38.947

34.175 34.184 34.781 35.395 36.023 36.662 37.308 37.956 38.602 39.242 39.870 40.482 41.073 41.636 42.166 42.653 43.083 43.438 43.687 43.775 43.576 42.617 39.756

0.20038 0.20029 0.19502 0.19075 0.18729 0.18451 0.18228 0.18050 0.17909 0.17797 0.17709 0.17640 0.17586 0.17542 0.17504 0.17469 0.17432 0.17387 0.17326 0.17232 0.17075 0.16731 0.15938

0.051318 0.051354 0.053742 0.056118 0.058489 0.060874 0.063296 0.065783 0.068357 0.071031 0.073812 0.076698 0.079686 0.082776 0.085974 0.089297 0.092780 0.096484 0.10052 0.10510 0.11074 0.11928

0.059719 0.059756 0.062208 0.064682 0.067201 0.069802 0.072534 0.075455 0.078618 0.082078 0.085888 0.090115 0.094850 0.10023 0.10650 0.11404 0.12355 0.13638 0.15548 0.18870 0.26594 0.70016

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

1120.0 1119.2 1068.3 1017.7 967.61 918.33 869.85 822.11 775.00 728.39 682.14 636.12 590.17 544.15 497.89 451.23 404.00 355.90 306.37 254.06 196.05 127.23 0

−0.38145 −0.38136 −0.37370 −0.36352 −0.35119 −0.33678 −0.32011 −0.30082 −0.27839 −0.25204 −0.22073 −0.18299 −0.13675 −0.079015 −0.0052732 0.091533 0.22306 0.41006 0.69376 1.1714 2.1419 5.1434 11.931

145.24 145.15 139.12 133.32 127.74 122.36 117.17 112.14 107.27 102.53 97.922 93.414 88.995 84.644 80.341 76.063 71.781 67.464 63.075 58.581 54.062 51.767

2153.6 2139.7 1479.1 1106.2 867.31 702.27 582.15 491.22 420.20 363.25 316.57 277.54 244.34 215.64 190.46 168.04 147.78 129.20 111.81 95.095 78.146 57.956

Saturated Properties 15.594 15.590 15.331 15.069 14.804 14.535 14.262 13.984 13.699 13.406 13.104 12.791 12.465 12.121 11.758 11.368 10.945 10.478 9.9483 9.3237 8.5279 7.2558 5.0171 0.00027611 0.00028055 0.00075481 0.0017896 0.0038201 0.0074704 0.013574 0.023188 0.037603 0.058360 0.087278 0.12651 0.17865 0.24685 0.33512 0.44874 0.59505 0.78498 1.0363 1.3818 1.8973 2.8805 5.0171

0.064126 0.064142 0.065228 0.066362 0.067550 0.068798 0.070116 0.071512 0.072999 0.074593 0.076311 0.078179 0.080227 0.082499 0.085050 0.087965 0.091364 0.095439 0.10052 0.10725 0.11726 0.13782 0.19932 3621.7 3564.4 1324.8 558.79 261.77 133.86 73.669 43.125 26.593 17.135 11.458 7.9043 5.5976 4.0511 2.9840 2.2285 1.6805 1.2739 0.96498 0.72368 0.52707 0.34717 0.19932

126.79 126.84 130.05 133.11 135.98 138.63 141.01 143.06 144.73 145.98 146.75 146.99 146.63 145.61 143.88 141.33 137.86 133.33 127.57 120.33 111.25 99.370 0

373.57 370.78 234.43 160.10 116.94 90.215 72.584 60.236 51.130 44.137 38.613 34.169 30.561 27.621 25.230 23.301 21.768 20.578 19.687 19.033 18.448 17.050 11.931

3.0801 3.0921 3.8934 4.6952 5.4978 6.3018 7.1080 7.9176 8.7324 9.5551 10.389 11.241 12.118 13.035 14.011 15.081 16.303 17.780 19.711 22.525 27.365 40.137

6.8294 6.8353 7.2319 7.6253 8.0147 8.3993 8.7786 9.1524 9.5209 9.8853 10.247 10.611 10.980 11.363 11.771 12.219 12.735 13.358 14.164 15.300 17.140 21.336 (Continued)

2-237

2-238 TABLE 2-127 Temperature K

Thermodynamic Properties of R-134a, 1,1,1,2-Tetrafluoroethane (Continued ) Pressure MPa

Density mol/dm3

Volume dm3/mol

Entropy kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity mPa⋅s

Int. energy kJ/mol

Enthalpy kJ/mol

10.955 16.873

10.962 16.880

0.061955 0.088519

0.081787 0.086506

0.12301 0.13060

968.03 743.31

−0.35132 −0.26099

37.073 39.124 45.154 52.096

39.037 41.348 48.032 55.610

0.17830 0.18716 0.20860 0.22818

0.070161 0.073781 0.086248 0.098386

0.080931 0.083445 0.095065 0.10695

145.63 154.76 175.31 192.97

46.198 29.047 12.552 6.7852

0.067479 0.079009 0.088775

10.933 20.597 25.980

11.001 20.676 26.069

0.061846 0.10281 0.12117

0.081812 0.089915 0.095165

0.12291 0.13695 0.15252

972.08 619.10 439.31

−0.35256 −0.16746 0.12101

128.11 91.627 74.978

2.0729 2.5555 3.3352

40.695 44.290 51.597

42.768 46.846 54.933

0.17460 0.18694 0.20785

0.090164 0.090315 0.099891

0.11623 0.10603 0.11116

140.54 159.63 185.14

22.877 13.885 7.0297

15.374 17.989 23.806

12.343 13.936 16.917

14.880 12.804 9.8674 2.0736

0.067202 0.078103 0.10134 0.48225

10.839 20.385 31.397 48.647

11.175 20.776 31.904 51.058

0.061371 0.10203 0.13765 0.18734

0.081929 0.089864 0.10066 0.10791

0.12246 0.13495 0.17178 0.15381

989.55 651.41 320.01 148.25

−0.35768 −0.19924 0.59952 7.9048

129.56 94.015 63.012 28.574

915.11 277.35 109.32 20.974 966.05 295.02 128.79 46.711

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Single-Phase Properties 200.00 246.79

0.10000 0.10000

246.79 275.00 350.00 425.00

0.10000 0.10000 0.10000 0.10000

200.00 275.00 312.54

1.0000 1.0000 1.0000

312.54 350.00 425.00

1.0000 1.0000 1.0000

200.00 275.00 350.00 425.00

5.0000 5.0000 5.0000 5.0000

14.805 13.501 0.050898 0.044972 0.034753 0.028455 14.819 12.657 11.264 0.48242 0.39132 0.29983

0.067543 0.074068 19.647 22.236 28.775 35.143

127.78 104.04 9.2899 11.540 17.537 23.539

868.18 380.27 9.7687 10.906 13.823 16.650 876.60 262.84 162.71

200.00 275.00 350.00 425.00

10.000 10.000 10.000 10.000

14.954 12.967 10.478 6.1370

0.066874 0.077121 0.095440 0.16295

10.727 20.149 30.642 43.563

11.395 20.920 31.597 45.193

0.060796 0.10115 0.13537 0.17038

0.082085 0.089868 0.099573 0.11141

0.12196 0.13304 0.15486 0.20870

1010.3 687.36 400.60 177.89

−0.36339 −0.22964 0.21924 3.0434

131.31 96.744 68.919 44.888

200.00 275.00 350.00 425.00

30.000 30.000 30.000 30.000

15.216 13.479 11.662 9.7202

0.065720 0.074190 0.085750 0.10288

10.326 19.398 29.071 39.385

12.298 21.624 31.644 42.471

0.058683 0.098210 0.13038 0.15838

0.082769 0.090220 0.098885 0.10808

0.12047 0.12865 0.13885 0.14967

1084.1 801.47 582.52 425.63

−0.38053 −0.30014 −0.15240 0.10364

137.79 105.87 82.955 67.154

1211.0 364.87 183.26 107.03

275.00 350.00 425.00

70.000 70.000 70.000

14.181 12.797 11.494

0.070517 0.078141 0.087004

18.373 27.492 37.066

23.310 32.961 43.157

0.093839 0.12484 0.15121

0.091314 0.099542 0.10829

0.12519 0.13226 0.13963

962.41 787.10 661.39

−0.35619 −0.30093 −0.23655

119.84 99.868 86.640

521.91 277.09 181.77

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Tillner-Roth, R., and Baehr, H. D., “An International Standard Formulation of the Thermodynamic Properties of 1,1,1,2-Tetrafluoroethane (HFC-134a) for Temperatures from 170 K to 455 K at Pressures up to 70 MPa,” J. Phys. Chem. Ref. Data 23:657–729, 1994. The source for viscosity is Huber, M. L., Laesecke, A., and Perkins, R. A., “Model for the Viscosity and Thermal Conductivity of Refrigerants, Including a New Correlation for the Viscosity of R134a,” Ind. Eng. Chem. Res. 42:3163–3178, 2003. The source for thermal conductivity is Perkins, R. A., Laesecke, A., Howley, J., Ramires, M. L. V., Gurova, A. N., and Cusco, L., “Experimental Thermal Conductivity Values for the IUPAC Round-Robin Sample of 1,1,1,2-Tetrafluoroethane (R134a),” NISTIR, 2000. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. Typical uncertainties are 0.05% for density, 0.02% for vapor pressure, 0.5% to 1% for heat capacity, 0.05% for vapor speed of sound, and 1% for liquid speed of sound, except in the critical region. The uncertainty in viscosity is 1.5% along the saturated-liquid line, 3% in the liquid phase, 0.5% in the dilute gas, 3% to 5% in the vapor phase, and 5% in the supercritical region, rising to 8% at pressures above 40 MPa. Below 200 K, the uncertainty is 8%. The uncertainty in thermal conductivity is 5%.

FIG. 2-14 Pressure-enthalpy diagram for Refrigerant 134a. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of Tillner-Roth, R., and H. D. Baehr, “An International Standard Formulation of the Thermodynamic Properties of 1,1,1,2-Tetrafluoroethane (HFC-134a) Covering Temperatures from 170 K to 455 K at Pressures up to 70 MPa,” J. Phys. Chem. Ref. Data 23(5): 657–729, 1994.

2-239

2-240 TABLE 2-128 Temperature K

Thermodynamic Properties of R-143a, 1,1,1-Trifluoroethane Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

−0.43936 −0.42914 −0.41402 −0.39585 −0.37472 −0.35034 −0.32211 −0.28906 −0.24979 −0.20231 −0.14368 −0.069548 0.026895 0.15683 0.34002 0.61491 1.0681 1.9469 4.3897 12.397

Saturated Properties 161.34 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 345.86

0.0010749 0.0025084 0.0059324 0.012629 0.024624 0.044602 0.075908 0.12252 0.18902 0.28049 0.40251 0.56112 0.76276 1.0144 1.3234 1.6983 2.1483 2.6850 3.3250 3.7618

161.34 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 345.86

0.0010749 0.0025084 0.0059324 0.012629 0.024624 0.044602 0.075908 0.12252 0.18902 0.28049 0.40251 0.56112 0.76276 1.0144 1.3234 1.6983 2.1483 2.6850 3.3250 3.7618

15.832 15.583 15.291 14.994 14.692 14.384 14.069 13.745 13.410 13.062 12.698 12.314 11.904 11.461 10.975 10.426 9.7846 8.9829 7.7913 5.1285 0.00080362 0.0017832 0.0039967 0.0081006 0.015110 0.026311 0.043269 0.067850 0.10227 0.14916 0.21175 0.29409 0.40144 0.54109 0.72367 0.96617 1.2991 1.7898 2.6696 5.1285

0.063163 0.064174 0.065399 0.066693 0.068062 0.069519 0.071077 0.072753 0.074570 0.076556 0.078751 0.081208 0.084004 0.087249 0.091119 0.095914 0.10220 0.11132 0.12835 0.19499 1244.4 560.78 250.20 123.45 66.180 38.007 23.111 14.738 9.7783 6.7041 4.7225 3.4004 2.4910 1.8481 1.3818 1.0350 0.76974 0.55871 0.37458 0.19499

4.4138 5.2969 6.3240 7.3629 8.4164 9.4869 10.576 11.685 12.817 13.973 15.156 16.368 17.615 18.903 20.239 21.638 23.125 24.750 26.688 29.429

4.4138 5.2971 6.3244 7.3637 8.4181 9.4900 10.581 11.694 12.831 13.995 15.188 16.414 17.680 18.991 20.360 21.801 23.344 25.048 27.114 30.163

0.026403 0.031735 0.037606 0.043223 0.048626 0.053849 0.058915 0.063848 0.068665 0.073385 0.078027 0.082607 0.087149 0.091675 0.096221 0.10083 0.10559 0.11065 0.11659 0.12527

0.068393 0.068179 0.068405 0.068990 0.069825 0.070836 0.071969 0.073190 0.074475 0.075809 0.077186 0.078605 0.080078 0.081625 0.083293 0.085172 0.087455 0.090641 0.096654

0.10179 0.10225 0.10325 0.10460 0.10621 0.10803 0.11005 0.11227 0.11474 0.11750 0.12066 0.12435 0.12879 0.13438 0.14180 0.15244 0.16980 0.20591 0.35704

1058.1 1016.7 969.14 921.61 874.04 826.46 778.88 731.28 683.65 635.90 587.94 539.61 490.70 440.95 389.93 337.04 281.21 220.39 149.32 0

25.521 25.895 26.340 26.796 27.262 27.736 28.213 28.693 29.170 29.641 30.102 30.548 30.972 31.366 31.715 32.000 32.183 32.184 31.732 29.429

26.859 27.302 27.824 28.355 28.892 29.431 29.968 30.498 31.018 31.521 32.003 32.456 32.872 33.240 33.544 33.758 33.837 33.684 32.977 30.163

0.16552 0.16118 0.15705 0.15370 0.15100 0.14881 0.14704 0.14560 0.14444 0.14349 0.14270 0.14202 0.14141 0.14081 0.14017 0.13940 0.13838 0.13682 0.13384 0.12527

0.044397 0.046371 0.048691 0.051040 0.053424 0.055867 0.058395 0.061026 0.063766 0.066612 0.069560 0.072606 0.075756 0.079035 0.082489 0.086214 0.090400 0.095488 0.10298

0.052938 0.055037 0.057550 0.060156 0.062886 0.065796 0.068954 0.072428 0.076287 0.080611 0.085515 0.091184 0.097932 0.10632 0.11743 0.13359 0.16076 0.22018 0.47999

137.57 140.62 143.91 146.92 149.60 151.89 153.71 155.02 155.74 155.81 155.15 153.70 151.36 148.04 143.59 137.85 130.56 121.34 109.29 0

385.09 262.77 176.43 124.70 92.835 72.442 58.764 49.133 42.049 36.657 32.456 29.136 26.498 24.406 22.765 21.499 20.526 19.682 18.259 12.397

Single-Phase Properties 200.00 225.63

0.10000 0.10000

225.63 300.00 400.00 500.00 600.00

0.10000 0.10000 0.10000 0.10000 0.10000

200.00 289.48

1.0000 1.0000

289.48 300.00 400.00 500.00 600.00

1.0000 1.0000 1.0000 1.0000 1.0000

200.00 300.00 400.00 500.00 600.00

5.0000 5.0000 5.0000 5.0000 5.0000

8.4143 11.198

8.4211 11.205

0.048616 0.061709

0.069829 0.072648

0.10620 0.11128

874.45 752.07

−0.37493 −0.30416

28.483 33.380 41.260 50.551 61.004

30.268 35.833 44.566 54.698 65.987

0.14619 0.16745 0.19247 0.21503 0.23558

0.059863 0.070758 0.086121 0.099065 0.10950

0.070868 0.079793 0.094695 0.10751 0.11790

154.52 179.93 207.36 231.13 252.55

52.958 18.414 7.5341 4.1010 2.5191

0.067956 0.087067

8.3891 18.835

8.4570 18.922

0.048489 0.091441

0.069866 0.081543

0.10604 0.13406

879.27 443.55

−0.37736 0.14902

1.8765 2.0285 3.1249 4.0544 4.9391

31.346 32.269 40.778 50.244 60.781

33.223 34.298 43.903 54.298 65.720

0.14084 0.14449 0.17212 0.19527 0.21607

0.078861 0.077834 0.087343 0.099519 0.10975

0.10583 0.099455 0.098681 0.10927 0.11891

148.24 155.53 198.53 227.30 251.11

24.503 20.787 7.7199 4.0976 2.4913

14.806 11.380 2.2504 1.3639 1.0491

0.067539 0.087876 0.44436 0.73318 0.95318

8.2811 19.812 38.004 48.802 59.789

8.6188 20.251 40.225 52.468 64.554

0.047943 0.094764 0.15165 0.17903 0.20106

0.070021 0.082741 0.093496 0.10135 0.11075

0.10541 0.13222 0.13815 0.11872 0.12364

900.01 452.11 159.25 213.49 246.86

−0.38724 0.11636 8.1026 3.8903 2.2996

14.694 13.888 0.056043 0.040759 0.030247 0.024114 0.020066 14.715 11.485 0.53292 0.49298 0.32001 0.24665 0.20246

0.068054 0.072006 17.843 24.534 33.061 41.469 49.836

200.00 300.00 400.00 500.00 600.00

10.000 10.000 10.000 10.000 10.000

14.913 11.776 6.3531 3.0122 2.1596

0.067054 0.084916 0.15740 0.33199 0.46305

8.1545 19.382 33.679 46.933 58.580

8.8250 20.231 35.253 50.252 63.211

0.047292 0.093258 0.13608 0.16976 0.19339

0.070195 0.082583 0.095653 0.10303 0.11178

0.10473 0.12585 0.17697 0.13206 0.12945

924.61 514.06 196.98 211.16 248.28

−0.39776 −0.037998 2.9315 3.0876 1.9304

200.00 300.00 400.00 500.00 600.00

50.000 50.000 50.000 50.000 50.000

15.598 13.358 11.268 9.4018 7.8978

0.064113 0.074862 0.088747 0.10636 0.12662

7.3673 17.612 28.859 40.839 53.306

10.573 21.355 33.296 46.157 59.637

0.042937 0.086486 0.12077 0.14943 0.17399

0.070934 0.083360 0.096003 0.10668 0.11548

0.10170 0.11389 0.12454 0.13213 0.13720

1089.7 794.12 590.09 478.93 431.69

−0.44295 −0.33796 −0.20571 −0.077157 −0.0052131

14.343 12.767 11.435 10.314

0.069721 0.078330 0.087453 0.096952

16.500 27.298 38.923 51.227

23.472 35.131 47.668 60.923

0.081539 0.11502 0.14296 0.16711

0.084059 0.097186 0.10821 0.11716

0.11166 0.12126 0.12921 0.13566

1008.9 833.69 723.22 656.57

−0.40055 −0.35302 −0.31534 −0.28902

300.00 400.00 500.00 600.00

100.00 100.00 100.00 100.00

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., and Jacobsen, R. T., “An International Standard Formulation for the Thermodynamic Properties of 1,1,1-Trifluoroethane (HFC-143a) for Temperatures from 161 to 450 K and Pressures to 50 MPa,” J. Phys. Chem. Ref. Data 29(4):521–552, 2000. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The estimated uncertainties of properties calculated using the equation of state are 0.1% in density, 0.5% in heat capacities, 0.02% in the speed of sound for the vapor at pressures less than 1 MPa, 0.5% in speed of sound elsewhere, and 0.1% in vapor pressure, except in the critical region.

2-241

2-242

TABLE 2-129

Thermodynamic Properties of R-404A

Temperature K

Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

200.00 205.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 305.00 310.00 315.00 320.00 325.00 330.00 335.00 340.00 345.00 345.27

0.022649 0.030989 0.041658 0.055101 0.071804 0.092293 0.11713 0.14693 0.18232 0.22397 0.27258 0.32888 0.39363 0.46763 0.55168 0.64664 0.75338 0.87280 1.0059 1.1536 1.3169 1.4970 1.6950 1.9122 2.1499 2.4096 2.6932 3.0027 3.3414 3.7150 3.7348

14.209 14.059 13.907 13.755 13.600 13.444 13.286 13.126 12.963 12.796 12.627 12.453 12.275 12.092 11.904 11.709 11.508 11.298 11.078 10.848 10.605 10.346 10.069 9.7686 9.4384 9.0688 8.6431 8.1285 7.4362 5.7429 4.9400

0.070377 0.071131 0.071905 0.072703 0.073527 0.074380 0.075265 0.076185 0.077145 0.078147 0.079197 0.080301 0.081465 0.082697 0.084006 0.085402 0.086899 0.088513 0.090266 0.092182 0.094295 0.096652 0.099314 0.10237 0.10595 0.11027 0.11570 0.12302 0.13448 0.17413 0.20243

10.353 10.948 11.544 12.144 12.746 13.353 13.963 14.578 15.199 15.824 16.456 17.094 17.738 18.390 19.049 19.717 20.394 21.081 21.780 22.490 23.215 23.956 24.717 25.500 26.310 27.157 28.054 29.026 30.147 32.108 32.875

200.00 205.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 305.00

0.021264 0.029285 0.039592 0.052629 0.068883 0.088879 0.11318 0.14240 0.17718 0.21817 0.26610 0.32169 0.38571 0.45896 0.54225 0.63645 0.74245 0.86115 0.99353 1.1406 1.3034 1.4830

29.920 30.185 30.451 30.718 30.987 31.256 31.525 31.795 32.063 32.330 32.596 32.859 33.119 33.375 33.626 33.872 34.111 34.342 34.563 34.773 34.968 35.147

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

10.355 10.950 11.547 12.148 12.751 13.359 13.972 14.590 15.213 15.842 16.478 17.120 17.770 18.429 19.096 19.772 20.460 21.159 21.870 22.597 23.339 24.101 24.885 25.695 26.538 27.423 28.365 29.396 30.597 32.755 33.631

0.058867 0.061803 0.064678 0.067498 0.070269 0.072995 0.075679 0.078326 0.080939 0.083520 0.086073 0.088600 0.091104 0.093589 0.096056 0.098510 0.10095 0.10339 0.10583 0.10826 0.11071 0.11317 0.11566 0.11818 0.12075 0.12341 0.12619 0.12918 0.13261 0.13874 0.14126

0.076939 0.077522 0.078116 0.078719 0.079326 0.079940 0.080558 0.081183 0.081815 0.082456 0.083107 0.083770 0.084446 0.085137 0.085846 0.086574 0.087326 0.088104 0.088914 0.089761 0.090653 0.091603 0.092625 0.093744 0.094998 0.096455 0.098241 0.10064 0.10445 0.11650

31.555 31.853 32.152 32.451 32.749 33.046 33.340 33.633 33.922 34.208 34.489 34.765 35.034 35.296 35.550 35.794 36.028 36.249 36.455 36.645 36.814 36.960

0.16521 0.16408 0.16307 0.16217 0.16138 0.16068 0.16006 0.15952 0.15903 0.15861 0.15823 0.15789 0.15759 0.15732 0.15707 0.15684 0.15661 0.15639 0.15616 0.15592 0.15566 0.15536

0.058696 0.059968 0.061245 0.062526 0.063815 0.065113 0.066424 0.067750 0.069095 0.070463 0.071855 0.073276 0.074728 0.076214 0.077737 0.079300 0.080909 0.082567 0.084282 0.086062 0.087917 0.089863

Sound speed m/s

Joule-Thomson K/MPa

0.11881 0.11915 0.11965 0.12028 0.12103 0.12188 0.12282 0.12386 0.12499 0.12621 0.12754 0.12899 0.13057 0.13229 0.13419 0.13630 0.13866 0.14133 0.14438 0.14793 0.15211 0.15715 0.16339 0.17139 0.18212 0.19751 0.22197 0.26871 0.40392 8.2559

859.89 831.56 804.42 778.20 752.69 727.72 703.16 678.91 654.88 631.01 607.23 583.50 559.77 535.99 512.13 488.15 464.02 439.69 415.13 390.28 365.11 339.56 313.56 287.00 259.73 231.53 201.95 170.20 134.59 89.976 0

−0.34161 −0.33384 −0.32460 −0.31394 −0.30185 −0.28830 −0.27318 −0.25636 −0.23766 −0.21683 −0.19356 −0.16749 −0.13814 −0.10493 −0.067104 −0.023728 0.026418 0.084928 0.15392 0.23626 0.33594 0.45865 0.61280 0.81141 1.0757 1.4433 1.9881 2.8807 4.6353 10.564 12.409

0.068032 0.069509 0.071021 0.072573 0.074172 0.075826 0.077546 0.079344 0.081232 0.083226 0.085343 0.087604 0.090033 0.092660 0.095524 0.098671 0.10217 0.10609 0.11056 0.11574 0.12186 0.12929

138.13 139.28 140.34 141.29 142.12 142.84 143.43 143.88 144.18 144.33 144.32 144.14 143.77 143.22 142.46 141.49 140.29 138.85 137.16 135.19 132.92 130.34

88.073 77.215 68.305 60.948 54.835 49.721 45.413 41.761 38.642 35.962 33.645 31.630 29.871 28.327 26.970 25.773 24.718 23.789 22.972 22.256 21.633 21.094

Cp kJ/(mol⋅K)

Saturated Properties

0.013010 0.017550 0.023271 0.030378 0.039095 0.049667 0.062359 0.077463 0.095292 0.11619 0.14055 0.16879 0.20137 0.23885 0.28183 0.33102 0.38725 0.45152 0.52501 0.60922 0.70599 0.81772

76.866 56.979 42.971 32.919 25.579 20.134 16.036 12.909 10.494 8.6063 7.1149 5.9247 4.9659 4.1867 3.5483 3.0210 2.5823 2.2148 1.9047 1.6414 1.4165 1.2229

310.00 315.00 320.00 325.00 330.00 335.00 340.00 345.00 345.27

1.6806 1.8975 2.1351 2.3950 2.6789 2.9893 3.3299 3.7109 3.7348

226.65

0.10000

227.41 300.00 400.00 500.00

0.10000 0.10000 0.10000 0.10000

289.79

1.0000

290.23 300.00 400.00 500.00

1.0000 1.0000 1.0000 1.0000

300.00 400.00 500.00

5.0000 5.0000 5.0000

0.94761 1.1001 1.2815 1.5019 1.7781 2.1438 2.6882 4.2113 4.9400

1.0553 0.90903 0.78032 0.66583 0.56239 0.46645 0.37199 0.23746 0.20243

35.304 35.435 35.530 35.578 35.558 35.429 35.084 33.615 32.875

37.078 37.159 37.196 37.173 37.065 36.824 36.323 34.496 33.631

0.074669

13.554

13.561

31.386 36.596 45.121 55.103

0.090189

0.15501 0.15459 0.15408 0.15343 0.15257 0.15136 0.14946 0.14379 0.14126

0.091922 0.094123 0.096513 0.099162 0.10220 0.10585 0.11074 0.12022

0.13856 0.15062 0.16713 0.19141 0.23111 0.30867 0.53035 8.6291

127.41 124.10 120.38 116.21 111.51 106.19 100.03 90.307 0

20.630 20.234 19.889 19.571 19.233 18.763 17.851 14.130 12.409

0.073887

0.080143

0.12218

719.55

−0.28348

33.188 39.050 48.428 59.250

0.16038 0.18269 0.20956 0.23365

0.065742 0.076875 0.092844 0.10612

0.076645 0.085907 0.10141 0.11456

143.14 166.24 191.81 213.92

47.558 16.998 6.9229 3.7455

21.750

21.840

0.10572

0.088879

0.14425

416.16

1.8916 2.0323 3.1292 4.0571

34.573 35.486 44.644 54.804

36.464 37.518 47.773 58.861

0.15615 0.15972 0.18922 0.21391

0.084363 0.083854 0.094142 0.10659

0.11078 0.10554 0.10545 0.11631

137.07 143.42 183.69 210.41

10.994 2.2256 1.3561

0.090955 0.44932 0.73741

22.770 41.867 53.389

23.225 44.113 57.076

0.10919 0.16875 0.19774

0.089725 0.10069 0.10859

0.14193 0.14547 0.12579

427.56 148.00 198.35

0.11428 7.6582 3.5826

Single-Phase Properties 13.392 0.055492 0.040750 0.030243 0.024113 11.088 0.52866 0.49205 0.31957 0.24648

18.021 24.540 33.066 41.471

0.15078 22.936 19.634 7.1401 3.7496

300.00 400.00 500.00

10.000 10.000 10.000

11.371 6.1241 2.9622

0.087944 0.16329 0.33758

22.323 37.557 51.539

23.203 39.190 54.915

0.10763 0.15323 0.18852

0.089307 0.10301 0.11046

0.13525 0.18569 0.13925

489.01 184.17 198.11

−0.035312 2.8522 2.8527

300.00 400.00 500.00

25.000 25.000 25.000

12.107 9.2730 6.6326

0.082594 0.10784 0.15077

21.419 34.286 47.758

23.484 36.982 51.527

0.10432 0.14304 0.17548

0.089393 0.10166 0.11215

0.12713 0.14227 0.14633

614.12 381.56 292.53

−0.22002 0.20064 0.65319

300.00 400.00 500.00

50.000 50.000 50.000

12.867 10.834 9.0225

0.077719 0.092300 0.11083

20.472 32.538 45.317

24.358 37.153 50.859

0.10057 0.13731 0.16786

0.090168 0.10251 0.11339

0.12262 0.13302 0.14051

753.19 559.24 455.37

−0.32391 −0.19415 −0.070101

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., “Pseudo Pure-Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C,” Int. J. Thermophys. 24(4):991–1006, 2003. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated heat capacities and speed of sound values is 0.5%. Uncertainties of bubble and dew point pressures are 0.5%.

2-243

2-244 TABLE 2-130

Thermodynamic Properties of R-407C

Temperature K

Pressure MPa

200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 359.35

0.019158 0.035795 0.062640 0.10366 0.16353 0.24755 0.36157 0.51193 0.70540 0.94916 1.2507 1.6182 2.0599 2.5851 3.2038 3.9255 4.6317

200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 359.35

0.011312 0.022624 0.041929 0.072846 0.11979 0.18793 0.28317 0.41203 0.58173 0.80008 1.0757 1.4179 1.8375 2.3470 2.9627 3.7100 4.6317

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa −0.31996 −0.30662 −0.28934 −0.26790 −0.24161 −0.20937 −0.16951 −0.11964 −0.056172 0.026372 0.13683 0.29038 0.51547 0.87274 1.5203 3.0499 10.947

Saturated Properties 17.036 16.697 16.352 15.999 15.637 15.264 14.877 14.472 14.045 13.591 13.102 12.567 11.969 11.278 10.435 9.2661 5.2600 0.0068643 0.013151 0.023450 0.039384 0.062913 0.096374 0.14256 0.20484 0.28739 0.39560 0.53670 0.72101 0.96439 1.2939 1.7642 2.5260 5.2600

0.058698 0.059892 0.061156 0.062503 0.063949 0.065512 0.067218 0.069099 0.071198 0.073576 0.076322 0.079573 0.083552 0.088671 0.095832 0.10792 0.19011 145.68 76.041 42.644 25.391 15.895 10.376 7.0147 4.8820 3.4796 2.5278 1.8632 1.3869 1.0369 0.77283 0.56682 0.39588 0.19011

8.8272 9.9359 11.051 12.175 13.312 14.464 15.632 16.822 18.035 19.278 20.555 21.877 23.255 24.711 26.287 28.110 32.145

8.8283 9.9380 11.055 12.182 13.323 14.480 15.657 16.857 18.085 19.348 20.651 22.006 23.427 24.940 26.594 28.534 33.025

0.050593 0.056002 0.061189 0.066188 0.071026 0.075728 0.080314 0.084805 0.089223 0.093590 0.097931 0.10228 0.10668 0.11119 0.11596 0.12137 0.13372

0.070988 0.071320 0.071817 0.072410 0.073074 0.073803 0.074597 0.075463 0.076412 0.077458 0.078624 0.079950 0.081509 0.083453 0.086157 0.090943

0.11073 0.11118 0.11203 0.11319 0.11465 0.11641 0.11853 0.12111 0.12427 0.12822 0.13331 0.14013 0.14989 0.16541 0.19551 0.28993

956.60 903.06 851.40 801.12 751.77 703.01 654.53 606.09 557.44 508.32 458.46 407.51 354.98 300.07 241.20 174.57 0

30.051 30.504 30.957 31.409 31.857 32.298 32.728 33.145 33.544 33.918 34.259 34.556 34.790 34.931 34.916 34.578 32.145

31.699 32.224 32.745 33.259 33.761 34.248 34.715 35.157 35.568 35.940 36.263 36.523 36.696 36.745 36.595 36.047 33.025

0.16726 0.16412 0.16151 0.15933 0.15749 0.15593 0.15460 0.15343 0.15240 0.15144 0.15051 0.14956 0.14852 0.14727 0.14560 0.14299 0.13372

0.048920 0.050967 0.053143 0.055439 0.057839 0.060328 0.062897 0.065542 0.068266 0.071085 0.074027 0.077140 0.080507 0.084283 0.088801 0.095065

0.057805 0.060200 0.062854 0.065784 0.069010 0.072563 0.076500 0.080917 0.085971 0.091920 0.099203 0.10861 0.12170 0.14208 0.18030 0.28700

149.59 152.36 154.78 156.79 158.33 159.36 159.80 159.60 158.69 156.99 154.41 150.83 146.11 140.03 132.24 122.09 0

109.12 88.122 72.006 59.560 49.904 42.378 36.483 31.840 28.163 25.236 22.898 21.024 19.516 18.284 17.206 15.951 10.947

Single-Phase Properties 200.00 229.25

0.10000 0.10000

236.25 300.00 400.00 500.00

0.10000 0.10000 0.10000 0.10000

291.84

1.0000

297.47 300.00 400.00 500.00

1.0000 1.0000 1.0000 1.0000

300.00 400.00 500.00

5.0000 5.0000 5.0000

8.8253 12.091

8.8312 12.097

0.050583 0.065819

0.070990 0.072363

0.11072 0.11310

956.99 804.85

−0.32010 −0.26966

31.690 35.535 42.554 50.849

33.574 37.991 45.862 54.997

0.15814 0.17467 0.19722 0.21756

0.056928 0.063341 0.076588 0.088895

0.067764 0.072378 0.085147 0.097330

157.81 179.00 205.99 229.27

53.242 20.041 7.7925 4.0471

0.074050

19.510

19.584

0.094388

0.077662

0.12906

499.23

2.0105 2.0465 3.1425 4.0637

34.177 34.384 42.101 50.576

36.187 36.431 45.244 54.639

0.15075 0.15156 0.17694 0.19786

0.073268 0.072744 0.078067 0.089416

0.097199 0.095419 0.089213 0.099001

155.15 156.77 198.26 225.88

13.412 2.1880 1.3504

0.074559 0.45703 0.74050

20.240 39.458 49.289

20.613 41.743 52.992

0.096862 0.15675 0.18193

0.078093 0.086188 0.091753

0.12762 0.12964 0.10811

507.10 161.10 213.00

0.027202 8.5257 3.9036

17.038 16.026 0.053062 0.040722 0.030231 0.024109 13.504 0.49738 0.48865 0.31821 0.24608

0.058692 0.062399 18.846 24.557 33.079 41.479

0.044233 23.442 22.566 7.9701 4.0390

300.00 400.00 500.00

10.000 10.000 10.000

13.740 7.1029 2.9957

0.072780 0.14079 0.33381

19.898 34.426 47.547

20.626 35.834 50.885

0.095679 0.13888 0.17282

0.077756 0.090433 0.094263

0.12301 0.20031 0.12254

558.94 184.71 207.67

−0.063246 3.3408 3.3327

300.00 400.00 500.00

25.000 25.000 25.000

14.443 10.899 7.3363

0.069238 0.091752 0.13631

19.146 30.990 43.479

20.877 33.284 46.886

0.092972 0.12855 0.15889

0.077634 0.087056 0.096319

0.11624 0.13223 0.13592

672.43 399.92 289.22

−0.19834 0.28513 0.97116

300.00 400.00 500.00

50.000 50.000 50.000

15.220 12.648 10.260

0.065703 0.079064 0.097468

18.302 29.255 40.787

21.587 33.209 45.660

0.089730 0.12310 0.15086

0.078160 0.087179 0.096753

0.11176 0.12077 0.12761

802.78 579.57 457.54

−0.28843 −0.12975 0.047330

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., “Pseudo Pure-Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C,” Int. J. Thermophys. 24(4):991–1006, 2003. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated heat capacities and speed of sound values is 0.5%. Uncertainties of bubble and dew point pressures are 0.5%.

2-245

2-246 FIG. 2-15

Pressure-enthalpy diagram for Refrigerant 407C. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the mixture model of Lemmon, E. W., and R. T. Jacobsen, “Equations of State for Mixtures of R-32, R-125, R-134a, R-143a, and R-152a,” J. Phys. Chem. Ref. Data 33: 593–620, 2004.

TABLE 2-131 Thermodynamic Properties of R-410A Temperature K

Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

200.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 305.00 310.00 315.00 320.00 325.00 330.00 335.00 340.00 344.49

0.029160 0.053727 0.071143 0.092819 0.11946 0.15182 0.19070 0.23697 0.29152 0.35531 0.42933 0.51461 0.61223 0.72330 0.84899 0.99048 1.1490 1.3260 1.5226 1.7404 1.9809 2.2456 2.5364 2.8550 3.2037 3.5848 4.0009 4.4556 4.9012

19.510 19.093 18.881 18.667 18.449 18.229 18.005 17.776 17.543 17.305 17.062 16.812 16.555 16.290 16.016 15.732 15.436 15.127 14.802 14.459 14.095 13.704 13.282 12.816 12.294 11.685 10.930 9.8413 6.3240

0.051256 0.052375 0.052962 0.053571 0.054202 0.054858 0.055542 0.056255 0.057002 0.057786 0.058611 0.059482 0.060406 0.061388 0.062439 0.063567 0.064785 0.066109 0.067559 0.069160 0.070948 0.072969 0.075293 0.078025 0.081343 0.085578 0.091491 0.10161 0.15813

7.0380 8.0188 8.5112 9.0052 9.5012 9.9997 10.501 11.006 11.514 12.026 12.543 13.065 13.593 14.127 14.669 15.218 15.776 16.344 16.924 17.516 18.123 18.747 19.392 20.064 20.772 21.531 22.376 23.414 25.988

200.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 305.00 310.00 315.00 320.00

0.029010 0.053489 0.070844 0.092447 0.11900 0.15125 0.19000 0.23611 0.29049 0.35407 0.42786 0.51287 0.61019 0.72092 0.84622 0.98729 1.1454 1.3218 1.5179 1.7351 1.9749 2.2390 2.5291 2.8472

26.495 26.835 27.002 27.167 27.329 27.488 27.645 27.798 27.947 28.092 28.232 28.367 28.496 28.619 28.733 28.839 28.935 29.019 29.090 29.144 29.178 29.189 29.170 29.112

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

7.0395 8.0217 8.5149 9.0101 9.5077 10.008 10.512 11.019 11.530 12.047 12.568 13.096 13.630 14.172 14.722 15.281 15.851 16.432 17.026 17.636 18.263 18.911 19.583 20.287 21.032 21.837 22.742 23.867 26.763

0.040995 0.045781 0.048098 0.050370 0.052600 0.054791 0.056948 0.059073 0.061169 0.063240 0.065289 0.067318 0.069331 0.071331 0.073321 0.075304 0.077284 0.079266 0.081254 0.083253 0.085270 0.087314 0.089398 0.091537 0.093762 0.096123 0.098732 0.10194 0.11022

0.062260 0.062050 0.062014 0.062020 0.062066 0.062151 0.062271 0.062426 0.062615 0.062837 0.063092 0.063380 0.063701 0.064057 0.064451 0.064884 0.065363 0.065893 0.066483 0.067147 0.067901 0.068773 0.069800 0.071046 0.072616 0.074717 0.077843 0.083650

0.097942 0.098396 0.098729 0.099138 0.099628 0.10020 0.10088 0.10165 0.10253 0.10353 0.10466 0.10594 0.10738 0.10902 0.11088 0.11300 0.11543 0.11825 0.12156 0.12550 0.13029 0.13630 0.14413 0.15493 0.17109 0.19853 0.25685 0.46832

929.01 879.84 855.20 830.52 805.81 781.06 756.26 731.41 706.48 681.45 656.31 631.02 605.55 579.88 553.95 527.72 501.14 474.14 446.66 418.60 389.87 360.33 329.82 298.10 264.83 229.46 190.98 147.49 0

−0.30179 −0.28524 −0.27544 −0.26446 −0.25217 −0.23841 −0.22300 −0.20574 −0.18637 −0.16459 −0.14006 −0.11232 −0.080861 −0.045000 −0.0039006 0.043515 0.098651 0.16337 0.24022 0.33275 0.44607 0.58788 0.77028 1.0135 1.3544 1.8665 2.7232 4.4554 9.7623

28.125 28.530 28.726 28.919 29.107 29.290 29.468 29.640 29.806 29.965 30.116 30.258 30.392 30.515 30.626 30.725 30.809 30.876 30.925 30.951 30.951 30.920 30.850 30.732

0.14644 0.14345 0.14212 0.14087 0.13972 0.13864 0.13762 0.13667 0.13577 0.13492 0.13411 0.13333 0.13259 0.13187 0.13116 0.13047 0.12978 0.12908 0.12837 0.12764 0.12688 0.12606 0.12517 0.12418

0.042482 0.044604 0.045719 0.046862 0.048026 0.049206 0.050400 0.051603 0.052814 0.054033 0.055260 0.056497 0.057747 0.059014 0.060302 0.061618 0.062969 0.064364 0.065814 0.067335 0.068945 0.070671 0.072551 0.074643

0.052236 0.055055 0.056590 0.058205 0.059899 0.061674 0.063533 0.065483 0.067535 0.069705 0.072011 0.074481 0.077148 0.080057 0.083265 0.086846 0.090901 0.095568 0.10104 0.10760 0.11566 0.12589 0.13943 0.15831

164.41 167.03 168.16 169.16 170.03 170.75 171.32 171.73 171.97 172.04 171.93 171.62 171.11 170.39 169.45 168.27 166.84 165.16 163.20 160.94 158.36 155.44 152.13 148.40

Saturated Properties

0.017797 0.031567 0.041089 0.052763 0.066925 0.083936 0.10420 0.12814 0.15625 0.18905 0.22714 0.27117 0.32190 0.38018 0.44702 0.52357 0.61123 0.71170 0.82707 0.95997 1.1138 1.2933 1.5048 1.7576

56.190 31.678 24.338 18.953 14.942 11.914 9.5972 7.8039 6.4000 5.2895 4.4026 3.6877 3.1066 2.6303 2.2371 1.9100 1.6360 1.4051 1.2091 1.0417 0.89779 0.77322 0.66456 0.56894

113.67 90.100 80.508 72.155 64.889 58.571 53.077 48.299 44.137 40.508 37.336 34.560 32.123 29.979 28.087 26.412 24.924 23.598 22.410 21.338 20.365 19.470 18.632 17.826

2-247

(Continued)

2-248 TABLE 2-131 Thermodynamic Properties of R-410A (Continued ) Temperature K

Pressure MPa

Density mol/dm3

Volume dm3/mol

Int. energy kJ/mol

325.00 330.00 335.00 340.00 344.49

3.1955 3.5766 3.9935 4.4504 4.9012

2.0668 2.4582 2.9848 3.7974 6.3240

0.48384 0.40681 0.33503 0.26334 0.15813

29.002 28.817 28.510 27.951 25.988

221.45

0.10000

221.53 300.00 400.00 500.00

0.10000 0.10000 0.10000 0.10000

280.32

1.0000

280.42 300.00 400.00 500.00

1.0000 1.0000 1.0000 1.0000

300.00 400.00 500.00

5.0000 5.0000 5.0000

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Saturated Properties (Continued) 30.548 30.272 29.848 29.123 26.763

0.12305 0.12169 0.11995 0.11740 0.11022

0.077041 0.079915 0.083629 0.089197

0.18670 0.23464 0.33370 0.65947

144.16 139.30 133.59 126.39 0

17.018 16.153 15.123 13.641 9.7623

0.051020

0.062030

0.099271

823.36

−0.26104 69.827 19.643 7.7467 4.0758

Single-Phase Properties 18.604 0.056810 0.040605 0.030202 0.024099

0.053751

9.1541

27.217 31.028 36.670 43.331

28.977 33.491 39.981 47.480

0.14051 0.15794 0.17654 0.19323

0.047215 0.050980 0.061554 0.071249

0.058714 0.059877 0.070067 0.079663

169.44 198.35 227.37 252.59

0.063641

15.253

15.317

0.075429

0.064913

0.11314

526.05

1.8849 2.1460 3.1769 4.0808

28.848 30.151 36.304 43.106

30.733 32.297 39.481 47.187

0.13041 0.13580 0.15648 0.17364

0.061731 0.057548 0.062713 0.071665

0.087169 0.075210 0.073258 0.081012

168.16 180.65 220.92 249.79

14.870 1.9755 1.3185

0.067248 0.50621 0.75845

17.202 34.349 42.072

17.539 36.880 45.864

0.082188 0.13813 0.15821

0.066139 0.068570 0.073521

0.11773 0.097588 0.087959

472.56 192.34 239.51

0.17344 7.6786 3.7957 0.036775 5.0121 3.3106

15.713 0.53054 0.46599 0.31478 0.24505

17.603 24.628 33.111 41.495

9.1488

0.046760 26.279 20.254 7.7768 4.0343

300.00 400.00 500.00

10.000 10.000 10.000

15.342 5.7949 2.8642

0.065180 0.17257 0.34914

16.830 30.845 40.710

17.482 32.570 44.202

0.080897 0.12363 0.14982

0.065435 0.074099 0.075667

0.11125 0.16518 0.098492

533.86 182.45 233.93

300.00 400.00 500.00

25.000 25.000 25.000

16.289 11.685 7.4115

0.061392 0.085582 0.13493

16.058 26.530 37.197

17.592 28.670 40.570

0.078110 0.10987 0.13644

0.065000 0.072157 0.078574

0.10273 0.11830 0.11515

658.09 379.59 291.31

−0.14678 0.50709 1.2724

300.00 400.00 500.00

50.000 50.000 50.000

17.287 14.049 11.128

0.057845 0.071182 0.089864

15.231 24.722 34.526

18.123 28.281 39.019

0.074923 0.10409 0.12804

0.065499 0.072480 0.079657

0.097459 0.10533 0.10880

792.80 566.13 449.76

−0.26163 −0.063564 0.13566

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., “Pseudo Pure-Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C,” Int. J. Thermophys. 24(4):991–1006, 2003. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated heat capacities and speed of sound values is 0.5%. Uncertainties of bubble and dew point pressures are 0.5%.

TABLE 2-132

Opteon™ YF (R-1234yf)

Saturation Properties—Temperature Table Temp [°C]  −40 −39 −38 −37 −36 −35 −34 −33 −32 −31 −30 −29 −28 −27 −26 −25 −24 −23 −22 −21 −20 −19 −18 −17 −16 −15 −14 −13 −12 −11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3

Pressure [kPa]  62.367 65.454 68.661 71.992 75.450 79.039 82.761 86.620 90.620 94.764 99.056 103.500 108.098 112.856 117.775 122.861 128.117 133.548 139.155 144.945 150.921 157.086 163.444 170.001 176.759 183.724 190.898 198.287 205.895 213.726 221.783 230.072 238.597 247.363 256.373 265.632 275.144 284.915 294.948 305.249 315.821 326.670 337.800 349.216

Volume [m3/kg] Liquid vf

Vapor vg

0.000774 0.000776 0.000777 0.000779 0.000781 0.000782 0.000784 0.000786 0.000787 0.000789 0.000791 0.000793 0.000794 0.000796 0.000798 0.000800 0.000801 0.000803 0.000805 0.000807 0.000809 0.000811 0.000813 0.000815 0.000817 0.000818 0.000820 0.000822 0.000824 0.000826 0.000829 0.000831 0.000833 0.000835 0.000837 0.000839 0.000841 0.000843 0.000846 0.000848 0.000850 0.000852 0.000855 0.000857

0.2635 0.2519 0.2409 0.2304 0.2205 0.2111 0.2022 0.1937 0.1857 0.1780 0.1708 0.1639 0.1573 0.1511 0.1451 0.1394 0.1340 0.1289 0.1240 0.1193 0.1148 0.1105 0.1065 0.1026 0.0988 0.0953 0.0919 0.0886 0.0855 0.0825 0.0796 0.0769 0.0742 0.0717 0.0693 0.0670 0.0647 0.0626 0.0605 0.0586 0.0567 0.0548 0.0531 0.0514

Density [kg/m3] Liquid df 1291.9 1289.2 1286.5 1283.8 1281.0 1278.3 1275.6 1272.8 1270.1 1267.3 1264.5 1261.8 1259.0 1256.2 1253.4 1250.5 1247.7 1244.9 1242.0 1239.2 1236.3 1233.4 1230.5 1227.6 1224.7 1221.8 1218.8 1215.9 1212.9 1209.9 1207.0 1203.9 1200.9 1197.9 1194.9 1191.8 1188.7 1185.6 1182.5 1179.4 1176.3 1173.1 1170.0 1166.8

Enthalpy [kJ/kg]

Vapor dg

Liquid hf

Latent hfg

3.795 3.970 4.152 4.340 4.535 4.737 4.946 5.162 5.386 5.617 5.855 6.102 6.357 6.620 6.891 7.171 7.460 7.758 8.066 8.383 8.709 9.046 9.392 9.750 10.117 10.496 10.885 11.286 11.699 12.123 12.559 13.008 13.469 13.943 14.431 14.931 15.446 15.974 16.517 17.074 17.647 18.234 18.837 19.457

151.1 152.2 153.4 154.6 155.7 156.9 158.1 159.3 160.4 161.6 162.8 164.0 165.2 166.4 167.6 168.8 170.0 171.2 172.4 173.7 174.9 176.1 177.3 178.6 179.8 181.0 182.3 183.5 184.8 186.0 187.3 188.5 189.8 191.0 192.3 193.6 194.9 196.1 197.4 198.7 200.0 201.3 202.6 203.9

185.5 185.0 184.5 184.0 183.5 183.0 182.5 182.0 181.5 181.0 180.5 180.0 179.5 178.9 178.4 177.9 177.4 176.8 176.3 175.7 175.2 174.6 174.1 173.5 172.9 172.4 171.8 171.2 170.6 170.0 169.5 168.9 168.3 167.7 167.0 166.4 165.8 165.2 164.6 163.9 163.3 162.6 162.0 161.3

Entropy [kJ/kg⋅K] Vapor hg

Liquid sf

336.6 337.3 337.9 338.6 339.3 339.9 340.6 341.3 342.0 342.6 343.3 344.0 344.7 345.3 346.0 346.7 347.4 348.0 348.7 349.4 350.1 350.7 351.4 352.1 352.7 353.4 354.1 354.7 355.4 356.1 356.7 357.4 358.0 358.7 359.4 360.0 360.7 361.3 362.0 362.6 363.3 363.9 364.6 365.2

0.807 0.812 0.817 0.822 0.827 0.832 0.837 0.842 0.847 0.852 0.857 0.861 0.866 0.871 0.876 0.881 0.886 0.891 0.895 0.900 0.905 0.910 0.915 0.919 0.924 0.929 0.934 0.939 0.943 0.948 0.953 0.958 0.962 0.967 0.972 0.976 0.981 0.986 0.991 0.995 1.000 1.005 1.009 1.014

Vapor sg 1.603 1.603 1.602 1.602 1.601 1.601 1.600 1.600 1.600 1.599 1.599 1.599 1.598 1.598 1.598 1.598 1.598 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.598 1.598 1.598 1.598 1.598 1.598

Temp [°C]  −40 −39 −38 −37 −36 −35 −34 −33 −32 −31 −30 −29 −28 −27 −26 −25 −24 −23 −22 −21 −20 −19 −18 −17 −16 −15 −14 −13 −12 −11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3

2-249

(Continued)

2-250 TABLE 2-132 Opteon™ YF (R-1234yf) (Continued ) Saturation Properties—Temperature Table Volume [m3/kg] Temp [°C]  4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Pressure [kPa] 

Liquid vf

Vapor vg

360.923 372.925 385.227 397.833 410.750 423.981 437.532 451.408 465.613 480.152 495.031 510.255 525.828 541.756 558.044 574.697 591.721 609.120 626.901 645.068 663.626 682.582 701.940 721.707 741.887 762.487 783.511 804.966 826.857 849.190 871.971 895.206 918.900 943.060 967.691 992.800 1018.393 1044.476 1071.055 1098.137 1125.728 1153.834 1182.462 1211.618

0.000859 0.000862 0.000864 0.000867 0.000869 0.000872 0.000874 0.000877 0.000879 0.000882 0.000884 0.000887 0.000890 0.000893 0.000895 0.000898 0.000901 0.000904 0.000907 0.000910 0.000913 0.000916 0.000919 0.000922 0.000925 0.000928 0.000932 0.000935 0.000938 0.000942 0.000945 0.000949 0.000952 0.000956 0.000960 0.000963 0.000967 0.000971 0.000975 0.000979 0.000983 0.000988 0.000992 0.000996

0.0498 0.0482 0.0467 0.0452 0.0439 0.0425 0.0412 0.0400 0.0387 0.0376 0.0365 0.0354 0.0343 0.0333 0.0323 0.0314 0.0305 0.0296 0.0288 0.0279 0.0271 0.0264 0.0256 0.0249 0.0242 0.0235 0.0229 0.0222 0.0216 0.0210 0.0204 0.0199 0.0193 0.0188 0.0183 0.0178 0.0173 0.0168 0.0164 0.0159 0.0155 0.0151 0.0147 0.0143

Density [kg/m3] Liquid df 1163.6 1160.4 1157.2 1153.9 1150.6 1147.3 1144.0 1140.7 1137.4 1134.0 1130.6 1127.2 1123.8 1120.3 1116.9 1113.4 1109.9 1106.3 1102.8 1099.2 1095.5 1091.9 1088.2 1084.5 1080.8 1077.1 1073.3 1069.5 1065.7 1061.8 1057.9 1054.0 1050.0 1046.0 1042.0 1037.9 1033.8 1029.6 1025.5 1021.2 1017.0 1012.6 1008.3 1003.9

Enthalpy [kJ/kg]

Vapor dg

Liquid hf

Latent hfg

20.092 20.744 21.413 22.100 22.804 23.526 24.267 25.027 25.807 26.606 27.425 28.266 29.127 30.011 30.916 31.845 32.796 33.772 34.772 35.797 36.848 37.925 39.029 40.161 41.321 42.510 43.729 44.979 46.260 47.573 48.920 50.301 51.717 53.169 54.658 56.186 57.753 59.360 61.010 62.702 64.440 66.223 68.053 69.933

205.2 206.5 207.8 209.1 210.5 211.8 213.1 214.4 215.8 217.1 218.5 219.8 221.2 222.5 223.9 225.2 226.6 228.0 229.3 230.7 232.1 233.5 234.9 236.3 237.7 239.1 240.5 241.9 243.4 244.8 246.2 247.6 249.1 250.5 252.0 253.4 254.9 256.4 257.8 259.3 260.8 262.3 263.8 265.3

160.7 160.0 159.3 158.7 158.0 157.3 156.6 155.9 155.2 154.5 153.8 153.0 152.3 151.6 150.8 150.1 149.3 148.5 147.7 147.0 146.2 145.4 144.6 143.7 142.9 142.1 141.2 140.4 139.5 138.7 137.8 136.9 136.0 135.1 134.1 133.2 132.3 131.3 130.3 129.4 128.4 127.4 126.3 125.3

Entropy [kJ/kg⋅K] Vapor hg

Liquid sf

365.9 366.5 367.2 367.8 368.4 369.1 369.7 370.3 371.0 371.6 372.2 372.8 373.4 374.1 374.7 375.3 375.9 376.5 377.1 377.7 378.3 378.9 379.5 380.0 380.6 381.2 381.8 382.3 382.9 383.4 384.0 384.5 385.1 385.6 386.1 386.7 387.2 387.7 388.2 388.7 389.2 389.7 390.1 390.6

1.019 1.023 1.028 1.033 1.037 1.042 1.047 1.051 1.056 1.061 1.065 1.070 1.075 1.079 1.084 1.088 1.093 1.098 1.102 1.107 1.112 1.116 1.121 1.125 1.130 1.135 1.139 1.144 1.148 1.153 1.158 1.162 1.167 1.171 1.176 1.181 1.185 1.190 1.194 1.199 1.204 1.208 1.213 1.217

Vapor sg 1.599 1.599 1.599 1.599 1.599 1.600 1.600 1.600 1.600 1.601 1.601 1.601 1.601 1.602 1.602 1.602 1.602 1.603 1.603 1.603 1.603 1.604 1.604 1.604 1.605 1.605 1.605 1.605 1.606 1.606 1.606 1.606 1.607 1.607 1.607 1.607 1.608 1.608 1.608 1.608 1.608 1.608 1.609 1.609

Temp [°C]  4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

1241.310 1271.543 1302.325 1333.663 1365.563 1398.032 1431.079 1464.709 1498.931 1533.751 1569.178 1605.219 1641.882 1679.174 1717.104 1755.680 1794.911 1834.805 1875.370 1916.617 1958.553 2001.189 2044.535 2088.600 2133.395 2178.931 2225.219 2272.271 2320.100 2368.717 2418.137 2468.375 2519.445

0.001001 0.001005 0.001010 0.001014 0.001019 0.001024 0.001029 0.001034 0.001040 0.001045 0.001051 0.001056 0.001062 0.001068 0.001075 0.001081 0.001088 0.001094 0.001101 0.001109 0.001116 0.001124 0.001132 0.001141 0.001149 0.001159 0.001168 0.001178 0.001189 0.001199 0.001211 0.001223 0.001236

0.0139 0.0135 0.0132 0.0128 0.0125 0.0121 0.0118 0.0115 0.0112 0.0109 0.0106 0.0103 0.0100 0.0098 0.0095 0.0092 0.0090 0.0087 0.0085 0.0082 0.0080 0.0078 0.0076 0.0073 0.0071 0.0069 0.0067 0.0065 0.0063 0.0061 0.0059 0.0057 0.0055

999.4 994.9 990.4 985.8 981.1 976.4 971.6 966.7 961.8 956.8 951.7 946.6 941.3 936.0 930.6 925.1 919.5 913.7 907.9 901.9 895.8 889.6 883.2 876.7 870.0 863.1 856.1 848.8 841.4 833.7 825.7 817.5 809.0

71.863 73.846 75.884 77.978 80.130 82.343 84.619 86.961 89.371 91.852 94.407 97.040 99.754 102.552 105.438 108.418 111.496 114.676 117.964 121.367 124.891 128.544 132.332 136.266 140.355 144.611 149.044 153.671 158.505 163.566 168.874 174.454 180.333

266.8 268.3 269.9 271.4 272.9 274.5 276.0 277.6 279.2 280.7 282.3 283.9 285.5 287.1 288.8 290.4 292.1 293.7 295.4 297.1 298.8 300.5 302.2 304.0 305.7 307.5 309.3 311.1 313.0 314.8 316.7 318.6 320.5

124.3 123.2 122.1 121.0 119.9 118.8 117.7 116.5 115.3 114.1 112.9 111.7 110.4 109.1 107.8 106.5 105.1 103.7 102.3 100.9 99.4 97.9 96.3 94.8 93.1 91.5 89.8 88.0 86.2 84.3 82.4 80.4 78.4

391.1 391.5 392.0 392.4 392.8 393.3 393.7 394.1 394.5 394.9 395.2 395.6 395.9 396.3 396.6 396.9 397.2 397.5 397.7 398.0 398.2 398.4 398.6 398.7 398.9 399.0 399.1 399.1 399.2 399.2 399.1 399.0 398.9

1.222 1.227 1.231 1.236 1.241 1.245 1.250 1.254 1.259 1.264 1.269 1.273 1.278 1.283 1.287 1.292 1.297 1.302 1.307 1.311 1.316 1.321 1.326 1.331 1.336 1.341 1.346 1.351 1.356 1.361 1.366 1.372 1.377

1.609 1.609 1.609 1.609 1.609 1.609 1.609 1.610 1.610 1.610 1.609 1.609 1.609 1.609 1.609 1.609 1.609 1.609 1.608 1.608 1.608 1.607 1.607 1.606 1.606 1.605 1.605 1.604 1.603 1.602 1.601 1.600 1.599

48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 (Continued)

2-251

2-252 TABLE 2-132

Opteon™ YF (R-1234yf) (Continued )

Superheated Vapor—Constant Pressure Tables V = Volume in m3/kg

H = Enthalpy in kJ/kg

S = Entropy in kJ/kg⋅K

Saturation Properties in Light Gray

Absolute Pressure, kPa

V

90

100

101.325

110 

−32.15°C

−29.78°C

−29.49°C

−27.60°C

S

V

S

V

H

S

V

H

Temp [°C] 

0.1869

341.9

H

1.600

0.1693

343.5

H

1.599

0.1672

343.7

1.599

0.1548

344.9

1.598

S Temp [°C] 

−30 −25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115

0.1888 0.1933 0.1978 0.2022 0.2066 0.2110 0.2153 0.2197 0.2240 0.2283 0.2325 0.2368 0.2410 0.2453 0.2495 0.2537 0.2579 0.2621 0.2663 0.2705 0.2746 0.2788 0.2830 0.2871 0.2913 0.2954 0.2996 0.3037 0.3078 0.3120

343.6 347.7 351.8 355.9 360.1 364.3 368.6 372.9 377.3 381.7 386.1 390.6 395.2 399.8 404.4 409.1 413.8 418.5 423.3 428.2 433.0 438.0 442.9 447.9 453.0 458.1 463.2 468.4 473.6 478.8

1.607 1.623 1.640 1.656 1.672 1.688 1.704 1.719 1.735 1.750 1.766 1.781 1.796 1.811 1.826 1.841 1.855 1.870 1.884 1.899 1.913 1.927 1.942 1.956 1.970 1.984 1.997 2.011 2.025 2.038

0.1732 0.1773 0.1813 0.1853 0.1893 0.1932 0.1971 0.2010 0.2049 0.2088 0.2126 0.2165 0.2203 0.2241 0.2279 0.2317 0.2355 0.2393 0.2431 0.2468 0.2506 0.2544 0.2581 0.2619 0.2656 0.2693 0.2731 0.2768 0.2805

347.4 351.5 355.6 359.9 364.1 368.4 372.7 377.1 381.5 386.0 390.5 395.0 399.6 404.2 408.9 413.6 418.4 423.2 428.0 432.9 437.9 442.8 447.8 452.9 458.0 463.1 468.3 473.5 478.7

1.615 1.631 1.647 1.664 1.680 1.695 1.711 1.727 1.742 1.758 1.773 1.788 1.803 1.818 1.833 1.847 1.862 1.877 1.891 1.905 1.920 1.934 1.948 1.962 1.976 1.990 2.003 2.017 2.031

0.1708 0.1748 0.1788 0.1828 0.1867 0.1906 0.1945 0.1983 0.2022 0.2060 0.2098 0.2136 0.2174 0.2211 0.2249 0.2286 0.2324 0.2361 0.2399 0.2436 0.2473 0.2510 0.2547 0.2584 0.2621 0.2658 0.2695 0.2731 0.2768

347.3 351.5 355.6 359.8 364.1 368.4 372.7 377.1 381.5 385.9 390.4 395.0 399.6 404.2 408.9 413.6 418.4 423.2 428.0 432.9 437.8 442.8 447.8 452.9 458.0 463.1 468.3 473.5 478.7

1.614 1.630 1.646 1.663 1.679 1.694 1.710 1.726 1.741 1.757 1.772 1.787 1.802 1.817 1.832 1.846 1.861 1.876 1.890 1.904 1.919 1.933 1.947 1.961 1.975 1.989 2.002 2.016 2.030

0.1567 0.1604 0.1642 0.1678 0.1715 0.1751 0.1787 0.1822 0.1858 0.1893 0.1929 0.1964 0.1999 0.2034 0.2068 0.2103 0.2138 0.2172 0.2207 0.2241 0.2275 0.2310 0.2344 0.2378 0.2412 0.2446 0.2480 0.2514 0.2548

347.1 351.2 355.4 359.6 363.9 368.2 372.5 376.9 381.3 385.8 390.3 394.9 399.5 404.1 408.8 413.5 418.3 423.1 427.9 432.8 437.8 442.7 447.7 452.8 457.9 463.0 468.2 473.4 478.7

1.607 1.623 1.640 1.656 1.672 1.688 1.704 1.719 1.735 1.750 1.765 1.781 1.796 1.811 1.825 1.840 1.855 1.869 1.884 1.898 1.912 1.927 1.941 1.955 1.969 1.982 1.996 2.010 2.024

−30 −25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115

Absolute Pressure, kPa

V

120

130

140

150

−25.56°C

−23.65°C

−21.85°C

−20.15°C

S

V

V

H

S

V

H

Temp [°C] 

0.1426

346.3

H

1.598

0.1322

347.6

H

1.598

S

0.1233

348.8

1.597

0.1155

349.9

1.597

S Temp [°C] 

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

0.1430 0.1464 0.1499 0.1533 0.1566 0.1600 0.1633 0.1666 0.1699 0.1731 0.1764 0.1796 0.1828 0.1861 0.1893 0.1925 0.1956 0.1988 0.2020 0.2051 0.2083 0.2114 0.2146 0.2177 0.2209 0.2240 0.2271 0.2302 0.2334 0.2365

346.8 350.9 355.1 359.4 363.6 367.9 372.3 376.7 381.1 385.6 390.1 394.7 399.3 403.9 408.6 413.4 418.1 422.9 427.8 432.7 437.6 442.6 447.6 452.7 457.8 462.9 468.1 473.3 478.6 483.9

1.600 1.616 1.633 1.649 1.665 1.681 1.697 1.712 1.728 1.743 1.759 1.774 1.789 1.804 1.819 1.833 1.848 1.863 1.877 1.892 1.906 1.920 1.934 1.948 1.962 1.976 1.990 2.003 2.017 2.031

0.1346 0.1378 0.1409 0.1441 0.1472 0.1503 0.1533 0.1564 0.1594 0.1624 0.1655 0.1684 0.1714 0.1744 0.1773 0.1803 0.1832 0.1862 0.1891 0.1920 0.1949 0.1978 0.2007 0.2037 0.2065 0.2094 0.2123 0.2152 0.2181

350.7 354.9 359.1 363.4 367.7 372.1 376.5 380.9 385.4 390.0 394.5 399.1 403.8 408.5 413.2 418.0 422.8 427.7 432.6 437.5 442.5 447.5 452.6 457.7 462.8 468.0 473.2 478.5 483.8

1.610 1.626 1.642 1.659 1.675 1.690 1.706 1.722 1.737 1.752 1.768 1.783 1.798 1.813 1.827 1.842 1.857 1.871 1.885 1.900 1.914 1.928 1.942 1.956 1.970 1.984 1.997 2.011 2.025

0.1244 0.1274 0.1304 0.1333 0.1362 0.1391 0.1420 0.1448 0.1477 0.1505 0.1533 0.1561 0.1589 0.1616 0.1644 0.1671 0.1699 0.1726 0.1753 0.1781 0.1808 0.1835 0.1862 0.1889 0.1916 0.1943 0.1970 0.1997 0.2023

350.4 354.6 358.9 363.2 367.5 371.9 376.3 380.8 385.3 389.8 394.4 399.0 403.6 408.3 413.1 417.9 422.7 427.6 432.5 437.4 442.4 447.4 452.5 457.6 462.7 467.9 473.1 478.4 483.7

1.603 1.620 1.636 1.653 1.669 1.684 1.700 1.716 1.731 1.747 1.762 1.777 1.792 1.807 1.822 1.836 1.851 1.865 1.880 1.894 1.908 1.922 1.937 1.950 1.964 1.978 1.992 2.005 2.019

0.1156 0.1184 0.1212 0.1240 0.1267 0.1294 0.1321 0.1348 0.1375 0.1401 0.1428 0.1454 0.1480 0.1506 0.1532 0.1557 0.1583 0.1609 0.1634 0.1660 0.1685 0.1711 0.1736 0.1761 0.1786 0.1812 0.1837 0.1862 0.1887

350.1 354.3 358.6 362.9 367.3 371.7 376.1 380.6 385.1 389.6 394.2 398.8 403.5 408.2 413.0 417.7 422.6 427.4 432.4 437.3 442.3 447.3 452.4 457.5 462.6 467.8 473.1 478.3 483.6

1.598 1.614 1.631 1.647 1.663 1.679 1.695 1.710 1.726 1.741 1.756 1.772 1.787 1.801 1.816 1.831 1.846 1.860 1.875 1.889 1.903 1.917 1.931 1.945 1.959 1.973 1.987 2.000 2.014

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 (Continued)

2-253

2-254 TABLE 2-132

Opteon™ YF (R-1234yf) (Continued )

Superheated Vapor—Constant Pressure Tables V = Volume in m3/kg

H = Enthalpy in kJ/kg

S = Entropy in kJ/kg⋅K

Saturation Properties in Light Gray

Absolute Pressure, kPa

V

160

170

180

190  

−18.54°C

−17.00°C

−15.53°C

−14.12°C

H

S

V

H

S

V

H

S

V

H

S

Temp [°C] 

0.1086

351.0

1.597

0.1026

352.1

1.597

0.0972

353.0

1.597

0.0923

354.0

1.597

Temp [°C] 

−15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130

0.1105 0.1132 0.1158 0.1184 0.1210 0.1235 0.1261 0.1286 0.1311 0.1335 0.1360 0.1385 0.1409 0.1433 0.1458 0.1482 0.1506 0.1530 0.1554 0.1578 0.1602 0.1626 0.1649 0.1673 0.1697 0.1720 0.1744 0.1767 0.1791 0.1815

354.1 358.4 362.7 367.1 371.5 375.9 380.4 384.9 389.4 394.0 398.7 403.3 408.1 412.8 417.6 422.4 427.3 432.2 437.2 442.2 447.2 452.3 457.4 462.6 467.7 473.0 478.2 483.5 488.9 494.2

1.609 1.625 1.641 1.658 1.674 1.689 1.705 1.721 1.736 1.751 1.766 1.782 1.796 1.811 1.826 1.841 1.855 1.870 1.884 1.898 1.912 1.926 1.940 1.954 1.968 1.982 1.995 2.009 2.023 2.036

0.1036 0.1061 0.1086 0.1111 0.1135 0.1159 0.1183 0.1207 0.1231 0.1254 0.1277 0.1301 0.1324 0.1347 0.1370 0.1393 0.1415 0.1438 0.1461 0.1483 0.1506 0.1528 0.1551 0.1573 0.1595 0.1618 0.1640 0.1662 0.1684 0.1706

353.8 358.1 362.4 366.8 371.2 375.7 380.2 384.7 389.3 393.9 398.5 403.2 407.9 412.7 417.5 422.3 427.2 432.1 437.1 442.1 447.1 452.2 457.3 462.5 467.6 472.9 478.1 483.4 488.8 494.2

1.603 1.620 1.636 1.653 1.669 1.684 1.700 1.716 1.731 1.747 1.762 1.777 1.792 1.807 1.821 1.836 1.850 1.865 1.879 1.894 1.908 1.922 1.936 1.950 1.963 1.977 1.991 2.004 2.018 2.031

0.0974 0.0998 0.1022 0.1045 0.1069 0.1092 0.1114 0.1137 0.1160 0.1182 0.1204 0.1226 0.1248 0.1270 0.1292 0.1313 0.1335 0.1356 0.1378 0.1399 0.1420 0.1442 0.1463 0.1484 0.1505 0.1526 0.1547 0.1568 0.1589 0.1610

353.5 357.8 362.2 366.6 371.0 375.5 380.0 384.5 389.1 393.7 398.4 403.0 407.8 412.5 417.3 422.2 427.1 432.0 437.0 442.0 447.0 452.1 457.2 462.4 467.6 472.8 478.1 483.4 488.7 494.1

1.598 1.615 1.632 1.648 1.664 1.680 1.696 1.711 1.727 1.742 1.757 1.772 1.787 1.802 1.817 1.832 1.846 1.861 1.875 1.889 1.903 1.917 1.931 1.945 1.959 1.973 1.987 2.000 2.014 2.027

0.0942 0.0965 0.0987 0.1009 0.1031 0.1053 0.1074 0.1096 0.1117 0.1138 0.1159 0.1180 0.1201 0.1222 0.1242 0.1263 0.1283 0.1303 0.1324 0.1344 0.1364 0.1384 0.1405 0.1425 0.1445 0.1465 0.1485 0.1505 0.1524

357.6 362.0 366.4 370.8 375.3 379.8 384.3 388.9 393.5 398.2 402.9 407.6 412.4 417.2 422.1 427.0 431.9 436.9 441.9 446.9 452.0 457.1 462.3 467.5 472.7 478.0 483.3 488.6 494.0

1.610 1.627 1.643 1.659 1.675 1.691 1.707 1.722 1.738 1.753 1.768 1.783 1.798 1.813 1.827 1.842 1.856 1.871 1.885 1.899 1.913 1.927 1.941 1.955 1.969 1.982 1.996 2.010 2.023

−15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130

Absolute Pressure, kPa 200

210

 −12.77°C V

H

220 −10.22°C

 −11.47°C S

V

H

230  −9.01°C

S

V

H

S

V

H

S

Temp [°C] 

0.0879

354.9

1.597

0.0839

355.7

1.597

0.0802

356.6

1.597

0.0769

357.4

1.597

Temp [°C] 

−10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135

0.0891 0.0913 0.0934 0.0956 0.0977 0.0997 0.1018 0.1039 0.1059 0.1079 0.1099 0.1119 0.1139 0.1159 0.1178 0.1198 0.1217 0.1237 0.1256 0.1275 0.1295 0.1314 0.1333 0.1352 0.1371 0.1390 0.1409 0.1428 0.1447 0.1466

357.3 361.7 366.1 370.6 375.1 379.6 384.2 388.7 393.4 398.0 402.7 407.5 412.3 417.1 421.9 426.8 431.8 436.7 441.7 446.8 451.9 457.0 462.2 467.4 472.6 477.9 483.2 488.5 493.9 499.3

1.606 1.623 1.639 1.655 1.671 1.687 1.703 1.718 1.733 1.749 1.764 1.779 1.794 1.809 1.823 1.838 1.852 1.867 1.881 1.895 1.909 1.923 1.937 1.951 1.965 1.979 1.992 2.006 2.019 2.032

0.0845 0.0866 0.0887 0.0907 0.0927 0.0947 0.0967 0.0987 0.1006 0.1025 0.1045 0.1064 0.1083 0.1101 0.1120 0.1139 0.1158 0.1176 0.1195 0.1213 0.1231 0.1250 0.1268 0.1286 0.1305 0.1323 0.1341 0.1359 0.1377 0.1395

357.0 361.5 365.9 370.4 374.9 379.4 384.0 388.6 393.2 397.9 402.6 407.3 412.1 417.0 421.8 426.7 431.6 436.6 441.6 446.7 451.8 456.9 462.1 467.3 472.5 477.8 483.1 488.5 493.8 499.3

1.602 1.618 1.635 1.651 1.667 1.683 1.699 1.714 1.730 1.745 1.760 1.775 1.790 1.805 1.819 1.834 1.849 1.863 1.877 1.891 1.906 1.920 1.934 1.947 1.961 1.975 1.988 2.002 2.015 2.029

0.0803 0.0824 0.0843 0.0863 0.0883 0.0902 0.0921 0.0940 0.0958 0.0977 0.0995 0.1013 0.1032 0.1050 0.1068 0.1086 0.1103 0.1121 0.1139 0.1157 0.1174 0.1192 0.1209 0.1227 0.1244 0.1261 0.1279 0.1296 0.1313 0.1331

356.8 361.2 365.7 370.1 374.7 379.2 383.8 388.4 393.0 397.7 402.4 407.2 412.0 416.8 421.7 426.6 431.5 436.5 441.5 446.6 451.7 456.8 462.0 467.2 472.4 477.7 483.0 488.4 493.8 499.2

1.597 1.614 1.631 1.647 1.663 1.679 1.695 1.710 1.726 1.741 1.756 1.771 1.786 1.801 1.816 1.830 1.845 1.859 1.874 1.888 1.902 1.916 1.930 1.944 1.958 1.971 1.985 1.998 2.012 2.025

0.0785 0.0804 0.0823 0.0842 0.0860 0.0878 0.0896 0.0914 0.0932 0.0950 0.0967 0.0985 0.1002 0.1020 0.1037 0.1054 0.1071 0.1088 0.1105 0.1122 0.1139 0.1155 0.1172 0.1189 0.1206 0.1222 0.1239 0.1255 0.1272

360.9 365.4 369.9 374.4 379.0 383.6 388.2 392.9 397.6 402.3 407.0 411.8 416.7 421.6 426.5 431.4 436.4 441.4 446.5 451.6 456.7 461.9 467.1 472.3 477.6 482.9 488.3 493.7 499.1

1.610 1.627 1.643 1.659 1.675 1.691 1.707 1.722 1.737 1.753 1.768 1.783 1.798 1.812 1.827 1.841 1.856 1.870 1.884 1.899 1.913 1.927 1.940 1.954 1.968 1.981 1.995 2.008 2.022

−10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 (Continued)

2-255

2-256 TABLE 2-132

Opteon™ YF (R-1234yf) (Continued )

Superheated Vapor—Constant Pressure Tables V = Volume in m3/kg

H = Enthalpy in kJ/kg

S = Entropy in kJ/kg⋅K

Saturation Properties in Light Gray

Absolute Pressure, kPa

V

240

250

260

270

 −7.84°C

−6.70°C

−5.60°C

 −4.54°C

S

V

H

S

H

S

Temp [°C] 

0.0738

358.2

H

1.597

S

0.0710

V

358.9

H

1.597

0.0684

359.6

1.597

0.0659

V

360.3

1.597

Temp [°C] 

−5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140

0.0749 0.0768 0.0786 0.0804 0.0822 0.0840 0.0857 0.0874 0.0891 0.0908 0.0925 0.0942 0.0959 0.0976 0.0992 0.1009 0.1025 0.1041 0.1058 0.1074 0.1090 0.1106 0.1122 0.1138 0.1154 0.1170 0.1186 0.1202 0.1218 0.1234

360.7 365.2 369.7 374.2 378.8 383.4 388.0 392.7 397.4 402.1 406.9 411.7 416.5 421.4 426.3 431.3 436.3 441.3 446.4 451.5 456.6 461.8 467.0 472.3 477.5 482.9 488.2 493.6 499.0 504.5

1.606 1.623 1.639 1.656 1.672 1.687 1.703 1.719 1.734 1.749 1.764 1.779 1.794 1.809 1.824 1.838 1.852 1.867 1.881 1.895 1.909 1.923 1.937 1.951 1.965 1.978 1.992 2.005 2.019 2.032

0.0716 0.0734 0.0752 0.0769 0.0787 0.0804 0.0821 0.0837 0.0854 0.0870 0.0887 0.0903 0.0919 0.0935 0.0951 0.0967 0.0983 0.0998 0.1014 0.1030 0.1045 0.1061 0.1076 0.1092 0.1107 0.1122 0.1138 0.1153 0.1168 0.1184

360.4 364.9 369.5 374.0 378.6 383.2 387.9 392.5 397.2 402.0 406.8 411.6 416.4 421.3 426.2 431.2 436.2 441.2 446.3 451.4 456.5 461.7 466.9 472.2 477.4 482.8 488.1 493.5 499.0 504.4

1.603 1.619 1.636 1.652 1.668 1.684 1.700 1.715 1.731 1.746 1.761 1.776 1.791 1.806 1.820 1.835 1.849 1.864 1.878 1.892 1.906 1.920 1.934 1.948 1.961 1.975 1.989 2.002 2.015 2.029

0.0686 0.0703 0.0721 0.0738 0.0754 0.0771 0.0787 0.0803 0.0819 0.0835 0.0851 0.0867 0.0882 0.0898 0.0913 0.0928 0.0944 0.0959 0.0974 0.0989 0.1004 0.1019 0.1034 0.1049 0.1064 0.1078 0.1093 0.1108 0.1123 0.1137

360.2 364.7 369.2 373.8 378.4 383.0 387.7 392.4 397.1 401.8 406.6 411.4 416.3 421.2 426.1 431.1 436.1 441.1 446.2 451.3 456.4 461.6 466.8 472.1 477.4 482.7 488.0 493.4 498.9 504.3

1.599 1.616 1.632 1.649 1.665 1.681 1.696 1.712 1.727 1.743 1.758 1.773 1.788 1.802 1.817 1.832 1.846 1.861 1.875 1.889 1.903 1.917 1.931 1.945 1.958 1.972 1.986 1.999 2.012 2.026

0.0675 0.0691 0.0708 0.0724 0.0740 0.0756 0.0772 0.0787 0.0803 0.0818 0.0833 0.0848 0.0863 0.0878 0.0893 0.0907 0.0922 0.0937 0.0951 0.0966 0.0980 0.0995 0.1009 0.1023 0.1038 0.1052 0.1066 0.1080 0.1094

364.4 369.0 373.6 378.2 382.8 387.5 392.2 396.9 401.7 406.5 411.3 416.1 421.0 426.0 430.9 435.9 441.0 446.1 451.2 456.3 461.5 466.7 472.0 477.3 482.6 488.0 493.4 498.8 504.3

1.612 1.629 1.645 1.661 1.677 1.693 1.709 1.724 1.739 1.755 1.770 1.785 1.799 1.814 1.829 1.843 1.858 1.872 1.886 1.900 1.914 1.928 1.942 1.956 1.969 1.983 1.996 2.010 2.023

−5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140

Absolute Pressure, kPa

V

280

290

300

310 

−3.50°C

−2.49°C

−1.51°C

−0.55°C

S

V

H

S

H

S

Temp [°C] 

0.0637

361.0

H

1.597

S

0.0615

V

361.7

H

1.597

0.0596

362.3

1.598

0.0577

V

362.9

1.598

Temp [°C] 

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145

0.0648 0.0664 0.0680 0.0696 0.0712 0.0727 0.0742 0.0757 0.0772 0.0787 0.0802 0.0816 0.0831 0.0845 0.0860 0.0874 0.0888 0.0902 0.0916 0.0930 0.0944 0.0958 0.0972 0.0986 0.1000 0.1013 0.1027 0.1041 0.1055 0.1068

364.2 368.8 373.4 378.0 382.6 387.3 392.0 396.7 401.5 406.3 411.1 416.0 420.9 425.8 430.8 435.8 440.9 445.9 451.1 456.2 461.4 466.6 471.9 477.2 482.5 487.9 493.3 498.7 504.2 509.7

1.609 1.626 1.642 1.658 1.674 1.690 1.706 1.721 1.736 1.752 1.767 1.782 1.797 1.811 1.826 1.840 1.855 1.869 1.883 1.897 1.911 1.925 1.939 1.953 1.966 1.980 1.993 2.007 2.020 2.033

0.0623 0.0639 0.0655 0.0670 0.0685 0.0700 0.0715 0.0730 0.0744 0.0758 0.0773 0.0787 0.0801 0.0815 0.0829 0.0842 0.0856 0.0870 0.0884 0.0897 0.0911 0.0924 0.0938 0.0951 0.0964 0.0978 0.0991 0.1004 0.1017 0.1031

363.9 368.5 373.2 377.8 382.4 387.1 391.8 396.6 401.4 406.2 411.0 415.9 420.8 425.7 430.7 435.7 440.8 445.8 451.0 456.1 461.3 466.5 471.8 477.1 482.4 487.8 493.2 498.6 504.1 509.6

1.606 1.622 1.639 1.655 1.671 1.687 1.703 1.718 1.734 1.749 1.764 1.779 1.794 1.808 1.823 1.838 1.852 1.866 1.880 1.894 1.909 1.922 1.936 1.950 1.964 1.977 1.991 2.004 2.017 2.031

0.0600 0.0616 0.0631 0.0646 0.0661 0.0675 0.0690 0.0704 0.0718 0.0732 0.0746 0.0759 0.0773 0.0786 0.0800 0.0813 0.0827 0.0840 0.0853 0.0866 0.0879 0.0892 0.0905 0.0918 0.0931 0.0944 0.0957 0.0970 0.0983 0.0996

363.7 368.3 372.9 377.6 382.2 386.9 391.7 396.4 401.2 406.0 410.9 415.7 420.6 425.6 430.6 435.6 440.6 445.7 450.9 456.0 461.2 466.4 471.7 477.0 482.3 487.7 493.1 498.6 504.0 509.6

1.603 1.619 1.636 1.652 1.668 1.684 1.700 1.715 1.731 1.746 1.761 1.776 1.791 1.806 1.820 1.835 1.849 1.864 1.878 1.892 1.906 1.920 1.934 1.947 1.961 1.975 1.988 2.002 2.015 2.028

0.0579 0.0594 0.0609 0.0623 0.0638 0.0652 0.0666 0.0680 0.0693 0.0707 0.0720 0.0733 0.0747 0.0760 0.0773 0.0786 0.0799 0.0812 0.0825 0.0837 0.0850 0.0863 0.0875 0.0888 0.0901 0.0913 0.0926 0.0938 0.0950 0.0963

363.4 368.1 372.7 377.4 382.0 386.8 391.5 396.2 401.0 405.9 410.7 415.6 420.5 425.5 430.5 435.5 440.5 445.6 450.7 455.9 461.1 466.3 471.6 476.9 482.3 487.6 493.0 498.5 504.0 509.5

1.600 1.616 1.633 1.649 1.665 1.681 1.697 1.713 1.728 1.743 1.758 1.773 1.788 1.803 1.818 1.832 1.847 1.861 1.875 1.889 1.903 1.917 1.931 1.945 1.958 1.972 1.986 1.999 2.012 2.026

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145

2-257

2-258

PHYSICAL AnD CHEMICAL DATA

FIG. 2-16

Pressure-enthalpy diagram for Refrigerant 1234yf. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M.O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology). Provided by Chemours.

THERMODYnAMIC PROPERTIES TABLE 2-133 Thermophysical Properties of Saturated Seawater Temp., °C

Pressure, bar

v, (m3/kg)103

cp, kJ/(kg⋅K)

µ, Ns/m2

k, W/(m⋅K)

NPr

105κ, 1/bar

0 1 2 3 4

0.005993 0.006438 0.006916 0.007427 0.007970

1.000158 1.000099 1.000057 1.000033 1.000025

4.000 4.000 4.000 4.000 4.001

0.001884 0.001827 0.001772 0.001720 0.001669

0.560 0.563 0.565 0.567 0.569

13.46 12.98 12.55 12.13 11.74

5.06 5.02 4.98 4.95 4.92

5 6 7 8 9

0.008548 0.009163 0.009816 0.010511 0.011248

1.000033 1.000057 1.000096 1.000149 1.000261

4.001 4.001 4.002 4.002 4.002

0.001620 0.001574 0.001529 0.001486 0.001445

0.571 0.574 0.576 0.578 0.580

11.35 10.97 10.62 10.29 9.97

4.89 4.86 4.83 4.80 4.78

10 11 12 13 14

0.01203 0.01286 0.01374 0.01467 0.01566

1.000298 1.000392 1.000500 1.000620 1.000727

4.003 4.003 4.003 4.004 4.004

0.001405 0.001367 0.001330 0.001294 0.001259

0.582 0.584 0.586 0.588 0.590

9.70 9.37 9.09 8.81 8.54

4.76 4.74 4.72 4.70 4.68

15 16 17 18 19

0.01671 0.01781 0.01898 0.02022 0.02153

1.000899 1.001055 1.001224 1.001404 1.001595

4.005 4.005 4.006 4.006 4.007

0.001226 0.001195 0.001165 0.001136 0.001107

0.592 0.594 0.595 0.597 0.599

8.29 8.06 7.82 7.62 7.41

4.66 4.65 4.63 4.62 4.60

20 21 22 23 24

0.02291 0.02437 0.02591 0.02753 0.02924

1.001796 1.002009 1.002232 1.002465 1.002708

4.007 4.007 4.008 4.008 4.009

0.001080 0.001054 0.001029 0.001005 0.000981

0.600 0.602 0.604 0.605 0.607

7.21 7.02 6.82 6.66 6.48

4.59 4.57 4.56 4.55 4.54

25 26 27 28 29

0.03104 0.03294 0.03494 0.03705 0.03926

1.002961 1.003224 1.003496 1.003778 1.004069

4.009 4.009 4.010 4.010 4.011

0.000958 0.000936 0.000915 0.000895 0.000875

0.608 0.609 0.611 0.612 0.614

6.31 6.16 6.01 5.86 5.72

4.53 4.52 4.51 4.50 4.49

30

0.04159

1.004369

4.011

0.000855

0.615

5.58

4.48

κ = (−1/V)(∂v/∂p)T ⋅ 105. Thus, at 0°C, the compressibility is 5.06 × 10−5/bar. For further information see, for instance, Bromley, LeR. A., J. Chem. Eng. Data, 12, 2 (1967): 202–206; 13, 1 (1968): 60–62 and 13, 3: 399–402; 15, 2 (1970): 246–253; and A.I.Ch.E.J., 20, 2 (1974): 326–335. Thermal conductivity data sources include Castelli, V. J., E. M. Stanley, et al., Deep Sea Res., 211 (1974): 311–318; Levy, F. L., Int. J. Refrig., 5, 3 (1982): 155–159. For velocity of sound, see, for instance, U.S. Naval Oceanographic Office SP 58, 1962 (50 pp.). More recent information is contained in UNESCO technical papers. See Marine Science No. 38, 1981 (6 pp.) and No. 44, 1983 (53 pp.). For sea ice properties, see Fukusako, S., Int. J. Thermophys., 11, 2 (1990): 353–372.

2-259

FIG. 2-17

Enthalpy-concentration diagram for aqueous sodium hydroxide at 1 atm. Reference states: enthalpy of liquid water at 32°F and vapor pressure is zero; partial molal enthalpy of infinitely dilute NaOH solution at 64°F and 1 atm is zero. [W.L. McCabe, Trans. Am. Inst. Chem. Eng., 31: 129 (1935).]

FIG. 2-18 Enthalpy-concentration diagram for aqueous sulfuric acid at 1 atm. Reference states: enthalpies of pure-liquid components at 32°F and vapor pressures are zero. Note: It should be observed that the weight basis includes the vapor, which is particularly important in the two-phase region. The upper ends of the tie lines in this region are assumed to be pure water. (O.A. Hougen and K.M. Watson, Chemical Process Principles, part I, Wiley, New York, 1943.)

2-260

THERMODYnAMIC PROPERTIES TABLE 2-134

Temp., °F

Saturated Solid/Vapor Water* Volume, ft3/lb

Enthalpy, Btu/lb

Entropy, Btu/(lb)(°F)

Pressure, lb/in2 abs.

Solid

Vapor

Solid

Vapor

Solid

Vapor

−160 −150 −140 −130 −120

4.949.−8 1.620.−7 4.928.−7 1.403.−6 3.757.−6

0.01722 0.01723 0.01724 0.01725 0.01726

3.607.+9 1.139.+9 3.864.+8 1.400.+8 5.386.+7

−222.05 −218.82 −215.49 −212.08 −208.58

990.38 994.80 999.21 1003.63 1008.05

−0.4907 −0.4801 −0.4695 −0.4590 −0.4485

3.5549 3.4387 3.3301 3.2284 3.1330

−110 −100 −90 −80 −70

9.517.−6 2.291.−5 5.260.−5 1.157.−4 2.443.−4

0.01728 0.01729 0.01730 0.01731 0.01732

2.189.+7 9.352.+6 4.186.+6 1.955.+6 9.501.+5

−204.98 −201.28 −197.49 −193.60 −189.61

1012.47 1016.89 1021.31 1025.73 1030.15

−0.4381 −0.4277 −0.4173 −0.4069 −0.3965

3.0434 2.9591 2.8796 2.8045 2.7336

−60 −50 −45 −40 −35

4.972.−4 9.776.−4 1.354.−3 1.861.−3 2.540.−3

0.01734 0.01735 0.01736 0.01737 0.01737

4.788.+5 2.496.+5 1.824.+5 1.343.+5 9.961.+4

−185.52 −181.34 −179.21 −177.06 −174.88

1034.58 1039.00 1041.21 1043.42 1045.63

−0.3862 −0.3758 −0.3707 −0.3655 −0.3604

2.6664 2.6028 2.5723 2.5425 2.5135

−30 −25 −20 −15 −10

3.440.−3 4.627.−3 6.181.−3 8.204.−3 1.082.−2

0.01738 0.01739 0.01739 0.01740 0.01741

7.441.+4 5.596.+4 4.237.+4 3.228.+4 2.475.+4

−172.68 −170.46 −168.21 −165.94 −163.65

1047.84 1050.05 1052.26 1054.47 1056.67

−0.3552 −0.3501 −0.3449 −0.3398 −0.3347

2.4853 2.4577 2.4308 2.4046 2.3791

−5 0 5 10 15

1.419.−2 1.849.−2 2.396.−2 3.087.−2 3.957.−2

0.01741 0.01742 0.01743 0.01744 0.01744

1.909.+4 1.481.+4 1.155.+4 9.060.+3 7.144.+3

−161.33 −158.98 −156.61 −154.22 −151.80

1058.88 1061.09 1063.29 1065.50 1067.70

−0.3295 −0.3244 −0.3193 −0.3142 −0.3090

2.3541 2.3297 2.3039 2.2827 2.2600

16 18 20 22 24

4.156.−2 4.581.−2 5.045.−2 5.552.−2 6.105.−2

0.01745 0.01745 0.01745 0.01746 0.01746

6.817.+3 6.210.+3 5.662.+3 5.166.+3 4.717.+3

−151.32 −150.34 −149.36 −148.38 −147.39

1068.14 1069.02 1069.90 1070.38 1071.66

−0.3080 −0.3060 −0.3039 −0.3019 −0.2998

2.2555 2.2466 2.2378 2.2291 2.2205

26 28 30 31 32

6.708.−2 7.365.−2 8.080.−2 8.461.−2 8.858.−2

0.01746 0.01746 0.01747 0.01747 0.01747

4.311.+3 3.943.+3 3.608.+3 3.453.+3 3.305.+3

−146.40 −145.40 −144.40 −143.90 −143.40

1072.53 1073.41 1074.29 1074.73 1075.16

−0.2978 −0.2957 −0.2937 −0.2927 −0.2916

2.2119 2.2034 2.1950 2.1908 2.1867

∗Condensed from Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, 1967 and 1972. Reproduced by permission. The validity of many standard reference tables has been critically reviewed by Jancso, Pupezin, and van Hook, J. Phys. Chem., 74 (1970):2984. Current information on the properties of solid, vapor, and liquid water properties can be found at http://www.iapws.org. The notation 4.949.−8, 3.607.+9, etc., means 4.949 × 10−8, 3.607 × 109, etc.

2-261

2-262

TABLE 2-135 Thermodynamic Properties of Water Temperature K

Pressure MPa

Density mol/dm3

273.16 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 647.1

0.000612 0.000992 0.001920 0.003537 0.006231 0.010546 0.017213 0.027188 0.041682 0.062194 0.090535 0.12885 0.17964 0.24577 0.33045 0.43730 0.57026 0.73367 0.9322 1.1709 1.4551 1.7905 2.1831 2.6392 3.1655 3.7690 4.4569 5.2369 6.1172 7.1062 8.2132 9.448 10.821 12.345 14.033 15.901 17.969 20.265 22.064

55.497 55.501 55.440 55.315 55.139 54.919 54.662 54.371 54.049 53.698 53.321 52.918 52.490 52.038 51.563 51.064 50.541 49.994 49.421 48.824 48.199 47.545 46.861 46.145 45.393 44.603 43.770 42.889 41.954 40.956 39.885 38.725 37.456 36.048 34.451 32.577 30.210 26.729 17.874

273.16 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440

0.000612 0.000992 0.001920 0.003537 0.006231 0.010546 0.017213 0.027188 0.041682 0.062194 0.090535 0.12885 0.17964 0.24577 0.33045 0.43730 0.57026 0.73367

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

0 0.51875 1.2742 2.0278 2.7808 3.5339 4.2873 5.0414 5.7964 6.5526 7.3104 8.0701 8.8320 9.5966 10.364 11.136 11.911 12.692 13.477 14.269 15.068 15.875 16.690 17.515 18.352 19.200 20.064 20.943 21.841 22.762 23.709 24.688 25.707 26.777 27.917 29.160 30.585 32.422 36.314

1.1E-05 0.51877 1.2742 2.0279 2.7810 3.5340 4.2876 5.0419 5.7972 6.5538 7.3121 8.0725 8.8354 9.6013 10.371 11.144 11.923 12.706 13.496 14.293 15.098 15.913 16.737 17.573 18.421 19.285 20.165 21.065 21.987 22.935 23.915 24.932 25.996 27.119 28.324 29.648 31.180 33.180 37.548

0 0.001876 0.004527 0.007082 0.009551 0.011941 0.014260 0.016511 0.018700 0.020830 0.022906 0.024932 0.026911 0.028847 0.030743 0.032602 0.034427 0.036222 0.037988 0.039729 0.041448 0.043147 0.044830 0.046498 0.048156 0.049807 0.051454 0.053102 0.054756 0.056422 0.058106 0.059821 0.061577 0.063396 0.065309 0.067371 0.069715 0.072737 0.079393

42.785 42.954 43.201 43.446 43.690 43.931 44.169 44.404 44.634 44.860 45.079 45.291 45.496 45.691 45.876 46.050 46.211 46.359

45.055 45.280 45.609 45.936 46.261 46.582 46.900 47.212 47.519 47.819 48.111 48.393 48.665 48.924 49.170 49.400 49.613 49.807

0.16494 0.16174 0.15741 0.15344 0.14981 0.14647 0.14339 0.14054 0.13791 0.13546 0.13317 0.13104 0.12904 0.12715 0.12537 0.12369 0.12208 0.12054

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

0.075978 0.075669 0.075095 0.074412 0.073645 0.072811 0.071927 0.071008 0.070070 0.069124 0.068180 0.067247 0.066331 0.065438 0.064570 0.063731 0.062920 0.062140 0.061390 0.060671 0.059984 0.059327 0.058702 0.058109 0.057548 0.057023 0.056536 0.056089 0.055690 0.055347 0.055071 0.054881 0.054808 0.054902 0.055258 0.056100 0.058152 0.064521

0.076023 0.075688 0.075429 0.075320 0.075294 0.075317 0.075373 0.075456 0.075567 0.075708 0.075883 0.076098 0.076357 0.076664 0.077026 0.077447 0.077934 0.078495 0.079136 0.079869 0.080706 0.081662 0.082757 0.084013 0.085464 0.087149 0.089124 0.091464 0.094275 0.097713 0.10201 0.10754 0.11491 0.12526 0.14100 0.16852 0.23108 0.46736

1402.3 1434.1 1472.1 1501.4 1523.2 1538.7 1548.7 1553.9 1554.8 1552.0 1545.8 1536.5 1524.3 1509.5 1492.2 1472.5 1450.6 1426.5 1400.4 1372.2 1342.0 1309.8 1275.7 1239.6 1201.5 1161.3 1119.1 1074.6 1027.9 978.54 926.44 871.23 812.49 749.57 681.27 604.73 513.19 400.66 0

−0.24142 −0.23515 −0.22720 −0.22024 −0.21393 −0.20804 −0.20241 −0.19690 −0.19140 −0.18581 −0.18005 −0.17404 −0.16769 −0.16092 −0.15366 −0.14581 −0.13728 −0.12794 −0.11767 −0.10631 −0.09369 −0.07959 −0.06372 −0.04578 −0.02534 −0.00189 0.025264 0.057002 0.094527 0.13949 0.19425 0.26220 0.34857 0.46172 0.61660 0.84473 1.2251 1.9542 3.7410

561.04 574.04 592.73 610.28 626.05 639.71 651.18 660.55 668.00 673.76 678.02 681.00 682.83 683.64 683.52 682.53 680.70 678.05 674.59 670.28 665.12 659.07 652.06 644.05 634.95 624.68 613.15 600.26 585.95 570.21 553.08 534.74 515.43 495.46 475.03 454.10 432.51 414.93

1791.2 1433.7 1084.0 853.84 693.54 577.02 489.49 421.97 368.77 326.10 291.36 262.69 238.77 218.60 201.43 186.68 173.91 162.77 152.98 144.31 136.58 129.64 123.37 117.66 112.42 107.57 103.05 98.792 94.746 90.857 87.074 83.342 79.600 75.773 71.759 67.382 62.244 55.247

0.025553 0.025657 0.025816 0.025982 0.026158 0.026350 0.026568 0.026821 0.027118 0.027469 0.027883 0.028372 0.028944 0.029608 0.030369 0.031230 0.032187 0.033234

0.033947 0.034073 0.034270 0.034483 0.034716 0.034980 0.035287 0.035653 0.036091 0.036617 0.037249 0.038004 0.038903 0.039963 0.041203 0.042634 0.044269 0.046114

409.00 413.92 420.99 427.89 434.63 441.18 447.54 453.68 459.58 465.22 470.57 475.61 480.32 484.67 488.65 492.22 495.39 498.12

Cv kJ/(mol⋅K)

Saturated Properties

0.000269 0.000426 0.000797 0.001420 0.002424 0.003978 0.006304 0.009681 0.014448 0.021014 0.029859 0.041537 0.056683 0.076014 0.10034 0.13055 0.16765 0.21276

0.018019 0.018018 0.018038 0.018078 0.018136 0.018209 0.018294 0.018392 0.018502 0.018623 0.018754 0.018897 0.019051 0.019217 0.019394 0.019583 0.019786 0.020003 0.020234 0.020482 0.020748 0.021033 0.021340 0.021671 0.022030 0.022420 0.022847 0.023316 0.023836 0.024417 0.025072 0.025823 0.026698 0.027741 0.029026 0.030697 0.033101 0.037413 0.055948 3711.0 2345.4 1254.3 704.01 412.60 251.39 158.62 103.30 69.213 47.586 33.491 24.075 17.642 13.156 9.9666 7.6601 5.9649 4.7002

592.65 477.26 351.65 264.35 203.74 161.25 130.92 108.77 92.178 79.440 69.427 61.373 54.749 49.181 44.405 40.237 36.550 33.259

17.071 17.442 18.031 18.673 19.369 20.117 20.922 21.784 22.707 23.695 24.750 25.875 27.074 28.347 29.699 31.128 32.638 34.230

9.2163 9.3815 9.6414 9.9195 10.213 10.518 10.833 11.157 11.487 11.823 12.162 12.504 12.848 13.192 13.538 13.883 14.228 14.573

450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 647.1

0.93220 1.1709 1.4551 1.7905 2.1831 2.6392 3.1655 3.7690 4.4569 5.2369 6.1172 7.1062 8.2132 9.4480 10.821 12.345 14.033 15.901 17.969 20.265 22.064

0.26711 0.33209 0.40925 0.50035 0.60738 0.73265 0.87884 1.0491 1.2473 1.4780 1.7471 2.0620 2.4325 2.8720 3.3994 4.0434 4.8497 5.9009 7.3737 9.8331 17.874

3.7438 3.0113 2.4435 1.9986 1.6464 1.3649 1.1379 0.95318 0.80174 0.67659 0.57238 0.48497 0.41110 0.34819 0.29417 0.24732 0.20620 0.16946 0.13562 0.10170 0.055948

55.317 53.212

0.018078 0.018793

46.492 46.609 46.708 46.788 46.848 46.885 46.898 46.883 46.838 46.758 46.641 46.478 46.264 45.988 45.636 45.188 44.613 43.855 42.801 41.095 36.314

49.982 50.134 50.263 50.367 50.442 50.487 50.500 50.475 50.411 50.302 50.142 49.925 49.641 49.278 48.819 48.242 47.506 46.550 45.238 43.156 37.548

0.11907 0.11764 0.11627 0.11493 0.11362 0.11233 0.11105 0.10979 0.10852 0.10724 0.10595 0.10462 0.10324 0.10180 0.10026 0.098600 0.096755 0.094631 0.092029 0.088324 0.079393

0.034362 0.035561 0.036821 0.038137 0.039503 0.040920 0.042391 0.043920 0.045519 0.047197 0.048968 0.050848 0.052856 0.055017 0.057361 0.059939 0.062831 0.066197 0.070465 0.077576

0.048177 0.050469 0.053005 0.055809 0.058919 0.062388 0.066289 0.070723 0.075827 0.081789 0.088873 0.097461 0.10813 0.12178 0.13994 0.16540 0.20384 0.26923 0.40819 0.94736

500.41 502.24 503.60 504.45 504.78 504.55 503.71 502.23 500.05 497.10 493.31 488.58 482.79 475.80 467.41 457.33 445.11 429.99 410.21 379.64 0

30.307 27.653 25.265 23.118 21.187 19.450 17.886 16.475 15.197 14.035 12.973 11.997 11.093 10.248 9.4499 8.6837 7.9329 7.1743 6.3669 5.3854 3.7410

35.904 37.663 39.512 41.455 43.502 45.666 47.969 50.442 53.130 56.102 59.456 63.341 67.981 73.721 81.108 91.052 105.17 126.66 163.44 250.01

−0.22024 −0.17843

610.32 678.97

67.038 47.254 19.298 10.567 6.6444 4.5167 3.2280 2.3885 1.8122 1.4006

25.053 27.008 35.861 46.367 57.964 70.385 83.466 97.085 111.15 125.58

−0.22022 −0.16113 −0.11435

610.73 684.10 673.37

29.473 19.741 10.615 6.6387 4.5077 3.2212 2.3837 1.8089 1.3982

36.427 38.799 47.636 58.735 70.983 84.000 97.573 111.57 125.89

−0.22012 −0.16222 −0.04945 0.047232

612.54 686.54 646.52 604.15

14.917 15.261 15.606 15.952 16.300 16.653 17.011 17.377 17.755 18.149 18.563 19.007 19.489 20.024 20.634 21.350 22.229 23.374 25.018 27.938

Single-Phase Properties 300 372.76

0.1 0.1

372.76 400 500 600 700 800 900 1000 1100 1200

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

0.032769 0.030397 0.024154 0.020086 0.017201 0.015044 0.013369 0.012030 0.010936 0.010024

2.0295 7.5214

0.007081 0.02347

0.074406 0.067921

0.075315 0.075938

45.138 45.900 48.619 51.387 54.256 57.240 60.347 63.581 66.941 70.426

48.190 49.189 52.759 56.365 60.069 63.887 67.827 71.893 76.085 80.402

0.13257 0.13516 0.14313 0.14970 0.15541 0.16050 0.16514 0.16943 0.17342 0.17718

0.02801 0.02717 0.02717 0.028103 0.029225 0.030431 0.031687 0.032963 0.034228 0.035458

0.037444 0.036170 0.035693 0.036513 0.037592 0.038778 0.040024 0.041293 0.042554 0.043781

0.018070 0.019209 0.020307

2.0263 9.5914 13.717

2.0444 9.6106 13.737

0.007077 0.028834 0.038518

0.074353 0.065422 0.061169

0.075270 0.076628 0.079348

3.5015 3.9749 4.8861 5.7547 6.6074 7.4524 8.2932 9.1313 9.9677

46.529 48.111 51.123 54.087 57.121 60.258 63.511 66.885 70.380

50.030 52.086 56.009 59.842 63.729 67.710 71.804 76.016 80.347

0.11863 0.12295 0.13011 0.13602 0.14121 0.14590 0.15021 0.15422 0.15799

0.034718 0.030084 0.029002 0.029629 0.030651 0.031821 0.033051 0.034290 0.035504

0.048846 0.041065 0.038358 0.038495 0.039301 0.040358 0.041522 0.042719 0.043905

0.018038 0.019167 0.021614 0.023175

2.0204 9.5643 17.474 20.685

2.1106 9.6601 17.582 20.801

0.007057 0.028766 0.046415 0.052622

0.074119 0.065337 0.058082 0.056215

0.075070 0.076438 0.083643 0.090740

1501.5 1543.5 471.99 490.31 548.31 598.61 643.92 685.47 724.03 760.17 794.33 826.85

12.256 13.285 17.270 21.407 25.564 29.669 33.685 37.592 41.382 45.054

2-263

1 1 1

453.03 500 600 700 800 900 1000 1100 1200

1 1 1 1 1 1 1 1 1

300 400 500 537.09

5 5 5 5

537.09 600 700

5 5 5

1.4072 1.1320 0.91269

0.71063 0.88340 1.0957

46.785 49.734 53.286

50.338 54.151 58.765

0.10762 0.11436 0.12148

0.046699 0.034611 0.031678

0.079952 0.051045 0.043318

498.04 561.07 624.59

14.362 10.407 6.5536

55.203 54.653 62.680

18.032 21.062 25.547

5 5 5 5 5

0.77805 0.68224 0.60918 0.55109 0.50355

1.2853 1.4658 1.6416 1.8146 1.9859

56.576 59.855 63.197 66.632 70.172

63.002 67.183 71.405 75.705 80.101

0.12714 0.13207 0.13652 0.14061 0.14444

0.031683 0.032430 0.033447 0.034565 0.035704

0.041848 0.041922 0.042571 0.043465 0.044458

674.39 717.57 756.57 792.63 826.45

4.4532 3.1856 2.3599 1.7924 1.3865

73.950 86.626 99.971 113.64 127.51

29.806 33.891 37.821 41.606 45.257

0.28559 0.25158 0.20466 0.17377 0.15134 0.13418 0.12058 0.10951 0.10032 55.439 52.173 46.267 43.151

1503.0 1511.3 1392.0

853.83 282.91

300 400 453.03

800 900 1000 1100 1200

55.340 52.060 49.243

30.517 32.898 41.401 49.786 58.136 66.471 74.799 83.123 91.444 99.763

2.0277 7.5196

501.02 535.74 592.58 640.55 683.48 722.85 759.50 794.01 826.77 1509.8 1520.9 1250.0 1087.8

853.67 218.80 150.24 15.021 17.051 21.329 25.550 29.687 33.718 37.630 41.420 45.088 853.00 219.84 118.27 100.01

(Continued)

2-264

TABLE 2-135 Temperature K

Thermodynamic Properties of Water (Continued ) Pressure MPa

Density mol/dm3

300 400 500 584.15

10 10 10 10

55.561 52.312 46.517 38.213

584.15 600 700 800 900 1000 1100 1200

10 10 10 10 10 10 10 10

Volume dm3/mol

Int. energy kJ/mol

Enthalpy kJ/mol

Entropy kJ/(mol⋅K)

Cv kJ/(mol⋅K)

Cp kJ/(mol⋅K)

Sound speed m/s

Joule-Thomson K/MPa

Therm. cond. mW/(m⋅K)

Viscosity µPa⋅s

Single-Phase Properties (Continued )

3.0787 2.7628 1.9625 1.6157 1.3945 1.2345 1.1111 1.0119

0.017998 0.019116 0.021497 0.026169

2.0131 9.5311 17.389 25.105

2.1931 9.7222 17.604 25.367

0.007031 0.028682 0.046244 0.060543

0.073834 0.065233 0.058028 0.054835

0.074829 0.076208 0.082910 0.11032

1518.2 1532.7 1271.3 847.33

−0.21999 −0.16351 −0.05669 0.29540

614.81 689.57 651.64 526.83

852.28 221.13 119.55 81.795

0.32482 0.36195 0.50956 0.61893 0.71709 0.81002 0.90002 0.98820

45.852 47.183 52.145 55.851 59.334 62.798 66.314 69.910

49.100 50.802 57.241 62.040 66.505 70.898 75.314 79.792

0.10117 0.10405 0.11405 0.12046 0.12572 0.13035 0.13456 0.13846

0.055964 0.047271 0.034838 0.033089 0.033219 0.033947 0.034908 0.035954

0.128640 0.092535 0.051779 0.045603 0.044062 0.043952 0.044427 0.045164

472.51 503.34 602.20 662.61 710.98 753.03 791.02 826.16

9.9124 9.4382 6.3228 4.3529 3.1289 2.3241 1.7683 1.3695

76.543 71.110 69.301 78.476 90.516 103.50 116.73 130.00

20.267 21.036 25.704 30.054 34.176 38.111 41.882 45.506

300 400 500 600 700 800 900 1000 1100 1200

100 100 100 100 100 100 100 100 100 100

57.573 54.500 49.914 43.935 36.179 26.768 19.073 14.734 12.246 10.631

0.017369 0.018349 0.020034 0.022761 0.027640 0.037359 0.052429 0.067868 0.081656 0.094062

1.8921 9.0423 16.289 23.820 31.916 40.700 48.805 55.188 60.470 65.222

3.6290 10.877 18.292 26.097 34.680 44.435 54.048 61.975 68.635 74.628

0.006516 0.027360 0.043895 0.058109 0.071320 0.084331 0.095669 0.10404 0.11039 0.11561

0.069812 0.063582 0.057324 0.052776 0.049610 0.047143 0.043932 0.041345 0.040131 0.039810

0.071696 0.073086 0.075607 0.081104 0.091576 0.10108 0.088057 0.071678 0.062539 0.057826

1667.9 1717.3 1555.7 1300.4 1020.0 813.97 765.30 792.50 832.67 872.28

−0.21618 −0.17905 −0.12564 −0.02079 0.21155 0.65939 1.0399 1.0944 0.98401 0.83544

654.50 741.80 730.42 645.83 510.14 351.46 257.03 232.07 223.70 219.07

856.88 243.50 138.92 101.51 79.363 62.042 53.250 51.518 52.497 54.415

300 400 500 600 700 800 900 1000 1100 1200

500 500 500 500 500 500 500 500 500 500

63.750 60.862 57.695 54.316 50.847 47.385 44.018 40.814 37.834 35.124

0.015686 0.016431 0.017332 0.018411 0.019667 0.021104 0.022718 0.024501 0.026432 0.028470

1.5247 7.9635 14.264 20.481 26.606 32.615 38.492 44.233 49.839 55.312

9.3678 16.179 22.930 29.687 36.439 43.167 49.851 56.484 63.055 69.547

0.003746 0.023347 0.038412 0.050731 0.061141 0.070124 0.077998 0.084987 0.091251 0.096900

0.063403 0.059634 0.055769 0.052734 0.050315 0.048442 0.047068 0.046126 0.045537 0.045218

0.068296 0.067603 0.067522 0.067584 0.067436 0.067080 0.066596 0.066041 0.065356 0.064451

2228.6 2258.7 2200.7 2093.8 1970.5 1850.1 1743.4 1655.7 1589.3 1543.9

−0.19915 −0.19486 −0.18339 −0.16883 −0.15188 −0.13256 −0.11124 −0.08910 −0.06907 −0.05511

763.82 929.09 1096.6 1097.9 935.15 738.72 572.49 445.17 350.97 282.78

1089.4 320.18 189.08 141.83 118.47 104.70 95.388 88.418 83.021 78.952

400 500 600 700 800 900 1000 1100 1200

1000 1000 1000 1000 1000 1000 1000 1000 1000

65.942 63.253 60.572 57.937 55.384 52.937 50.611 48.415 46.349

0.015165 0.015810 0.016509 0.017260 0.018056 0.018890 0.019759 0.020655 0.021575

7.4792 13.357 19.141 24.836 30.435 35.938 41.354 46.695 51.976

22.644 29.167 35.650 42.096 48.491 54.828 61.113 67.350 73.551

0.019833 0.034391 0.046212 0.056150 0.064689 0.072155 0.078776 0.084722 0.090117

0.057934 0.055063 0.053055 0.051393 0.050059 0.049062 0.048373 0.047942 0.047713

0.065743 0.064967 0.064676 0.064219 0.063663 0.063101 0.062594 0.062176 0.061861

2718.6 2677.2 2602.3 2513.7 2423.7 2338.7 2261.5 2193.2 2133.6

−0.19303 −0.19158 −0.18789 −0.18439 −0.18105 −0.17779 −0.17459 −0.17139 −0.16808

1172.7 2199.5 3250.5 3202.2 2408.7 1610.7 1052.9 703.41 487.61

329.93 190.55 137.73 108.98 91.430 80.198 72.716 67.520 63.774

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Wagner, W., and Pruss, A., “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2):387–535, 2002. The source for viscosity is International Association for the Properties of Water and Steam, Revised Release on the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance, IAPWS, 1997. The source for thermal conductivity is the International Association for the Properties of Water and Steam, Revised Release on the IAPS Formulation 1985 for the Thermal Conductivity of Ordinary Water Substance, IAPWS, 1998. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainty in density of the equation of state is 0.0001% at 1 atm in the liquid phase, and 0.001% at other liquid states at pressures up to 10 MPa and temperatures to 423 K. In the vapor phase, the uncertainty is 0.05% or less. The uncertainties rise at higher temperatures and/or pressures, but are generally less than 0.1% in density except at extreme conditions. The uncertainty in pressure in the critical region is 0.1%. The uncertainty of the speed of sound is 0.15% in the vapor and 0.1% or less in the liquid, and increases near the critical region and at high temperatures and pressures. The uncertainty in isobaric heat capacity is 0.2% in the vapor and 0.1% in the liquid, with increasing values in the critical region and at high pressures. The uncertainties of saturation conditions are 0.025% in vapor pressure, 0.0025% in saturated-liquid density, and 0.1% in saturatedvapor density. The uncertainties in the saturated densities increase substantially as the critical region is approached. For the uncertainties in the viscosity and thermal conductivity, see the IAPWS Release.

THERMODYnAMIC PROPERTIES TABLE 2-136 Thermodynamic Properties of Water Substance along the Melting Line T, °C

103 v f , m3/kg

h f , kJ/kg

s f , kJ/kg⋅K

cpf , kJ/kg⋅K

cmelt , kJ/kg⋅K

106α f , K−1

106K f ,T bar−1

0.0100 0.0026 −0.3618 −0.7410 −1.1249

1.00021 1.00016 0.99770 0.99523 0.99278

0 0.0719 3.5140 6.9794 10.3964

0 −0.0001 −0.0054 −0.0110 −0.0167

4.219 4.218 4.196 4.174 4.152

3.969 3.970 3.997 4.023 4.047

−67.42 −67.17 −54.92 −42.52 −30.24

50.90 50.88 50.30 49.73 49.17

200 250 300 400 500

−1.5166 −1.9151 −2.3206 −3.1532 −4.0156

0.99037 0.98798 0.98562 0.98098 0.97643

13.7648 17.0843 20.3547 26.7472 32.9403

−0.0225 −0.0285 −0.0347 −0.0474 −0.0607

4.132 4.112 4.092 4.056 4.022

4.070 4.092 4.113 4.150 4.184

−18.05 −5.93 6.12 30.09 53.97

48.63 48.11 47.59 46.61 45.68

600 800 1000

−4.909 −6.790 −8.803

0.97196 0.96326 0.95493

38.932 50.300 60.836

−0.0747 −0.1046 −0.1371

3.992 3.937 3.893

4.215 4.270 4.320

77.87 126.18 175.98

44.80 43.19 41.74

P, bar 6.117 × 10 1.01325 50 100 150

–3t

Condensed from U. Grigull, Private communication, January 18, 1995. Materials prepared at Technical University München, Germany by U. Grigull and S. Marek. For a table as a function of temperature, see Grigull, U. and S. Marek, Warme u. Stoff., 30 (1994): 1–8. t = the triple point (at 6.117 × 10−3 bar, 0.01°C); vf = 0.0010021 m3/kg: α f = −67.42 × 10−6/K. Other equations for properties are given by Jones, F. E. and G. L. Harris, J. Res. N.I.S.T., 97, 3 (1992): 335–340, and by Wagner, W. and A. Pruss, J. Phys. Chem. Ref. Data, 22, 3 (1993): 783–787. Steam tables include Walker, W. A., U.S. Naval Ordn. Lab. rept. NOLTR NOLTR-66-217 = AD 651105 (0–1000 bar, 0–150°C), 1967 (72 pp.); Grigull, U., J. Straub, et al., Steam Tables in S.I. Units (0.01–1000 bar, 0–1000°C), Springer-Verlag, Berlin, 1990 (133 pp.); Tseng, C. M., T. A. Hamp, et al., Atomic Energy of Canada rept. (30 props, sat liq & vap., 1–220 bar), AECL-5910 1977 (90 pp.). For dissociation, see e.g., Knonicek, V., Rozpr. Cesko Acad Ved., Rada techn ved (0.01–100 bar, 1000–5000 K). 77, 1 (1967). The proceedings of the 10th international conference on the properties of steam were edited by Sytchev, V. V. and A. A. Aleksandrov, Plenum, NY, 1984; and for the 11th conference by Pichal, M. and O. Sifner, Hemisphere, 1989 (550 pp.). Current information on the properties of solid, vapor, and liquid water properties can be found at http://www.iapws.org. For electrical conductivity, see e.g., Marshall, W. L., J. Chem. Eng. Data, 32 (1987): 221–226.

2-265

2-266

PHYSICAL AnD CHEMICAL DATA

TRAnSPORT PROPERTIES Introduction The tables and nomographs in this subsection are organized roughly with mass transport properties first (surface tension, viscosity, diffusion coefficient) followed by thermal transport properties. Unit Conversions For this subsection, the following unit conversions are applicable: Diffusivity: to convert square centimeters per second to square feet per hour, multiply by 3.8750; to convert square meters per second to square feet per hour, multiply by 38,750. Pressure: to convert bars to pounds-force per square inch, multiply by 14.504. Temperature: °F = 9⁄5°C + 32; °R = 9⁄5 K. Thermal conductivity: to convert watts per meter-kelvin to British thermal unit–feet per hour–square foot–degree Fahrenheit, multiply by 0.57779; and to convert British thermal unit–feet per hour–square foot–degree Fahrenheit to watts per meter-kelvin, multiply by 1.7307. Viscosity: to convert pascal-seconds to centipoise, multiply by 1000. Additional References An extensive coverage of the general pressure and temperature variation of thermal conductivity is given in the monograph by Vargaftik, N. B., L. P. Filippov, A. A. Tarzimanov and E. E. Totskiy, Thermal Conductivity of Liquids and Gases (in Russian), Standards Press, Moscow, 1978, now published in English translation by CRC Press, Miami, Fla. For a similar work on viscosity, see Stephan and Lucas, Viscosity of Dense Fluids, Plenum, New York and London, 1979. Tables and polynomial fits for refrigerants in both the gaseous and the liquid states are contained in ASHRAE Handbook—Fundamentals, SI ed., ASHRAE, Atlanta, 2005. Other sources for viscosity include Fischer & Porter Co. catalog 10-A-94, “Fluid Densities and Viscosities,” 1953 (200 industrial fluids in 48 pp.) and

TABLE 2-137

MASS TRAnSPORT PROPERTIES

Surface Tension r (dyn/cm) of Various Liquids

Compound Acetic acid Acetone Aniline

Benzene

Benzonitrile Bromobenzene n-Butane Carbon disulfide Carbon tetrachloride

Chlorobenzene

D. van Velzen, R. L. Cardozo et al., EURATOM Ispra, Italy rept. 4735 e, 1972 (160 pp.). Liquid viscosity, 314 cpds, is summarized in I&EC Fundtls., 11 (1972): 20–26. Five hundred forty-nine binary and ternary systems are discussed in Skubla, P., Coll. Czech. Chem. Commun., 46 (1981): 303–339. See also Duhne, C. R., Chem. Eng. (NY), 86: 15 (July 16, 1979): 83–91 (equations and 326 liquids); and Rao, K. V. K., Chem. Eng. (NY), 90, 11 (May 30, 1983): 90–91 (nomograph, 87 liquids). For rheology, non-Newtonian behavior, see, for instance, Barnes, H., The Chem. Engr. (UK), (June 24, 1993): 17–23; Hyman, W. A., I&EC Fundtls., 16 (1976): 215–218; and Ferguson, J., and Z. Kemblowski, Applied Fluid Rheology, Elsevier, 1991 (325 pp.). Other sources for thermal conductivity include Ho, C. Y., R. W. Powell et al., J. Phys. Chem. Ref. Data, 1 (1972) and 3, suppl. 1 (1974); Childs, Ericks et al., N.B.S. Monogr. 131, 1973; Jamieson, D. T., J. B. Irving et al., Liquid Thermal Conductivity, H.M.S.O., Edinburgh, Scotland, 1975 (220 pp.). Other references include B. Poling, J. Prausnitz, and J. O’Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, 2000; N.B. Vargaftik, Y.K. Vinogradov, and V.S. Yargin, Handbook of Physical Properties of Liquids and Gases, Begell House, New York, 1996; Carl Yaws, Chemical Properties Handbook: Physical, Thermodynamics, Environmental Transport, Safety & Health Related Properties for Organic & Inorganic Chemicals, McGraw-Hill, New York, 1998; and M.R. Riazi, Characterization and Properties of Petroleum Fractions, ASTM, West Conshohocken, Pa., 2005. Free web resources include the NIST Webbook at http://webbook.nist.gov and the KDB (Korea thermophysical properties) database at http://www.cheric.org/ research/kdb/.

T, K

σ

293 333 298 308 318 293 313 333 353 293 313 333 353 293 323 363 293 323 373 203 233 293 293 313 288 308 328 348 368 293 323 373

27.59 23.62 24.02 22.34 21.22 42.67 40.5 38.33 36.15 28.88 26.25 23.67 21.2 39.37 35.89 31.26 35.82 32.34 26.54 23.31 19.69 12.46 32.32 29.35 27.65 25.21 22.76 20.31 17.86 33.59 30.01 24.06

Compound p-Cresol Cyclohexane Cyclopentane Diethyl ether 2,3-Dimethylbutane Ethyl acetate

Ethyl benzoate Ethyl bromide Ethyl mercaptan Formamide n-Heptane

T, K

σ

313 373 293 313 333 293 313 288 303 293 313 293 313 333 353 373 293 313 333 283 303 288 303 298 338 373 293 313 333 353

34.88 29.32 25.24 22.87 20.49 22.61 19.68 17.56 16.2 17.38 15.38 23.97 21.65 19.32 17 14.68 35.04 32.92 30.81 25.36 23.04 23.87 22.68 57.02 53.66 50.71 20.14 18.18 16.22 14.26

Compound

T, K

σ

Isobutyric acid

293 313 333 363 293 323 373 423 473 293 313 333 313 333 373 293 313 333 363 293 313 333 353 373 293 313 333

25.04 23.2 21.36 18.6 24.62 20.05 12.9 6.3 0.87 22.56 20.96 19.41 39.27 37.13 32.96 23.71 22.15 20.6 18.27 29.98 26.83 24.68 22.53 20.38 37.21 34.6 31.98

Methyl formate

Methyl alcohol Phenol n-Propyl alcohol

n-Propyl benzene

Pyridine

Methyl formate values from D. B. Macleod, Trans. Faradaay Soc. 19:38, 1923. All others from J. J. Jasper, J. Phys. Chem. Ref. Data 1:841, 1972.

TABLE 2-138 Cmpd. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) Name

Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride

Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4 CF4

CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5 75-73-0

Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 153.8227 88.0043

C1

C2

1.9703E-05 1.4230E-07 1.5640E-08 1.0939E-05 3.1005E-08 4.7754E-07 1.2025E-06 6.5230E-07 1.7154E-07 2.4910E-08 1.4250E-06 4.1855E-08 1.7531E-07 9.2121E-07 2.5082E-08 3.1340E-08 1.1184E-07 7.4266E-08 3.4647E-05 3.7790E-07 6.9022E-08 1.5600E-07 4.0138E-08 1.3874E-06 7.3534E-08 2.2320E-07 6.2597E-08 6.5411E-08 6.0259E-07 2.6960E-07 3.4387E-08 7.5626E-08 7.0728E-08 1.4031E-06 1.2114E-07 6.9744E-07 4.2898E-08 1.0500E-06 1.0060E-07 3.4205E-07 5.4539E-08 3.1378E-08 2.7856E-06 4.2200E-05 1.2566E-08 1.8178E-05 2.1480E-06 5.8204E-08 1.1127E-06 3.1370E-06 2.1709E-06

0.17646 0.7574 1.078 0.23466 0.9762 0.60273 0.4952 0.579 0.7418 0.98882 0.5039 0.9806 0.72 0.60529 0.96663 0.9676 0.8002 0.8289 0.12396 0.6005 0.84014 0.7181 0.90735 0.4434 0.93798 0.7146 0.9115 0.92914 0.5309 0.6715 0.94604 0.83521 0.84383 0.4611 0.76972 0.5462 0.91349 0.4867 0.77881 0.59764 0.88896 0.96513 0.377 0.10118 1.0939 0.17513 0.46 0.9262 0.5338 0.3742 0.45853

C3 1564.6 272.14 1209.5 23.139 327.16 291.4 410.8 138.4 108.3 30.8 176.17 83.24 7.9 152.43 91.197 3260.2 409 74.746 180 34.714 678.22 184.9

199.64 134.7 71.798 64.391 537 92.661 305.25 358.7 95.108 234.21 43.687 663.14 2840 2110.6 290 44.581 94.7 491.5 208

C4

Tmin, K

Viscosity at Tmin

Tmax, K

Viscosity at Tmax

149.78 353.33 289.81 200.15 178.45 229.32 192.40 185.45 286.15 189.63 80.00 195.41 235.65 83.78 403.00 278.68 442.29 395.45 260.28 321.35 257.85 458.15 243.95 342.20 265.85 429.24 154.25 179.44 136.95 164.25 134.86 220.00 196.15 183.85 158.45 87.80 134.26 167.62 199.65 185.30 157.46 133.02 147.43 176.80 267.95 161.30 194.67 161.11 68.15 250.33 89.56

4.166E-06 6.842E-06 7.053E-06 5.386E-06 4.329E-06 5.208E-06 6.468E-06 4.174E-06 7.679E-06 4.455E-06 5.508E-06 6.378E-06 5.122E-06 6.742E-06 8.274E-06 7.077E-06 1.089E-05 8.578E-06 5.104E-06 5.324E-06 5.680E-06 9.122E-06 5.151E-06 6.186E-06 1.383E-05 1.187E-05 6.182E-06 8.126E-06 3.340E-06 4.553E-06 3.559E-06 5.157E-06 4.580E-06 3.961E-06 3.772E-06 1.795E-06 3.770E-06 4.044E-06 4.216E-06 3.424E-06 3.833E-06 3.520E-06 3.329E-06 4.175E-06 5.692E-06 3.144E-06 9.749E-06 5.048E-06 4.434E-06 8.361E-06 5.132E-06

1000 1000 1000 1000 1000 1000 600 1000 1000 1000 2000 1000 1000 3273.1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 600 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 800 1000 1000 1000 1500 800 1250 1000 1000

2.600E-05 2.093E-05 2.681E-05 2.504E-05 2.571E-05 2.314E-05 1.923E-05 2.523E-05 2.532E-05 2.306E-05 6.227E-05 3.551E-05 2.154E-05 1.205E-04 1.992E-05 2.486E-05 2.441E-05 2.087E-05 1.915E-05 1.698E-05 2.129E-05 1.886E-05 2.045E-05 1.768E-05 2.967E-05 2.623E-05 3.397E-05 4.009E-05 1.966E-05 2.457E-05 2.369E-05 2.260E-05 2.259E-05 2.207E-05 2.259E-05 2.325E-05 2.360E-05 2.229E-05 1.993E-05 1.720E-05 2.427E-05 2.466E-05 1.893E-05 2.211E-05 2.404E-05 1.959E-05 5.203E-05 2.693E-05 4.654E-05 2.789E-05 4.267E-05

2-267

(Continued)

2-268

TABLE 2-138 Cmpd. no. 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) (Continued ) Name

Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Diisopropyl amine Diisopropyl ether Diisopropyl ketone

Formula Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O

CAS 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0

Mol. wt. 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19 102.17476 114.18546

C1

C2

2.6000E-07 1.0650E-07 3.5554E-08 1.6960E-07 6.2860E-08 4.7100E-08 3.8802E-07 1.4427E-07 8.7371E-08 1.4305E-07 3.3699E-07 3.7385E-08 1.0881E-06 6.7700E-08 7.9581E-08 5.2312E-08 1.3326E-06 2.3619E-07 3.0260E-07 1.7578E-06 3.9150E-08 3.5018E-05 2.6400E-08 7.1748E-08 5.5065E-08 6.1192E-08 3.2720E-08 5.6914E-07 2.4999E-07 1.4125E-07 1.1379E-07 2.9444E-07 7.7147E-08 2.3340E-07 1.6030E-07 1.5913E-07 2.0135E-07 1.4321E-07 7.6787E-07 1.4906E-07 1.1989E-07 3.3628E-08 4.3184E-07 1.9480E-06 6.5492E-08 2.7228E-06 4.3934E-07 7.7484E-07 4.1380E-07 1.6910E-07 9.2797E-08

0.7423 0.7942 0.98455 0.7693 0.907 0.911 0.6367 0.7438 0.80775 0.7451 0.60751 0.98433 0.48359 0.8367 0.8376 0.89422 0.4537 0.67465 0.64991 0.4265 0.91427 0.11725 0.9487 0.7982 0.8341 0.82546 0.9302 0.50744 0.6878 0.8097 0.8502 0.728 0.79906 0.714 0.763 0.7639 0.73421 0.7785 0.5741 0.7617 0.79108 0.9426 0.6035 0.41 0.86232 0.39531 0.64867 0.57978 0.5999 0.7114 0.7819

C3 98.3 94.7 96.6

205.08 166.15 98.538 159.8 221.17 330.86 36.7 104.97 58.008 445 139 167.14 370.34 22.264 3394.6 71 109.38 79.56 77.434 39.13 273.3 0.5962 83.243 93.816 154.74 80.765 260 205 193.14 111.98 98.159 276.16 105.9 84.37 39.587 247 495.8 59.455 445.07 169.64 198.7 269.5 124 93.399

C4

Tmin, K

Viscosity at Tmin

Tmax, K

Viscosity at Tmax

200.00 227.95 136.75 209.63 175.43 150.35 155.97 285.39 304.19 307.93 177.14 245.25 182.48 279.69 296.60 242.00 169.67 179.28 138.13 145.59 189.64 285.00 243.51 304.55 280.05 206.89 247.56 229.15 60.00 210.15 282.85 370.10 175.30 248.39 256.15 326.14 176.19 237.49 178.01 200.00 172.71 301.15 223.35 156.85 169.20 154.56 215.00 136.95 357.05 187.65 204.81

8.900E-06 5.611E-06 4.506E-06 7.091E-06 6.820E-06 4.533E-06 4.175E-06 6.113E-06 6.687E-06 6.731E-06 3.480E-06 8.411E-06 4.797E-06 6.671E-06 6.917E-06 5.714E-06 3.778E-06 4.409E-06 3.369E-06 4.150E-06 4.238E-06 5.262E-06 3.755E-06 5.070E-06 4.715E-06 3.632E-06 4.761E-06 4.091E-06 4.137E-06 7.685E-06 1.038E-05 1.538E-05 3.278E-06 5.850E-06 6.127E-06 8.313E-06 5.487E-06 7.164E-06 5.895E-06 5.515E-06 4.742E-06 6.450E-06 5.364E-06 3.720E-06 4.046E-06 5.148E-06 8.001E-06 5.478E-06 8.016E-06 4.218E-06 4.089E-06

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 900 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 480 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

3.992E-05 2.348E-05 3.195E-05 3.143E-05 3.307E-05 2.547E-05 2.618E-05 2.108E-05 2.108E-05 2.120E-05 1.834E-05 3.355E-05 2.308E-05 1.928E-05 2.346E-05 2.381E-05 2.118E-05 2.191E-05 2.309E-05 2.441E-05 2.118E-05 1.791E-05 1.729E-05 1.604E-05 1.622E-05 1.701E-05 1.944E-05 1.488E-05 1.744E-05 3.502E-05 3.696E-05 3.895E-05 1.781E-05 2.569E-05 2.588E-05 2.611E-05 2.887E-05 2.824E-05 3.175E-05 2.599E-05 2.611E-05 2.176E-05 2.239E-05 2.212E-05 2.388E-05 2.891E-05 3.317E-05 3.547E-05 2.055E-05 2.049E-05 1.881E-05

103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156

1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan

C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O

534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9

90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396

4.4172E-08 3.9833E-08 1.9377E-06 2.7570E-07 6.8567E-07 7.8220E-07 8.4576E-07 9.9104E-07 3.2282E-08 2.6800E-06 3.5538E-06 5.0372E-07 5.2195E-08 4.7238E-08 5.2854E-07 8.6101E-08 3.9554E-08 2.7334E-07 2.8451E-08 1.2900E-07 6.3440E-08 2.9236E-07 2.5906E-07 1.0613E-07 3.2140E-06 4.9340E-07 4.2231E-07 6.3441E-08 9.2371E-08 1.6175E-07 4.1070E-07 2.1696E-06 2.0789E-06 1.3744E-07 8.6706E-08 2.8132E-07 4.3403E-08 6.7610E-07 2.5704E-08 7.9129E-08 1.3974E-07 1.0498E-07 8.5992E-08 5.5300E-07 5.1539E-07 2.6635E-05 6.3600E-07 2.1174E-07 4.0868E-06 3.9346E-08 1.5948E-05 6.8290E-08 5.0702E-08 6.4320E-07

0.91098 0.91566 0.4093 0.6841 0.52542 0.4994 0.487 0.4723 0.97742 0.3975 0.3766 0.54462 0.85584 0.90849 0.6112 0.8345 0.892597 0.7393 0.93622 0.744 0.8287 0.62458 0.67988 0.8066 0.3572 0.5924 0.58154 0.8369 0.7908 0.7163 0.57143 0.3812 0.4163 0.7557 0.83923 0.6792 0.94806 0.5804 0.94738 0.79565 0.74266 0.76988 0.8427 0.6061 0.5726 0.15779 0.6638 0.7087 0.35526 1.0027 0.21516 0.8774 0.9114 0.5854

492.69 133.2 278.82 371.6 398 436.89 534 1176.1 227.44 69.036 302.85 167.86 129.93 117.03 219.5 702.84 98.902 52.7 667 239.17 239.21 73.63 102.32 142.27 230.06 577.77 352.7 122.8 75.512 238.46 354.9 83.193 98.58 100.41 58.148 273.66 288.76 2173.5 61.6 157.42 651.07 1151.1 54.864 325.3

3590

159.95 226.10 240.91 180.96 145.19 392.70 402.94 396.58 188.44 131.65 212.72 160.00 274.18 122.93 174.88 291.67 413.79 284.95 300.03 210.15 263.57 309.58 90.35 200.00 189.60 192.15 178.20 238.45 258.15 175.15 161.84 134.71 169.41 284.29 260.15 329.00 160.65 193.55 155.15 180.00 140.00 204.15 125.26 199.25 145.65 167.55 53.48 357.88 129.95 131.35 155.15 275.60 281.45 187.55

4.497E-06 5.701E-06 6.006E-06 5.563E-06 3.211E-06 7.936E-06 7.900E-06 7.957E-06 5.405E-06 3.688E-06 4.097E-06 3.300E-06 5.089E-06 3.739E-06 4.544E-06 6.231E-06 8.569E-06 1.226E-05 5.933E-06 4.429E-06 3.511E-06 3.214E-06 2.643E-06 6.029E-06 4.632E-06 4.953E-06 3.673E-06 4.733E-06 5.344E-06 3.392E-06 3.103E-06 2.659E-06 5.714E-06 6.863E-06 7.150E-06 8.359E-06 5.356E-06 5.069E-06 3.058E-06 3.371E-06 3.219E-06 4.224E-06 3.441E-06 5.768E-06 2.994E-06 4.277E-06 4.148E-06 9.491E-06 3.832E-06 5.237E-06 5.608E-06 7.882E-06 8.658E-06 5.037E-06

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

2.388E-05 2.224E-05 2.194E-05 2.744E-05 2.021E-05 1.796E-05 1.749E-05 1.801E-05 2.762E-05 2.722E-05 2.202E-05 1.766E-05 1.804E-05 2.511E-05 2.766E-05 2.350E-05 1.884E-05 3.995E-05 1.831E-05 1.970E-05 1.593E-05 1.284E-05 2.583E-05 2.651E-05 2.274E-05 2.384E-05 1.893E-05 1.915E-05 1.975E-05 1.989E-05 1.729E-05 1.914E-05 2.726E-05 2.264E-05 2.655E-05 2.477E-05 3.032E-05 2.750E-05 1.787E-05 1.781E-05 2.150E-05 1.946E-05 2.742E-05 2.857E-05 2.088E-05 2.496E-05 5.873E-05 2.446E-05 2.880E-05 4.009E-05 3.277E-05 2.776E-05 2.749E-05 2.768E-05

2-269

(Continued)

2-270

TABLE 2-138 Cmpd. no. 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206

Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) (Continued ) Name

Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene

Formula He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10

CAS

Mol. wt.

C1

C2

7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9

4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329

3.2530E-07 3.1338E-07 4.2392E-05 6.6720E-08 1.3633E-08 2.5720E-07 3.4649E-05 8.9656E-08 8.8629E-08 7.7509E-08 4.6970E-08 5.9501E-07 1.2463E-07 4.0986E-05 1.7514E-07 1.2145E-08 1.5773E-07 1.0652E-07 9.7820E-08 9.8882E-08 8.0060E-08 5.2127E-07 4.3636E-08 2.9986E-07 5.5562E-07 2.3489E-07 1.7970E-07 9.1700E-08 4.9240E-07 1.2780E-08 4.5101E-14 3.9314E-08 1.1202E-07 5.2542E-08 6.7978E-05 9.1130E-08 5.2546E-07 3.0663E-07 8.0599E-08 1.3226E-06 1.1630E-06 1.6480E-06 5.6409E-07 7.4106E-08 4.0824E-07 2.4344E-08 1.8690E-07 8.9348E-08 5.0602E-07 8.5423E-07

0.7162 0.6238 0.1011 0.82837 1.0595 0.6502 0.10705 0.78236 0.78376 0.81089 0.8932 0.52758 0.7322 0.10349 0.70737 1.0861 0.7189 0.77022 0.7772 0.7755 0.81293 0.5444 0.90747 0.62647 0.5337 0.7151 0.685 0.9273 0.6702 1.0631 3.0005 1.0134 0.7822 0.88063 0.092766 0.8222 0.59006 0.69655 0.8392 0.4885 0.4787 0.4444 0.5863 0.82436 0.5923 0.97376 0.7096 0.80197 0.55258 0.47389

C3 −9.6 692.2 3420 85.752 248.6 2900.7 100.14 100.18 69.927 57.6 274.02 395 3180.6 157.14 163.3 105.85 99.53 99.825 65.274 237.01 42.32 178.17 244.38 205.05 −0.59 157.7 340 −521.83

C4 107

6000

140

76,111

100.3 4637.3 93.57 105.67 205 77.332 504.3 316 510.66 231.9 83.086 208.22 −91.597 192 77.653 199.82 239.34

18,720

Tmin, K

Viscosity at Tmin

Tmax, K

Viscosity at Tmax

20.00 295.13 229.80 182.57 265.83 239.15 220.00 234.15 238.15 154.12 229.92 192.22 291.31 214.93 177.83 269.25 228.55 223.00 217.35 217.50 133.39 170.05 192.62 141.25 183.65 274.69 13.95 206.45 200.00 300.00 285.50 250.00 227.15 177.95 409.15 288.15 90.69 240.00 301.15 250.00 170.45 196.32 179.69 260.75 159.53 150.00 450.15 155.95 135.58 139.39

3.530E-06 3.254E-06 4.625E-06 3.391E-06 5.052E-06 4.440E-06 4.351E-06 4.485E-06 4.550E-06 3.169E-06 4.832E-06 3.932E-06 3.274E-06 4.523E-06 3.631E-06 5.294E-06 4.567E-06 4.650E-06 4.397E-06 4.403E-06 2.871E-06 3.567E-06 4.235E-06 2.947E-06 3.851E-06 7.460E-06 6.517E-07 1.285E-05 9.594E-06 2.576E-06 9.931E-06 1.058E-05 5.415E-06 5.037E-06 9.629E-06 7.242E-06 3.470E-06 7.523E-06 7.714E-06 6.505E-06 4.769E-06 4.781E-06 5.167E-06 5.515E-06 3.572E-06 2.621E-06 1.000E-05 3.422E-06 3.083E-06 3.263E-06

2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1673.15 3000 800 1000 425 472.68 480 1000 1000 1000 1000 1000 1000 1000 800 800 1000 1000 1000 1000 1000 1000 1000 1000 1000

7.561E-05 1.377E-05 1.928E-05 1.878E-05 2.056E-05 1.838E-05 1.861E-05 1.812E-05 1.809E-05 1.962E-05 2.124E-05 1.787E-05 1.399E-05 2.004E-05 2.005E-05 2.201E-05 1.945E-05 1.970E-05 1.909E-05 1.907E-05 2.064E-05 1.811E-05 2.209E-05 1.928E-05 1.782E-05 4.225E-05 4.330E-05 4.512E-05 4.358E-05 4.421E-06 2.019E-05 2.050E-05 2.261E-05 2.304E-05 2.289E-05 2.440E-05 2.800E-05 3.128E-05 2.464E-05 2.125E-05 2.045E-05 2.350E-05 2.628E-05 2.034E-05 2.021E-05 2.190E-05 2.109E-05 2.111E-05 1.918E-05 1.820E-05

207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259

2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol

C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N CH3NO2 N 2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O

78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9

66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255

5.6844E-07 3.9342E-08 4.9950E-08 4.0748E-08 3.7330E-07 4.8806E-08 6.5281E-07 8.5736E-08 2.4000E-07 2.0000E-07 9.0798E-07 3.7026E-08 3.9771E-08 1.9770E-07 2.6098E-07 2.6552E-08 8.6219E-08 6.9755E-06 1.5035E-07 9.4257E-08 3.1573E-07 1.9250E-07 1.0826E-07 8.6077E-08 1.6370E-07 4.8890E-07 7.2131E-08 1.1164E-06 1.0546E-07 1.0871E-07 9.6050E-07 9.0981E-07 3.5642E-07 4.4941E-08 5.8223E-08 3.8926E-07 7.1455E-07 1.5779E-07 7.6460E-07 6.4318E-07 7.1900E-07 2.4391E-07 6.5592E-07 8.2005E-07 4.0700E-07 2.1150E-06 1.4670E-06 3.0465E-07 3.8518E-05 1.0344E-07 1.8105E-08 1.2000E-07 3.5879E-05

0.553 0.91086 0.89479 0.92709 0.6177 0.92549 0.5294 0.80277 0.68 0.704 0.495 0.92849 0.92242 0.7453 0.68276 0.98316 0.83591 0.3154 0.7338 0.7845 0.66404 0.7091 0.77382 0.81669 0.76706 0.6096 0.80319 0.4537 0.77106 0.78135 0.4856 0.49288 0.6327 0.90199 0.88057 0.63159 0.49832 0.73224 0.5476 0.5389 0.6659 0.702 0.6081 0.61423 0.6485 0.4642 0.5123 0.62218 0.10867 0.77301 0.99668 0.74 0.10109

227.18 44.662 256.5 310.59 100.77 210 187 355.89

131.22 133.4 72.564 1034.5 108.5 90.183 173.59 109 93.349 71.294 107.97 342.23 99.437 374.74 93.745 70.639 381 260.08 232.2 48.298 169.45 303.31 112.15 284 400.16 5.3 280 54.714 114.58 367.5 305.7 125.4 705.34 3502.7 220.47 180 3258.2

160.15 157.48 175.30 183.45 187.35 139.05 146.58 299.15 280.15 269.15 130.73 146.62 115.00 182.55 160.00 186.48 167.23 174.15 150.00 189.15 256.15 127.93 180.15 171.64 150.18 224.95 240.00 119.55 176.00 150.00 298.97 132.81 185.65 133.97 160.17 116.34 249.95 164.55 278.65 353.43 30.00 183.63 63.15 66.46 244.60 182.30 110.00 305.04 267.30 219.66 285.55 268.15 238.15

3.893E-06 3.947E-06 4.052E-06 5.112E-06 3.993E-06 4.698E-06 2.934E-06 6.232E-06 6.331E-06 6.062E-06 2.722E-06 3.800E-06 3.165E-06 5.574E-06 4.551E-06 4.534E-06 4.341E-06 5.117E-06 3.448E-06 3.901E-06 7.481E-06 3.242E-06 3.968E-06 4.065E-06 4.450E-06 5.265E-06 4.162E-06 2.366E-06 3.707E-06 3.707E-06 6.727E-06 3.423E-06 4.316E-06 3.725E-06 3.908E-06 3.196E-06 5.057E-06 3.938E-06 8.264E-06 7.125E-06 5.884E-06 3.752E-06 4.372E-06 3.964E-06 5.756E-06 8.854E-06 7.618E-06 3.231E-06 5.013E-06 3.335E-06 5.074E-06 4.499E-06 4.250E-06

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 600 1000 1000 1000 1000 1000 1000 1000 1000 1000 3273.1 1000 1970 1000 1000 1000 1500 1000 1000 1000 1000 1000 1000

2.112E-05 2.125E-05 2.312E-05 2.463E-05 2.118E-05 2.917E-05 1.930E-05 1.994E-05 2.175E-05 2.181E-05 2.046E-05 2.259E-05 2.327E-05 3.009E-05 2.573E-05 2.364E-05 2.588E-05 3.029E-05 2.157E-05 1.951E-05 2.642E-05 2.327E-05 2.076E-05 2.265E-05 2.956E-05 2.456E-05 1.685E-05 1.865E-05 1.983E-05 2.242E-05 1.312E-05 2.174E-05 2.288E-05 2.284E-05 2.434E-05 2.612E-05 1.714E-05 2.232E-05 2.616E-05 1.900E-05 1.573E-04 2.432E-05 6.432E-05 5.122E-05 2.625E-05 4.000E-05 5.737E-05 1.314E-05 1.812E-05 1.767E-05 1.769E-05 1.688E-05 1.694E-05 (Continued)

2-271

2-272

TABLE 2-138 Cmpd. no. 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309

Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) (Continued ) Name

1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol

Formula C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2

CAS 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6

Mol. wt. 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442

C1

C2

6.6329E-08 3.8673E-08 6.1447E-07 3.2095E-07 3.9500E-05 3.1191E-08 1.5557E-08 1.7520E-07 3.4163E-05 8.0901E-08 6.1515E-11 5.0324E-05 3.3253E-08 5.7084E-07 6.3032E-05 1.1010E-06 1.1960E-07 4.0828E-08 4.3300E-05 6.3412E-08 1.0971E-08 1.8903E-07 1.1749E-07 2.4630E-07 1.1640E-07 1.6378E-06 8.8646E-08 2.7467E-08 4.1022E-08 5.7650E-07 4.3478E-07 1.0094E-07 8.5360E-08 4.3511E-08 6.0758E-07 4.9054E-08 7.9420E-07 1.2003E-06 5.4749E-07 3.8397E-05 1.4807E-08 9.6891E-06 2.1372E-07 1.6200E-07 3.0387E-07 7.3919E-07 6.0741E-07 3.5532E-08 7.9457E-08 4.5430E-08

0.82027 0.91142 0.50705 0.61839 0.10787 0.92925 1.0299 0.6941 0.10661 0.79062 1.8808 0.077611 0.9351 0.52446 0.10487 0.5634 0.84797 0.8766 0.098676 0.84758 1.11 0.7031 0.7649 0.6653 0.7615 0.44337 0.81492 0.97555 0.90585 0.53498 0.5272 0.799 0.80872 0.908 0.53845 0.90125 0.5491 0.494 0.53893 0.10821 1.0733 0.24601 0.6894 0.7285 0.61945 0.5423 0.5863 0.95654 0.84656 0.9173

C3

C4

76.204 50.646 287.19 709.09 3390 55.092 206.8 3028 99.338 3604.6 32.426 271.76 4210.1 96.3 212.68 3090 41.718 175.9 103.78 208.7 107.94 636.11 85.198

235.2 238.27 103.1 88.273 102.73 173.45 415.8 479.78 283.52 2510.9 1537.6 178.57 117 210.35 263.73 367.29 65.878 61

–26,218

Tmin, K

Viscosity at Tmin

Tmax, K

Viscosity at Tmax

191.91 253.05 223.15 301.31 251.65 216.38 289.65 257.65 241.55 252.85 255.55 171.45 223.95 193.55 462.65 54.35 80.15 283.07 191.59 143.42 239.15 410.95 200.00 196.29 234.18 108.02 160.75 197.45 167.45 163.83 372.38 314.06 243.15 404.15 136.87 85.47 200.00 187.35 199.00 165.00 252.45 180.37 178.15 188.36 173.55 87.89 180.25 142.61 159.95 213.15

3.542E-06 4.995E-06 4.170E-06 3.266E-06 4.955E-06 3.677E-06 5.338E-06 4.583E-06 4.530E-06 4.611E-06 2.075E-06 3.406E-06 4.579E-06 3.757E-06 1.188E-05 3.773E-06 4.922E-06 3.288E-06 4.246E-06 3.305E-06 4.793E-06 9.111E-06 4.452E-06 4.003E-06 5.079E-06 2.813E-06 3.638E-06 4.766E-06 4.242E-06 3.621E-06 6.010E-06 7.514E-06 5.324E-06 8.072E-06 3.788E-06 2.702E-06 4.732E-06 4.471E-06 3.914E-06 4.114E-06 5.607E-06 3.652E-06 3.802E-06 4.540E-06 3.350E-06 2.093E-06 4.203E-06 4.085E-06 4.132E-06 4.832E-06

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1500 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

1.781E-05 1.996E-05 1.585E-05 1.345E-05 1.896E-05 1.813E-05 1.913E-05 1.755E-05 1.771E-05 1.733E-05 2.700E-05 1.868E-05 2.057E-05 1.681E-05 2.496E-05 6.371E-05 4.184E-05 1.436E-05 2.093E-05 2.124E-05 2.346E-05 2.068E-05 2.098E-05 2.019E-05 2.023E-05 2.176E-05 2.275E-05 2.320E-05 2.141E-05 1.879E-05 1.340E-05 2.283E-05 2.093E-05 2.090E-05 2.135E-05 2.480E-05 2.490E-05 2.461E-05 1.765E-05 2.309E-05 2.457E-05 2.089E-05 2.122E-05 2.223E-05 1.812E-05 2.477E-05 2.550E-05 2.632E-05 2.583E-05 2.418E-05

310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345

Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene

C6H4O2 F4Si C8H8 C4H6O4 O2S F6S O3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10

106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3

108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165

1.1085E-07 2.1671E-07 6.3863E-07 5.7821E-05 6.8630E-07 5.3986E-07 3.9067E-06 3.9218E-05 7.0859E-07 5.1567E-09 3.7780E-07 5.0784E-07 8.5988E-08 8.1458E-07 1.0300E-06 8.7268E-07 2.7081E-07 3.5585E-08 2.4110E-07 1.2434E-06 7.8498E-07 6.8812E-07 1.1070E-07 8.2418E-07 3.4066E-08 2.8471E-08 3.5940E-08 5.9537E-08 1.3880E-07 6.7484E-07 2.3790E-07 3.6429E-08 1.7096E-08 6.8293E-07 8.3436E-07 9.3485E-07

0.8008 0.76757 0.5254 0.099467 0.6112 0.6349 0.3845 0.12589 0.51971 1.1561 0.6533 0.5614 0.82841 0.50257 0.5497 0.49397 0.6955 0.8987 0.6845 0.4832 0.49855 0.51063 0.746 0.4931 0.95252 0.96571 0.9052 0.81842 0.7599 0.5304 0.71517 0.95924 1.1146 0.52199 0.49713 0.47683

152.51 16.28 295.1 4409.6 217 34.5 470.1 3861.1 652.24 271.01 328.55 68.172 380.29 569.4 323.79 187.93 165.3 223 447.7 362.79 330.88 72.4 371.44 43.528 30.83 125 90.245 98 230.17 102.84

324.17 365.86 371.96

19,000

388.85 250.00 242.54 460.85 197.67 205.15 297.93 700.15 329.35 279.01 164.65 237.38 176.99 373.96 234.94 178.18 236.50 267.76 158.45 156.08 247.79 229.33 165.78 387.91 398.40 354.00 247.57 288.45 180.35 173.15 119.36 178.35 273.16 225.30 247.98 286.41

9.439E-06 1.410E-05 5.158E-06 1.007E-05 8.280E-06 9.790E-06 1.355E-05 1.373E-05 4.837E-06 3.465E-06 4.006E-06 4.592E-06 4.520E-06 7.930E-06 6.049E-06 4.008E-06 6.756E-06 3.344E-06 3.210E-06 3.689E-06 4.975E-06 4.520E-06 3.488E-06 7.958E-06 9.208E-06 7.581E-06 3.506E-06 4.677E-06 4.659E-06 4.459E-06 3.907E-06 5.260E-06 8.882E-06 4.735E-06 5.225E-06 6.037E-06

1000 500 1000 1000 1000 5000 694.19 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1073.15 1000 1000 1000

2.429E-05 2.475E-05 1.858E-05 2.125E-05 3.844E-05 1.195E-04 2.883E-05 1.925E-05 1.554E-05 1.516E-05 2.710E-05 1.847E-05 2.461E-05 1.900E-05 2.926E-05 2.000E-05 2.782E-05 1.517E-05 2.230E-05 2.418E-05 1.803E-05 1.760E-05 1.786E-05 1.812E-05 2.352E-05 2.179E-05 1.660E-05 1.558E-05 2.407E-05 2.140E-05 3.016E-05 2.749E-05 4.082E-05 1.898E-05 1.894E-05 1.836E-05

The vapor viscosity is calculated by μ = C1T C2/(1 + C3/T + C4/T 2) where μ is the viscosity in Pa∙s and T is the temperature in K. Viscosities are at either 1 atm or the vapor pressure, whichever is lower. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.

2-273

2-274

TABLE 2-139 Eqn

Cmpd. no.

101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

Viscosity of Inorganic and Organic Liquids (Pa∙s) Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide

Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO

CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0

Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101

C1 −10.976 1.5525 −9.03 −20.457 −14.918 5.4711 6.224 −12.032 −28.12 −0.24126 −20.077 −6.743 −15.407 −8.8685 −12.632 7.5117 −8.4562 −12.947 −23.268 −148.6 −14.152 −11.46 −11.459 −9.9265 16.775 −20.611 −5.0539 −16.615 −10.143 17.844 −7.2471 −393.86 −390.03 −82.851 −16.323 −10.773 −10.346 −10.335 −17.488 −23.802 −10.807 −10.903 −3.4644 −6.4551 −9.817 −11.13 18.775 −10.306 −4.9735

C2 755.12 1376.4 1212.3 1638.6 1023.4 143.99 −151.8 867.34 2280.2 350.57 285.15 598.3 1518.7 204.29 2668.2 294.68 1024.4 2557.9 1880.5 8377.2 2652 1497 1334.4 1576.3 -314 1656.5 645.8 931.44 472.79 −310.2 534.82 19,042 18,609 4481.8 3141.7 591.61 522.3 521.39 1478.2 1887.2 966.74 932.82 334.5 744.7 1388 1084.1 −402.92 703.01 97.67

C3 −2.0126 −0.322 1.3834 0.5961 −2.4432 −2.6554 0.19534 2.3956 −1.5676 1.784 −0.7341 0.60172 −0.38305

C4

C5

−6.238E-22 −3.690E-27

10 10

−1.294E-22

10

1.7994 20.559

−0.0000133

2

−0.043397 0.00049694 −0.21119 −3.9763 1.4415 −0.87689 0.94366 −0.028241 −4.5058 −0.57469 59.978 60.014 11.182

−4.6625E-27 −0.049479 −0.055844 −0.000020943

10 1 1 2

−6.9171E-26

10

−2.794 −0.30635

−0.011847 −0.013184 0.91828 1.8479 −0.014851 0.023034 −1.0811 −0.67524 −0.238 −4.6854 −1.1088

Tmin, K

Viscosity at Tmin

149.78 353.33 289.81 200.15 190 229.32 193.15 185.45 286.15 189.63 59.15 195.41 235.65 83.78 403 278.68 258.27 395.52 260.28 321.35 257.85 275.65 243.95 342.2 265.85 242.43 154.25 179.44 136.95 250 134.86 220 196.15 190 238 87.8 134.26 167.62 250 200 157.46 133.02 147.43 176.8 267.95 161.3 216.58 161.58 68.15

2.647E-03 1.728E-03 1.265E-03 7.159E-03 1.655E-03 7.616E-04 1.958E-04 1.773E-03 1.359E-03 1.340E-03 3.430E-04 5.240E-04 3.429E-03 2.950E-04 2.451E-03 7.761E-04 2.047E-03 1.534E-03 2.393E-03 5.369E-03 2.092E-02 1.886E-03 2.513E-03 1.427E-03 1.353E-03 2.842E-03 5.065E-03 1.464E-03 1.081E-03 2.547E-04 2.243E-03 2.020E+02 4.410E+04 2.602E-01 4.404E-02 1.769E-02 1.483E-03 6.810E-04 1.496E-03 1.030E-02 8.716E-03 2.287E-02 1.369E-03 3.223E-03 2.561E-03 1.217E-02 2.488E-04 2.592E-03 2.688E-04

Tmax, K 294.15 494.3 391.05 412.7 329.44 354.81 273.15 353.22 460 350.45 130 393.15 426.73 150 563.15 545 442.29 600.8 464.15 664 478.6 458.15 472.03 723.15 350 429.24 393.15 363.15 284 400 420 544 540.8 391.9 372.9 335.6 276.87 274.03 399.26 456.46 373.15 358.13 373.15 347.94 436.42 390.74 303.15 441.6 131.37

Viscosity at Tmax 2.229E-04 2.895E-04 3.890E-04 2.874E-04 2.351E-04 2.100E-04 9.819E-05 2.181E-04 2.086E-04 2.191E-04 4.276E-05 4.858E-05 2.736E-04 3.823E-05 3.730E-04 7.106E-05 3.333E-04 1.683E-04 2.836E-04 2.614E-04 1.821E-04 2.121E-04 1.788E-04 1.076E-04 6.021E-04 3.310E-04 1.751E-04 2.060E-04 1.773E-04 4.880E-05 3.566E-05 3.441E-04 2.890E-04 3.845E-04 3.715E-04 1.222E-04 1.982E-04 2.022E-04 2.521E-04 2.359E-04 2.475E-04 2.851E-04 1.271E-04 2.570E-04 3.087E-04 2.351E-04 5.652E-05 1.643E-04 6.515E-05

101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 100 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Diisopropyl amine

CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N

56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9

153.8227 88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19

−8.0738 −9.9212 −9.5412 0.15772 10.9222 −14.109 10.39 10.27183 −15.458 −914.12 −377.23 −851.12 −24.988 −11.794 −3.4968 −33.763 280.87 −44.877 −11.641 −3.2612 −4.1508 −3.524 −11.338 4.1184 −97.663 −12.305 −69.985 −15.868 −11.464 −2.3633 0.000001348 −10.457 −17.582 −10.013 10.027 −114.7 −30.6 31.63 −8.991 15.312 −13.071 −10.872 −11.269 −375.21 −17.57 10.197 −5.135 10.501 −10.072 −17.723 −1.7366

1121.1 300.5 456.62 540.5 −118.895 1049.2 −134.38 −67.2235 1086 38,855 17,909 36,686 1807.9 992.33 397.94 2497.2 −31,869 3227.7 1154.3 614.16 599.77 342.54 1304.1 629.98 4342.7 2324.1 5818.8 1434.8 1510.1 791.93 1101.1 1635.4 921.31 206 4905.4 2153.4 −1080 870.2 −41.12 940.03 1033.1 1195.3 17,177 1385.7 −63.8 667.5 −52.181 710.48 850.2 599.8

−0.4726

−1.6075 −3.305 0.5377 −3.262 −3.1664 0.654 139.11 55.565 129.13 2.0556 −1.1087 3.2236 −38.837 4.887 0.066511 −1.156 −1.0308 −1.1599 0.000092396 −2.2076 13.645 −0.055494 8.0715 0.68071 −0.012754 −1.2272

−0.00014757 −0.00004841 −0.00013329

3,994,500

2 2 2

−2.002

−0.000019319

2

−0.000020577

2

−3.6367

0.5

−1.1719E-18

7

−0.0031354 0.9932 −3.1607 16.358 2.9371 −6.114 −0.2805 −3.919 0.3733 −0.00067435 0.012736 66.66 0.85647 −3.226 −0.8553 −3.3459 −0.14677 1.0601 −1.4237

250 89.56 172.12 250 136.75 209.63 175.43 150.35 250 273.15 293.15 273.15 200 245.25 182.48 279.69 296.6 242 200 225 138.13 145.59 189.64 285 240.05 304.55 285 206.89 247.56 229.15 20.35 210.15 282.85 220.6 175.3 248.39 256.15 326.14 176.19 237.49 208.38 192.5 172.71 293.15 223.35 200 225 154.56 179.6 137 250

2.032E-03 1.408E-03 1.020E-03 1.422E-03 2.026E-03 1.970E-03 7.234E-04 2.362E-03 5.514E-04 8.438E-02 9.548E-03 9.674E-02 6.363E-03 4.317E-04 8.345E-04 1.264E-03 6.328E-02 8.960E-03 4.017E-03 1.122E-03 7.531E-03 9.601E-04 1.155E-02 2.134E-03 2.741E-03 6.798E-03 1.937E-02 4.975E-03 4.364E-03 3.786E-03 1.348E-06 5.331E-03 2.042E-03 2.919E-03 5.931E-03 2.463E-03 2.726E-03 8.543E-04 4.076E-03 1.839E-03 1.406E-03 4.051E-03 1.381E-02 8.128E-01 1.190E-03 7.359E-04 1.113E-03 1.229E-03 1.030E-03 1.832E-03 7.479E-04

455 145.1 333.72 540 423.15 353.2 416.25 423.15 308.85 564.68 558.04 563.72 400 320.12 367.94 443.04 520.08 428.58 373.15 325 405.6 318.4 431.95 481.65 494.16 543.15 503 443.75 512.35 505.6 20.35 381.15 404.51 488.8 414.15 547.16 453.57 447.21 330.45 400 373.93 361.25 369.52 589.28 329.1 373.15 365.25 343.15 283.65 343.15 357.05

2.030E-04 3.897E-04 2.822E-04 1.291E-04 8.727E-05 3.410E-04 6.726E-05 1.190E-04 2.767E-04 1.793E-05 1.514E-04 2.992E-05 2.881E-04 1.676E-04 1.278E-04 2.070E-04 1.652E-04 4.402E-04 2.877E-04 3.167E-04 1.416E-04 1.080E-04 2.440E-04 2.718E-04 1.292E-04 2.304E-04 2.727E-04 2.064E-04 1.848E-04 2.167E-04 1.348E-06 5.071E-04 5.120E-04 2.951E-04 1.989E-04 1.565E-04 3.761E-04 3.039E-04 3.407E-04 2.557E-04 2.374E-04 3.301E-04 3.495E-04 1.090E-04 2.260E-04 1.141E-04 2.354E-04 1.026E-04 2.257E-04 6.050E-05 2.193E-04

2-275

(Continued)

2-276

TABLE 2-139 Eqn 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101

Viscosity of Inorganic and Organic Liquids (Pa∙s) (Continued )

Cmpd. no.

Name

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

Diisopropyl ether Diisopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane

Formula C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si

CAS 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9

Mol. wt. 102.17476 114.18546 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506

C1 −11.5 −15.097 −10.968 −10.631 0.10842 −10.93 7.2565 −10.716 −11.796 −11.344 −10.577 −10.62 −20.425 −12.08 152.9 −17.641 −37.347 −16.0542 −46.166 −12.373 −15.404 −134.91 −18.315 −7.0046 7.875 14.354 19.822 −13.563 −40.706 −12.24 −15.485 −22.11 −6.894 1.8878 −53.908 −290.36 −11.012 −8.521 −9.8417 −13.037 −11.311 −11.331 −11.452 −9.7574 −8.9215 0.7109 −11.499

C2 993 1426.9 885.49 1086.4 300.2 699.5 221.4 1140.5 1463.5 1168.9 1172.6 448.99 1515.5 1112.2 −10,183 1067.5 2835 2221.79 3086.2 2017.5 1390 6054.2 2283.5 276.38 781.98 −154.6 −0.12598 1208.6 3035 1836.4 1325.6 1673 818.6 78.865 4030.8 14,251 967.4 634.2 876.4 2346 1337.2 908.46 1172.7 729.43 950.8 386.51 1122.6

C3

C4

C5

0.022 0.51512

−1.6831 −2.7946 −0.047736 0.04513 −0.14244 0.000083967 1.4444 0.09654 −22.709

50,373,000,000

−4

1.0317 3.7937 0.63829 5.104 0.5564 19.337 0.95485 −0.6087 −3.0418 −3.7887 −4.9793 0.377 4.2655 0.021868 0.6432 1.641 −0.5941 −2.1554 5.9704 42.486 −0.3314 −0.1708 −0.02982 0.00042478 −0.00010095 −0.14912 −0.32687 −1.7754

−0.00002443

2

−3.11E-18

7

−0.000040369

2

Tmin, K

Viscosity at Tmin

187.65 204.81 159.95 226.1 240.91 200 220 239.66 223.16 184.99 188.44 131.65 240 160 274.18

2.258E-03 4.569E-03 4.375E-03 2.950E-03 3.796E-04 5.917E-04 1.103E-03 1.992E-03 5.311E-03 8.315E-03 6.093E-03 7.398E-04 2.041E-03 9.669E-03 6.023E-02

341.45 397.55 337.45 366.15 371 308.15 331.13 392.7 484.92 396.58 382.9 248.31 425.15 362.93 612.8

2.110E-04 2.194E-04 2.378E-04 4.695E-04 1.186E-04 1.734E-04 2.509E-04 3.045E-04 1.541E-04 2.956E-04 2.336E-04 1.490E-04 2.981E-04 2.147E-04 1.109E-04

225 291.67 413.79 284.95 293.15 260 262.15 309.58 90.35 200 220 192.15 178.2 250 258.15 250 200 253.15 104 284.29 260.15 250 160.65 245 155.15 180 140 204.15 125.26 250 200 167.55

6.696E-04 2.253E-03 1.071E-03 1.525E-03 4.124E-03 9.454E-04 3.002E-03 4.242E-03 1.247E-03 1.315E-02 1.132E-03 1.727E-03 8.012E-03 6.643E-03 6.705E-03 1.319E-03 6.406E-03 9.605E-04 6.334E-04 2.487E-03 1.305E-01 7.909E-04 1.918E-03 7.435E-04 8.035E+00 1.765E-02 7.908E-03 3.319E-03 9.520E-03 9.848E-04 1.156E-03 8.239E-03

310.48 464 559.2 374.65 613.44 382.35 526.4 616.93 300 440 473.15 289.73 413.1 486.55 466.95 394.65 404.94 378.15 250 483.15 576 329 283.85 345 510.1 417.15 326.15 386.55 308.15 372.25 337.01 371.05

2.528E-04 3.547E-04 3.214E-04 4.610E-04 1.134E-04 2.118E-04 1.220E-04 2.078E-04 3.587E-05 1.416E-04 9.061E-05 2.236E-04 2.326E-04 3.109E-04 2.822E-04 2.533E-04 2.956E-04 2.599E-04 6.142E-05 1.723E-04 1.276E-04 3.123E-04 2.863E-04 2.486E-04 2.165E-04 2.522E-04 1.949E-04 2.207E-04 2.626E-04 2.480E-04 2.086E-04 2.089E-04

Tmax, K

Viscosity at Tmax

101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101

149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198

Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate

F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2

7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3

37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924

8.18 −10.064 −10.118 −10.501 −7.6591 −74.521 −48.529 −10.923 −9.6312 −19.991 −9.5468 −98.159 −40.543 −66.654 −125.81 −9.3874 −13.929 −10.819 −11.812 −2.7947 −20.182 0.1369 −56.569 −46.402 −39.324 −82.705 −11.445 −13.684 −10.903 −4.2684 −10.073 −4.7263 −3.7464 −75.781 −11.661 −11.633 −116.34 −21.927 353.99 −10.905 −11.497 −31.157 −117.73 −14.527 −6.1572 −25.317 −4.648 13.557 −2.8737 10.848

−75.6 1058.7 464.42 427.78 603.36 5081.5 3394.7 894.63 −3.841 2245.1 1147.2 3592.6 3328.3 5325.8 7996 1204.9 1321.9 841.33 1291.9 563.86 2203.5 633.77 2140.5 3448.6 3841 7404.9 1187.2 1283.4 796.19 647.6 1123.3 594.43 624.2 4175.4 24.7 316.38 3834.6 1266.5 13,928 762.11 1365.7 1926 9943.3 1497.7 178.15 1789.2 1832 −187.3 301.35 75

−3.5148 −0.17162 0.0086309 −0.53378 9.0873 5.3903 −0.00068418 −1.458 1.1982 −0.23251 14.197 4.1804 7.66 16.412 −0.32618 0.40382 0.076469 −1.1636 1.2289 −1.6659 7.5175 5.0849 3.6933 6.4721 0.0029076 0.33755 −1.0087 −0.16515 −0.86247 −1.084 9.6508 −0.261 0.56191 16.864 1.5927 −41.717 −0.11863 0.036966 2.925 14.589 0.51747 −0.95239 2.069 −1.2191 −3.6592 −1.2271 −3.297

−1.065E-08

10

−0.000029555

2

−2.2512E-28 −7.6643E-17

9.9041 6

−0.000017676

2

−2.12E-30 1.5016

10.485 0.41014

−7.27E-09 −4.10E-16

3 10

−2.5875E-10 −2962

−9.0606E-24

4 −0.5

10

53.48 232.15 129.95 131.35 155.15 273.15 281.45 200 2.2 295.13 229.8 180.15 265.83 239.15 220 234.15 250 154.12 229.92 192.22 291.31 214.93 174.65 269.25 228.55 223 217.35 217.5 133.39 170.05 192.62 141.25 183.65 274.69 13.95 185.15 158.97 259.83 189.79 187.68 250 250 409.15 288.15 90.69 175.47 301.15 250 170.45 275

7.317E-04 1.599E-03 1.438E-03 7.450E-04 1.560E-03 7.171E-03 2.319E-03 1.575E-03 3.628E-06 3.814E-03 2.971E-03 4.341E-03 9.242E-03 8.805E-02 3.856E-01 2.427E-03 1.642E-03 4.701E-03 3.097E-03 2.528E-03 3.536E-03 2.849E-03 2.379E-03 5.854E-03 8.570E-02 4.919E-01 2.561E-03 2.563E-03 7.197E-03 3.550E-03 6.035E-03 8.332E-03 2.483E-03 1.451E-03 2.546E-05 9.207E-04 1.003E-03 2.754E-04 1.545E-03 5.726E-04 2.938E-03 6.737E-04 3.386E-03 1.664E-03 2.063E-04 1.193E-02 3.995E-03 6.135E-04 6.045E-04 6.126E-04

140 453.15 235.45 194.82 253.85 493 373.71 304.5 5.1 575.3 426.15 432.16 496.15 448.6 432.9 421.15 424.18 429.92 450.09 447.2 564.15 401.15 406.08 478.85 429.9 412.4 400.7 396.65 336.63 432 425.81 412 435 522.52 33 206.45 318.15 298.85 368.92 350 450 453.15 580 434.15 188 337.85 478.15 425 373.15 400

5.954E-05 1.542E-04 2.900E-04 2.587E-04 2.645E-04 3.829E-04 5.444E-04 3.392E-04 2.532E-06 2.088E-04 2.580E-04 1.003E-04 3.754E-04 3.190E-04 2.707E-04 2.040E-04 2.318E-04 1.417E-04 2.087E-04 1.777E-04 2.054E-04 2.563E-04 1.164E-04 4.019E-04 3.343E-04 3.274E-04 2.108E-04 2.185E-04 1.959E-04 1.377E-04 2.172E-04 2.083E-04 1.368E-04 2.191E-04 3.906E-06 8.206E-04 5.777E-05 1.821E-04 1.185E-04 8.089E-05 2.649E-04 1.214E-04 4.281E-04 3.582E-04 2.262E-05 3.442E-04 2.392E-04 1.198E-04 8.846E-05 1.636E-04 (Continued)

2-277

2-278

TABLE 2-139 Eqn 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101

Cmpd. no. 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247

Viscosity of Inorganic and Organic Liquids (Pa∙s) (Continued ) Name Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon

Formula CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne

CAS 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9

Mol. wt. 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797

C1 −17.044 −21.971 −10.481 −12.596 −1.035 −46.377 −10.755 −8.4453 −3.6585 −11.278 −10.97 −1.8842 −12.206 −12.002 −11.358 −6.1534 −6.6904 −6.6915 −1.8553 −4.8515 −6.7424 −10.517 −11.104 −1.0598 −10.842 −39.641 −11.27 −11.394

C2

C3

1074 2267.4 648.37 889.11 1048.5 4169.6 705.48 639.21 441.1 949.12 1067.3 433.58 1141.7 1009.7 1213.1 3219 3150.5 3173.2 612.62 679.07 788.86 745.32 627.18 520.68 863.65 2113.3 888.42 1168.7

0.84203 1.4173 −0.041947 0.20469 −1.5474 4.7 −0.011113 −0.38409 −1.0547 −0.00012343 −0.017484 −1.3238 0.15014

−11.216 −11.272 −11.075 −10.628 −0.099 −12.579 −12.86 −11.391 −13.912 400.35 −10.385 −4.841 −10.705 −10.569

737.75 1048.9 990.72 645 496 2224.2 946.91 1090.8 797.09 −30,387 599.59 696.7 788.94 952.38

−11.632 −13.415 −10.34 −19.308 −17.945

1251.6 1050.5 519.61 1822.5 115.57

C4

C5

−1.4494 −1.392 −1.3046 −1.3774 −0.93238 −0.69862 0.036581 −1.4961 −0.00074603 4.308 0.024736 −0.007539 0.019308 0.00030493 0.025885 −1.5939 0.26191 1.0752E-07 0.45308 −56.971 −0.046088 −0.9194 −0.048383 −0.063873 0.071692 0.33157 −0.013899 1.218 1.428

550,680,000

0

−2.14E-17

−3

0

10

Tmin, K

Viscosity at Tmin

179.69 288.15 159.53 150 298.15 155.95 135.58 139.39 160.15 157.48 175.3 183.45 200 139.05 146.58 299.15 280.15 269.15 248.15 146.62 168.54 275 160 186.48 167.23 250 188 189.15

1.236E-03 2.299E-03 1.321E-03 3.542E-03 1.774E-03 5.989E+01 3.675E-03 3.164E-03 1.915E-03 5.239E-03 6.930E-03 1.628E-03 3.339E-03 8.734E-03 4.587E-02 2.584E-02 3.729E-02 1.107E-01 9.288E-04 7.669E-03 3.539E-03 4.070E-04 9.133E-04 2.266E-03 3.409E-03 6.104E-04 1.637E-03 5.222E-03

273.15 472.65 314 310 450.15 404.15 304.3 311.7 390.15 343.31 396.58 364 375.9 353.6 457.68 548.8 491.2 493.6 353.15 433.6 420.8 314.7 280.5 535.5 339.8 304.9 331.7 389.15

2.275E-04 2.149E-04 1.739E-04 1.928E-04 2.859E-04 3.891E-04 2.034E-04 1.841E-04 1.476E-04 2.006E-04 2.286E-04 2.035E-04 2.539E-04 1.066E-04 1.653E-04 8.025E-05 1.360E-04 2.356E-04 2.742E-04 1.301E-04 1.129E-04 2.891E-04 1.731E-04 7.577E-05 2.474E-04 3.134E-04 2.143E-04 2.170E-04

127.93 180.15 171.64 150.18 260 240 119.55 176 110 295.56 132.81 250 133.97 160.17

4.722E-03 4.305E-03 4.977E-03 2.022E-03 8.635E-04 3.646E-02 2.506E-02 5.554E-03 1.072E-02 5.334E-03 2.253E-03 8.002E-04 6.390E-03 7.103E-03

303.92 367.55 553.1 279.11 400 518.15 333.41 372 310.95 451.21 266.25 352.6 312.2 368.69

1.703E-04 2.212E-04 9.292E-05 2.826E-04 2.229E-04 2.519E-04 2.038E-04 2.120E-04 1.588E-04 1.006E-04 2.270E-04 2.593E-04 2.127E-04 2.333E-04

249.95 164.55 151.15 353.43 25.09

1.972E-03 4.801E-03 9.377E-04 9.077E-04 1.602E-04

438.65 328.2 278.65 633.15 44.13

2.382E-04 2.502E-04 1.929E-04 1.892E-04 2.706E-05

Tmax, K

Viscosity at Tmax

101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101

248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299

Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde

C2H5NO2 N2 F3N CH3NO2 N2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O

79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6

75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914

−4.438 16.004 −9.5556 19.329 −246.65 −16.403 −4.3492 −68.54 −48.851 −39.863 −98.854 −11.069 −11.319 −2.3409 −22.688 −2.5373 −98.805 −60.795 −0.22128 −145.99 −11.736 −20.804 −11.19 −11.498 −3.8552 −27.978 −4.1476 −10.94 −19.299 −8.2185 −53.509 −37.067 −36.561 −16.456 −11.055 −2.8695 −10.667 −6.9168 −11.677 −1.7273 −3.7241 −22.472 −15.822 −11.31 195.25 −6.3528 −17.156 23.467 −8.8918 −11.208 −5.9402

746.5 −181.61 981.64 −381.68 3150.3 2119.5 1052.7 3165.3 4095 4089 7183.8 1081.7 1428 715.52 2466 900.91 3905.5 4617.8 3018.4 9296.7 1415.2 1834.6 1057.4 1362.1 684.22 2915.1 94.04 415.96 2088.6 919.43 1836.6 2856.7 3542.2 3209.9 1005.3 596.32 659.56 818.76 1091.2 424.34 516.54 2566.9 3301.8 1280 −11,072 240.85 646.25 116.07 2357.6 1079.8 617.95

−0.9385 −5.1551

200 63.15

3.420E-03 2.633E-04

387.22 124

3.027E-04 3.331E-05

−0.19453 −4.8618 49.98 0.6881 −1.0035 9.0919 5.294 3.7631 12.283

244.6 210 109.5 305.04 267.3 218.15 285.55 280 238.15 191.91 253.05 223.15 301.31 251.65 211.15 289.65 280 241.55 252.85 255.55 171.45 223.95 193.55 462.65 54.36 77.55 283.07 191.59 143.42 270 253.15 200 250 234.18 108.02 220 197.45 167.45 163.83 372.38 291.45 243.15 404.15 136.87 85.47 146.95 185.26 199 165

1.344E-03 2.065E-04 3.858E-04 4.012E-03 2.432E-03 3.306E-03 1.030E-02 1.733E-02 2.310E-01 4.372E-03 3.026E-03 3.206E-03 3.926E-03 2.555E-03 2.629E-03 6.652E-03 1.472E-02 1.856E-01 2.161E-03 2.039E-03 6.587E-03 4.837E-03 3.614E-03 6.539E-04 7.170E-04 3.787E-03 3.486E-03 3.532E-03 3.529E-03 3.773E-03 1.649E-02 6.660E-01 9.009E-04 1.024E-03 1.045E-02 1.643E-03 3.745E-03 2.322E-03 1.902E-03 1.920E-03 1.119E-02 2.368E-03 1.229E-03 5.772E-04 9.458E-03 2.069E+01 3.917E-01 3.083E-03 2.522E-03

374.35 283.09 180.05 603.15 465.52 593.15 528.75 486.25 471.7 420.02 492.95 487.2 589.86 445.15 454.96 512.85 468.35 452.9 446.15 440.65 453.52 472.19 468 516 150 208.8 543.84 375.15 465.15 458.95 410.95 392.2 375.46 375.14 303.22 385.15 399.79 378 415.2 610.03 555.4 522.4 557.65 298.15 360 370.35 355.3 508.8 322.15

3.078E-04 7.730E-05 3.791E-05 2.068E-04 2.606E-04 4.997E-05 3.670E-04 2.823E-04 3.334E-04 2.048E-04 1.912E-04 2.172E-04 2.057E-04 2.614E-04 1.111E-04 3.576E-04 2.902E-04 5.409E-04 1.913E-04 2.075E-04 1.422E-04 1.999E-04 1.868E-04 4.399E-04 6.990E-05 1.300E-04 2.091E-04 2.539E-04 4.796E-05 3.510E-04 3.842E-04 2.557E-04 2.354E-04 2.232E-04 2.051E-04 2.385E-04 2.463E-04 1.898E-04 9.980E-05 2.849E-04 5.134E-05 1.420E-04 1.986E-04 1.416E-04 4.275E-05 4.735E-04 4.892E-04 1.133E-04 2.470E-04

−0.022545 −1.222 1.5703 −1.2685 14.103 7.028 −2.8054 19.285 0.0003618 1.3403

−0.22541

1

−0.000013519

2

−0.000025112

2

0.000013141

2

−0.000019627

2

0.015575 −1.0071 2.3374 −1.207 1.1091 −0.42363 7.1409 3.7344 3.3364

−8.0487E-37

12.84

0.0039301 −1.2025 −0.59628 0.10658 −1.342 −1.1167 1.5749

−29.084 −0.58229 1.1101 −5.3372 −0.91376 −0.74183

−7.3439E-11 2,880,100,000

4 −4.0267

2-279

(Continued)

2-280

TABLE 2-139 Eqn 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101

Cmpd. no. 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345

Viscosity of Inorganic and Organic Liquids (Pa∙s) (Continued ) Name Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene

Formula C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O2S F6S O3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10

CAS

Mol. wt.

79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3

74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165

C1

C2

C3

−23.931 −6.698 17.797 −9.8074 −18.282 −92.082 −73.735 −5.7244 −10.153 −804.54 −14.846

1834.6 753.58 −252.43 1010.4 1549.7 1907.3 2668.2 638.2 840.71 30,487 1829.4

1.9124 −0.63783 −4.291 −0.25697 1.0454 15.639 10.993 −0.76415 −0.093763 130.79 0.3729

−22.675 −104.32 46.223 3.8305 −88.793 −11.566 −215.09 −136.73 −10.321 −118.86 −10.843 5.5351 −16.671 −226.08 0.388 −111.98 −3.7067 10.142 −11.756 −9.6461 −12.928 −4.0309 −10.707 −11.504 52.176 −69.778 −22.407 −2.2333 0.26297 −10.37 −52.843 −11.91 −15.489 −7.381

1758 9615.1 −1378 41.21 6400.7 2843.2 11,612 6421.3 900.92 5829.5 1165.2 632.38 1342.5 6805.7 736.5 5468.6 585.78 −130.41 1483.1 1281.2 1137.5 990.76 1818.5 3301 −4951.9 5905.2 1462.8 320.37 276.55 823.31 3703.6 1094.9 1393.5 911.7

1.6701 12.587 −8.7475 −2.1342 10.709 31.849 19.493 −0.069128 16.605 −2.6576 0.8388 37.542 −1.7063 15.579 −1.0926 −3.2199 −0.040387 −0.29478 0.25725 −1.1771 −0.39102 −8.5676 8.0214 1.7006 −1.2915 −1.7282 5.866 0.13825 0.63711 −0.54152

C4

C5

−0.043098 −0.018364

1 1

−0.15449

1

−0.026882 −0.00002297

1 2

−0.000016991

2

−0.060853

1

−0.000016992

2

−3.6929E-28

10

570,980

−5.879E-29

−2

10

Tmin, K

Viscosity at Tmin

252.45 180.37 250 188.36 200 87.89 180.25 142.61 159.95 213.15 388.85

2.275E-03 2.928E-03 1.002E-03 3.060E-03 6.774E-03 1.549E-02 5.852E-03 6.477E-03 4.641E-03 9.502E+02 3.642E-04

414.32 370.25 473.15 321 432.39 333.15 353.97 325.71 340.87 500.8 454

3.430E-04 2.172E-04 1.045E-04 2.908E-04 2.357E-04 5.147E-05 2.810E-04 2.784E-04 2.656E-04 3.307E-04 1.965E-04

242.54 460.85 225 223.15 289.95 700.15 329.35 277.65 164.65 237.4 293.15 373.96 250 178.18 236.5 267.67 250 200 247.79 229.33 165.78 172.22 398.4 353.15 247.57 288.45 225 173.15 130 178.35 273.16 225.3 247.98 286.41

1.919E-03 1.913E-03 6.900E-04 5.388E-04 2.477E-03 5.502E-04 1.736E-02 3.350E-03 5.505E-03 1.183E-02 1.040E-03 1.999E-04 1.269E-03 1.569E-02 2.955E-03 3.399E-03 6.135E-04 5.156E-04 2.495E-03 3.477E-03 8.636E-03 1.305E-02 2.150E-03 1.167E-02 3.240E-03 2.089E-02 1.237E-03 8.764E-04 2.425E-03 3.171E-03 1.702E-03 1.834E-03 1.735E-03 7.021E-04

418.31 591 400 318.69 318.15 795.28 723.15 554.4 373.15 576 303.15 454 393.15 383.78 387 540 359.05 308.15 449.27 442.53 541.15 387.91 676.8 625 511.2 590.15 345.65 364 400 434.52 646.15 413.1 418.1 413.1

2.268E-04 4.426E-04 6.557E-05 2.383E-04 9.456E-04 3.385E-04 1.522E-04 1.170E-04 2.446E-04 1.458E-04 9.125E-04 8.859E-05 2.625E-04 2.428E-04 3.798E-04 1.520E-04 2.028E-04 1.612E-04 1.663E-04 1.942E-04 4.530E-05 2.049E-04 3.288E-04 1.601E-04 1.569E-04 1.856E-04 2.654E-04 1.273E-04 8.272E-05 2.086E-04 5.028E-05 2.189E-04 2.459E-04 2.169E-04

Tmax, K

Viscosity at Tmax

Except for deuterium, the liquid viscosity is calculated by Eqn 101: µ = exp(C1 + C2/T + C3 ln T + C4T C5) where µ is the viscosity in Pa∙s and T is the temperature in K. Viscosity is either 1 atm or the vapor pressure, whichever is higher. For deuterium, liquid viscosity is calculated by Eqn 100: µ = C1 + C2T + C3T 2 + C4T 3 + C5T 4 where µ is the viscosity in Pa∙s and T is the temperature in K. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.

TRAnSPORT PROPERTIES TABLE 2-140 Viscosities of Liquids: Coordinates for Use with Fig. 2-19 Liquid Acetaldehyde Acetic acid, 100% Acetic acid, 70% Acetic anhydride Acetone, 100% Acetone, 35% Acetonitrile Acrylic acid Allyl alcohol Allyl bromide Allyl iodide Ammonia, 100% Ammonia, 26% Amyl acetate Amyl alcohol Aniline Anisole Arsenic trichloride Benzene Brine, CaCl2, 25% Brine, NaCl, 25% Bromine Bromotoluene Butyl acetate Butyl acrylate Butyl alcohol Butyric acid Carbon dioxide Carbon disulfide Carbon tetrachloride Chlorobenzene Chloroform Chlorosulfonic acid Chlorotoluene, ortho Chlorotoluene, meta Chlorotoluene, para Cresol, meta Cyclohexanol Cyclohexane Dibromomethane Dichloroethane Dichloromethane Diethyl ketone Diethyl oxalate Diethylene glycol Diphenyl Dipropyl ether Dipropyl oxalate Ethyl acetate Ethyl acrylate Ethyl alcohol, 100% Ethyl alcohol, 95% Ethyl alcohol, 40% Ethyl benzene Ethyl bromide 2-Ethyl butyl acrylate Ethyl chloride Ethyl ether Ethyl formate 2-Ethyl hexyl acrylate Ethyl iodide Ethyl propionate Ethyl propyl ether Ethyl sulfide Ethylene bromide Ethylene chloride Ethylene glycol Ethylidene chloride Fluorobenzene Formic acid

X

Y

15.2 12.1 9.5 12.7 14.5 7.9 14.4 12.3 10.2 14.4 14.0 12.6 10.1 11.8 7.5 8.1 12.3 13.9 12.5 6.6 10.2 14.2 20.0 12.3 11.5 8.6 12.1 11.6 16.1 12.7 12.3 14.4 11.2 13.0 13.3 13.3 2.5 2.9 9.8 12.7 13.2 14.6 13.5 11.0 5.0 12.0 13.2 10.3 13.7 12.7 10.5 9.8 6.5 13.2 14.5 11.2 14.8 14.5 14.2 9.0 14.7 13.2 14.0 13.8 11.9 12.7 6.0 14.1 13.7 10.7

4.8 14.2 17.0 12.8 7.2 15.0 7.4 13.9 14.3 9.6 11.7 2.0 13.9 12.5 18.4 18.7 13.5 14.5 10.9 15.9 16.6 13.2 15.9 11.0 12.6 17.2 15.3 0.3 7.5 13.1 12.4 10.2 18.1 13.3 12.5 12.5 20.8 24.3 12.9 15.8 12.2 8.9 9.2 16.4 24.7 18.3 8.6 17.7 9.1 10.4 13.8 14.3 16.6 11.5 8.1 14.0 6.0 5.3 8.4 15.0 10.3 9.9 7.0 8.9 15.7 12.2 23.6 8.7 10.4 15.8

Liquid Glycerol, 100% Glycerol, 50% Heptane Hexane Hydrochloric acid, 31.5% Iodobenzene Isobutyl alcohol Isobutyric acid Isopropyl iodide Kerosene Linseed oil, raw Mercury Methanol, 100% Methanol, 90% Methanol, 40% Methyl acetate Methyl acrylate Methyl i-butyrate Methyl n-butyrate Methyl chloride Methyl ethyl ketone Methyl formate Methyl iodide Methyl propionate Methyl propyl ketone Methyl sulfide Naphthalene Nitric acid, 95% Nitric acid, 60% Nitrobenzene Nitrogen dioxide Nitrotoluene Octane Octyl alcohol Pentachloroethane Pentane Phenol Phosphorus tribromide Phosphorus trichloride Propionic acid Propyl acetate Propyl alcohol Propyl bromide Propyl chloride Propyl formate Propyl iodide Refrigerant R-22 Sodium Sodium hydroxide, 50% Stannic chloride Succinonitrile Sulfur dioxide Sulfuric acid, 110% Sulfuric acid, 100% Sulfuric acid, 98% Sulfuric acid, 60% Sulfuryl chloride Tetrachloroethane Thiophene Titanium tetrachloride Toluene Trichloroethylene Triethylene glycol Turpentine Vinyl acetate Vinyl toluene Water Xylene, ortho Xylene, meta Xylene, para

X

Y

2.0 6.9 14.1 14.7 13.0 12.8 7.1 12.2 13.7 10.2 7.5 18.4 12.4 12.3 7.8 14.2 13.0 12.3 13.2 15.0 13.9 14.2 14.3 13.5 14.3 15.3 7.9 12.8 10.8 10.6 12.9 11.0 13.7 6.6 10.9 14.9 6.9 13.8 16.2 12.8 13.1 9.1 14.5 14.4 13.1 14.1 17.2 16.4 3.2 13.5 10.1 15.2 7.2 8.0 7.0 10.2 15.2 11.9 13.2 14.4 13.7 14.8 4.7 11.5 14.0 13.4 10.2 13.5 13.9 13.9

30.0 19.6 8.4 7.0 16.6 15.9 18.0 14.4 11.2 16.9 27.2 16.4 10.5 11.8 15.5 8.2 9.5 9.7 10.3 3.8 8.6 7.5 9.3 9.0 9.5 6.4 18.1 13.8 17.0 16.2 8.6 17.0 10.0 21.1 17.3 5.2 20.8 16.7 10.9 13.8 10.3 16.5 9.6 7.5 9.7 11.6 4.7 13.9 25.8 12.8 20.8 7.1 27.4 25.1 24.8 21.3 12.4 15.7 11.0 12.3 10.4 10.5 24.8 14.9 8.8 12.0 13.0 12.1 10.6 10.9

2-281

2-282

PHYSICAL AnD CHEMICAL DATA

FIG. 2-19 Nomograph for viscosities of liquids at 1 atm. For coordinates see Table 2-141. To convert centipoise to pascalseconds, multiply by 0.001.

TRAnSPORT PROPERTIES

2-283

TABLE 2-141 Diffusivities of Pairs of Gases and Vapors (1 atm) Dv in cm2/s Substance Acetic acid Acetone n-Amyl alcohol sec-Amyl alcohol Amyl butyrate Amyl formate i-Amyl formate Amyl isobutyrate Amyl propionate Aniline Anthracene Argon Benzene Benzidine Benzyl chloride n-Butyl acetate i-Butyl acetate n-Butyl alcohol i-Butyl alcohol Butyl amine i-Butyl amine i-Butyl butyrate i-Butyl formate i-Butyl isobutyrate i-Butyl proprionate i-Butyl valerate Butyric acid i-Butyric acid Cadmium Caproic acid i-Caproic acid Carbon dioxide

Carbon disulfide Carbon monoxide Carbon tetrachloride Chlorobenzene Chloroform Chloropicrin m-Chlorotoluene o-Chlorotoluene p-Chlorotoluene Cyanogen chloride Cyclohexane n-Decane Diethylamine 2,3-Dimethyl butane Diphenyl n-Dodecane Ethane Ethanol Ether (diethyl) Ethyl acetate Ethyl alcohol Ethyl benzene Ethyl n-butyrate Ethyl i-butyrate Ethylene Ethyl formate Ethyl propionate Ethyl valerate Eugenol Formic acid Helium n-Heptane n-Hexane Hexyl alcohol Hydrogen

Temp., °C 0 0 0 30 0 0 0 0 0 0 30 0 20 0 0 0 0 0 0 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20 25 500‡ 0 0 450‡ 0 30 0 25 0 0 0 0 15 45 90 0 15 0 126 0 0 0 0 30 0 0 0 0 0 0 0 0 0 0 0 20 38 15 0 0 25 500

Air

A

H2

0.1064 .109 .0589 .072 .040 .0543 .058 .0419 .046 .0610 .075 .0421

0.416 .361 .235

.077 .0298 .066 .058 .0612 .0703 .088 .0727 .0821 .0853 .0468 .0705 .0457 .0529 .0424 .067 .0679

.306

O2

N2

CO2

N2O

CH4

C2H6

C2H4

n-C4H10

i-C4H10

0.0716 .0422

.171 .1914

.0347

0.194 0.0797

.0528

.2364 .2716

.0425 .0476

.2771

.0483

.185

.0327

.191 .203 .173 .264 .271

.0364 .0366 .0308 .0476 .0471 .17

.050 .0513 .138

.550

.139

0.096 .163

.0996∗

0.153 .00215†

.9 .0892

.369 .651 .293

.185 1.0 0.0636

.319

.0744

.063 .137

0.116

.075 .091 .088 .054 .059 .051 .111 0.0719

.0760

.086 .306

.0841

.0884 .0657

.301

.0753

.0751

.0610 .308 .459 .377 .298 .273

.0778 .0715 .089 .102 .0658 .0579 .0591 .0840 .068 .0512 .0377 .1308

.0813 .0686 .0546 .0487

.375

.0685

.224 .229 .486 .337 .236 .205

.0407 .0413 .0573 .0450 .0367

.510

.0874

Ref. 8 6, 16 8 5 8 8 8 8 8 8 5 8 18 8, 15 8 8 8 8 8 5 8 8 8 8 8 8 8 8 8 8 13 8 8 8 19 1, 9 18 8 8 18 16, 17 5 6 10 8 8 8 10 3 6 3 8 3 8 3 8 20 7, 8 8 5 8 8 8 8 8 8 4, 8 8 8 8 8 19

.641 .705 .066§ .0663 .0499 .611

.290 .200

.0753 .697 4.2

.0757 .674

.0351 .550 .646

.535

.625

0.459 .537

0.486 .726

0.272

0.277

3 8 8 2 18 (Continued)

2-284

PHYSICAL AnD CHEMICAL DATA

TABLE 2-141

Diffusivities of Pairs of Gases and Vapors (1 atm) (Continued ) Dv in cm2/s

Substance

Temp., °C

Air

Hydrogen cyanide Hydrogen peroxide Iodine Mercury Mesitylene Methane Methyl acetate Methyl alcohol Methyl butyrate Methyl i-butyrate Methyl cyclopentane Methyl formate Methyl propionate Methyl valerate Naphthalene Nitrogen

0 60 0 0 0 500 0 0 0 0 15 0 0 0 0 0 25 0 0 30 0 0 0 0 0 0 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 25 0 30 0

0.173 .188 .07 .112 .056

Nitrous oxide n-Octane Oxygen Phosgene Propionic acid Propyl acetate n-Propyl alcohol i-Propyl alcohol n-Propyl benzene i-Propyl benzene n-Propyl bromide i-Propyl bromide Propyl butyrate Propyl formate n-Propyl iodide i-Propyl iodide n-Propyl isobutyrate i-Propyl isobutyrate Propyl propionate Propyl valerate Safrol i-Safrol Sulfur hexafluoride Toluene Trimethyl carbinol 2,2,4-Trimethyl pentane 2,2,3-Trimethyl heptane n-Valeric acid i-Valeric acid Water

H2

O2

N2

CO2

N 2O

CH4

C2H6

C2H4

n-C4H10

0.0731 .0872 .0735 0.0569 .0513

18 0.0567 .0879 .0446 .0451

0.0742

0.0758

.295

.0528 0.181 0.165 .096

0.535 .0505 0.0642 .178 .095 .0829 .067 .085 .0818 .101 .0481 .0489 .085 .0902 .0530 .0712 .079 .0802 .0549 .059 .057 .0466 .0434 .0455

.271 .697

0.0705

0.0710 0.181

.139

.330

.0588

.315

.0577

.206 .281

.0364 .0490

.212

.0388

.212 .189

.0395 .0341

.418 .076 .088 .087

0.071

0.0618

.288

0.0688

.270 0.050 0.0544 0.220

.212 .75

Ref. 10 11 8, 12, 14 8, 12, 13 8

1.1 .333 .506 .242 .257 .318

i-C4H10

0.070 .13

0.53

.084 .132 .0633 .0639

30 90 0 0 0 450

A

0.148

0.163

0.0960

0.0908

8 8 8 8 3 8 8 8 8 8 2 8 8 3 8 10 8 8 8 8 5 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 4, 8 5 8

0.0705

3

0.0684

3 8 8 8, 20 18

.0376 .138 1.3

∗ 320 mmHg. † 40 atm. ‡ Also at other temperatures. § Strong function of concentration. References 1 Amdur, Irvine, Mason, and Ross, J. Chem. Phys., 20, 436 (1952). 2 Boyd, Stein, Steingrimsson, and Rumpel, J. Chem. Phys., 19, 548 (1951). 3 Cummings and Ubbelohde, J. Chem. Soc. (London), 1953, p. 3751. 4 Fairbanks and Wilke, Ind. Eng. Chem., 42, 471 (1950). 5 Gilliland, Ind. Eng. Chem., 26, 681 (1934). 6 Gorynnova and Kuvskinskii, Zhur. Tekh. Fiz., 18, 1421 (1948). 7 Hansen, Dissertation, Jena, 1907. 8 International Critical Tables, vol. 5, p. 62. 9 Jeffries and Drickamer, J. Chem. Phys., 22, 436 (1954). 10 Klotz and Miller, J. Am. Chem. Soc., 69, 2557 (1947). 11 McMurtrie and Keyes, J. Am. Chem. Soc., 70, 3755 (1948). 12 Mullaly and Jacques, Phil. Mag., 48, 6, 1105 (1924). 13 Spier, Physica, 6 (1939): 453; 7, 381 (1940). 14 Topley and Whytlaw-Gray, Phil. Mag., 4, 873 (1927). 15 Trautz and Ludwig, Ann. Physik, 5, 5, 887 (1930). 16 Trautz and Muller, Ann. Physik, 22, 353 (1935). 17 Trautz and Ries, Ann. Physik, 8, 163 (1931). 18 Walker and Westenberg, J. Chem. Phys., 32, 136 (1960). 19 Westenberg and Walker, J. Chem. Phys., 26, 1753 (1957). 20 Winkelmann, Wied. Ann., 22, 152 (1884); 23, 203 (1884); 26, 105 (1885); 33, 445 (1888); 36, 92 (1889).

TRAnSPORT PROPERTIES Table 2-143 has a representative selection of diffusion coefficients. The subsection “Prediction and Correlation of Physical Properties” should be consulted for estimation techniques.

TABLE 2-142

Diffusivities in Liquids (25çC)

Dilute solutions and 1 atm unless otherwise noted; use DLµ/T = constant to estimate effect of temperature; ∗ indicates that reference gives effect of concentration.

Solute

Solvent

DL × 105, sq cm/sec

Acetal∗ Acetamide∗ Acetamide∗ Acetic acid Acetic acid Acetic acid Acetic acid Acetic acid Acetic acid∗ Acetonitrile Acetylene Allyl alcohol∗ Allyl alcohol Ammonia∗ i-Amyl alcohol∗ i-Amyl alcohol Benzene Benzene (50 mole %) Benzene (50 mole %) Benzene (50 mole %) Benzene (50 mole %) Benzene (50 mole %) Benzene (50 mole %) Benzoic acid Benzoic acid Benzoic acid Benzoic acid Benzoic acid Bromine Bromine Bromine Bromobenzene Bromoform∗ Bromoform Bromoform Bromoform∗ Bromoform Bromoform n-Butanol Caffeine Carbon dioxide Carbon dioxide Carbon disulfide (50 mole %, 200 atm.) Carbon disulfide (50 mole %, 200 atm.) Carbon disulfide (50 mole %, 218 atm.) Carbon disulfide (50 mole %, 200 atm.) Carbon disulfide (50 mole %, 100 atm.) Carbon disulfide (50 mole %, 50 atm.) Carbon disulfide (50 mole %, 200 atm.) Carbon disulfide (50 mole %) Carbon tetrachloride Carbon tetrachloride∗ Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride∗ Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride Chloral∗ Chloral hydrate

Ethanol Ethanol Water Acetone Benzene Carbon tetrachloride Ethylene glycol Toluene Water Water Water Ethanol Water Water Ethanol Water Carbon tetrachloride n-Decane 2,4-Dimethyl pentane n-Dodecane n-Heptane n-Hexadecane n-Octadecane Acetone Benzene Carbon tetrachloride Ethylene glycol Toluene Benzene Carbon disulfide Water Benzene Acetone i-Amyl alcohol Ethanol Ethyl ether Methanol n-Propanol Water Water Ethanol Water n-Butanol i-Butanol Chlorobenzene 2,4-Dimethyl pentane n-Heptane Methyl cyclohexane n-Octane Toluene Benzene Cyclohexane Decalin Dioxane Ethanol n-Heptane Kerosene Methanol i-Octane Tetralin Ethanol Water

1.25 0.68 1.19 3.31 2.11 1.49 0.13 2.26 1.24 1.66 1.78, 2.11 1.06 1.19 1.7, 2.0, 2.3 0.87 1.0 1.53 1.72 2.49 1.40 2.47 0.96 0.86 2.62 1.38 0.91 0.043 1.49 2.7 4.1 1.3 2.30 2.90 0.53 1.08 3.62 2.20 0.94 0.96 0.63 4.0 1.96 3.57 2.42 3.00 3.63 3.0 3.5 3.10 2.06 2.04 1.49 0.776 1.02 1.50 3.17 0.961 2.30 2.57 0.735 0.68 0.77

Estimated possible, error, ± %1 5 5 3

3 5 5 6 5 8

5

5 6 6 1

3 2 2 2 2 2 2 2 2 2 5 7

Ref. 11 11 11 4 1, 4 4 4 4 11 11 1, 24 11 11 1, 11 11 11, 25 7 26 26 26 26 26 26 4 4 4 4 4 11 11 11 25 11 11 11 11 23 11 1, 11, 18, 25 11 11 1, 3, 5, 20, 24, 28 14 14 14 14 14 14 14 14 7, 9 9, 10∗ 9 9 9, 10∗ 9 9 9 9 9 11 11 (Continued)

2-285

2-286

PHYSICAL AnD CHEMICAL DATA TABLE 2-142 Diffusivities in Liquids (25çC) (Continued ) Dilute solutions and 1 atm unless otherwise noted; use DL µ /T = constant to estimate effect of temperature; ∗ indicates that reference gives effect of concentration.

Solute Chlorine Chlorobenzene Chloroform Chloroform Cinnamic acid Cinnamic acid Cinnamic acid Cinnamic acid 1,1′-Dichloropropanol Dicyanodiamide∗ Diethyl ether Diethyl ether 2,4-Dimethyl pentane (50 mole %) 2,4-Dimethyl pentane (50 mole %) Ethanol∗ Ethyl acetate Ethylene dichloride Formic acid Formic acid Formic acid Formic acid Formic acid Formic acid Glucose Glycerol Glycerol Glycerol∗ n-Heptane (50 mole %) n-Heptane (50 mole %) n-Heptane (50 mole %) n-Heptane (50 mole %) Hexamethylene tetramine Hydrogen chloride∗ Hydrogen Hydrogen sulfide Hydroquinone∗ Hydroquinone∗ Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine∗ Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodobenzene Lactose∗ Maltose∗ Mannitol∗ Methanol Nicotine∗ Nitric acid∗ Nitrobenzene Nitrogen Nitrous oxide Oxalic acid∗

Solvent

DL × 105, sq cm/sec

Water Benzene Benzene Ethanol Acetone Benzene Carbon tetrachloride Toluene Water Water Benzene Water n-Dodecane n-Hexadecane Water Ethyl benzoate Benzene Acetone Benzene Carbon tetrachloride Ethylene glycol Toluene Water Water i-Amyl alcohol Ethanol Water n-Dodecane n-Hexadecane n-Octadecane n-Tetradecane Water Water Water Water Ethanol Water Acetic acid Anisole Benzene Bromobenzene Carbon disulfide Carbon tetrachloride Chloroform Cyclohexane Dioxane Ethanol Ethyl acetate Ethyl ether Ethylene bromide n-Heptane n-Hexane Mesitylene Methanol Methyl cyclohexane n-Octane Tetrabromoethane n-Tetradecane Toluene m-Xylene Ethanol Water Water Water Water Water Water Carbon tetrachloride Water Water Water

1.44 2.66 2.50 1.38 2.41 1.12 0.76 2.41 1.0 1.18 2.73 0.85 1.44 0.88 1.28 0.94 2.8 3.77 2.28 1.89 0.094 2.65 1.37 0.69 0.12 0.56 0.94 1.58 1.00 0.92 1.29 0.67 3.10 5.85 (4.4) 1.61 0.53 0.88, 1.12 1.13 1.25 1.98 1.25 3.2 1.45 2.30 1.80 1.07 1.30 2.2 3.61 0.93 3.4, 2.5 4.15 1.49 1.74 2.1 2.76 2.0 0.96 2.1 1.82 1.09 0.49 0.48 0.65 1.6 0.60 2.98 1.00 1.9 1.8 1.61

Estimated possible, error, ± %1 4 6 3

6 4

4

10 6 6

3 5

10 8 3

3 5 5 5 8 2

2

Ref. 1, 28 25 1, 25 11 4 4 4 4 11 11 25 2 26 26 1, 7, 9,∗ 11,∗ 22 6 1, 25 4 4 4 4 11 11 11 11 1, 11∗ 26 26 26 26 11 4, 11,∗ 12∗ 1, 11, 24(?) 1 11 2, 11∗ 11 11 9, 19, 23 4, 11, 19 11, 19, 23 9, 11, 19 11, 23 4 9 4, 11∗ 11, 19 11 11 9, 11, 19 4, 9 9 19 4 4 11 4 11 9, 11 11 11 11 11 1, 7, 11 11 11 7 1, 24 1, 11 11

TRAnSPORT PROPERTIES TABLE 2-142

Diffusivities in Liquids (25çC) (Continued )

Dilute solutions and 1 atm unless otherwise noted; use DL µ /T = constant to estimate effect of temperature; ∗ indicates that reference gives effect of concentration.

Solute Oxygen Oxygen Oxygen Pentaerythritol∗ Phenol Phenol Phenol Phenol Phenol Phenol n-Propanol Pyridine∗ Pyridine Pyrogallol Raffinose∗ Resorcinol∗ Resorcinol∗ Saccharose∗ Stearic acid∗ Succinic acid∗ Sucrose Sulfur dioxide Sulfuric acid∗ Tartaric acid∗ 1,1,2,2-Tetrabromoethane Toluene Toluene Toluene Toluene Toluene Urea Urea Urethane Water

Solvent Glycerol∗-water (106 poise) Sucrose∗-water (125 poise) Water Water i-Amyl alcohol Benzene Carbon disulfide Chloroform Ethanol Ethyl ether Water Ethanol Water Water Water Ethanol Water Water Ethanol Water Water Water Water Water 1,1,2,2-Tetrachloroethane n-Decane n-Dodecane n-Heptane n-Hexane n-Tetradecane Ethanol Water Water Glycerol

DL × 105, sq cm/sec

Estimated possible, error, ± %1

Ref.

0.24

13

0.25

13

2.5 0.77 0.2 1.68 3.7 2.0 0.89 3.9 1.1 1.24 0.76 0.74 0.41 0.46 0.87 0.49 0.65 0.94 0.56 1.7 1.97 0.80 0.61 2.09 1.38 3.72 4.21 1.02 0.73 1.37 1.06 0.021

References 1 Arnold, J. Am. Chem. Soc., 52, 3937 (1930). 2 Calvet, J. Chim. Phys., 44, 47 (1947). 3 Carlson, J. Am. Chem. Soc., 33, 1027 (1911). 4 Chang and Wilke, J. Phys. Chem., 59, 592 (1955). 5 Davidson and Cullen, Trans. Inst. Chem. Eng., 35, 51 (1957). 6 Dummer, Z. Anorg. Chem., 109, 31 (1949). 7 Gerlach, Ann. Phys. (Leipzig), 10, 437 (1931). 8 Gosting and Akeley, J. Am. Chem. Soc., 74, 2058 (1952). 9 Hammond and Stokes, Trans. Faraday Soc., 49, 890 (1953); 49, 886 (1953). 10 Hammond and Stokes, Trans. Faraday Soc., 52, 781 (1956). 11 International Critical Tables, vol. 5, p. 63. 12 James, Hollingshead, and Gordon, J. Chem. Phys., 7, 89 (1939); 7, 836 (1939). 13 Jordon, Ackermann, and Berger, J. Am. Chem. Soc., 78, 2979 (1956). 14 Koeller and Drickamer, J. Chem. Phys., 21, 575 (1953). 15 Kolthoff and Miller, J. Am. Chem. Soc., 63, 1013 (1941).

20  4

 3  7  7  4  5  4  4  5  6  3 10  4

 2

1, 3, 15, 21, 24 11 11 1 11 11 11 11 1, 7, 11 11 11 11 11 11 11 11 11 11 2, 27 15, 17 11 11 11 4 4 4 4 4 11 8, 11 11, 25 16

2-287

2-288

PHYSICAL AnD CHEMICAL DATA

THERMAL TRAnSPORT PROPERTIES

TABLE 2-143

Transport Properties of Selected Gases at Atmospheric Pressure* Thermal conductivity, W/(m ⋅ K) Temperature, K

Substance

Viscosity, 10–4 Pa ⋅ s Temperature, K

250

300

400

500

Acetone Acetylene Benzene

0.0080 0.0162 0.0077

0.0115 0.0213 0.0104

0.0201 0.0332 0.0195

0.0310 0.0452 0.0335

600

Bromine CCl4 Chlorine

0.0038 0.0053 0.0071

0.0048 0.0067 0.0089

0.0067 0.0099 0.0124

0.0126 0.0156

0.0190

Deuterium Propylene R 22 SO2

0.122 0.0114 0.0080 0.0078

0.141 0.0168 0.0109 0.0096

0.176 0.0226 0.0170 0.0143

0.0430 0.0230 0.0200

0.0580 0.0290 0.0256

250

0.0561 0.0524

0.111 0.073 0.109

Prandtl number, dimensionless Temperature, K

300

400

500

600

0.077 0.104 0.076

0.101 0.135 0.101

0.128 0.164 0.127

0.156 0.154

0.101 0.136

0.203 0.131 0.178

0.260 0.162 0.218

0.291 0.191 0.259

0.126 0.087 0.129 0.129

0.153 0.115 0.168 0.175

0.178 0.141

0.201

0.217

0.256

250

300

400

0.860 0.820

0.797 0.771

0.762 0.760

500

∗An approximate interpolation scheme is to plot the logarithm of the viscosity or the thermal conductivity versus the logarithm of the absolute temperature. At 250 K the viscosity of gaseous argon is to be read as 1.95 × 10–5 Pa ⋅ s = 0.0000195 N ⋅ s/m2.

TABLE 2-144

Prandtl number of Air* Pressure, bar

Temperature, K

1

5

10

20

30

40

50

60

70

80

90

100

80 90 100 120 140

mix 0.796 0.786 0.773 0.763

2.31 1.76 0.872 0.813 0.782

2.32 1.77 1.54 0.89 0.82

2.35 1.78 1.53 1.44 0.94

2.37 1.79 1.53 1.65 1.20

2.40 1.81 1.53 1.54 1.59

2.42 1.82 1.53 1.48 2.14

2.45 1.83 1.53 1.43 2.43

2.48 1.85 1.53 1.40 2.07

2.51 1.87 1.54 1.38 1.78

2.54 1.89 1.54 1.36 1.62

2.57 1.91 1.55 1.34 1.52

160 180 200 240 280

0.754 0.745 0.738 0.724 0.710

0.765 0.754 0.743 0.727 0.711

0.78 0.763 0.749 0.729 0.713

0.84 0.792 0.766 0.737 0.717

0.92 0.830 0.788 0.746 0.721

1.03 0.876 0.812 0.756 0.726

1.13 0.932 0.841 0.767 0.731

1.25 1.00 0.87 0.78 0.737

1.37 1.07 0.90 0.80 0.742

1.65 1.14 0.95 0.81 0.75

1.83 1.20 0.97 0.81 0.75

1.72 1.25 1.00 0.82 0.76

300 350 400 450 500

0.705 0.699 0.694 0.691 0.689

0.707 0.699 0.694 0.691 0.689

0.708 0.699 0.694 0.691 0.689

0.712 0.701 0.695 0.691 0.689

0.715 0.703 0.696 0.692 0.689

0.717 0.705 0.697 0.692 0.690

0.721 0.707 0.698 0.693 0.690

0.725 0.709 0.699 0.693 0.690

0.728 0.711 0.700 0.694 0.690

0.732 0.712 0.701 0.695 0.691

0.737 0.714 0.703 0.695 0.691

0.742 0.716 0.704 0.696 0.691

600 700 800 900 1000

0.690 0.696 0.705 0.709 0.711

0.690 0.696 0.704 0.709 0.711

0.690 0.695 0.704 0.708 0.711

0.689 0.695 0.704 0.708 0.711

0.689 0.695 0.704 0.708 0.711

0.689 0.695 0.703 0.708 0.710

0.689 0.695 0.703 0.708 0.710

0.689 0.695 0.703 0.708 0.710

0.689 0.695 0.703 0.708 0.710

0.690 0.695 0.702 0.708 0.709

0.690 0.695 0.702 0.708 0.709

0.690 0.695 0.702 0.708 0.709

∗Compiled by P. E. Liley from tables of specific heat at constant pressure, thermal conductivity, and viscosity given in SI units for integral kelvin temperatures and pressures in bars by Vasserman. Thermophysical Properties of Air and Its Components and Thermophysical Properties of Liquid Air and Its Components. Nauka, Moscow, and in translated form by the National Bureau of Standards, Washington. The number of significant figures given above reflects the similar numbers appearing for the constituent properties in the source references. While reasonable agreement occurs for atmospheric pressure with some other works, the fragmentary data available for the saturated, etc., states show large deviations.

TABLE 2-145 Eqn

Cmpd. no.

102 102 100 100 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 100 102 102 102

1 2 3 3 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 45 46 47

Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)] Name Acetaldehyde Acetamide Acetic acid Acetic acid Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyric acid Butyronitrile Carbon dioxide

Formula C2H4O C2H5NO C2H4O2 C2H4O2 C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H8O2 C4H7N CO2

CAS 75-07-0 60-35-5 64-19-7 64-19-7 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 107-92-6 109-74-0 124-38-9

Mol. wt. 44.05256 59.0672 60.052 60.052 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 88.1051 69.1051 44.0095

C1 1.0943E-07 0.00013195 2.4148 1.0879 3.3901E-06 3.1289E-06 −26.8 8.3653E-07 0.000075782 0.024098 0.0009265 −0.000861 0.00031417 9.6608E-06 0.00059858 0.000633 0.025389 0.00001652 0.00047951 0.0001163 1.3917E-06 0.0001235 0.00023476 0.00096451 0.00015525 2.8646E-06 1.0404E-06 0.00027085 0.00099879 5.7816E-07 0.000088221 −20890 0.051094 0.00014035 −918.39 0.0011484 4.5894E-06 0.000096809 0.000067737 0.000078576 5.86E-09 0.1807 0.00097826 0.9719 0.000037269 9.9652E-07 0.7873 9.2069E-08 1.3751E-06 3.69

C2 2.0279 0.97 −0.020867 −0.0038977 1.9588 1.4618 0.9098 1.6481 1.0327 0.3285 0.7035 0.77281 0.7786 1.3799 0.7527 0.6221 0.28547 1.3117 0.7818 0.9705 1.5389 0.9495 0.8639 0.69225 0.9446 1.4098 1.4685 0.7932 0.71894 1.6666 1.0273 0.9593 0.45253 1.0032 −0.21199 0.87647 1.4484 1.1153 1.0709 1.0565 2.376 0.0082225 0.78643 −0.111 1.1427 1.6558 −0.0036161 2.0312 1.5786 −0.3838

C3 728.3 0.000059409 3.6227E-06 36053

C4

−5.4718E-08 14,086,000

126,500,000 −36.227 1325.3 627.58 −2555.2 −0.7116

31,432 577,830 112,460

354.04 70 1018.3 491 463.4 740

241,830

778.7 187.8 519.99 715.78 −391.35

2121.7

1,228,600 189,410

193,840 278,930 156,820

278.33 2358.4

165,880

75.316 −93,820,000,000 5455.5 711.66 334420 3253.7

99,063 1,979,800 −2,884,200,000

781.82 −65.881 14.63 −401.32 −129.42 1531.5 1167.2 −43.844

129,390 105,920 69,280 1,691,500 67,115 3,163,200 79,421

5.6641E-06

−2.8451E-09

964

1,860,000

Tmin, K 294.15 494.3 391.05 458.15 541.5 412.7 329.44 339.09 189.35 325.84 414.15 298.15 70 200 426.73 90 563.15 339.15 442.29 522.4 464.15 579.24 478.6 458.15 472.03 373.15 300 429.24 311.49 273 284 268.74 272.65 469.57 481.38 370.7 372.9 266.91 273.15 274.03 273 456.46 371.61 358.13 281.22 347.94 436.42 706.95 390.74 194.67

Thermal cond. at Tmin 0.01110 0.02189 0.06749 0.06258 0.03925 0.02084 0.01363 0.01238 0.01011 0.01534 0.02027 0.00929 0.00603 0.01446 0.01809 0.00585 0.02317 0.01407 0.01861 0.02090 0.01767 0.02213 0.02167 0.01936 0.02071 0.01123 0.00452 0.01302 0.00723 0.00664 0.01172 0.01281 0.01357 0.02672 0.02110 0.02097 0.02435 0.01252 0.01105 0.01200 0.00783 0.02151 0.01832 0.01749 0.01268 0.01610 0.05147 0.05647 0.01698 0.00887

Tmax, K 1000 1000 458.15 541.5 1000 1000 1000 1000 1000 1000 1000 1000 2000 900 1000 3273.1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 500 1000 1000 1000 1000 1000 1000 1000 1000 712.94 1000 1000 1273.15 1257 800 1000 1000 1000 1000 1000 706.95 1000 1000 1500

Thermal cond. at Tmax 0.13269 0.06206 0.06259 0.03955 0.11105 0.07600 0.11362 0.07358 0.09545 0.08028 0.06867 0.11525 0.11675 0.11523 0.06796 0.09525 0.05618 0.09542 0.06427 0.05452 0.05758 0.04899 0.06636 0.06398 0.06171 0.06347 0.00956 0.04495 0.04267 0.05779 0.09071 0.16809 0.13799 0.08383 0.08332 0.06536 0.10161 0.12049 0.13926 0.13704 0.07634 0.07465 0.08610 0.08470 0.09644 0.09245 0.05647 0.11421 0.07484 0.09025

2-289

(Continued)

2-290

TABLE 2-145 Eqn

Cmpd. no.

102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102

48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)] (Continued ) Name Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane

Formula CS2 CO CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2

CAS 75-15-0 630-08-0 56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6

Mol. wt. 76.1407 28.0101 153.8227 88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997

C1 0.0003467 0.00059882 0.00016599 0.000092004 0.0009993 0.0004783 4.91778E-07 0.00043073 −3263.77 0.01652 0.00009154 0.00019307 0.00018648 0.00019063 1.6743E-07 0.000014433 −449910 0.000000859 0.0032207 −1095.5 0.0000901 9.5461E-06 0.0010949 −91.383 0.0000813 1.9749E-06 −668.4 3.3251E-09 −0.3072 0.000027232 0.00012058 0.000016707 0.00028527 0.00021231 0.00015878 0.00021302 0.0032694 −1067.8 −1420 −1520.8 0.0001315 0.00021054 0.0014796 0.000057603 0.000062435 −11,633 0.00001706 −0.0044894 0.0018097 0.000059249

C2 0.7345 0.6863 0.94375 1.0164 0.5472 0.8994 1.70639 0.83878 0.0675 0.44154 1.0681 0.9248 0.9302 0.9282 1.8369 1.2104 0.27364 1.7709 0.5991 −0.023408 1.0897 1.4641 0.71644 0.89718 1.0674 1.5349 0.9323 2.4876 0.489 1.257 1.0111 1.2128 0.9874 0.8052 0.8636 0.8719 0.58633 0.754 0.7614 0.754 1.0113 0.9574 0.69531 1.1148 1.103 0.4621 1.248 0.6155 0.67406 1.0713

C3 479 57.13 1449.6 270.83 458.6 1845.5 −232.008 1874.5 −46,803,200 2444.42 746.6 710 709.37 716.91 −449.46 −10,001,000,000 243 608.69 498, 780 655 632.62 175.55 −283,310,000 697.6 −4,071,000,000 −124.9 −67,500 751.7 740 −206.08 −200.51 649.51 659.5 1620 1259.9 −3,036,100,000 −4,504,000,000 −433,2800,000 1023.8 1414 2657.4 849.98 913.43 −3,793,900,000 −112.8 −3266.3 1179.7 101.84

C4 501.92

163,000 46603.4 −25,000,700,000 793,392

112,760 −9.8654E+12 509,290 −7,835,500,000

346,040

−29,400,000

153,850 21,807

300,890

77,960 174,850 45,974

Tmin, K 273.15 70 349.79 145.1 200 400 285.45 334.33 248.95 319.67 308.85 475.43 464.15 475.13 380 251.9 285.66 325 434 428.58 356.12 273 317.38 240.37 431.95 481.65 447.3 543.15 504 443.75 512.35 447.15 233.15 381.15 404.51 370.1 323.15 446.23 453.57 447.21 330.45 356.59 312.9 361.25 369.52 541.54 273.15 200 365.25 248.95

Thermal cond. at Tmin 0.00776 0.00576 0.00812 0.00505 0.00551 0.01579 0.01004 0.00854 0.00801 0.01285 0.01222 0.02316 0.02230 0.02319 0.01534 0.01164 0.01356 0.01380 0.02399 0.02291 0.01914 0.01061 0.01360 0.01061 0.02022 0.02590 0.02173 0.02746 0.02590 0.02149 0.02709 0.02092 0.11474 0.00940 0.01077 0.00687 0.01244 0.01561 0.01507 0.01564 0.01132 0.01177 0.00847 0.01220 0.01222 0.03044 0.01148 0.00764 0.01743 0.01016

Tmax, K 1000 1500 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1500 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 600 1000 1000

Thermal cond. at Tmax 0.03745 0.08724 0.04595 0.08108 0.03002 0.07935 0.07943 0.04920 0.07246 0.08232 0.08389 0.06716 0.06736 0.06762 0.08181 0.06174 0.14994 0.14198 0.09535 0.12704 0.10116 0.14429 0.10148 0.15854 0.07629 0.07948 0.10286 0.11029 0.09389 0.09175 0.07482 0.07667 0.44547 0.03351 0.03729 0.03356 0.07330 0.06430 0.06066 0.06417 0.07025 0.06498 0.04931 0.06881 0.06647 0.07463 0.09804 0.05181 0.08089 0.08447

102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102

98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

1,2-Difluoroethane Difluoromethane Diisopropyl amine Diisopropyl ether Diisopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene

C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C 2 H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F

624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6

66.04997 52.02339 101.19 102.17476 114.18546 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032

2.4194E-06 0.000013015 0.00051305 0.00019879 −8.5357 0.00046265 3.7962E-06 0.00021761 1.6085 0.000034741 0.008856 0.013298 0.012144 0.00022578 0.059975 0.014449 0.000022421 0.00012822 0.0011808 0.00023614 0.00064761 0.00402358 6.4032E-07 0.00014629 0.0001123 0.000005719 −375.32 0.000073869 −0.010109 1.3575E-07 0.3935 0.000017537 0.00002012 0.00017727 829.29 0.0000748 0.0043244 8.6806E-06 0.1655 −8145800 0.00077079 −0.0003788 508 2.5804E-06 0.0052833 0.00021652 −152400 0.0015251 1.0507E-07 5.8174E-08 2.7142E-06 0.00012144 0.000053432

1.4456 1.1897 0.8076 0.9423 −0.0056423 0.81968 1.4462 0.9187 −0.1103 1.1646 0.4215 0.3692 0.3854 0.892 0.2667 0.3612 1.2137 0.9324 0.742 0.9204 0.7716 0.57548 1.7194 0.9377 0.9958 1.4699 1.0708 1.1689 0.6475 1.9681 0.0131 1.3144 1.1513 0.9428 1.0156 1.1103 0.5429 1.4559 0.1798 −0.30502 0.7713 1.115 0.9023 1.4669 0.52982 0.94192 −0.049106 0.70243 1.9854 2.0116 1.4281 0.93831 1.1576

360.19 306.8 1882.1 539.34

154,510 106,230 −65,622,000 104,530

217 2160.3 −99.956 −50.645 0.1027 52.191 697 1018.6 595.22 −146.91 752.5 1131 638 1013.3 3598.32

132,070 2,989,300 130,820 764,580 852,540 803,590

745.89 183.2 579.4 −8,783,600,000 500.73 −7332 1380 560.65 −89.583 712.4 8,955,300,000 686 333.67 299.72 3827.9 1,832,500,000 446.16 −5641 2,170,000,000

1,098,800 728,130 131,830 6400 82,563

98,000

−268,000 1,710,000 125,410

570,470 −29,403 1,600,000 −1.1842E+13 197,930

1415.7 632.16 80,955,000 1347.5

−9.3122E+11 35,085

−372.68

57,690

760.75

378,180

303.65 221.5 357.05 328.05 397.55 337.45 366.15 300.13 280.03 331.13 392.7 402.94 396.58 382.9 248.31 425.15 362.93 556.85 253.55 310.48 462.15 559.2 337.85 531.46 279.65 489.47 616.93 184.55 293.15 273.15 289.73 409.35 486.55 466.95 394.65 404.95 376.62 170 390.41 470.45 329 273.15 327.46 500.66 417.15 326.15 386.55 308.15 400 273.15 371.05 70 357.88

0.00938 0.00803 0.01836 0.01598 0.02015 0.01554 0.01936 0.01288 0.01845 0.01581 0.01884 0.01948 0.01952 0.01613 0.01139 0.02001 0.01797 0.01981 0.01291 0.01520 0.02059 0.02063 0.01427 0.02188 0.01055 0.02354 0.02563 0.00886 0.01475 0.00847 0.01622 0.02007 0.01855 0.02306 0.01583 0.02180 0.01832 0.00879 0.02272 0.02513 0.01610 0.01004 0.01426 0.02353 0.01967 0.01717 0.01889 0.01487 0.01540 0.01133 0.01268 0.00654 0.01546

993.65 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1500 1000 1000 1000 1000 1000 1000 1000 768.01 1000 1000 1000 1000 1000 1000 990.21 1000 1000 1000 1000 1000 1000 1000 590.92 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 550 1000 700 600

0.05206 0.04826 0.08967 0.09444 0.13085 0.08099 0.08279 0.09199 0.12209 0.10506 0.09500 0.09196 0.09376 0.06310 0.19458 0.07539 0.09962 0.04587 0.09296 0.08319 0.06379 0.04661 0.05855 0.05449 0.08515 0.09301 0.06968 0.15807 0.13417 0.10681 0.10532 0.09859 0.05524 0.06973 0.10314 0.09505 0.09659 0.06613 0.08915 0.09896 0.09659 0.18063 0.11921 0.06492 0.07348 0.08882 0.12768 0.08195 0.09499 0.03690 0.05223 0.05675 0.03874

2-291

(Continued)

2-292

TABLE 2-145 Eqn

Cmpd. no.

102 102 102 102 100 100 102 102 102 102 102 102 100 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102

151 152 153 154 155 155 155 156 157 158 159 160 161 161 162 163 164 165 166 167 168 169 170 171 172 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196

Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)] (Continued ) Name Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Formic acid Formic acid Furan Helium-4 Heptadecane Heptanal Heptane Heptanoic acid Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate

Formula C2H5F CH3F CH2O CH3NO CH2O2 CH2O2 CH2O2 C4H4O He C17H36 C7H14O C7H16 C7H14O2 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2

CAS 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 64-18-6 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9

Mol. wt. 48.0595 34.03292 30.02598 45.04062 46.0257 46.0257 46.0257 68.07396 4.0026 240.46774 114.18546 100.20194 130.185 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854

C1 6.3522E-06 0.000048998 5.2201E-06 0.00025893 −0.8303 1.8897 0.00072291 −644950 0.00226 −114.41 1.4326E-06 −0.070028 −0.088162 4.449E-08 −0.061993 0.00018818 1348.6 2049.3 0.00002133 0.0083145 0.000060732 0.000004438 1.5427E-06 −650.5 12,049,00,000 6.1268E-08 −4935500 0.00018361 −1.2158 −0.33262 0.000064256 6.9682E-06 0.074318 0.000058116 0.000011631 0.00043196 0.002653 0.00049725 0.001865 4.6496E-06 0.000034629 1.381E-07 0.000214 0.00028183 4.8284E-06 0.00019847 8.3983E-06 5.7992E-07 0.034177 −25343

C2 1.346 1.0175 1.417 0.9083 0.0046141 −0.006901 1.8898 0.2862 0.7305 1.0566 1.5896 0.38068 0.00065022 2.133 0.2792 0.96338 1.0313 1.0323 1.2885 0.51862 1.0586 1.4949 1.5824 0.8053 −4.0059 2.0874 −0.1653 0.97199 0.026637 0.12054 1.1355 1.347 0.30035 1.0724 1.2753 0.86603 0.7452 0.63088 0.49755 1.3669 1.1224 1.8379 0.9248 0.92094 1.3599 0.9284 1.4268 1.7862 0.3312 −0.1934

C3

723.6 −5.7466E-06 6.4407E-06 4,877,600 −16,794,000,000 −18.63 −2,211,400,000

C4

−1,889,300,000 −1.7372E+13 440

−7049.9 −1.2803E-06

−2,400,500 9.1349E-10

−3336 696.02 14,832,000,000 22,983,000,000 487.8 2253 −102.79 682

−1,642,000

−1,412,100,000 −1668.8 1,563,100,000 677.05 −1711.6 −2472.6 445.15 −214.35 4470.1 −77.165 −202.84 641.48 12 331.62 358 −210.76 18.744 −352.09 698 619.17

532,590 143,140

722,550 −1.5752E+13 −13,176,000 −5,493,400 64,810 110,480 1,775,800 123,900 122,990

58,295 46,041

678.69 −49.654 2070 11,164,000

1,195,600 −67,259,000,000

Tmin, K 235.45 194.82 253.85 493 420 470 537.9 304.5 30 575.3 426.15 339.15 496.15 643.11 449.45 432.9 420.55 424.18 366.79 450.09 372.93 560.01 401.15 339.09 478.85 641.42 429.9 412.4 273 273 336.63 354.35 425.81 344.48 357.67 386.65 22 206.45 190 273.15 350 212.8 427.85 304.92 580 434.15 111.63 273 478.15 330.09

Thermal cond. at Tmin 0.00990 0.01047 0.01333 0.02930 0.09392 0.06898 0.04120 0.01367 0.03124 0.02454 0.02168 0.01583 0.03085 0.04349 0.02345 0.02501 0.01943 0.01951 0.01845 0.02289 0.01827 0.02568 0.02031 0.01704 0.03317 0.04435 0.02220 0.02421 0.00775 0.00800 0.01644 0.01485 0.02151 0.01679 0.01506 0.02828 0.01718 0.00551 0.00880 0.00985 0.02356 0.00724 0.02206 0.01804 0.02766 0.02176 0.01263 0.01303 0.02498 0.01415

Tmax, K 1000 1000 1000 1000 470 537.9 1000 1000 2000 1000 1000 1000 643.11 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 641.42 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1600 600 700 673.15 450 600 1000 1000 1000 1000 600 684.37 1000 1000

Thermal cond. at Tmax 0.06933 0.05529 0.09304 0.07973 0.06890 0.04118 0.11296 0.13631 0.58820 0.07649 0.08413 0.11493 0.04346 0.11150 0.10722 0.08616 0.11287 0.11145 0.10518 0.07899 0.08751 0.08055 0.08620 0.12003 0.04435 0.11206 0.11104 0.09022 0.10523 0.10980 0.10850 0.08546 0.08167 0.09155 0.08466 0.10430 0.64299 0.01812 0.03213 0.04185 0.03160 0.03258 0.07497 0.10081 0.05801 0.07210 0.08425 0.06726 0.07895 0.11878

102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102

197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249

Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen

C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2

74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9

40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134

0.00026544 0.4734 −55.13 0.000023963 0.0002509 0.0008968 0.0001799 2054.5 0.00019098 0.00021736 0.00015498 0.000023993 0.079414 0.000065855 1333.1 0.00037057 0.0000719 0.00011359 0.069565 0.075448 0.0024385 0.0040082 0.0019845 0.00041077 0.00024036 −4202700 0.0034805 −800040 0.00020053 −2483300 0.0026136 2.1191 −5935000 0.0071536 0.00002653 0.00072502 0.0001813 0.000061119 0.93312 0.089772 1.1776E-06 −488.1 −200.9 0.011136 0.0023574 12.248 0.21276 0.0002084 0.00032359 0.000091828 0.0011385 0.0011282 0.00033143

0.8921 −0.1111 1.065 1.1308 0.899 0.7742 0.9457 0.90109 0.9341 0.9171 0.9364 1.1976 0.23442 1.072 0.9962 0.81367 1.1274 1.0311 0.1633 0.155 0.61774 0.54462 0.6393 0.75688 0.93177 −0.1524 0.61906 −0.2285 0.95381 −0.046517 0.62 −0.19015 −0.089497 0.53907 1.1631 0.7395 0.92912 1.0861 −0.1172 0.18501 1.6618 0.8877 −0.1321 0.4831 0.67434 −0.5611 −0.022299 0.93034 0.8892 1.0345 0.6646 0.6895 0.7722

222.19 533.57 −448,200,000 −67.272 253.4 456 704.6 8,760,500,000 84.07 112.3 15.366 58.59 2671.9 −36.369 12,317,000,000 609.17 667 709.27 208.7 218.44 223.01 242.12 227.11 591.5 588.14 2,084,600,000 1810.8 248,100,000 644.42 1,313,100,000 1631.7 1453.4 3,098,800,000 2700.7 29.996 365.68 793.45 −59.592 1154.3 639.23 −1,448,500,000 104,000 21,70.3 1804.1 −1067 −194.68 364.832 623.22 731.78 8.7 679.11 16.323

79,869 1,649,600 125,720 149,500 230,640

155,720 177,690 137,400 35,667 1,366,100 106,430

1,209,500 1,252,500 477,570 559,040 434,120

−1.4577E+13 166,290 −1.5034E+12 −1.5798E+13 126,720 3,575,500 −2.7994E+13 241,730 32,519 204,360 141,260 2,961,700 1,114,700

−846,000,000 281,220 155,660 2,715,200 1,708,700 73,041

238,800 373.72

249.94 353.35 266.82 472.65 314 273.15 450.15 404.15 304.3 311.71 305.4 273.15 396.58 302.15 375.9 281.85 374.08 441.15 438.15 440.15 344.96 348.64 338.05 314.7 273 352.79 339.8 300 331.7 389.65 312 303.92 367.55 171.64 273.15 373.45 518.15 333.41 372 261.43 333.82 266.25 350 312.2 368.69 216.25 438.65 328.2 278.65 491.14 30 387.22 63.15

0.01154 0.01569 0.01259 0.01784 0.01326 0.01198 0.02266 0.02116 0.01348 0.01320 0.01304 0.01173 0.01966 0.01468 0.01495 0.01155 0.02056 0.02322 0.02415 0.02435 0.01592 0.01544 0.01501 0.01109 0.01419 0.01546 0.01653 0.01369 0.01729 0.01869 0.01221 0.01606 0.01760 0.00459 0.01171 0.01680 0.02383 0.01606 0.01828 0.01273 0.01839 0.01276 0.01402 0.01648 0.01802 0.01108 0.01969 0.01638 0.01493 0.02243 0.00846 0.01580 0.00602

1000 1000 650 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 766.87 1000 1000 1000 1000 1000 1000 1000 1000 1000 3273.1 1000 2000

0.09675 0.06904 0.07917 0.05588 0.08902 0.11176 0.07253 0.11843 0.09771 0.09504 0.08664 0.08586 0.07960 0.10120 0.10543 0.06357 0.10399 0.08238 0.08888 0.08908 0.10227 0.09578 0.09888 0.04813 0.09447 0.11740 0.08415 0.13148 0.08863 0.12433 0.06864 0.09451 0.12847 0.07516 0.07704 0.07637 0.06195 0.10242 0.08117 0.11701 0.07325 0.15513 0.10886 0.09079 0.08398 0.09590 0.07255 0.08958 0.09273 0.06730 0.24616 0.06887 0.11638

2-293

(Continued)

2-294

TABLE 2-145 Eqn

Cmpd. no.

102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 100 102 102 102 102 102 102 102 102 102 102 102 102 102 102 100 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102

250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297

Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)] (Continued ) Name Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol

Formula F3N CH3NO2 N2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O

CAS 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0

Mol. wt. 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095

C1 2.1443 0.00003135 0.001096 0.0004096 0.000049571 0.00000175 −0.065771 46.08 −30.715 0.00016806 0.000021269 0.047041 0.000016681 −291.08 0.00000166 −8758 −0.20973 3.2003E-08 −0.0030238 0.00016915 −0.0020184 8.1833E-08 0.0000133 −3965.5 0.000060734 2.7969E-06 0.00044994 0.0043147 4.7796E-06 0.00000113 −684.4 0.44736 7.5284E-08 2896 0.00019575 −0.01719 22.775 2.7081E-06 0.00022307 0.00011261 0.000052415 0.00025623 0.00010167 0.038846 0.00016675 0.0000593 0.000061629 −1.12 −613.84 7.3907E-07

C4

Tmin, K

1860.3 −91.6 540 45.6 3332.3

1,216,700 128,000

−3482.3 −2460.2 8107 713.67 662.21 2460.6 −199.41 −6,019,900,000

−1,580,300 1,867,000 −156,830,000

144.09 374.35 182.3 121.38 603.05 465.52 423.97 528.75 485.2 471.7 420.02 492.95 423.85 589.86 445.15 339 512.85 637.35 468.35 452.9 446.15 440.65 394.41 472.19 399.35 516 80 161.85 543.84 375.15 273.15 458.95 706.95 410.9 392.2 273 273 303.22 385.15 399.79 313.33 329.27 610.03 454.99 439.43 557.65 238.65 231.11 370.35 355.3

C2 −0.30545 1.1119 0.667 0.7509 1.2652 1.5534 0.27198 −1.0037 −0.1075 0.96876 1.2943 0.29733 1.218 1.0615 1.5669 0.8448 0.0012201 2.18 0.8745 0.97238 1.0027 2.0418 1.3554 0.5213 1.0516 1.3164 0.7456 0.47999 1.4851 1.6323 0.764 −0.0019667 2.0589 0.8985 0.9692 0.4832 1.0019 1.5493 0.93358 1.034 1.0948 1.0073 0.988 0.2392 0.91777 1.046 1.0731 0.10972 0.7927 1.7419

C3

−27,121,000,000 −2.1843E-06

1,367,200 144,580

1.3942E-09

−13352 698.55 −20406 504.59 −1,851,900,000 −124.91

158,300

56.699 700.09 643.13 −1,055,000,000 2.9973E-06 12,735,000,000 664.04 −3798 191,000,000 41.075 794.16 693.05 −51.09 1423.7 797 985.81 730.1 765.5 1.8579 −9834.6 −1,157,400,000

−1.4141E-09

−1,235,000 8301.3

101,160

937,170

70,128 −7,535,800

Thermal cond. at Tmin 0.00648 0.01365 0.00891 0.01094 0.02502 0.02440 0.02130 0.02815 0.02436 0.02603 0.02051 0.02559 0.01981 0.02491 0.02345 0.01503 0.02955 0.04157 0.02380 0.02545 0.02046 0.02050 0.01926 0.02505 0.01967 0.01041 0.00691 0.00931 0.02529 0.01799 0.01288 0.03938 0.05537 0.02084 0.02372 0.00877 0.00898 0.01546 0.01890 0.02019 0.01517 0.01653 0.02490 0.02183 0.01669 0.01864 0.00980 0.01114 0.02135 0.02049

Tmax, K 1000 1000 1000 750 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 637.35 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 1000 1000 1000 1000 706.95 1000 990.95 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 720.25 1000

Thermal cond. at Tmax 0.06377 0.06553 0.07133 0.05567 0.07147 0.08003 0.10597 0.11042 0.09895 0.07904 0.09772 0.07598 0.07956 0.07395 0.08333 0.11053 0.04157 0.11097 0.10288 0.08229 0.10597 0.10923 0.10295 0.07845 0.08394 0.02488 0.12655 0.06990 0.08299 0.08912 0.12707 0.05536 0.11308 0.11087 0.09509 0.12002 0.12082 0.11472 0.07858 0.08412 0.09608 0.11119 0.05208 0.06936 0.05461 0.04615 0.09526 0.14599 0.07034 0.12428

102 102 100 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102

298 299 300 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345

Propenylcyclohexene Propionaldehyde Propionic acid Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene

C9H14 C3H6O C3H6O2 C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C 3 H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O2S F6S O3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10

13511-13-2 123-38-6 79-09-4 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3

122.20746 58.07914 74.0785 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165

0.00010242 9.0711E-07 1.0014 1.8905E-07 1.1671E-06 1325.3 0.2833 0.16992 0.0000449 740.1 0.00018367 0.0087425 0.0001666 −5678600 0.0000955 0.010048 5.5263E-06 10.527 0.00048883 1.0702 3.4082E-06 0.000078652 −163.62 9.5521E-06 0.00007754 0.00085604 0.000015235 0.00013384 0.00002392 0.0000952 5.3701E-06 0.000106 0.00027648 0.000098408 0.00008498 0.00001758 0.000020248 0.00020544 0.00018189 0.038012 2498.8 −3279500 0.000054197 −229.41 3510.8 6.2041E-06 3.0593E-09 4.9707E-06 9.9305E-08

1.0486 1.6709 −0.0045954 1.93 1.6033 1 0.055046 0.021288 1.2018 0.9732 0.9627 0.51733 0.9765 −0.045252 0.928 0.4033 1.344 −0.7732 0.6518 −0.2348 1.3647 0.95174 0.9193 1.4561 1.0778 0.7297 1.2816 0.98115 1.2694 1.0423 1.4751 1.0161 0.901 1.0452 1.061 1.3114 1.2284 0.87137 0.88744 0.68615 0.95209 −0.12941 1.0632 0.59582 0.225 1.3973 2.4182 1.3787 1.9229

701.56 7.1517E-06

12,235,000,000 1325.9 −54.484 421 5,646,000,000 646.01 2358.1 706 2,615,700,000 63.6 553.74

−3.5878E-09

1,817,600 1,624,800

334,590 −3.5415E+13 685,570

−1333 −117.08 2010.4

1,506,400 78,863 1,277,000

−282.82 −1,087,600,000 662.22 729 531.99 −111.88 645.95 537 1243.3 599.09 91 167.68 720.49 708 392.9 −174.72 807.3 803.39 34,663 20,167,000,000 1,710,400,000 −70.589 −169,430,000 401,720,000

289,490

−569.28 −225.64 −469.93

213,840 124,120

132,900 132,200

147,800

8,721,900 −1.2727E+13 90,617

121,060 66,786 113,460

431.65 322.15 414.32 616.15 370.25 374.65 321 432.39 225.45 353.97 325.71 340.87 460.75 454 333.55 418.31 591 250 273.15 317.9 795.28 373.15 526.73 339.12 480.77 394.27 379.44 357.31 383.78 387 508.62 273.15 273.15 449.27 442.53 355.15 387.91 629.6 625 469.08 520.3 345.65 278.25 259.25 363.85 273.16 320 320 320

0.02262 0.01407 0.06993 0.04578 0.01532 0.01520 0.01709 0.02022 0.01054 0.01403 0.01616 0.01654 0.02624 0.02593 0.01761 0.01837 0.02934 0.00745 0.01163 0.01386 0.03097 0.00950 0.02517 0.01564 0.02395 0.01801 0.01964 0.01525 0.01901 0.01125 0.02422 0.01018 0.01280 0.02238 0.02098 0.01846 0.02001 0.02474 0.02410 0.02259 0.02486 0.01515 0.01123 0.00963 0.01198 0.01574 0.00867 0.01492 0.01019

1000 1000 616.15 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 702.45 1000 1000 900 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1073.15 1000 1000 1000

0.08421 0.09340 0.04578 0.11657 0.07534 0.10832 0.10000 0.07658 0.12737 0.10893 0.08624 0.08439 0.08302 0.12665 0.03837 0.07276 0.05949 0.03969 0.04587 0.04930 0.04233 0.05598 0.08615 0.13419 0.07676 0.07579 0.10528 0.07139 0.10007 0.05684 0.08942 0.09680 0.10734 0.07816 0.07583 0.10847 0.10079 0.04675 0.04635 0.09798 0.08899 0.12177 0.08222 0.08300 0.04135 0.10652 0.09965 0.08084 0.09060

2-295

Except for acetic acid, butyric acid, formic acid, heptanoic acid, octanoic acid, pentanoic acid, propionic acid, the vapor thermal conductivity is calculated by Eqn 102: k = C1T C2/(1 + C3/T + C4/T 2) where k is the thermal conductivity in W/(m∙K) and T is the temperature in K. Thermal conductivities are at either 1 atm or the vapor pressure, whichever is lower. Eqn 100, used for the limited temperature ranges as noted for the associating compounds above, k = C1 + C2T + C3T 2 + C4T 3 Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.

2-296

PHYSICAL AnD CHEMICAL DATA

TABLE 2-146

Thermophysical Properties of Miscellaneous Saturated Liquids Temperature, °C

Substance

Property

Acetaldehyde ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr Acetic acid

−50

−40

−30

−20

−10

863 2.05 460 0.211 4.47

852 2.08 404 0.206 4.08

840 2.11 358 0.200 3.78

828 2.14 321 0.195 3.52

816 2.17 290 0.189 3.33

0 804 2.20 263 0.184 3.14

10 794 2.24 241 0.182 2.97

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

20

30

40

50

60

70

80

90

100

972

960

783 2.28 222 0.180 2.81 1049 2.031 1210 0.173 14.2

1039

1028

1018

1006

995

984

1102 0.170

1010 0.168

795 0.167

600 0.165

0.163

0.161

Aniline

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

— — — — —

— — — — —

— — — — —

— — — — —

— — — — —

1039 2.024 10200 0.186 111

1030 2.047 6500 0.184 72

1022 2.071 4400 0.182 50

1013 2.093 3160 0.180 36.7

1005 2.113 2370 0.177 28.3

996 2.132 1850 0.174 22.7

987 2.17 1510 0.171 19.2

978 2.20 1270 0.169 16.5

969 2.23 1090 0.168 14.5

960 2.27 935 0.167 12.7

951 2.32 825 0.167 11.5

Butanol

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

845 1.947 34700 0.175 3860

841 1.996 22400 0.174 2570

837 2.046 14700 0.173 1740

833 2.100 10300 0.172 1260

829 2.153 7400 0.171 930

825 2.202 5190 0.170 670

817 2.262 3870 0.168 120

810 2.345 2950 0.167 41

803 2.437 2300 0.166 33.8

797 2.524 1780 0.165 27.2

791 2.621 1410 0.164 22.5

784

776

768

760

753

1140 0.163

930 0.162

760 630 535 0.161 0.160 0.159

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

1362 0.988 630 0.194 3.21

1348 0.989 580 0.190 3.02

1334 0.990 535 0.186 2.85

1320 0.991 496 0.182 2.70

1306 0.993 463 0.178 2.58

1292 0.996 435 0.174 2.49

1278 1.004 405 0.170 2.39

1263 1.017 375 0.166 2.30

350 0.161

330 0.158

0.156

0.154

0.152

0.150

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

— — — — —

— — — — —

— — — — —

— — — — —

— — — — —

— — — — —

789 2.068 1175 0.122 19.9

779 2.081 980 0.120 17.0

769 2.094 820 0.119 14.4

759 2.106 710 0.118 12.7

750 2.119 605 0.117 11.0

740

731

721

540 0.116

0.114

0.112

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

2.01 6400 0.188 68.4

2.04 4790 0.186 52.5

2.08 3650 0.184 41.3

2.13 2825 0.181 33.2

2.19 2220 0.179 27.2

806 2.27 1770 0.177 22.7

798 2.35 1470 0.175 19.7

789 2.43 1200 0.173 16.9

781 2.52 1000 0.171 14.7

776 2.62 835 0.168 13.0

763 2.73 700 0.165 11.6

754 2.83 590 0.162 10.3

745 2.93 500 0.159 9.2

735 3.03 435 0.156 8.4

725 3.19 370 0.153 7.7

716 3.30 314 0.151 6.9

947

935

924

912

888

876

863

851

838

825

811

797

580

510

901 2.01 455 0.145 6.3

400 0.142

370 0.139

345 0.136

310 0.133

280 0.130

250 230 220 0.127 0.123 0.119

Carbon disulfide

Cyclohexane

Ethanol

Ethyl acetate

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) 1090 k (W/m⋅K) Pr

Ethylamine

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

761 2.95 580 0.204 8.39

750 2.97 500 0.201 7.39

739 2.98 435 0.199 6.51

729 3.00 390 0.196 5.97

718 3.01 350 0.194 5.43

707 3.03 320 0.191 5.08

695

683

671

658

646

633

620

607

Ethyl ether

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

790 2.135 550 0.159 7.39

780 2.156 470 0.155 6.54

769 2.179 410 0.151 5.92

758 2.205 365 0.147 5.48

747 2.233 330 0.144 5.12

736 2.265 290 0.140 4.69

725 2.299 265 0.139 4.38

714 2.332 233 0.134 4.05

702 2.36 214 0.129 3.92

689 2.39 197 0.125 3.77

676 2.43 181 0.120 3.67

666 2.47 166 0.116 3.54

653 2.51 153 0.112 3.43

640

625

611

140

129

118

Ethyl iodide

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

0.656 0.663 0.670 0.677 730 0.092 5.37

0.684 655 0.090 4.98

0.691 590 0.088 4.63

0.698 539 0.086 4.30

0.705 495 0.085 4.11

0.712 455 0.083 3.90

0.718 420 0.081 3.72

0.724 390 0.080 3.53

Ethylene glycol

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

1127 2.272 57000 0.254 510

1120 2.327 33300 0.255 305

1113 2.381 20200 0.256 190

1106 2.431 13400 0.258 126

1099 2.484 9100 0.259 87.3

1092 2.536 7070 0.260 69.0

1085 2.586 4000

1077 2.636 3450

1070 1063 1056 2.685 2.734 2.779 3000 2440 2000

Formic acid

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

1241

1231

1220

1209

1196

1184

1170

1156

1140

0.265

2260 0.261

1800 0.257

1470 0.257

1220 0.253

1030 0.250

890 0.246

780 0.243

680 615 550 0.240 0.236 0.232

1124

1108

TRAnSPORT PROPERTIES

2-297

TABLE 2-146 Thermophysical Properties of Miscellaneous Saturated Liquids (Continued ) Temperature, °C Substance Gasoline

Glycerol

Kerosene

Property

−50

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) 1710 k (W/m⋅K) 0.131 Pr ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

—

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) 1150 k (W/m⋅K) Pr

−40

1400 0.128 —

−30

−20

−10

784 1.88 1170 990 0.125 0.123 15.1

775 1.92 850 0.121 13.5

—

—

—

0

20

30

40

50

60

70

759 2.02 645 0.118 11.0

751 2.06 530 0.116 9.41

743 2.11 464 0.114 8.59

735 2.15 410 0.112 7.87

721 2.20 367 0.110 7.34

717 2.25 330 0.108 6.88

708 2.30 298 0.106 6.47

1276

1270

1248 2.457

1242 2.504

2.548

2.588

2.625 2.657 2.686

4.0.+6

1260 2.393 1.5.+6 0.284 12650

1254 2.406

1.2.+7

0.285

0.287

0.288

0.289

0.291

0.293 0.294 0.295

2.28 73

2.32 66

2.35 60

2.38 55

767 1.97 735 0.120 12.1

725

500

360

275

781 1.91 215 0.140 2.93

10

774 1.96 173 0.139 2.44

767 2.02 149 0.139 2.17

760 2.07 126 0.138 1.89

754 2.13 108 0.138 1.67

748 2.18 95 0.137 1.51

742 2.23 83 0.137 1.35

80

90

100

699 2.35 270 0.104 6.10

690 2.41 246 0.102 5.81

681 2.46 225 0.100 5.54

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k(W/m⋅K) Pr

2.30 2305 0.225 23.6

2.32 1800 0.222 18.8

2.35 1410 0.219 15.1

2.37 1170 0.216 12.9

2.40 975 0.212 11.0

2.42 820 0.209 9.53

2.45 692 0.206 8.23

2.47 590 0.203 7.18

783 2.49 510 0.199 6.38

774 2.52 455 0.195 5.88

766 2.55 400 0.192 5.31

756 2.65 355 0.189 4.98

746 2.78 315 0.187 4.68

736 2.94 271 0.184 4.34

725 3.13 240 0.182 4.13

711 3.30 218 0.180 3.99

Methyl formate

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

1069 1.84 830 0.217 7.04

1056 1.86 711 0.213 6.21

1043 1.88 618 0.209 5.56

1030 1.90 544 0.205 5.04

1017 1.92 481 0.200 4.62

1003 1.95 430 0.195 4.30

989 1.99 380 0.191 3.96

975 2.03 345 0.186 3.77

960 2.08 315 0.180 3.64

944

929

913

897

880

863

845

Oil, castor

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

2,420,000 0.182

986,000 451,000 231,000 125,000 74,000 43,000 0.181 0.180 0.179 0.178 0.177 0.176 0.175 0.174 0.17

Methanol

Oil, olive

Pentane

Propanol

Sulfuric acid

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

138,000 0.170

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

693 2.060 489 0.142 7.14

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

849 1.955 20,200 13,500 9500 6900 0.167 0.166 0.165 236

684 2.084 428 0.139 6.42

674 2.110 379 0.136 5.88

665 2.137 339 0.132 5.49

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

Turpentine

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

923 1.535 1670 0.149 17.8

913 1.556 1345 0.147 14.2

904 1.579 1100 0.144 12.1

36,300 0.167

24,500 0.166

17,000 12,400 0.166 0.165 0.165 0.164 0.164

616

606

596

585

574

562

209 0.115

190 0.112

175 0.108

161 0.105

148 0.101

137 124 113 0.098 0.095 0.091

646 2.206 279 0.125 4.92

636 2.239 254 0.122 4.66

626 2.273 234 0.119 4.47

811

814

796

788

779

770

761

752

5110

819 2.219 3900

2900

2245

1720 0.171

1400 0.169

1130 0.168

921 0.167

760 0.165

630 508 447 0.164 0.163 0.162

1834 1.382 25,400

15,700

11,500

8820

7220

6090

5190

829 1.80 380 0.124 5.5

820 1.83 355 0.122 5.3

810 1.87 325 0.119 5.1

820

730

675

48,400 35,200 0.314 932 1.514 2120 0.152 21.1

52,000 0.168

656 2.167 307 0.128 5.20

ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr

Toluene

914 1.633 84,000 0.169 810

895 1.602 915 0.142 10.3

886 1.633 770 0.139 9.0

876 1.652 670 0.137 8.1

867 1.675 590 0.134 7.4

858 1.701 520 0.132 6.7

848 1.73 470 0.129 6.3

839 1.76 420 0.126 5.9

1.72 2250 0.130 29.8

1.76 1780 0.129 24.3

1.80 1490 0.128 20.9

1270 0.127 18.4

1070 0.126 16.1

1.93 925 0.125 14.3

550

747

800 1.92 295 0.117 4.8

538

743

790 1.97 270 0.114 4.7

2-298

TABLE 2-147 Cmpd. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)] Name

Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride

Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4 CF4

CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5 75-73-0

Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 153.8227 88.0043

C1 0.33515 0.39363 0.214 0.23638 0.2878 0.30755 0.33363 0.2703 0.2441 0.30751 0.28472 1.169 0.23494 0.1819 0.28485 0.23444 0.20996 0.2391 0.20603 0.25867 0.17847 0.2029 0.20316 0.19053 –0.2185 0.16983 0.1629 0.16143 0.21966 0.22231 0.27349 0.064621 –0.0032865 0.22888 0.18599 0.22153 0.21378 0.21153 0.21721 0.18707 0.21143 0.2069 0.22334 0.24962 0.1967 0.24077 0.4406 0.2333 0.2855 0.1589 0.20771

C2 –0.00055227 –0.00037053 –0.0001834 –0.00024263 –0.000427 –0.000402 –0.00083655 –0.0003764 –0.0002904 –0.000487 –0.0017393 –0.002314 –0.00026477 –0.0003176 –0.00025225 –0.00030572 –0.0002146 –0.0002325 –0.00021023 –0.00022516 –0.000065843 –0.0002226 –0.00019912 –0.00015145 0.0042143 –0.0001981 –0.00021198 –0.00021287 –0.0003436 –0.0003664 –0.00071267 0.00067625 0.0011463 –0.00025 –0.00017227 –0.00035023 –0.00035445 –0.00035056 –0.00026563 –0.00020037 –0.000258 –0.0002568 –0.0003515 –0.000325 –0.000168 –0.00028665 –0.0012175 –0.000275 –0.001784 –0.0001987 –0.00078883

C3

C4

C5

–0.00000411

–0.000017753 3.1041E-08

5.1555E-07 –1.0491E-06 –1.5525E-06

–2.0108E-11

Tmin, K 149.78 353.33 289.81 200.15 178.45 229.32 192.4 185.45 286.15 189.63 75 195.41 235.65 83.78 403 278.68 258.27 395.45 260.28 321.35 257.85 275.65 243.95 342.2 266 242.43 154.25 179.44 136.95 164.25 134.86 220 196.15 183.85 158.45 87.8 134.26 167.62 199.65 185.3 157.46 133.02 147.43 176.8 267.95 161.3 216.58 161.11 68.15 250.33 89.56

Thermal cond. at Tmin 0.2524 0.2627 0.1608 0.1878 0.2116 0.2154 0.1727 0.2005 0.1610 0.2152 0.1543 0.7168 0.1725 0.1264 0.1832 0.1492 0.1545 0.1472 0.1513 0.1863 0.1615 0.1415 0.1546 0.1387 0.1299 0.1218 0.1302 0.1232 0.1726 0.1621 0.1868 0.1626 0.1618 0.1829 0.1587 0.1908 0.1662 0.1528 0.1642 0.1499 0.1708 0.1727 0.1715 0.1922 0.1517 0.1945 0.1769 0.1890 0.1639 0.1092 0.1371

Tmax, K

Thermal cond. at Tmax

294.15 494.3 391.05 412.7 343.15 354.81 250 325.84 484.5 350.45 125 400.05 512.5 150 563.15 413.1 442.29 596 464.15 664 478.6 528.6 472.03 723.15 584 429.24 327 413.15 284 268.74 400 469.57 481.38 391 372.9 266.91 276.87 274.03 453.75 473.15 371.61 358.13 281.22 347.94 573.15 390.74 300 319.37 125 349.79 145.1

0.1727 0.2105 0.1423 0.1362 0.1413 0.1649 0.1245 0.1477 0.1034 0.1368 0.0673 0.2433 0.0993 0.0418 0.1428 0.1081 0.1150 0.1005 0.1085 0.1092 0.1470 0.0852 0.1092 0.0810 0.0316 0.0848 0.0936 0.0735 0.1221 0.1238 0.0709 0.1508 0.1888 0.1311 0.1218 0.1281 0.1156 0.1155 0.0967 0.0923 0.1156 0.1149 0.1245 0.1365 0.1004 0.1288 0.0754 0.1455 0.0625 0.0894 0.0933

2-299

52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106

Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Di–isopropyl amine Di–isopropyl ether Di–isopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine

Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N

7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3

70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19 102.17476 114.18546 90.121 104.14758 54.09044 45.08368

0.2246 0.1841 0.23779 0.1778 0.25381 0.21851 0.21232 0.18241 0.19186 0.17971 0.1855 0.37845 0.22262 0.19813 0.1715 0.17557 0.20926 0.2066 0.21776 0.24348 0.18374 0.21363 0.2063 0.206 0.236171 0.20237 0.20134 0.20839 1.264 0.1426 0.13622 0.17558 0.19418 0.16694 0.16994 0.16977 0.18881 0.214 0.23847 0.18 0.19653 0.0218 0.2587 0.2495 0.21065 0.27019 0.23171 0.37296 0.1844 0.19162 0.22076 0.22078 0.22998 0.22773 0.2454

–0.000064 –0.0001917 –0.000395209 –0.0002023 –0.000431803 –0.00033762 –0.0003149 –0.00011109 –0.0001303 –0.00012037 –0.00020895 –0.00069945 –0.00034082 –0.0002505 –0.0001255 –0.00012392 –0.00026037 –0.0002696 –0.00027783 –0.00042568 –0.0001925 –0.00023004 –0.00025 –0.0002 –0.00025 –0.00024187 –0.00020826 –0.00023622 –0.00016402 –0.0001179 –0.00022499 –0.00022246 –0.0001667 –0.0001637 –0.0001799 –0.00026083 –0.000266 –0.00033366 –0.00023144 –0.00025012 0.0010315 –0.00054343 –0.000407 –0.0002623 –0.000661 –0.00038503 –0.00088707 –0.000239 –0.0002762 –0.00027624 –0.00031271 –0.00030372 –0.00034804 –0.000338

–0.000000788

–0.000001355 4.2097E-07

3.443E-07 2.5762E-07

172.12 227.95 136.75 209.63 175.43 150.35 155.97 285.39 304.19 307.93 177.14 245.25 182.48 279.69 296.6 242 169.67 179.28 138.13 145.59 189.64 285 243.51 304.75 280.05 206.89 247.56 229.15 20.4 210.15 282.85 220.6 175.3 248.39 262.87 326.14 176.19 253.15 178.01 192.5 172.71 301.15 223.35 156.85 169.2 154.56 179.6 136.95 176.85 187.65 204.81 159.95 226.1 240.91 180.96

0.1902 0.1404 0.1837 0.1354 0.1781 0.1677 0.1632 0.1507 0.1522 0.1426 0.1485 0.2069 0.1604 0.1281 0.1343 0.1456 0.1651 0.1583 0.1794 0.1815 0.1472 0.1481 0.1454 0.1451 0.1662 0.1523 0.1498 0.1543 1.2640 0.1081 0.1029 0.1259 0.1552 0.1255 0.1269 0.1111 0.1429 0.1467 0.1791 0.1354 0.1533 0.2095 0.1583 0.1857 0.1663 0.1763 0.1626 0.2563 0.1421 0.1398 0.1642 0.1708 0.1613 0.1439 0.1842

410 404.87 348.15 400 333 393.15 386.7 475.43 464.15 475.13 413.15 251.9 285.66 353.87 563.15 428.58 356.12 322.4 333.15 240.37 431.95 481.65 447.3 543.15 503 443.75 512.35 447.15 20.4 498.4 404.51 370.1 523.15 446.23 351.71 548 416.9 356.59 325 438 457.6 673.15 453.15 433.15 365.25 363.15 372.8 302.56 357.05 400.1 460 337.45 366.15 300.13 403.15

0.0659 0.1065 0.1002 0.0969 0.1100 0.0858 0.0906 0.1296 0.1314 0.1225 0.0992 0.2023 0.1253 0.1095 0.1008 0.1225 0.1165 0.1197 0.1252 0.1412 0.1006 0.1028 0.0945 0.0974 0.1104 0.0950 0.0946 0.1028 1.2640 0.0609 0.0885 0.0923 0.0778 0.0926 0.1124 0.0712 0.0801 0.1191 0.1300 0.0786 0.0821 0.1022 0.0989 0.0732 0.1148 0.0756 0.0882 0.1282 0.0991 0.0811 0.0937 0.1153 0.1188 0.1233 0.1091 (Continued)

2-300

TABLE 2-147 Cmpd. no. 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156

Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)] (Continued ) Name

2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan

Formula C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O

CAS

Mol. wt.

C1

C2

79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9

86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396

0.1774 0.1807 0.18092 0.17675 0.21373 0.31174 0.26 0.17964 0.13905 0.25547 0.23942 0.3142 0.21956 0.3027 0.18686 0.2224 0.2047 0.2178 0.35758 0.2468 0.2501 0.30059 0.1999 0.20771 0.2175 0.21043 0.17662 0.18334 0.4194 0.36434 0.088067 0.3097 0.26957 0.2587 0.20954 0.19356 0.21928 0.22873 0.23392 0.2137 0.22717 0.19653 0.2758 0.20962 0.25866 0.48162 0.336003243 0.3847 0.302 0.2198

–0.0002436 –0.0002177 –0.0002108 –0.0002077 –0.0002447 –0.0005638 –0.000255 –0.000246 0.0001509 –0.0004411 –0.0003311 –0.00030809 –0.000209955 –0.0004827 –0.00014953 –0.000314 –0.0002326 –0.0002233 –0.0011458 –0.000264 –0.0003563 –0.000581 –0.00023823 –0.00021265 –0.0002407 –0.00024903 –0.0002014 –0.0002228 –0.001591 –0.0004433 0.00094712 –0.0004023 –0.0003984 –0.00033 –0.00022251 –0.00024102 –0.00032568 –0.0002913 –0.0003206 –0.0002515 –0.0003298 –0.00016907 –0.0016297 –0.00028034 –0.000498 –0.0010709 –0.00054 –0.0001065 –0.000108 –0.00031405

C3

C4

–3.978E-07

6.1866E-07

6.602E-07

0.000001306 –1.3114E-06

–1.6698E-07

0

0

C5

Tmin, K 145.19 239.66 223.16 184.99 188.44 131.65 250 160 273.15 122.93 174.88 291.67 413.79 284.95 300.03 210.15 263.57 309.58 90.35 159.05 189.6 192.15 178.2 238.45 258.15 175.15 161.84 134.71 104 284.29 260.15 195.2 160.65 193.55 155.15 180 140 204.15 125.26 199.25 145.65 167.55 53.48 238.15 129.95 131.35 155.15 275.7 281.45 187.55

Thermal cond. at Tmin 0.1420 0.1285 0.1339 0.1383 0.1676 0.2375 0.1963 0.1403 0.1506 0.2012 0.1815 0.2243 0.1327 0.1652 0.1420 0.1564 0.1434 0.1487 0.2591 0.2048 0.1825 0.2133 0.1574 0.1570 0.1554 0.1668 0.1440 0.1533 0.2681 0.2383 0.2457 0.2312 0.2056 0.1948 0.1750 0.1502 0.1737 0.1693 0.1938 0.1636 0.1791 0.1635 0.1886 0.1429 0.1939 0.3410 0.2522 0.3553 0.2716 0.1609

Tmax, K

Thermal cond. at Tmax

331.15 392.7 402.94 596.15 382.9 320.03 425.15 362.93 556.85 253.55 310.48 464 559.2 374.47 531.46 382 489.47 616.93 300 353.15 350.21 293.15 413.1 549.4 516.5 453.15 404.94 376.62 280 390.41 470.45 329 283.85 433.15 500.66 466.4 391.2 450.1 308.15 495 400.07 371.05 130 353.15 235.45 194.82 253.85 493 373.71 304.5

0.0967 0.0952 0.0960 0.0529 0.1200 0.1313 0.1516 0.0904 0.0997 0.1436 0.1366 0.1712 0.1022 0.1219 0.1074 0.1025 0.0909 0.0800 0.0695 0.1536 0.1253 0.1870 0.1015 0.0909 0.0932 0.0976 0.0951 0.0994 0.0763 0.1913 0.2434 0.1773 0.1565 0.1158 0.0981 0.0812 0.0919 0.0976 0.1351 0.0892 0.0952 0.1108 0.0639 0.1106 0.1414 0.2730 0.1989 0.3322 0.2616 0.1242

2-301

157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211

Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate

He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2

7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7

4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317

–0.013833 0.20926 0.22841 0.215 0.202 0.234063 0.21142 0.2026 0.2108 0.19664 0.2037 0.21098 0.20749 0.22832 0.22492 0.1855 0.230656 0.21391 0.21076 0.23493 0.19112 0.20996 0.2058 0.21492 0.2119 1.3675 –0.0917 0.234 0.8045 0.43454 0.7516 0.4842 0.21668 0.237 0.28231 0.2306 0.41768 0.2837 0.23743 0.2777 0.23648 0.26082 0.33446 0.22142 0.1983 0.21246 0.22284 0.17471 0.19447 0.19636 0.20385 0.22235 0.20698 0.20348 0.21748

0.022913 –0.0002215 –0.00026273 –0.000303 –0.0002 –0.00025 –0.00024793 –0.0002234 –0.000246 –0.00016623 –0.0002252 –0.00026652 –0.00021917 –0.00026482 –0.0003533 –0.000146 –0.00025 –0.00026042 –0.00024 –0.0002912 –0.000083519 –0.0002692 –0.0002324 –0.0002899 –0.00027048 –0.0015895 0.017678 –0.0004636 –0.002102 –0.0007008 –0.0010874 –0.001184 –0.0002556 –0.000332 –0.00024019 –0.00025201 –0.0024528 –0.000281 –0.0002362 –0.000417 –0.00041639 –0.0003506 –0.00067427 –0.00022759 –0.0002822 –0.00033581 –0.0002516 –0.0001256 –0.0002901 –0.000291 –0.0002874 –0.0003044 –0.00024439 –0.0003106 –0.00025913

–0.0054872

0.0004585

–2.5241E-07

–5.1407E-07

–0.000382

3.5588E-06

8.033E-07

–3.3324E-06

1.0266E-07

2.2 295.13 229.8 182.57 265.83 239.15 220 234.15 238.15 154.12 229.92 192.22 291.31 214.93 177.83 269.25 228.55 223 217.35 217.5 133.39 170.05 192.62 141.25 183.65 274.69 13.95 185.15 273.15 259.83 189.79 193.15 227.15 177.95 409.15 288.15 90.69 175.47 301.15 175.15 170.45 196.32 179.69 260.75 159.53 113.25 357.15 155.95 135.58 139.39 160.15 157.48 175.3 183.45 187.35

0.0149 0.1439 0.1680 0.1597 0.1488 0.1743 0.1569 0.1503 0.1522 0.1650 0.1519 0.1597 0.1436 0.1714 0.1621 0.1462 0.1735 0.1558 0.1586 0.1716 0.1708 0.1642 0.1610 0.1740 0.1622 0.9309 0.0754 0.1482 0.2303 0.2525 0.5452 0.2555 0.1586 0.1779 0.1840 0.1580 0.2245 0.2344 0.1663 0.2047 0.1655 0.1920 0.2392 0.1621 0.1533 0.1744 0.1330 0.1551 0.1551 0.1558 0.1578 0.1744 0.1641 0.1465 0.1689

4.8 575.3 426.15 371.58 496.15 573.15 432.9 553.15 424.05 366.79 450.09 372.93 560.01 401.15 370 603.15 575 412.4 400.85 466 336.63 354.35 425.81 344.48 357.67 623.15 31 290.62 323.15 298.85 394.45 292.42 482.75 305.55 580 530 180 337.85 478.15 386.15 249.94 421 283.15 547.9 314 368.13 480.9 404.15 304.3 311.7 305.4 463.15 396.58 302.15 493.15

0.0204 0.0818 0.1164 0.1024 0.1028 0.0908 0.1041 0.0790 0.1065 0.1017 0.1023 0.1116 0.0848 0.1221 0.0942 0.0974 0.0869 0.1065 0.1146 0.0992 0.1048 0.1146 0.1068 0.1151 0.1152 0.3770 0.0848 0.0993 0.1252 0.2251 0.3227 0.1380 0.0933 0.1356 0.1430 0.0970 0.0915 0.1888 0.1245 0.1167 0.1324 0.1132 0.2079 0.0967 0.1097 0.0888 0.1018 0.1239 0.1062 0.1057 0.1161 0.0814 0.1101 0.1096 0.0897 (Continued)

2-302

TABLE 2-147 Cmpd. no. 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262

Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)] (Continued ) Name

Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne

Formula CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N CH3NO2 N 2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16

CAS 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3

Mol. wt. 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334

C1

C2

0.24683 0.1791 0.21558 0.21839 0.21828 0.1929 0.20023 0.1994 0.21956 0.27304 0.2197 0.22136 0.3246 0.222 0.2301 0.2822 0.24154 0.2332 0.20978 0.26119 0.2583 0.20911 0.19334 0.21698 0.20455 0.21258 0.2802 0.22534 0.24817 0.21103 0.2774 0.19657 0.22526 0.28035 0.17096 0.2971 0.247 0.2654

–0.00038854 –0.0002291 –0.00022728 –0.00025776 –0.0002557 –0.0002492 –0.00025581 –0.00026149 –0.00032153 –0.0004518 –0.0002505 –0.00028938 –0.000468 –0.00032217 –0.00028899 –0.00042037 –0.0003774 –0.0003044 –0.00026468 –0.00038345 –0.000379 –0.00021852 –0.00028038 –0.00028998 –0.00036589 –0.00029864 –0.000786 –0.0002683 –0.0003774 –0.00025985 –0.00054608 –0.0002118 –0.00037235 –0.0004646 –0.00010059 –0.017356 –0.0002814 –0.001677

0.3276 0.10112 0.1878 0.21229 0.21905 0.209 0.204 0.240538 0.2081 0.20468 0.20244 0.20954

–0.000405 0.0010293 –0.00022 –0.00024013 –0.000264 –0.0002 –0.00025 –0.00022869 –0.00025738 –0.00021343 –0.00024588

C3

C4

C5

6.516E-07

1.1689E-07

0

0.0005911

–0.000007421

–0.00000943

0

Tmin, K

Thermal cond. at Tmin

Tmax, K

Thermal cond. at Tmax

139.05 273.15 299.15 280.15 269.15 130.73 146.62 168.54 182.55 160 186.48 167.23 174.15 188 189.15 256.15 127.93 180.15 171.64 150.18 290.15 208.2 119.55 176 113.54 298.97 132.81 185.65 133.97 160.17 116.34 249.95 164.55 151.15 353.43 25 183.63 63.15

0.1928 0.1165 0.1476 0.1462 0.1495 0.1603 0.1627 0.1553 0.1609 0.2008 0.1730 0.1730 0.2431 0.1614 0.1754 0.1745 0.1933 0.1784 0.1644 0.2036 0.1483 0.1636 0.1598 0.1659 0.1630 0.1233 0.1873 0.1755 0.1976 0.1694 0.2139 0.1436 0.1672 0.2101 0.1354 0.1167 0.1953 0.1595

281.85 374.08 548.8 484.2 484.8 344.95 348.64 338.05 314.7 341.34 352.79 339.8 373.15 390 451.42 312 370 435.9 357.91 279.11 363.45 555.2 389.25 432.3 400 404.96 395.2 475 373 368.69 216.25 438.65 328.2 341.1 646.97 44 387.22 124

0.1373 0.0934 0.0909 0.0936 0.0943 0.1069 0.1110 0.1110 0.1184 0.1188 0.1313 0.1230 0.1500 0.0964 0.0996 0.1510 0.1019 0.1005 0.1150 0.1542 0.1206 0.0878 0.0842 0.0916 0.0582 0.0916 0.0713 0.0979 0.1074 0.1152 0.1593 0.1037 0.1156 0.1219 0.1059 0.0457 0.1380 0.0575

244.6 277.59 110 305.04 267.3 219.66 285.55 268.15 238.15 191.91 253.05 223.15

0.2285 0.1011 0.1869 0.1452 0.1549 0.1510 0.1469 0.1735 0.1536 0.1553 0.1484 0.1547

374.35 277.59 176.4 603.05 465.52 423.97 528.75 578.65 471.7 420.02 492.95 423.85

0.1760 0.1011 0.0759 0.0796 0.1073 0.0971 0.0983 0.0959 0.1002 0.0966 0.0972 0.1053

2-303

263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317

Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid

C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O 2S F6S O 3S C8H6O4

593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0

254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084

0.2137 0.22273 0.2156 0.203 0.235281 0.20955 0.2132 0.21732 0.20467 0.2012 0.2095 0.26335 0.2741 0.17483 0.20649 0.23894 0.2537 0.1848 0.223042 0.21875 0.2161 0.21569 0.21361 0.20597 0.2086 0.22102 0.21282 0.13753 0.18831 0.16326 0.22946 0.23081 0.26755 0.23144 0.20161 0.1831 0.31721 0.1954 0.26743 0.2332 0.2632 0.18707 0.24719 0.2247 0.21706 0.2202 0.2152 0.26524

–0.0002252 –0.00025037 –0.00029483 –0.0002 –0.00025 –0.00023733 –0.0002494 –0.00024969 –0.0002675 –0.0002142 –0.00025334 –0.00022461 –0.00138 0.00075288 –0.00021911 –0.00029724 –0.000576 –0.0001434 –0.00025 –0.00027849 –0.00024866 –0.00024081 –0.00030777 –0.00024518 –0.00024536 –0.000322 –0.0002856 –0.000025247 –0.0001 –0.00017777 –0.00021345 –0.0004078 –0.00066457 –0.00025 –0.00021529 –0.00020275 –0.000528 –0.000164 –0.00033418 –0.0003096 –0.0004278 –0.00019846 –0.00048824 –0.000264 –0.00028952 –0.00028535 –0.0000497 –0.00028676

0.20215 0.27216 0.38218 0.2544 0.92882 0.3063

–0.0002201 –0.00023183 –0.0006254 –0.0006595 –0.0030803 –0.00028541

–2.5228E-06

0.000000344

2.774E-07

0.000000412

0.00000266

301.31 251.65 216.38 289.65 257.65 241.55 252.85 255.55 171.45 223.95 193.55 462.65 60 77.35 283.07 191.59 143.42 239.15 273.15 200 196.29 234.18 108.02 160.75 197.45 167.45 163.83 372.38 314.06 243.15 404.15 136.87 85.47 200 185.26 199 165 252.45 180.37 178.15 188.36 173.55 87.89 180.25 142.61 159.95 213.15 388.85

0.1458 0.1597 0.1518 0.1451 0.1709 0.1522 0.1501 0.1535 0.1588 0.1532 0.1605 0.1594 0.1913 0.2180 0.1445 0.1820 0.1782 0.1505 0.1548 0.1631 0.1673 0.1593 0.1804 0.1666 0.1602 0.1671 0.1660 0.1281 0.1569 0.1200 0.1432 0.1750 0.2128 0.1814 0.1617 0.1428 0.2301 0.1540 0.2072 0.1780 0.1972 0.1526 0.2043 0.1771 0.1758 0.1746 0.2046 0.1537

589.86 445.15 398.83 512.85 570.15 452.9 499 440.65 394.41 472.19 399.35 516 150 161.85 543.84 375.15 445 458.65 353.15 392.2 375.46 375.14 303.22 385.15 399.79 313.33 329.27 610.03 454.99 439.43 557.65 238.65 350 370.35 425 431.65 322.15 543.15 370.25 434.82 333.15 583.15 340.49 483.15 325.71 340.87 460.75 545

0.0809 0.1113 0.0980 0.1004 0.0927 0.1021 0.0888 0.1073 0.0992 0.1001 0.1083 0.1475 0.0671 0.2306 0.0873 0.1274 0.0655 0.1190 0.1348 0.1095 0.1227 0.1254 0.1203 0.1115 0.1105 0.1201 0.1188 0.1221 0.1428 0.0851 0.1104 0.1335 0.0689 0.1389 0.1101 0.0956 0.1471 0.1063 0.1437 0.0986 0.1664 0.0713 0.0810 0.0972 0.1228 0.1229 0.1923 0.1090

242.54 460.85 197.67 223.15 289.95 700.15

0.1488 0.1653 0.2586 0.1072 0.2593 0.1065

418.31 591 400 318.69 481.47 795.28

0.1101 0.1351 0.1320 0.0442 0.0624 0.0793 (Continued)

2-304 TABLE 2-147 Cmpd. no. 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345

Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)] (Continued ) Name

o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene

Formula C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10

CAS 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3

Mol. wt. 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165

C1 0.16853 0.20293 0.19428 0.14563 0.20414 0.17835 0.20571 0.20463 0.20731 0.20447 0.1918 0.23813 0.18854 0.19216 0.1659 0.16815 0.18421 0.19898 0.20515 0.218744 0.256 0.22838 0.2333 0.21831 –0.432 0.20044 0.19989 0.20003

C2 –0.00010817 –0.00021798 –0.000249 –0.0000536 –0.00021217 –0.00023704 –0.00020028 –0.00024252 –0.00024997 –0.00022612 –0.0002453 –0.00038397 –0.0001963 –0.0002105 –0.00022686 –0.00020535 –0.00016097 –0.00017659 –0.00023933 –0.00025 –0.0003542 –0.00035173 –0.00039223 –0.00029122 0.0057255 –0.00023544 –0.0002299 –0.00023573

C3

C4

–0.000008078 1.861E-09

C5

Tmin, K 329.35 279.01 164.65 237.38 176.98 373.96 234.94 178.18 236.5 267.76 158.45 156.08 247.79 229.33 165.78 172.22 398.4 354 247.57 281 180.35 173.15 119.36 178.35 273.16 225.3 247.98 286.41

Thermal cond. at Tmin 0.1329 0.1421 0.1533 0.1329 0.1666 0.0897 0.1587 0.1614 0.1482 0.1439 0.1529 0.1782 0.1399 0.1439 0.1283 0.1328 0.1201 0.1365 0.1459 0.1485 0.1921 0.1675 0.1865 0.1664 0.5672 0.1474 0.1429 0.1325

Tmax, K

Thermal cond. at Tmax

723.15 526.73 339.12 480.77 394.27 426 357.31 474.85 482 508.62 483.15 276.02 449.27 442.53 372.39 387.91 629.6 625 469.08 561.2 410 278.25 345.6 434.52 633.15 413.1 417.58 413.1

0.0903 0.0881 0.1098 0.1199 0.1205 0.0774 0.1341 0.0895 0.0868 0.0895 0.0733 0.1321 0.1003 0.0990 0.0814 0.0885 0.0829 0.0886 0.0929 0.0784 0.1108 0.1305 0.0978 0.0918 0.4272 0.1032 0.1039 0.1026

The liquid thermal conductivity is calculated by k = C1 + C2T + C3T2 + C4T3 + C5T4 where k is the thermal conductivity in W/(m∙K) and T is the temperature in K. Thermal conductivities are at either 1 atm or the vapor pressure, whichever is higher. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.

TRAnSPORT PROPERTIES TABLE 2-148

FIG. 2-20 and TABLE 2-148

Nomograph (right) for thermal conductivity of organic liquids. (From B.V. Mallu and Y.J. Rao, Hydroc. Proc. 78, 1988.)

2-305

2-306

PHYSICAL AnD CHEMICAL DATA

TABLE 2-149

Thermal-Conductivity-Temperature Table for Metals and nonmetals* Thermal conductivities tabulated in watts per meter-kelvin Temperature, K

Substance

20

40

60

80

7 38,000 470 47 240

32 13,500 230 196 100

300

400

500

121 2,300 110 810 45

174 850 80 1,400 31

160 380 60 1,650 24

125 300 48 1,490 22

55 237 32 480 18

36 273 26 272 16

26 240 22 196 14

20 237 20 146 12

165 900 400 250 4

305 250 570 450 9

400 150 450 380 16

327 120 250 250 18

230 110 180 190 19

170 110 158 160 20

45 105 111 120 23

25 104 90 100 25

15 101 87 85 27

Copper Gallium Gold Graphite† Graphite‡

19,000 2,200 2,800 27 81

10,700 640 1,500 108 420

2,100 250 520 135 1,630

850 200 380 81 2,980

570 170 350 54 4,290

483 140 345 39 4,980

413 100 327 15 3,250

398 85 315 10 2,000

Hastelloy Inconel Iridium Iron Lead

1 2 1,300 710 175

3 4 1,900 1,000 57

4 8 750 560 43

5 10 360 270 42

6 11 230 170 41

7 11 172 132 40

9 14 147 94 37

10 15 145 80 35

Magnesium Magnesium oxide Manganese Manganin Mercury

1,200 1,100 2 2 54

1,300 3,100 2 4 40

620 2,200 4 9 35

290 950 5 11 33

190 460 5 13 33

169 260 6 13 32

159 75 7 17 32

Molybdenum Nickel Nylon Palladium Platinum

150 2,600 0.04 1,200 1,200

280 1,700 0.10 610 490

350 570 0.17 160 130

250 290 0.20 100 92

210 200 0.23 88 82

179 158 0.25 80 79

PTFE§ Pyrex Quartz Rhodium Rubber

0.94 0.12 1,200 2,900

1.43 0.20 480 3,900

1.94 0.33 82 1,000 0.13

2.1 0.42 40 370 0.15

2.15 0.51 30 250 0.16

140

57

25

15

16,500 108 300

5,200 146 93

1,100 88 29

14

320 28

130 39 880

100

110

59

Alumina Aluminum Antimony Beryllium oxide Bismuth Boron Cadmium Chromium Cobalt Constantan

Selenium (axis) Silica Silver Tantalum Tellurium Tin Titanium Tungsten Uranium Zinc Zirconium

10

100

200

1000

1200

16 232

10 220

8 93

7 99

6 105

111

70

47

33

25

12 99 85 70 30

81

71

65

62

61

392

388

383

371

357

342

312 7 1,460

309 5 1,140

304 4 930

292 3 680

278 3 530

262 2 440

2 370

11

13

143 69 34

140 61 33

55 31

43 19

33 22

28 24

31 26

156 48 8 22 8

153 36 9 28 10

151 27 9 34 11

149 21

146 13

84 10

98 8

112 7

40 12

13

14

143 106 0.28 78 75

138 91 0.30 78 73

134 80

130 72

126 66

118 67

112 72

105 76

100 80

78 72

80 72

72

73

78

78

81

2.16 0.57

2.20 0.88

2.25 1.1

190 0.17

160 0.20

10

8

6

630 68 17

500 62 13

430 59 11

358 61

62

101 37 330 20 150 42

90 33 310 22 135 38

84 31 280 23 130 34

2.3 1.6

2.5 2.1

150 0.22

145 0.24

140 0.25

425 58 6

4 1.34 424 57 4

3 1.52 420 58 3

2 1.70 413 58 3

72 26 190 26 123 25

67 21 180 28 120 23

62 20 170 30 116 22

60 20 150 32 110 21

600

1.87 405 59

800

2.22 389 59

2.60 374 60

1400

19 140 110 21

∗ Especially at low temperatures, the thermal conductivity can often be markedly reduced by even small traces of impurities. This table, for the highest-purity specimens available, should thus be used with caution in applications with commercial materials. From Perry, Engineering Manual, 3d ed., McGraw-Hill, New York, 1976. A more detailed table appears as Section 5.5.6 in the Heat Exchanger Design Handbook, Hemisphere Pub. Corp., Washington, DC, 1983. † Parallel to basal plane. ‡ Perpendicular to basal plane. § Also known as Teflon, etc.

TRAnSPORT PROPERTIES TABLE 2-150

Thermal Conductivity of Chromium Alloys*

TABLE 2-151 Thermal Conductivity of Some Alloys at High Temperature*

k = Btu/(h⋅ft2)(°F/ft) American iron and steel institute type no. 301, 302, 302B, 303, 304, 316† 308 309, 310 321, 347 403, 406, 410, 414, 416† 430, 430F† 442 501, 502†

k at 212°F

k at 932°F

9.4 8.8 8.0 9.3 14.4 15.1 12.5 21.2

12.4 12.5 10.8 12.8 16.6 15.2 14.2 19.5

2-307

Thermal conductivity, Btu/( ft)(hr)(°R) °R

∗ Table 2-150 is based on information from manufacturers. † Shelton and Swanger (National Bureau of Standards), Trans. Am. Soc. Steel Treat., 21, 1061–1078 (1933).

Kovar

Advance

Monel

Hastelloy A

Inconel

Nichrome V

5.6 6.2 6.8 7.3 7.8

6.0 6.5 7.0 7.6 8.1

5.5 6.1 6.7 7.3 7.8

500 600 700 800 900

7.8 8.3 8.6 8.7 8.7

11.4 12.6 13.9 15.1

9.0 10.2 11.2 12.3 13.4

1000 1100 1200 1300 1400

8.9 9.2 9.5 9.8 10.2

16.4 17.6 18.8 20.0 21.2

14.4 15.4 16.5 17.6 18.7

8.4 9.0 9.5 10.1 10.7

8.6 9.1 9.7 10.2 10.8

8.4 9.0 9.5 10.1 10.7

1500 1600 1700 1800 1900

10.5 10.8 11.1 11.3 11.5

22.5 23.8 25.0 26.2 27.4

19.8 20.8 21.9 23.0 24.0

11.3 11.8 12.3 12.9 13.4

11.3 11.8 12.4 13.0 13.6

11.3 11.9 12.4 13.0 13.5

2000 2100 2200

11.8 12.1 12.3

28.7 30.0

25.1 26.1 27.2

14.0 14.6 15.1

14.0 14.5 15.0

14.1 14.7 15.3

∗Silverman, J. Metals, 5, 631 (1953). Copyright American Institute of Mining, Metallurgical and Petroleum Engineers, Inc.

TABLE 2-152

Thermophysical Properties of Selected nonmetallic Solid Substances

Material

Density, kg/m3

Alumina Asphalt Bakelite Beryllia Brick

3975 2110 1300 3000 1925

Brick, fireclay Carbon, amorphous Clay Coal Cotton

2640 1950 1460 1350 80

Diamond Granite Hardboard Magnesite Magnesia

3500 2630 1000 3025 3635

Emissivity

Specific heat, kJ/(kg⋅K)

Thermal conductivity, W/(m⋅K)

0.82 0.93

0.765 0.920 1.465 1.030 0.835

36 0.06 1.4 270 0.72

11.9 0.03 0.74 88 0.45

0.960 0.724 0.880 1.26 1.30

1.0 1.6 1.3 0.26 0.06

0.39 1.13 1.01 0.15 0.58

0.509 0.775 1.38 1.13 0.943

2300 2.79 0.15 4.0 48

1290 1.37 0.11 1.2 14

0.93 0.86 0.91 0.80

0.38 0.72

Oak Paper Pine Plaster board Plywood

770 930 525 800 540

0.90 0.83 0.84 0.91

Pyrex Rubber Rubber, foam Salt Sandstone

2250 1150 70 2150

0.92 0.92 0.90 0.34 0.59

Silica Sapphire Silicon carbide Soil

3975 3160 2050

Teflon Thoria Urethane foam Vermiculite

2200 4160 70 120

2.38 1.34 2.75

Thermal diffusivity, m2/s × 106

0.18 0.011 0.12 0.17 0.12

0.10 0.01 0.54

0.74 0.09

0.854 0.745

1.4 0.2 0.03 7.1 2.9

0.79 0.48 0.86 0.38

0.743 0.765 0.675 1.84

1.3 46 110 0.52

15 230 0.14

0.92 0.28

0.35 0.71 1.05 0.84

0.26 14 0.03 0.06

0.34 4.7 0.36 0.60

1.22 0.835 2.00

0.18

1.8

note: Difficulties of accurately characterizing many of the specimens mean that many of the values presented here must be regarded as being of order of magnitude only. For some materials, actual measurement may be the only way to obtain data of the required accuracy. To convert kilograms per cubic meter to pounds per cubic foot, multiply by 0.062428; to convert kilojoules per kilogram-kelvin to British thermal units per pounddegree Fahrenheit, multiply by 0.23885.

2-308

TABLE 2-153 Lower and Upper Flammability Limits, Flash Points, and Autoignition Temperatures for Selected Hydrocarbons LFL

UFL

Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Olefins Olefins Olefins Olefins Olefins Olefins Acetylenes

Group

Methane Ethane Propane n-Butane Isobutane n-Pentane Isopentane Neopentane n-Hexane n-Heptane 2,3-Dimethylpentane n-Octane 2,2,4-Trimethylpentane n-Nonane n-Decane Ethylene Propylene 1-Butene cis-2-Butene trans-2-Butene 1-Pentene Acetylene

Compound

74-82-8 74-84-0 74-98-6 106-97-8 75-28-5 109-66-0 78-78-4 463-82-1 110-54-3 142-82-5 565-59-3 111-65-9 540-84-1 111-84-2 124-18-5 74-85-1 115-07-1 106-98-9 590-18-1 624-64-6 109-67-1 74-86-2

CAS

CH4 C2H6 C3H8 C4H10 C4H10 C5H12 C5H12 C5H12 C6H14 C7H16 C7H16 C8H18 C8H18 C9H20 C10H22 C2H4 C3H6 C4H8 C4H8 C4H8 C5H10 C2H2

Formula

5.00 3.00 2.10 1.60 1.80 1.40 1.40 1.40 1.20 1.05 1.10 0.96 0.95 0.85 0.75 2.70 2.15 1.60 1.70 1.70 1.40 2.50

15.00 12.40 9.50 8.40 8.40 7.80 7.60 7.50 7.20 6.70 6.70 6.50 6.00 5.60 5.40 36.00 11.20 10.00 9.70 9.70 8.70 80.00

Flash point (K) 87.12 139.00 171.00 199.15 191.00 224.15 218.00 205.00 250.15 269.00 261.00 287.15 265.00 304.15 322.85 129.00 169.00 198.00 205.00 203.00 222.00 151.00

Acetylenes Acetylenes Aromatics Aromatics Aromatics Aromatics Aromatics Aromatics Cyclic hydrocarbons Cyclic hydrocarbons Cyclic hydrocarbons Cyclic hydrocarbons Cyclic hydrocarbons Cyclic hydrocarbons Cyclic hydrocarbons Alcohols Alcohols Alcohols Alcohols Alcohols Alcohols Alcohols Alcohols Alcohols Alcohols Aldehydes Aldehydes Aldehydes

Vinylacetylene Methylacetylene Benzene Toluene o-Xylene Ethylbenzene Cumene Anthracene Cyclopropane Furan Cyclopentadiene Cyclohexane Methylcyclohexane Phenol Dicyclopentadiene Methanol Ethanol Allyl Alcohol 1-Propanol Isopropanol 1-Butanol 2-Butanol 2-Methyl-1-propanol 2-Methyl-2-propanol Cyclohexanol Formaldehyde Acetaldehyde Acrolein

689-97-4 74-99-7 71-43-2 108-88-3 95-47-6 100-41-4 98-82-8 120-12-7 75-19-4 110-00-9 542-92-7 110-82-7 108-87-2 108-95-2 77-73-6 67-56-1 64-17-5 107-18-6 71-23-8 67-63-0 71-36-3 78-92-2 78-83-1 75-65-0 108-93-0 50-00-0 75-07-0 107-02-8

C4H4 C3H4 C6H6 C7H8 C8H10 C8H10 C9H12 C14H10 C3H6 C4H4O C5H6 C6H12 C7H14 C6H6O C10H12 CH4O C2H6O C3H6O C3H8O C3H8O C4H10O C4H10O C4H10O C4H10O C6H12O CH2O C2H4O C3H4O

2.20 1.70 1.20 1.10 1.10 1.00 0.88 0.60 2.40 2.00 1.70 1.30 1.15 1.70 0.80 7.18 3.30 2.50 2.10 2.00 1.70 1.70 1.70 1.84 1.20 7.00 4.00 2.80

31.70 57.30 8.00 7.10 6.40 6.70 6.50 5.20 10.40 23.00 14.60 7.80 6.70 8.60 6.30 36.50 19.00 18.00 14.00 12.70 11.30 9.80 11.00 9.00 11.10 73.00 30.00 31.00

211.00 192.00 262.00 279.15 305.15 296.15 309.15 458.15 180.00 237.00 227.00 255.93 269.15 352.15 318.15 284.15 286.15 294.00 297.59 285.15 310.50 296.15 302.32 284.26 334.15 219.80 232.00 247.15

Autoignition T (K) 810.00 745.00 723.00 561.00 733.15 516.00 693.15 723.15 498.00 477.00 608.15 479.00 684.15 478.00 474.00 723.15 728.15 657.00 598.00 597.00 546.00 578.15 Decomposes violently on heating. Forms explosive peroxides with air or oxygen. 613.15 833.15 753.15 736.15 703.15 697.00 813.15 771.00 663.15 913.15 518.15 523.15 988.00 783.15 737.00 696.00 651.00 644.00 728.75 616.00 663.15 681.15 751.00 573.15 697.15 449.15 507.00

Aldehydes Aldehydes Aldehydes Aldehydes Aldehydes Aldehydes Ethers Ethers Ethers Ethers Ketones Ketones Ketones Acids Acids Acids Esters Esters Esters Esters Esters Esters Esters Esters Esters Esters Inorganic Inorganic Inorganic Oxides Oxides Oxides Oxides Oxides Peroxides Sulfur containing Sulfur containing Sulfur containing Sulfur containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Bromides Glycols Glycols

Propanal trans-Crotonaldehyde cis-Crotonaldehyde 2-Methylpropanal Butanal Furfural Dimethyl ether Methyl vinyl ether Diethyl ether Diphenyl ether Acetone Methyl ethyl ketone Acetophenone Acetic acid Hydrogen cyanide Formic acid Methyl formate Ethyl formate Methyl acetate Vinyl acetate Ethyl acetate n-Propyl acetate Isopropyl acetate n-Butyl acetate Isobutyl acetate n-Pentyl acetate Hydrogen Ammonia Cyanogen Carbon monoxide Ethylene oxide 1,2-Propylene oxide 1,4-Dioxane Mesityl oxide Di-t-Butyl peroxide Carbon disulfide Hydrogen sulfide Carbonyl sulfide Dimethyl sulfide Methyl chloride Ethyl chloride Isopropyl chloride 1,2-Dichloroethane 1,2-Dichloropropane Dichloromethane 2-Chloroethanol Trichloroethylene Hexachloro-1,3-Butadiene Vinyl chloride Monochlorobenzene Benzyl chloride Bromomethane Ethylene glycol Diethylene glycol

123-38-6 123-73-9 15798-64-8 78-84-2 123-72-8 98-01-1 115-10-6 107-25-5 60-29-7 101-84-8 67-64-1 78-93-3 98-86-2 64-19-7 74-90-8 64-18-6 107-31-3 109-94-4 79-20-9 108-05-4 141-78-6 109-60-4 108-21-4 123-86-4 110-19-0 628-63-7 1333-74-0 7664-41-7 460-19-5 630-08-0 75-21-8 75-56-9 123-91-1 141-79-7 110-05-4 75-15-0 7783-06-4 463-58-1 75-18-3 74-87-3 75-00-3 75-29-6 107-06-2 78-87-5 75-09-2 107-07-3 79-01-6 87-68-3 75-01-4 108-90-7 100-44-7 74-83-9 107-21-1 111-46-6

C3H6O C4H6O C4H6O C4H8O C4H8O C5H4O2 C2H6O C3H6O C4H10O C12H10O C3H6O C4H8O C8H8O C2H4O2 CHN CH2O2 C2H4O2 C3H6O2 C3H6O2 C4H6O2 C4H8O2 C5H10O2 C5H10O2 C6H12O2 C6H12O2 C7H14O2 H2 H3N C2N2 CO C2H4O C3H6O C4H8O2 C6H10O C8H18O2 CS2 H2S COS C2H6S CH3Cl C2H5Cl C3H7Cl C2H4Cl2 C3H6Cl2 CH2Cl2 C2H5ClO C2HCl3 C4Cl6 C2H3Cl C6H5Cl C7H7Cl CH3Br C2H6O2 C4H10O3

2.60 2.10 2.10 1.60 1.90 2.10 3.30 2.60 1.70 0.80 2.60 1.80 1.10 4.00 5.60 12.00 5.20 2.76 3.13 2.60 2.18 1.80 1.76 1.40 1.42 1.10 4.00 15.00 6.60 12.50 3.00 2.20 2.00 1.30 0.74 1.30 4.00 12.00 2.20 8.10 3.80 2.80 4.50 3.30 14.00 4.90 12.00 2.90 3.60 1.30 1.10 10.10 3.10 1.70

17.00 15.50 15.50 11.00 12.50 19.30 26.20 39.00 46.00 6.00 13.00 11.00 6.70 19.90 40.00 38.00 23.00 15.70 14.00 13.40 11.50 8.00 7.20 7.60 8.00 7.10 75.00 28.00 32.00 74.20 100.00 35.50 22.00 8.80 8.20 50.00 44.00 29.00 19.70 17.20 15.40 10.70 16.00 14.50 22.00 15.90 29.00 15.70 33.00 9.60 7.10 16.00 42.00 37.00

243.15 286.15 285.93 254.15 262.15 333.15 193.00 217.15 228.15 388.15 253.15 264.15 350.15 312.04 255.00 323.15 247.00 254.15 260.15 265.37 269.00 283.71 274.82 298.15 291.00 310.15 14.00 209.00 214.00 71.00 225.00 236.00 284.15 301.00 277.15 243.15 167.00 186.00 237.15 203.00 223.15 238.15 286.00 286.15 265.00 328.15 305.15 389.00 205.00 301.15 333.15 230.00 384.15 413.15

500.15 505.00 505.00 478.00 503.15 589.00 499.15 560.15 433.15 891.15 738.15 789.00 843.15 700.00 811.00 753.00 729.00 728.15 775.00 700.00 700.00 723.00 733.15 694.00 696.00 633.15 793.15 924.00 984.00 882.00 702.00 703.15 453.15 618.00 Organic peroxides can ignite easily 363.15 533.15 477.00 478.15 905.00 802.00 866.00 686.00 830.00 888.15 698.15 683.15 883.15 745.00 911.00 858.15 800.00 669.00 636.15

2-309

(Continued)

2-310 TABLE 2-153 Lower and Upper Flammability Limits, Flash Points, and Autoignition Temperatures for Selected Hydrocarbons (Continued ) Group Glycols Amines Amines Amines Amines Amines Amines Amines Amines Amines Amines Amines Amines Amines Miscellaneous Miscellaneous Miscellaneous Miscellaneous Miscellaneous Miscellaneous Miscellaneous Miscellaneous

Compound Triethylene glycol Methylamine Ethylamine Dimethylamine Isopropylamine Trimethylamine Allylamine Diethylamine Tert-Butylamine Triethylamine Cyclohexylamine Monoethanolamine Diethanolamine Dimethylethanolamine Acrylonitrile Aniline Diborane Methyl methacrylate Styrene Biphenyl Methyl acrylate Phthalic anhydride

CAS 112-27-6 74-89-5 75-04-7 124-40-3 75-31-0 75-50-3 107-11-9 109-89-7 75-64-9 121-44-8 108-91-8 141-43-5 111-42-2 108-01-0 107-13-1 62-53-3 19287-45-7 80-62-6 100-42-5 92-52-4 96-33-3 85-44-9

Formula C6H14O4 CH5N C2H7N C2H7N C3H9N C3H9N C3H7N C4H11N C4H11N C6H15N C6H13N C2H7NO C4H11NO2 C4H11NO C3H3N C6H7N B2H6 C5H8O2 C8H8 C12H10 C4H6O2 C8H4O3

LFL

UFL

0.90 4.90 2.70 2.80 2.00 2.00 2.03 1.70 1.70 1.20 0.66 3.00 1.70 1.40 3.05 1.30 0.80 1.70 1.10 0.70 2.18 1.20

9.20 20.70 14.00 14.40 10.40 11.60 24.30 10.10 8.90 8.00 9.40 13.10 9.80 12.20 17.00 11.00 88.00 12.50 6.10 5.80 14.40 9.20

Flash point (K) 429.15 217.00 227.00 223.15 236.15 207.00 252.00 245.15 236.00 262.15 299.65 366.55 445.15 312.15 268.15 344.15 142.00 284.15 305.00 383.15 270.00 425.00

Autoignition T (K) 644.00 703.15 657.00 595.00 673.15 463.15 647.039 583.15 648.15 522.15 566.15 683.15 935.00 568.15 754.00 890.00 325.00 708.15 763.15 813.15 741.15 857.00

Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES

2-311

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES* InTRODUCTIOn Physical property values, sufficiently accurate for many engineering applications, can be estimated in the absence of reliable experimental data. The purpose of this section is to provide a set of recommended prediction methods for general engineering use. It is not intended to be a comprehensive review, and many additional methods are available in the literature. Methods recommended in this section were selected on the basis of accuracy, generality, and, in most cases, simplicity or ease of use. They generally correspond to the methods tested and given priority in the DIPPR 801 database project.* Properties included in this subsection are divided into 10 categories: (1) physical constants including critical properties, normal melting and boiling points, acentric factor, radius of gyration, dipole moment, refractive index, and dielectric constant; (2) liquid and solid vapor pressure; (3) thermal properties including enthalpy and Gibbs energy of formation and ideal gas entropy; (4) latent enthalpies of vaporization, fusion, and sublimation; (5) heat capacities for ideal and real gases, liquids, and solids; (6) densities of gas, liquid, and solid phases; (7) gas and liquid viscosity; (8) gas and liquid thermal conductivity; (9) surface tension; and (10) flammability properties including flash point, flammability limits, and autoignition temperature. Each of the 10 subsections gives a definition of the properties and a description of one or more recommended prediction methods. Each description lists the type of method, its uncertainty, its limitations, and the expected

*The Design Institute for Physical Properties (DIPPR) is an industrial consortium under the auspices of AIChE; Project 801, Evaluated Process Design Data, is a purecomponent database of industrially important compounds. Values and procedures used with permission of the DIPPR 801 Technical Committee.

uncertainty of the predicted value. A numerical example is also given to illustrate use of the method. For brevity, symbols used for physical properties and for variables and constants in the equations are defined under Nomenclature and are not necessarily defined after their first use except where doing so clarifies usage. A list of equation and table numbers in which variables appear is included in the Nomenclature section for quick crossreferencing. Although emphasis is on pure-component properties, some mixture estimation techniques have been included for physical constants, density, viscosity, thermal conductivity, surface tension, and flammability. Correlation and estimation of properties that are inherently multicomponent (e.g., diffusion coefficients, mixture excess properties, activity coefficients) are treated elsewhere in this handbook. UnITS The International System (SI) of metric units has been used throughout this section. Where possible, the estimation equations are set up in dimensionless groups to eliminate the need to specify units of variables and to facilitate unit conversions. For example, rather than use Pc as an equation variable, the dimensionless group (Pc/Pa) is used. When a value for Pc expressed in any units (say, Pc = 6.53 MPa) is inserted into this group, the result is dimensionless with an explicit indication of conversion factors that must be included, such as Pc 6.53 MPa  6.53 MPa   10 6 Pa  = = = 6.53 × 10 6   Pa Pa Pa   MPa  Appropriate unit conversion factors are found in Sec. 1 of this handbook.

nomenclature Physical constants h k NA R Properties

Definition Planck’s constant Boltzmann’s constant Avogadro’s number Gas constant

Value 6.626 × 10−34 J ⋅ s 1.3806 × 10−23 J/(molecule ⋅ K) 6.022 × 1026 molecule/kmol 8314.3 Pa ⋅ m3/(kmol ⋅ K)

Definition

Typical units

A, B, C AIT Avdw B, B(T) CP C op

Molecular principal moments of inertia Autoignition temperature Van der Waals area Second virial coefficient Isobaric molar heat capacity Ideal gas isobaric molar heat capacity

kg ⋅ m2 K m2/kmol m3/kmol J/(kmol ⋅ K) J/(kmol ⋅ K)

Cv Hi k LFL M n P P Pc Pr P* P*meas Pr* Pt* RD Rg So Ss Sr Svib

Constant-volume molar heat capacity Enthalpy of compound i Thermal conductivity Lower flammability limit Molecular weight Refractive index Pressure Parachor Critical pressure Reduced pressure; Pr = P/Pc Vapor pressure Measured vapor pressure value Reduced vapor pressure; Pr* = P*/Pc Vapor pressure at triple point Molar refraction Radius of gyration Ideal gas entropy Standard state entropy Rotational contribution to entropy Vibrational contribution to entropy

J/(kmol ⋅ K) J/kmol W/(m ⋅ K) % kg/kmol unitless Pa unitless Pa unitless Pa Pa unitless Pa cm3/mol m J/(kmol ⋅ K) J/(kmol ⋅ K) J/(kmol ⋅ K) J/(kmol ⋅ K)

2-312

PHYSICAL AnD CHEMICAL DATA nomenclature (Continued ) Properties

Definition

Typical units

T Tad Tb Tbr Tc TFP Tm Tmeas Tr UFL V Vc Vr wi xi yi Z Zc Zi ∆G of

Temperature Adiabatic flame temperature Normal boiling point temperature Reduced temperature at Tb; Tbr = Tb/Tc Critical temperature Flash point temperature Melting temperature T at which a dependent property was measured Reduced temperature; Tr = T/Tc Upper flammability limit Molar volume Critical volume Reduced volume; Vr = ZTr/Pr Mass fraction of component i Mole fraction of component i Mole fraction of component i in vapor phase Compressibility factor; Z = PV/RT Critical compressibility factor; Zc = PcVc/RTc Compressibility factor of reference fluid i Ideal gas standard Gibbs energy of formation

K K K unitless K K K K unitless % m3/kmol m3/kmol unitless unitless unitless unitless unitless unitless unitless J/kmol

∆G sf

Standard state Gibbs energy of formation

J/kmol

∆H of

Ideal gas standard enthalpy of formation

J/kmol

∆H sf

Standard state enthalpy of formation

J/kmol

DHfus DHrxn DHsub DHu ∆S sf

Enthalpy of fusion Enthalpy change per mole of reaction as written Enthalpy of sublimation Enthalpy of vaporization Standard state entropy of formation

J/kmol J/kmol J/kmol J/kmol J/(kmol ⋅ K)

∆S of

Ideal gas entropy of formation

J/(kmol ⋅ K)

DSfus DZv d e h ho m mr r ρc ρr ρS, ρL, ρV σ σm t tb fi w

Latent entropy of fusion Change in compressibility factor upon vaporization Solubility parameter Dielectric constant Viscosity Viscosity at low pressure Dipole moment Reduced dipole moment [defined in Eq. (2-66)] Molar density; r = V −1 Critical molar density; ρc = Vc−1 Reduced molar density; ρr = ρ/ρc Density of solid, liquid, vapor, respectively Surface tension Surface tension of mixture Complementary reduced temperature (1 − Tr) t at the normal boiling point (1 − Tbr) Volume fraction of component i Acentric factor

J/(kmol ⋅ K) unitless J1/2 ⋅ m−3/2 unitless Pa ⋅ s Pa ⋅ s D unitless kmol/m3 kmol/m3 unitless kmol/m3 mN/m mN/m unitless unitless unitless unitless

Equation variables

Definition

a a, b, c, . . . a, b, c ai a, b a, b ai, bi, di aα A, B, C, . . .

EoS constant GC values for Cp and h Correlation coefficients GC values Terms in second virial correlation Chickos correlation parameters GC values for liquid Cp EoS constant for mixture Correlation constants/parameters

A Ai b bi, ci, . . . bi

Factor in liquid k correlation o Constants in C p correlation EoS constant Reference EoS constants GC value for AIT

Appears in (Eq. 2-?) or [Table 2-?] (70), [172] (54), (57), (96), [174] (25), (27), (42), (43), (44), (69) (46), (96), [164], [174] (65) (42), (43), (44) (54), [166] (78) (2), (23), (24), (26), (28), (28a), (38), (40), (53), (54), (56), (69), (71), (82), (84), (86), (87), (94), (95), (100), (101), (102) (110), [176] (48), (49), (70) (70), [172] (69), [171] (129), [180]

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES nomenclature (Continued ) Equation variables

Definition

Appears in (Eq. 2-?) or [Table 2-?]

b B(i) C

EoS constant for mixture Second virial expansion term Number of components in mixture

C Ci

Parameter in modified Pachaiyappan method GC values for some methods

Cij (Cop)i Csj Cst Ctj fi F(i) F GI Gij gEc gEr h K m nhvy nA nE NG ni

Group-group intramolecular interaction pair GC values for ideal gas heat capacity Chickos GC value for C—H group Fuel concentration for stoichiometric combustion Chickos GC value for functional group Halogen correction for DHsub correlation Vapor pressure deviation function Factor in surface tension equation Group-group interaction correction term Adjustable mixture viscosity parameter UNIFAC combinatorial excess Gibbs energy UNIFAC residual excess Gibbs energy Parameter in Riedel vapor pressure equation Parameter in Riedel vapor pressure equation Parameter in modified Pachaiyappan method Number of non-hydrogen atoms Number of atoms in the molecule Number of occurrences of element E in compound Number of interacting groups Number of occurrences of group i

nf ns nx N

Number of different functional groups Number of C—H groups bonded to functional groups Number of halogen and H atoms Total number of groups in molecule

NC Nfi Ngi NH NCR NO NR NS Nsi NSi NX Pc q qi Qk ri r* Rk (So)i t tm1,i tm2,i Tc Tc,ij xP U* UFLi Z(0) Z(1) Zc,ij ZRA ZRA α, b, g, . . .

Number of C atoms Number of functional groups of type i Number of C—H groups of type i bonded to C Number of H atoms Number of CH2 groups forming cyclic paraffin Number of O atoms Number of nonaromatic rings Number of S atoms Number of C—H groups bonded to functional group Number of Si atoms Number of halogen atoms Pseudocritical pressure for mixture

(77) (62), (63), (64), (65) (74), (75), (76), (77), (78), (79), (80), (81), (98) (109) (9), (10), (11), (18), (86), [175], [173] (12), [156] (52), [165] (44), [162] (127), (128) (44), [163] (46), [164] (29) (118), (119) (9), (10), (11), (12) (97) (98) (98) (28a) (28a) (109) (11), (12), (18) (1), (34), (35), (51) (58) (12) (9), (10), (11), (13), (15), (16), (31), (46), (52), (54), (55), (86), (117), (124), (127), (129) (44) (44) (46) (18), (31) (46), (54), (57), (58), (86), (96), (117), (124), (127), (129) (123) (44) (44) (123) (43) (123) (43) (123) (44) (123) (123) (75)

Rackett equation power for Zc UNIFAC molecular surface area UNIFAC group surface area UNIFAC molecular volume Dimensionless separation distance UNIFAC group volume GC value for entropy Total number of functional groups First-order GC contribution for Tm Second-order GC contribution for Tm Pseudocritical temperature for mixture

(72), (80) following (99) following (99) following (99) (4) following (99) (31), [161] (44) (16), [158] (16), [159] (74), (75), (79)

Cross term in mixing rule Term in the Pailhes method [= log(1 atm/P)] Dimensionless intermolecular potential GC contribution Compressibility factor of simple fluid Acentric deviation term for Z Cross term in mixing rule Modified Rackett correlation parameter Modified Rackett parameter for mixture Correlation parameters for k

(79) (17) (4) (127), [178] (68), [169] (68), [170] (79) following (72) (80), (81) (107), (108), (110), [176]

2-313

2-314

PHYSICAL AnD CHEMICAL DATA nomenclature (Continued ) Equation variables

Appears in (Eq. 2-?) or [Table 2-?]

Definition EoS temperature-dependent function Parameter in Riedel vapor pressure equation Viscosity group-group interactions Reference EoS constant Stoichiometric coefficient for combustion Nonlinear correction term in correlation Reference EoS constant

α(Tr) αc αmn b b bi g d d DE DP DT DV (DHfo)i DPi Dpci Dsi DTad,i Dtci e e f n ni

= 0 for nonlinear molecules; = 1 for linear EoS parameter Contribution of element E to heat capacity GC contribution to Pc GC contribution to Tc GC contribution to Vc GC value for enthalpy of formation GC for Parachor Group i contribution to critical pressure GC value for group i Group i contribution to adiabatic flame temperature Group i contribution to critical temperature Lennard-Jones well depth parameter EoS parameter UNIFAC molecular volume fraction LFL enthalpic term Stoichiometric coefficient (+ for product and − for reactant) for compound i in reaction Frequency of vibrational mode j UNIFAC molecular surface fraction UNIFAC group surface fraction Characteristic rotational T of molecule Characteristic vibrational T of mode j Lennard-Jones size parameter Rotational external symmetry number Modified reduced dipole moment Parameter in Riedel vapor pressure equation Parameter in correlation of k for gases UNIFAC interaction factor Viscosity de-dimensionalizing factor Pseudo-acentric factor for mixture

nj q Q QA, QB, QC Qj σ σ µ*r y y ymn x ω

(70), [172] (28a) (99), [175] (69), [171] (122), (123), (128) (46), (57), [164], [167] (69), [171] (1), (35), before (50), (51) (70), [172] (58), [168] (7), [154] (6), [154] (8), [154] (31), [161] (117), [177] (15) (44), [162, 163] (124) (13) following (4) (70), [172] following (99) (126) (32), (33), (34) (50) following (99) following (99) before and following (35) (1), (35) following (4) following (35) (84), (85) (28a) (106), (107) (99) (88), (89), (90), (91), (92), (93) (76)

Acronyms and abbreviations

Definition

CC CS DIPPR EoS GC LJ MC MD QSPR

Computational chemistry Corresponding states Design Institute for Physical Properties Equation of state Group contributions Lennard-Jones Monte Carlo Molecular dynamics Quantitative structure-property relationships

GEnERAL REFEREnCES Prediction Methods [PGL4] Reid, R. C., J. M. Prausnitz, and B. E. Poling, The Properties of Gases and Liquids, 4th ed., McGraw-Hill, New York, 1987. [PGL5] Poling, B. E., J. M. Prausnitz, and J. P. O’Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, 2001.

Property Databases [DIPPR] Rowley, R. L., et al., DIPPR Data Compilation of Pure Chemicals Properties, Design Institute for Physical Properties, AIChE, New York, 2007. [TRC] TRC Thermodynamic Tables—Non-Hydrocarbons, Thermodynamics Research Center, The Texas A&M University System, College Station, Tex., extant 2004; TRC Thermodynamic Tables—Hydrocarbons, Thermodynamics Research Center, The Texas A&M University System, College Station, Tex., extant 2004. [JANAF] Chase, M. W., Jr., et al., “JANAF Thermochemical Tables,” J. Phys. Chem. Ref. Data, 14, suppl. 1, 1985.

[SWS] Stull, D. R., F. F. Westrum, Jr., and G. C. Sinke, The Chemical Thermodynamics of Organic Compounds, John Wiley & Sons, New York, 1969. [TDS] Daubert, T. E., and R. P. Danner, Technical Data Book—Petroleum Refining, 5th ed., American Petroleum Institute, Washington, extant 1994.

CLASSIFICATIOn OF ESTIMATIOn METHODS Physical property estimation methods may be classified into six general areas: (1) theory and empirical extension of theory, (2) corresponding states, (3) group contributions, (4) computational chemistry, (5) empirical and quantitative structure-property relations (QSPR) correlations, and (6) molecular simulation. A quick overview of each class is given below to provide context for the methods and to define the general assumptions, accuracies, and limitations inherent in each.

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES Theory and Empirical Extension of Theory Methods based on theory generally provide better extrapolation capability than empirical fits of experimental data. Assumptions required to simplify the theory to a manageable equation suggest accuracy limitations and possible improvements, if necessary. For example, the ideal gas isobaric heat capacity, rigorously obtained from statistical mechanics under the assumption of independent harmonic vibrational modes, is (Rowley, R. L., Statistical Mechanics for Thermophysical Property Calculations, Prentice-Hall, Englewood Cliffs, N.J., 1994) C op R

=

8 − δ 3 n A −6+δ + ∑ 2 j =1

2

Θ /T

e j  Θj   T  Θ j /T − 1)2 (e

(2-1)

0 nonlinear molecules δ = 1 linear molecules where Qj is the characteristic temperature for the jth vibrational frequency in a molecule of nA atoms. The temperature dependence of this equation is exact to the extent that the frequencies are harmonic. Extension of theory often requires introduction of empirical models and parameters in lieu of terms that cannot be rigorously calculated. Good accuracy is expected in the region where the model parameters were fitted to experimental data, but only limited accuracy when an empirical model is extrapolated to other conditions. For example, a simplified theory suggests that vapor pressure should have the form ln P * = A −

B T

(2-2)

where the empirical parameter B is given by B=

∆ Hυ R ∆ Zυ

(2-3)

and ∆Hυ and ∆Zυ are differences between the vapor and liquid enthalpies and compressibility factors, respectively. Equation (2-2) can be used to correlate vapor pressures over a moderate temperature range, but it is inadequate to represent vapor pressures over the whole liquid temperature range because ∆Hυ also varies with temperature. Corresponding States (CS) The principle of CS applies to conformal fluids [Leland, T. L., Jr., and P. S. Chappelear, Ind. Eng. Chem., 60 (1968): 15]. Two fluids are conformal if their intermolecular interactions are equivalent when scaled in dimensionless form. For example, the Lennard-Jones (LJ) intermolecular pair potential energy U can be written in dimensionless form as U* = 4(r∗−12 − r∗−6)

(2-4)

where r∗ = r/σ, U ∗ = U/ε, σ is the LJ size parameter, and ε is the LJ attractive well depth parameter. At equivalent scaled temperatures kT/ε (k is Boltzmann’s constant) and pressures Pσ3/ε, all LJ fluids will have identical dimensionless properties because the molecules interact through the identical scaled intermolecular potential given by Eq. (2-4). Generalization of this scaling principle is commonly done using critical temperature Tc and critical pressure Pc as scaling factors. At the same reduced coordinates (Tr = T/Tc and Pr = P/Pc) conformal fluids will have the same dimensionless properties. For example, Z = Z(Tr, Pr) where the compressibility factor is defined as Z = PV/RT. A correlation of experimental data for one fluid can then be used as the reference for the properties of all conformal fluids. Nonconformality is the main accuracy limitation. For instance, interactions between nonspherical or polar molecules are not adequately represented by Eq. (2-4), and so the scaled properties of these fluids will not conform to those of a fluid with interactions well represented by Eq. (2-4). A correction for nonconformality is usually made by the addition of one or more reference fluids whose deviations from the first reference fluid are used to characterize the effect of nonconformality. For example, in the Lee-Kesler method [Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510] n-octane is used as a second, nonspherical reference fluid, and deviations of n-octane scaled properties from those of the spherical reference fluid at equivalent reduced conditions are assumed to be a linear function of the acentric factor. Group Contributions (GCs) Physical properties generally correlate well with molecular structure. GC methods assume a summative behavior of the structural groups of the constituent molecules. For example, ethanol (CH3—CH2—OH) properties would be obtained as the sum of contributions from the —CH3, —CH2, and —OH groups. The contribution of each group is obtained by regression of experimental data that include as many different compounds containing that group as possible. Structural groups must be used exactly as defined in the original correlation of the groups. A general principle when parsing a structure into constituent groups is that

2-315

the more specific the group, the higher its priority. For example, the structural piece —COOCH3 in a methyl ester could be divided in more than one way, but if the —COO— and —CH3 groups are available in the method, then they should be used rather than the combination of the two less specific groups —(C == O)— and —O—. These latter group values were most likely regressed only from ketone and ether data, respectively. Excellent accuracy can usually be expected from GC methods in which the group values were regressed from large quantities of experimental data. However, if the ratio of the number of groups to regressed experimental data is large, significant errors can result when the method is applied to new compounds (extrapolation). Such excessive specificity in the group definitions leads to poor extrapolation capabilities even though the fit of the regressed data may have been excellent. First-order GC methods assume simple summations of the group values are adequate to represent the molecular value. Second-order effects, caused by steric and electron induction effects from neighboring groups, can alter group values. Second-order GC methods require considerably more experimental data to tune the method, and large tables of group values are required because differences in bonded neighbors require separate groups. Computational Chemistry (CC) Commercial software is available that solves the Schrödinger equation by using approximate forms of the wave function. Various levels of sophistication (termed model chemistry) for the wave function can be chosen at the expense of computational time. Results include structural information (bond lengths, bond angles, dihedral angles, etc.), electron/charge distribution information, internal vibrational modes ( for ideal gas properties), and energy of the molecule, valid for the chosen model chemistry. Because calculations are usually performed on individual molecules, the results are best suited for ideal gas properties. Relative energies for the same model chemistry are more accurately obtained than absolute energies, so enthalpies and entropies of reaction are also common industrial uses of CC predictions. Empirical QSPR Correlations Quantitative structure-property relationship (QSPR) methods correlate physical properties with molecular descriptors that characterize the structural and electronic character of the molecule. Large amounts of experimental data are used to statistically determine the most significant descriptors to be used in the correlation and their contributions. The resultant correlations are simple to apply if the descriptors are available. Descriptors must be generated by the user with computational chemistry software or obtained from some tabulation. QSPR methods are often very accurate for specific families of compounds for which the correlation was developed, but extrapolation to other families generally results in considerable loss of accuracy. Molecular Simulations Molecular simulations are useful for predicting properties of bulk fluids and solids. Molecular dynamics (MD) simulations solve Newton’s equations of motion for a small number (on the order of 103) of molecules to obtain the time evolution of the system. MD methods can be used for equilibrium and transport properties. Monte Carlo (MC) simulations use a model for the potential energy between molecules to simulate configurations of the molecules in proportion to their probability of occurrence. Statistical averages of MC configurations are useful for equilibrium properties, particularly for saturated densities, vapor pressures, etc. Property estimations using molecular simulation techniques are not illustrated in the remainder of this section as commercial software implementations are not commonly available. PHYSICAL COnSTAnTS Critical Properties The critical temperature Tc, pressure Pc, and volume Vc of a compound are important, widely used constants. They are important in determining the phase boundaries of a compound and (particularly Tc and Pc) are required input parameters for many property estimation methods, particularly CS methods. The critical temperature of a compound is the temperature above which a liquid phase cannot be formed, regardless of the system pressure. The critical pressure is the vapor pressure of the compound at the critical temperature. The molar critical volume is the volume occupied by 1 mol of a chemical at its critical temperature and pressure. The critical compressibility factor Zc is determined from the experimental or predicted values of the critical properties by its definition Zc =

PcVc RTc

(2-5)

Recommended Methods The Ambrose method is recommended for all three critical properties of hydrocarbons and n-alcohols. The Nannoolal method is recommended for all three critical properties of all other organic molecules. The Wilson-Jasperson method is a simple method also recommended for estimating Tc and Pc for organic and some inorganic chemicals.

2-316

PHYSICAL AnD CHEMICAL DATA

The first-order Wilson-Jasperson method often gives better results than the second-order method except strongly polar, hydrogen-bonding, and associating fluids. Method: Ambrose method. Reference: Ambrose, D., Natl. Phys. Lab. Report Chem. 92 (1978); Natl. Phys. Lab Report Chem. 98 (1979). Classification: Group contributions. Expected uncertainty: ~6 K for Tc (about 1 percent), ~2 bar for Pc (about 5 percent), ~8 cm3/mol for Vc (about 3 percent). Applicability: Organic compounds. Input data: Tb, M, group contributions DT, DP, and DV from Table 2-154. Description: A GC method with first-order contributions and corrections (delta Platt number) for branched alkanes. Variables Tc, Pc, and Vc are given by the following relations:

(

)

−1

 

Pc M 0.339 + ∑ ∆ P = bar kg/kmol

)

Tc = Tb 1 + 1.242 + ∑ ∆T 

(

Description: A GC method with first-order contributions. Variables Tc, Pc, and Vc are given by the following relations:     1  Tc = Tb  0.6990 + 0.8607      0.9889 +  ∑ niC i + GI   i   

(2-9)

−0.14041

 M   kg/kmol 

Pc = 2 kPa    0.00939 + ∑ niC i + GI 

(2-10)

i

(2-6) −2

Vc = 10 m3 /mol

(2-7)

Vc = 40 + ∑ ∆V cm /mol

(2-8)

3

i

i

i

n

-0.2266 hvy

+ 86.1539

(2-11)

where ni is the number of groups of type i; Ci are group contributions from Table 2-155; M is molecular weight; and GI is the total correction for groupgroup interactions calculated using GI =

Example Use the Ambrose method to estimate the critical constants of 2,2,4-trimethylpentane. Required data: From the DIPPR 801 database, Tb = 372.39 K and M = 114.229 kg/kmol. Structure:

∑n C + GI

-6

1 nhvy

NG

NG

i =1

j =1

C ij

∑ ∑ NG − 1

(2-12)

where Cji = Cij. The values for the interactions are shown in this format in Table 2-156. The sum of all group pairs within the molecule is divided by the number of nonhydrogen atoms, nhvy, and by 1 less than the number of interacting groups NG. In the example below, there are no group-group interactions. The calculation of GI using Eq. (2-12) is illustrated later in an example calculation for the normal boiling point.

Group contributions from Table 2-154:

Example Estimate the critical constants of o-xylene using the Nannoolal Group

ni

Alkyl carbons >CH— (correction) >C< (correction) Delta Platt no.

8 1 1 0

DT

DP

0.138 −0.043 −0.120 −0.023

0.226 −0.006 −0.030 −0.026

DV 55.1 −8 −17 —

Calculations using Eqs. (2-6), (2-7), and (2-8):

∑∆

T

Required input data: From the DIPPR 801 database, Tb = 417.58 K. From Table 2-155:

= (8) (0.138) + (1)(−0.043) + (1)(−0.120) = 0.941

Tc = Tb(1.4581) = (372.39 K)(1.4581) = 543.0 K

∑∆

P

= (8)(0.226) + (1)(−0.006) + (1)(−0.030) = 1.772

(

Pc M 0.339 + ∑ ∆ P = bar kg/kmol

∑∆

V

method. Structure:

)

−2

=

114.229 = 25.63 (0.339 + 1.772)2

Pc = 25.63 bar

= (8)(55.1) + (1)(−8) + (1)(−17) = 415.8

Group

ni

Ci (TC)

Ci (PC)

=C(a)} CH3−(a) =C(a)CH} (each) >C< (each) Double bonds (nonaromatic) Triple bonds Delta Platt number,b multiply by Aliphatic functional groups: }O} >CO }CHO }COOH }CO}O}OC} }CO}O} }NO2} }NH2 }NH} >N} }CN }S} }SH }SiH3 }O}Si(CH3)2 }F }Cl }Br }I Halogen correction in aliphatic compounds: F is present F is absent, but Cl, Br, I are present Aliphatic alcoholsc Ring compound increments (listed only when different from aliphatic values): }CH2}, >CH}, >C< >CH} in fused ring Double bond }O} }NH} }S} Aromatic compounds: Benzene Pyridine C4H4 ( fused as in naphthalene) }F }Cl }Br }I }OH Corrections for nonhalogenated substitutions: First Each subsequent Ortho pairs containing }OH Ortho pairs with no }OH Highly fluorinated aliphatic compounds: }CF3, }CF2}, >CF} }CF2}, >CF} (ring) >CF} (in fused ring) }H (monosubstitution) Double bond (nonring) Double bond (ring) (other increments as in nonfluorina ted compounds)

DT

DP

DV

0.138

0.226

55.1

−0.043 −0.120 −0.050 −0.200 −0.023

−0.006 −0.030 −0.065 −0.170 −0.026

−8 −17 −20 −40 —

0.138 0.220 0.220 0.578 1.156 0.330 0.370 0.208 0.208 0.088 0.423 0.105 0.090 0.200 0.496 0.055 0.055 0.055 0.055

0.160 0.282 0.220 0.450 0.900 0.470 0.420 0.095 0.135 0.170 0.360 0.270 0.270 0.460 — 0.223 0.318 0.500 —

20 60 55 80 160 80 78 30 30 30 80 55 55 119 — 14 45 67 90

0.125 0.055 d

e

0.090 0.030 −0.030 0.090 0.090 0.090

0.182 0.182 — — — —

0.448 0.448 0.220 0.080 0.080 0.080 0.080 0.198

0.924 0.850 0.515 0.183 0.318 0.600 0.850 −0.025

0.010 0.030 −0.080 −0.040

0 0.020 −0.050 −0.050

0.200 0.140 0.030 −0.050 −0.150 −0.030

0.550 0.420 — −0.350 −0.500 —

15 44.5 44.5 −15 10 — 30 f

a Ambrose, D., Correlation and Estimation of Vapour-Liquid Critical Properties. I. Critical Temperatures of Organic Compounds, Natl. Phys. Lab Report Chem. 92 (1978); Correlation and Estimation of Vapour-Liquid Critical Properties. II. Critical Pressures and Volumes of Organic Compounds, Natl. Phys. Lab Report Chem. 98 (1979). b The delta Platt number is defined as the Platt number of the isomer minus the Platt number of the corresponding alkane. (For n-alkanes the Platt number is n − 3.) The Platt number is the total number of groups of four carbon atoms three bonds apart [Platt, J. R., J. Chem. Phys., 15(1947): 419; 56(1952): 328]. This correction is used only for branched alkanes. c Includes naphthenic alcohols and glycols but not aromatic alcohols such as xylenol. d First determine the hydrocarbon homomorph, i.e., substitute }CH3 for each }OH and calculate ∑DT for this compound. Subtract 0.138 from ∑DT for each }OH substituted. Next, add 0.87 − 0.11n + 0.003n2 where n = [Tb/K (alcohol) − 314]/19.2. Exceptions include methanol (∑DT = 0), ethanol (∑DT = 0.939), and any alcohol whose value of n exceeds 10. e Determine the hydrocarbon homomorph as in footnote d. Calculate ∑Dp and subtract 0.226 for each }OH substituted. Add 0.100 − 0.013n, where n is computed as in footnote d. f When estimating the critical volumes of aromatic substances, use ring compound values, if available, and correct for double bonds.

2-317

2-318

PHYSICAL AnD CHEMICAL DATA

TABLE 2-155

Group Contributions for the nannoolal et al. Method for Critical Constantsa and normal Boiling Pointb

Table-specific nomenclature: (e) = connected to N, O, F, Cl; (ne) = not connected to N, O, F, Cl; (r) = in a ring; (c) = in a chain; (a) = aromatic, not necessarily carbon; (Ca) = aromatic carbon; b = any nonhydrogen atom ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 74

Group CH3—(ne) CH3—(e) CH3—(a) —C(c)H2— >C(c)H— >C(c)< >C(c)C(c)C(r)H— >C(r)< >C(r)C(r)C(r)Si< >SiCH— in a chain >C< in a chain >C< in a chain connected to at least one F, Cl, N, or O >C< in a chain connected to at least one aromatic carbon —CH2— in a ring >CH— in a ring >C< in a ring >C< in a ring; connected to at least one N, O, Cl, or F not in the ring >C< in a ring connected to at least one N or O which is part of the ring >C< in a ring connected to at least one aromatic carbon aromatic =CH— aromatic =C< not connected to O, N, Cl, or F aromatic =C< connected to O, N, Cl, or F aromatic =C< with three aromatic neighbors F— connected to C or Si F— on a C=C (vinyl fluoride) F— connected to C or Si substituted with at least one F and two other atoms F— connected to a C or Si substituted with one F or Cl and one other atom F— connected to C or Si already substituted with two F or Cl atoms F— connected to an aromatic carbon Cl— connected to C or Si not already substituted with F or Cl Cl— connected to C or Si already substituted with one F or Cl Cl— connected to C or Si already substituted with at least two F or Cl Cl— connected to aromatic C Cl— on a C=C (vinyl chloride) Br— connected to a nonaromatic C or Si Br— connected to an aromatic C I— connected to C or Si —OH connected to tertiary carbon —OH connected to secondary C or Si —OH connected to primary C or Si; chain >4 C or Si —OH connected to primary C or Si; chain (OC2)< (epoxide) NH2— connected to either C or Si NH2— connected to an aromatic C —NH— connected to two C or Si (secondary amine) >N— connected to three C or Si (tertiary amine) —COOH connected to C —COO— connected to two C (ester) HCOO— connected to C ( formic acid ester) —COO— in ring, C is connected to C (lactone) —CON< disubstituted amide —CONH— (monosubstituted amide) —CONH2 (amide) —CO— connected to two nonaromatic C (ketones) CHO— connected to nonaromatic C (aldehydes) —SH connected to C (thiols) —S— connected to two C —S—S— (disulfide) connected to two C —S— in an aromatic ring —C≡N (cyanide) connected to C >C=C< (both C have at least one non-H neighbor) noncyclic >C=C< connected to at least one aromatic C noncyclic >C=C< with at least one F, Cl, N, or O H2C=C< (1-ene) cyclic >C=C< —C≡C— HC≡C— (1-yne) —O—in an aromatic ring with aromatic C neighbors aromatic —N— in a five-member ring, free electron pair aromatic =N— in a six-member ring NO2— connected to aliphatic C NO2— connected to aromatic C >Si< >Si< connected to at least one O nitrate (esters of nitric acid) nitrites (esters of nitrous acid)

TC × 103

PC × 104

VC

NBP

41.8682 33.1371 −1.0710 40.0977 30.2069 −3.8778 52.8003 9.4422 21.2898 26.3513 −17.0459 51.7974 18.9549 −29.1568 16.1154 68.2045 68.1923 29.8039 15.6068 11.0757 18.1302 19.1772 20.8519 −24.0220 −1.3329 2.6113 15.5010 −16.1905 60.1907 5.2621 −21.5199 −8.6881 84.8567 79.3047 49.5968 130.1320 14.0159 12.5082 41.3490 18.3404 −50.6419 17.1780 −0.5820 199.9042 75.7089 58.0782 109.1930 102.1024

8.1620 5.5262 4.1660 5.2623 2.3009 −2.9925 3.4310 2.3665 3.4027 3.6162 −5.1299 4.1421 0.8765 −0.1320 2.1064 4.1826 3.5500 1.0997 0.7328 4.3757 3.4933 2.6558 1.6547 0.5236 −2.2611 −1.4992 0.4883 −0.9280 11.8687 −4.3170 −2.2409 −4.7841 −7.4244 −4.4735 −1.8153 −6.8991 −12.1664 2.0592 0.1759 −4.4164 −9.0065 −0.4086 2.3625 3.9873 4.3592 1.0266 0.4329 0.5172

28.7855 28.8811 26.7237 32.0493 32.1108 28.0534 33.7577 28.8792 24.8517 30.9323 5.9550 29.5901 20.2325 10.5669 19.4020 25.0434 5.6704 16.4118 −5.0331 1.5646 3.3646 1.0897 1.1084 19.3190 22.0457 23.9279 26.2582 36.7624 34.4110 36.0223 30.7004 48.2989 10.6790 5.6645 2.0869 3.7778 25.6584 11.6284 46.7680 13.2571 73.7444 20.5722 6.0178 40.3909 42.6733 36.1286

56.1572 44.2000 −7.1070 0.5887

0.1190 −2.3615 −9.4154 −8.2595

30.9229 25.5034 34.7699 38.0185

−7.7181 117.1330 45.1531

−4.9259 5.1666 7.1581

20.3127 43.7983

67.9821 45.4406 56.4059 −19.9737 36.0883 10.4146 18.9903 10.9495 82.6239

−6.2791 9.6413 3.4731 −2.2718 2.4489 −0.5403 8.3052 −4.7101 −5.0929

51.0710 48.1957 34.1240 40.9263 29.8612 4.7476 −25.3680 23.6094 34.8472

25.4209 72.5587

5.7270 2.7602

75.7193 69.5645

177.3066 251.8338 157.9527 239.4531 240.6785 249.5809 266.8769 201.0115 239.4957 222.1163 209.9749 250.9584 492.0707 244.3581 235.3462 315.4128 348.2779 367.9649 106.5492 49.2701 53.1871 78.7578 103.5672 −19.5575 330.9117 287.1863 267.4170 205.7363 292.5816 419.4959 377.6775 556.3944 349.9409 390.2446 443.8712 488.0819 361.4775 146.4836 820.7118 321.1759 441.4388 223.0992 126.2952 1080.3139 636.2020 642.0427 1142.6119 1052.6072 1364.5333 1487.4109 618.9782 553.8090 434.0811 461.5784 864.5074 304.3321 719.2462 475.7958 586.1413 500.2434 412.6276 475.9623 512.2893 422.2307 37.1936 453.3397 306.7139 866.5843 821.4141 282.0181 207.9312 920.3617 494.2668

64.3506

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-155

2-319

Group Contributions for the nannoolal Method for Critical Constantsa and normal Boiling Point b (Continued )

Table-specific nomenclature: (e) = connected to N, O, F, Cl; (ne) = not connected to N, O, F, Cl; (r) = in a ring; (c) = in a chain; (a) = aromatic, not necessarily carbon; (Ca) = aromatic carbon; b = any nonhydrogen atom ID 76 77 78 79 80 81 82 83 87 88 89 90 91 92 93 94 97 99 100 101 102 103 104 107 109 111 113 115

Group

Description

—C=O—O—C=O— COCl— >SiSnC=C=C< >C=C—C=CC=C—C=CSiN—(C=O)—N< (C,Si)2>N< (C,Si)2 F—(C,Si)(Cl)(b)2 —OCOO— >SO4 >S=O >N(C=O) (N)—C≡N >P< —ON=(C,Si)

TC × 103

anhydride connected to two C COCl— connected to C (acid chloride) >Si< connected to at least one F or Cl noncyclic carbonate OCN— connected to C or Si (cyanate) SCN— (thiocyanate) connected to C noncyclic sulfone connected to two C (sulfones) >Sn< connected to four carbons cumulated double bond conjugated double bond in a ring conjugated double bond in a chain CHO— connected to aromatic C (aldehydes) double-bonded amine connected to at least one C or Si —CO— connected to two C with at least one aromatic C (ketones) >Si< attached to two carbon or hydrogen peroxide —NH— connected to two C or Si, at least one aromatic (secondary amines) —CO connected to O and N (carbamate) —CO connected to two N (urea) Quaternary amine connected to four C or Si F— connected to C or Si with at least one Cl and two other atoms —CO connected to two O (carbonates) S(= O)2 connected to two O (sulfates) sulfoxide —CO connected to N —C≡N (cyanide) connected to N phosphorus connected to at least 1 C or S (phosphine) —ON= connected to C or Si (isoazole)

PC × 104

VC

NBP

164.3355

4.0458

157.3401 97.2830 153.7225

12.6786 0.2822

90.9726 62.3642 53.6350 24.7302

−23.9221 0.7043 12.6128 −10.2451

68.0701

38.4681

−4.0133

20.0440

63.6504 34.2058

−5.0403 3.2023

28.7127 55.3822

27.3441

−4.3834

29.3068

1.3231 764.9595

3.3971 58.9190

1.3597

36.0361

−5.1116

16.2688

32.1829 11.4437 −1.3023 −34.3037 −1.3798 −2.7180 11.3251 −4.7516 1.2823 6.7099

7.3149 4.1439 0.4387 −4.2678 4.8944 2.8103 −0.3035 0.0930 0.7061 −0.7246

−3.8033 27.5326 1.5807 −2.6235 −5.3091 −6.1909 3.2219 −6.3900 −3.5964 1.5196

−33.8201 −18.4815 −23.6024 −24.5802 −35.6113

−8.8457 −2.2542 −3.2460 −5.3113 1.0934

−4.6483 −5.0563 −6.3267 4.9392 2.8889

52.8789 27.1026

64.4616

1251.2675 778.9151 540.0895 879.7062 660.4645 1018.4865 1559.9840 510.4223 664.0903 957.6388 928.9954 560.1024 229.2288 606.1797 273.1755 201.3224 886.7613 1045.0343 –109.6269 111.0590 1573.3769 1483.1289 1379.4485 492.0707 971.0365 428.8911 612.9506

Corrections 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134

(C=O)—C([F,Cl]2,3) (C=O)—C([F,Cl]2,3)2 C—[F,Cl]3 (C)2—C—[F,Cl]2 No hydrogen One hydrogen (3,4) ring 5-ring Ortho pair(s) Meta pair(s) Para pair(s) ((C= )(C)C—CC3) C2C—CC2 C3C—CC2 C3C—CC3 C=C—C=O

carbonyl connected to C with two or more halogens carbonyl connected to two C, each with at least two halogens carbon with three halogens secondary carbon with two halogens component has no hydrogen component has one hydrogen a three- or four-member nonaromatic ring a five-member nonaromatic ring ortho- position counted only once and only if no meta or para pairs meta- position counted only once and only if no para or ortho pairs para- position counted only once and only if no meta or ortho pairs carbon with four carbon neighbors and one double-bonded carbon neighbor carbon with four carbon neighbors, two on each side carbon with five carbon neighbors carbon with six carbon neighbors —C=O connected to sp3 carbon

–82.2328 –247.8893 –20.3996 15.4720 –172.4201 –99.8035 –62.3740 –40.0058 –27.2705 –3.5075 16.1061 25.8348 35.8330 51.9098 111.8372 40.205

Nannoolal, Y., et al., Fluid Phase Equilib. 252 (2007): 1. Nannoolal, Y., et al., Fluid Phase Equilib. 226 (2004): 45.

a b

Description: A GC method with first- and some second-order contributions. Variables Tc, Pc, and Vc are given by the following relations:

Results:

Property Tc /K Pc /bar Vc /(cm3/mol)

DIPPR 801 recommendation 630.3 37.32 370

Nannoolal estimation

% Difference

628.9 36.24 370.6

−0.2 −2.9 0.2

Method: Wilson-Jasperson method. Reference: Wilson, G. M., and L. V. Jasperson, “Critical Constants Tc, Pc, Estimation Based on Zero, First and Second Order Methods,” AIChE Spring Meeting, New Orleans, La., 1996. Classification: Group contributions. Expected uncertainty: ~6 K or 1 percent for Tc; ~2 bar or 5 percent for Pc. Applicability: Organic and some inorganic compounds. Input data: M, Tb, group contributions Ci from Table 2-157, and molecular structure.

Tc =

Tb    0.048271 − 0.019846nr + ∑ nk ∆tc k + ∑ n j ∆tc j    k j

0.2

Pc 0.0186233(Tc /K) = bar exp(Y ) − 0.96601   Y = − 0.00922295 − 0.0290403nr + 0.041  ∑ nk ∆pc k + ∑ n j ∆pc j   k  j

(2-13)

(2-14)

(2-15)

where nr is the number of rings in the molecule; Dtck and Dpck are the firstorder group contributions tabulated in Table 2-157 with nk the number of such occurrences in the molecule; and Dtcj and Dpcj are the second-order

2-320

PHYSICAL AnD CHEMICAL DATA TABLE 2-156 Intermolecular Interaction Corrections for the nannoolal et al. Method for Critical Constantsa and normal Boiling Pointb

—OH :: —OH —OH :: —COOH —OH :: —O— —OH :: >(OC2)< —OH :: —COOC— —OH :: —CO— —OH :: —O(a)— —OH :: —S(na)— —OH :: —SH —OH :: —NH2 —OH :: >NH —OH :: —CN —OH :: =N(a)–(r6) —OH(a) :: —OH(a) —OH(a) :: —COOH —OH(a) :: —O— —OH(a) :: —COOC— —OH(a) :: —CHO —OH(a) :: —NH2 —OH(a) :: Nitrate —OH(a) :: =N(a)–(r6) —COOH :: —COOH —COOH :: —O— —COOH :: —COOC— —COOH :: —CO— —O— :: —O— —O— :: >(OC2)< —O— :: —COOC— —O— :: —CO— —O— :: —CHO —O— :: —O(a)— —O— :: —S(na)— —O— :: —NH2 —O— :: >NH —O— :: —CN —O— :: Nitrate >(OC2)< :: >(OC2)< >(OC2)< :: —CO— >(OC2)< :: —CHO —COOC— :: —COOC— —COOC— :: —CO— —COOC— :: —O(a)— —COOC— :: —NH2 —COOC— :: >NH —COOC— :: —CN —COOC— :: Nitrate —CO— :: —CO— —CO— :: —CHO —CO— :: —O(a)— —CO— :: —S(a)— —CO— :: >NH —CO— :: —CN —CO— :: Nitrate —CO— :: =N(a)–(r6) —CHO— :: —CHO— —CHO— :: —O(a)— —CHO— :: —S(a)— —CHO— :: Nitrate —O(a)— :: —NH2 —O(a)— :: =N(a)–(r5) —S(na)— :: —S(na)— —S(na)— :: —NH2 —S(a)— :: —CN —S(a)— :: =N(a)–(r5) —SH :: —SH —NH2 :: —NH2 —NH2 :: >NH —NH2 :: Nitrate —NH2 :: =N(a)–(r6) >NH :: >NH >NH :: =N(a)–(r6) —OCN :: —OCN —OCN :: Nitrate —CN :: =N(a)–(r6) Nitrate :: Nitrate =N(a)–(r6) :: =N(a)–(r6)

PC × 104

−434.8568

−5.6023

−146.7881

7.3373

19.7707

120.9166 −30.4354

69.8200 6.1331

−8.0423

144.4697

57.8350

97.5425

162.6878 707.4116 128.2740

2.6751 88.8752 −1.0295

−23.6366 −329.5074 −55.5112

−654.1363 −738.0515

25.8246 −125.5983

−37.2468

0.5195

−74.8680

1605.564

−78.2743

−413.3976

24.0243 −861.1528

−35.1998 43.9001

217.9243 −403.1196

131.7924

−19.7033

164.2930

−60.9217

−0.6754

−49.7641

22.1871

741.8565

366.2663

−32.3208

−57.1233 44.1062

−1866.097

Nannoolal, Y., et al., Fluid Phase Equilib. 252 (2007): 1. b Nannoolal, Y., et al., Fluid Phase Equilib. 226 (2004): 45.

a

VC

TC × 103

12.5371

−26.4556

NBP 291.7985 146.7286 135.3991 226.4980 211.6814 46.3754 435.0923 –74.0193 38.6974 314.6126 286.9698 306.3979 1334.6747 288.6155 –1477.9671 130.3742 −1184.9784 43.9722 797.4327 –1048.124 –614.3624 117.2044 612.8821 −183.2986 −55.9871 91.4997 178.7845 322.5671 15.6980 17.0400 329.0050 394.5505 124.3549 101.8475 293.5974 963.6518 1006.388 22.5208 163.5475 431.0990 22.5208 707.9404 182.6291 317.0200 517.0677 –205.6165 −303.9653 −391.3690 176.5481 381.0107 −215.3532 −574.2230 –3628.903 124.1943 562.1763 674.6858 397.575 140.9644 395.4093 –888.612 –11.9406 −562.306 −101.232 –348.740 217.6360 174.0258 510.3473 663.8009 27.2735 239.8076 758.9855 −356.5017 –263.0807 –370.9729 65.1432 –271.9449

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES group contributions, also tabulated in Table 2-157, with nj occurrences of these second-order groups in the molecule.

TABLE 2-157 Wilson-Jasperson First- and Second-Order Contributions for Critical Temperature and Pressurea First-order atom

Example Estimate Tc and Pc of sec-butanol by using the Wilson-Jasperson

method. Required input data: From DIPPR 801 database, Tb = 372.9 K. Structure:

Group contributions from Table 2-157: Group

nk

Dtck

Dpck

nj

Dtcj

Dpcj

H

10

0.002793

0.12660

—

—

—

O

1

0.020341

0.43360

—

—

—

C

4

0.008532

0.72983

—

—

—

−OH, C4 or less

—

—

1

—

0.0350

0

From Eqs. (2-13), (2-14), and (2-15):

∑ n ∆tc k

k

= (10)(0.002793) + (1)(0.020341) + (4)(0.008532) = 0.082399

Tc =

∑ n ∆pc k

k

Tb 372.9 K = = 534.25 K (0.048271 + 0.082399 + 0.0350)0.2 0.6980

= (10)(0.12660) + (1)(0.43360) + (4)(0.72983) = 4.61892

Y = − 0.00922295 + 0.041(4.61892) = 0.18015 Pc 0.0186233(Tc /K) (0.0186233)(534.25) = = = 43.00 bar exp(Y ) − 0.96601 exp(0.18015) − 0.96601

Results: Property

DIPPR 801 recommendation

Wilson-Jasperson estimation

% Difference

Tc /K

536.2

534.25

−0.4

43.00

2.3

Pc /bar

42.02

Normal Melting Point The normal melting point is defined as the temperature at which melting occurs at atmospheric pressure. Methods to estimate the melting point are not particularly effective because the melting point depends strongly on solid crystal structure and that structure is not effectively correlated with standard GC or CS methods. Recommended Method The method of Constantinou and Gani is recommended with caution. Reference: Constantinou, L., and R. Gani, AIChE J., 40 (1994): 1697. Classification: Group contributions. Expected uncertainty: 25 percent. Applicability: Organic compounds. Input data: First- and second-order group contributions from molecular structure. Description: A group contribution method given by  Tm = (102.425 K) ⋅ ln  ∑ ni t m1, i +  i

∑n t

j m 2, j

j

ni 2 1 1

tm1,i

Second-order group }OH, C4 or less }OH, C5 or more }O} }NH2, >NH, >N} }CHO >CO }COOH }COO} }CN }NO2 Organic halides (once per molecule) }SH, }S}, }SS} Siloxane bond

Dpck 0.12660 0.43400 0.91000 0.72983 0.44805 0.43360 0.32868 0.12600 6.05000 1.34000 1.22000 1.04713 0.97711 0.79600 1.19000 — — 1.42000 2.68000 1.20000 0.97151 1.11000 — 1.11000 2.71000 1.69000 1.95000 — 0.43000 1.31593 1.66000 6.33000 1.07000 — 1.08000 — — −0.08000 0.69000 2.05000 2.04000

Dtcj

Dpcj

0.0350 0.0100 −0.0075 −0.0040 0.0000 −0.0550 0.0170 −0.0150 0.0170 −0.0200 0.0020

0.00 0.00 0.00 0.00 0.50 0.00 0.50 0.00 1.50 1.00 0.00

0.0000 −0.0250

0.00 −0.50

As cited in PGL5.

Calculation using Eq. (2-16): Tm = (102.425 K) ln [(2)(0.4640) + 12.6275 + 1.5656] = 278 K

Example Estimate the melting point of 2,6-dimethylpyridine. Structure and group contributions:

Group

Dtck 0.002793 0.320000 0.019000 0.008532 0.019181 0.020341 0.008810 0.036400 0.088000 0.020000 0.012000 0.007271 0.011151 0.016800 0.014000 0.018600 0.059000 0.031000 0.007000 0.010300 0.012447 0.013300 −0.027000 0.175000 0.017600 0.007000 0.020000 0.010000 0.000000 0.005900 0.017000 −0.027500 0.219000 0.013000 0.011000 0.014000 −0.050000 0.000000 0.000000 0.007000 0.015000

(2-16)

where ni, nj = number of first- and second-order groups, respectively tm1,i = first-order group contributions from Table 2-158 tm2,i = second-order group contributions from Table 2-159

−CH3 −C5H3(N)− Six-member ring

H, D, T He B C N O F Ne Al Si P S Cl Ar Ti V Ga Ge As Se Br Kr Rb Zr Nb Mo Sn Sb Te I Xe Cs Hf Ta W Re Os Hg Bi Rn U

a

  

2-321

tm2,i

0.4640 12.6275 1.5656

The predicted value is 4 percent higher than the recommended experimental value of 267 K in the DIPPR 801 database. Normal Boiling Point The normal boiling temperature Tb is the temperature at which the vapor pressure of the liquid equals 101.325 kPa (1.0 atm). If there are sufficient vapor pressure data available, then Tb may be found from a regression of the data using an appropriate vapor pressure equation [e.g., Eqs. (2-24) to (2-28)]. If two or more vapor pressure values are available in the approximate temperature range of Tb, they can be used to obtain Tb by using Eq. (2-2) to linearly interpolate ln P* versus 1/T values. When one or more low-temperature vapor pressure points are available, a common occurrence, then the method of Pailhes can be used to estimate Tb.

2-322

PHYSICAL AnD CHEMICAL DATA TABLE 2-158 Group

First-Order Groups and Their Contributions for Melting Point * Group

tm1,i

TABLE 2-159

Group

tm1,i

}CH3 0.4640 }COOCH2} >CH2 0.9246 }OOCH >CH} 0.3557 }OCH3 >C< 1.6479 }OCH2} }CH=CH2 1.6472 }OCH< }CH=CH} 1.6322 }OCH2F >C=CH2 1.7899 }CH2NH2 >C=CH} 2.0018 >CHNH2 >C=C< 5.1175 }NHCH3 }CH=C=CH2 3.3439 }CH2NH} >ACH 1.4669 >CHNH} >AC} 0.2098 >NCH3 >ACCH3 1.8635 }NCH2} >ACCH2} 0.4177 >ACNH2 >ACCH< −1.7567 }C5H3(N)} }OH 3.5979 }CH2CN >ACOH 13.7349 }COOH }COCH3 4.8776 }CH2Cl }COCH2} 5.6622 >CHCl }CHO 4.2927 >CCl} }COOCH3 4.0823 }CHCl2 *Constantinou, L., and R. Gani, AIChE J., 40 (1994): 1697.

3.5572 4.2250 2.9248 2.0695 4.0352 4.5047 6.7684 4.1187 4.5341 6.0609 3.4100 4.0580 0.9544 10.1031 12.6275 4.1859 11.5630 3.3376 2.9933 9.8409 5.1638

}CCl3 >ACCl }CH2NO2 >CHNO2 >ACNO2 }CH2SH }I }Br }C≡CH }C≡C} >C=CCl} >ACF }CF3 }COO} }CCl2F }CClF2 }F (other) }CONH2 }CON(CH3)2 }CH3S >CH2S

tm1,i 10.2337 2.7336 5.5424 4.9738 8.4724 3.0044 4.6089 3.7442 3.9106 9.5793 1.5598 2.5015 3.2411 3.4448 7.4756 2.7523 1.9623 31.2786 11.3770 5.0506 3.1468

Second-Order Groups and Their Contributions for Melting Point*

Group

tm21,i

}CH(CH3)2 }C(CH3)3 }CH(CH3)CH(CH3)} }CH(CH3)C(CH3)2} }C(CH3)2C(CH3)2} Three-member ring Five-member ring Six-member ring Seven-member ring CHn=CHm}CHp=CHk [k, n, m, p = 0, 1, 2] CH3CHm=CHn [m, n = 0, 1, 2]

0.0381 −0.2355 0.4401 −0.4923 6.0650 1.3772 0.6824 1.5656 6.9709 1.9913

CH2CHm=CHn [m, n = 0, 1, 2]

−0.5870

CHCHm=CHn or CCHm=CHn [m, n = 0, 1, 2] Alicyclic side chain: CcyclicCm [m > 1] CH3CH3

−0.2361

CHCHO; CCHO

Group

0.2476

1.4880 2.0547 −0.2951

CH3COCH; CH3COC

−0.2986

Ccyclic(=O) 0.7143 ACCHO −0.6697 *Constantinou, L., and R. Gani, AIChE J., 40 (1994): 1697.

The most accurate method for prediction of normal boiling temperatures without experimental data is the Nannoolal method. Recommended Method Pailhes method. Reference: Pailhes, F., Fluid Phase Equilib., 41 (1988): 97. Classification: Group contributions. Expected uncertainty: ~3 K (1 to 2 percent). Applicability: Organic compounds. Input data: Molecular structure and one measured vapor pressure value * Pmeas (often at a low pressure). The method requires estimation of the reduced normal boiling point, Tbr, and Pc, which in the example below are obtained using the Wilson-Jasperson first-order method and the Ambrose method, respectively. Description: A simple group contribution method is given by  log(Pc /bar) + (1 − Tbr ) x P  2 Tb = Tmeas   − 3 x p − 1.49 x p log(Pc /bar)   where Tb = estimated normal boiling point Pc = critical pressure estimated from group contributions

−3.1034 28.4324 0.4838 0.0127 −2.3598 −2.0198 −0.5480 0.3189 0.9124 9.5209

CHm(OH)CHn(NHp) [m, n, p = 0, 1, 2, 3] CHm(NH2)CHn(NH2) [m, n = 0, 1, 2] CHm cyclic}NHp}CHn cyclic [m, n, p = 0, 1, 2] CHm}O}CHn=CHp [m, n, p = 0, 1, 2] AC}O}CHm [m = 0, 1, 2, 3] CHm cyclic}S}CHn cyclic [m, n = 0, 1, 2] CHm=CHn}F [m, n = 0, 1, 2] CHm=CHn}Br [m, n = 0, 1, 2] ACBr ACl

−2.8298

CH3COCH2

tm21,i

CHCOOH; CCOOH ACCOOH CH3COOCH; CH3COOC COCH2COO or COCHCOO or COCCOO CO}O}CO ACCOO CHOH COH CHm(OH)CHn(OH) [m, n = 0, 1, 2] CHm cyclic}OH [m = 0, 1]

(2-17)

2.7826 2.5114 1.0729 0.2476 0.1175 −0.2914 −0.0514 −1.6425 2.5832 −1.5511

xP = log(1 atm/P*meas) Tmeas = temperature at which experimental vapor pressure P*meas is known Example The vapor pressure of n-decylacetate (M = 200.32 kg/kmol) at 348.65 K is 106.66 Pa. Estimate the normal boiling point of this compound, using the Paihles method. Structure and group contributions from Tables 2-154 and 2-157:

Wilson-Jasperson Groups

ni

ni

DP,i

H

24

0.002793

−COO−

1

0.470

O

2

0.020341

C (alkyl)

11

0.226

C

12

0.008532

Δtci

Ambrose Groups

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES CHARACTERIZInG AnD CORRELATInG COnSTAnTS

Group contribution calculations using Eq. (2-13) for Tbr and Eq. (2-7) for Pc :

∑ n ∆tc i

i

= (24)(0.002793) + (2)(0.020341) + (12)(0.008532) = 0.210098

Acentric Factor The acentric factor of a compound w is defined in terms of the reduced vapor pressure evaluated at a reduced temperature of 0.7 as

Tbr = (0.048271 + 0.210098)0.2 = 0.7629

∑n ∆ i

P ,i

ω = − log Pr*

= (1)(0.470) + (11)(0.226) = 2.956

Pc =

200.32 bar = 18.450 bar (0.339 + 2.956)2

Calculation of auxiliary quantities:  101,325 Pa   1 atm  x P = log  ∗  = log   = 2.9777  Pmeas   106.66 Pa  Calculation of normal boiling point using Eq. (2-17):  log (18.450) + (1 − 0.7629)(2.9777)  Tb 2 = (348.65)   − 3(2.9777) − 1.49(2.9777) log(18.450) K   Tb = 520.94 K The estimated value is 0.7 percent higher than the DIPPR 801 recommended value of 517.15 K.

Recommended Method: Nannoolal method. Reference: Nannoolal, Y., J. Rarey, D. Ramjugernath, and W. Cordes, Fluid Phase Equilib., 226 (2004): 45. Classification: Group contributions. Expected uncertainty: ~7 K (about 2 percent). Applicability: Organic compounds. Input data: Ci values in Table 2-155; intramolecular group-group interactions Cij in Table 2-156; and the number of nonhydrogen atoms in the molecule. Description: A GC method that includes second-order corrections for steric effects and intramolecular interactions. Tb is calculated from

(2-18)

where nhvy = number of nonhydrogen (heavy) atoms ni = number of occurrences of group i Ci = group contribution from Table 2-155 GI = total group-group interaction as calculated using Eq. (2-12) and Table 2-156

−1.0000

(2-19)

Example Calculate the acentric factor of chlorobenzene with a known value for Tb.

Input information: From the DIPPR 801 database, Tb = 404.87 K, Tc = 632.35 K, and Pc = 45.1911 bar. Calculation of auxiliary quantities (see Eq. (2-28a) for these equations): Tbr =

Tb 404.87 = 0.64 = Tc 632.35

ψ = −35 + αc =

=

Example Estimate the normal boiling point of di-isopropanolamine by using the Nannoolal method. Structure:

Tr = 0.7

It is primarily used as a third parameter (in addition to Tc and Pc) in CS predictions as a measure of deviations from nonspherical molecular shape, hence the name, suggesting molecular interactions that are not between centers of molecules. However, as defined in Eq. (2-19), w also contains polarity information, and it increases with increasing polarity for molecules of similar size and shape. The value of w is close to zero for small, spherically shaped, nonpolar molecules (argon, methane, etc.). It increases in value with larger deviations of molecular shape from spherical (longer chain lengths, less chain branching, etc.) and with increasing molecular polarity. When possible, w should be obtained from experimental vapor pressure correlations by using Eq. (2-19), but an accurate estimation of w can be made by using the critical constants and a single vapor pressure point by application of CS vapor pressure equations. Recommended Method 1 Definition. Classification: Theory and empirical extension of theory. Expected uncertainty: Within 3 percent if an experimental vapor pressure correlation is available; within 10 percent from a predicted vapor pressure correlation. Applicability: Most organic compounds. Input data: Vapor pressure correlation or Tc, Pc, and Tb if an experimental vapor pressure correlation is unavailable. Description: Equation (2-19) is applied directly to the appropriate vapor pressure equation. A predictive vapor pressure equation can also be used as in the second example.

N

∑n ⋅ C + GI Tb i =1 i i + 84.3395 = 0.6583 K nhvy + 1.6868

2-323

K = 0.0838

36 36 + 42 ⋅ ln(Tbr ) − Tbr6 = −35 + + 42 ⋅ ln(0.64) − (0.64)6 = 2.4312 Tbr 0.64

(3.758) K ψ + ln( PC /1.01325bar) K ψ − ln(Tbr ) 45.1911  (3.758)( 0.0838 )(2.4312) + ln   1.01325  = 7.025 (0.0838)(2.4312) − ln(0.64)

D = K (α c − 3.758) = (0.0838)(7.025 − 3.758) = 0.2738 A = 35 D = 9.581 B = −36 D = −9.855 C = α c − 42 D = −4.473 Calculation using Eq. (2-28) at Tr = 0.7: ln( Pr ) = 9.581 −

Group contributions and values: Group

ni

Ci

Group total

}CH3

2

177.3066

354.6132

>C(c) 1) is the number of occurrences of that group in the molecule. Group

Example

Group

Gi

Example

Gi

0.2879 –OH(na) alcohol 0.2230 [S, N, P] = O thionyl chloride ketone 0.3615 –OH(a) phenol 0.0990 >C=O 0.3348 2-pyrrolidone 0.0075 >C=O ring –OH(C < 5)* ethanol –COO– ester −0.0650 –CHO aldehyde 0.1617 –COOH acid −0.5900 *Applied in addition to regular −OH group for molecules with fewer than 5 C atoms.

Example Calculate the dielectric constant of salicylaldehyde at 303 K. The structure of salicylaldehyde is shown below with the two different oxygen-containing groups and their contributions that are to be used in Eq. (2.23). O

−1

O Groups   A G µ δ ln ε = C 0 + C1   + C 2  2 vdw −1  + C 3  1/2 -3/2  + C 4 n 2 + ∑ i  m ⋅ kmol   D  J ⋅m  ki i

(2-23)

C0 −0.1694

HO

Group

Gi

ki

−CHO

0.1617

1

−OH(a)

0.0990

1

2-326

PHYSICAL AnD CHEMICAL DATA

Values of the input properties for Eq. (2.23) obtained from the DIPPR database are μ = 3.08794 D, Avdw = 8.43 × 108 m2/kmol, d = 21330 J1/2∙m−3/2, n = 1.57017. Equation (2.23) is then used to obtain the dielectric constant: 4.072 ln ε = −0.3416 + (0.5239) ( 3.08794 ) + 8.43 + (7.408 × 10 −5 )(21330) − (0.3248)(1.57017)2 + 0.1617 + 0.0990

C = αc − 42D

B = −36D

A = 35D

Values of the constant K [Vetere, A., Ind. Eng. Chem. Res., 30 (1991): 2487] are as follows: Class

ln e = 2.799 and e = 16.43 A few reported experimental values are 13.9 at 293 K, 17.1 at 303 K, and 18.35 at 293.15 K.

Value

Acids

K = −0.120 + 0.025h

Alcohols

K = 0.373 − 0.030h

All other organic compounds

K = 0.0838

VAPOR PRESSURE Liquids Vapor pressure is the equilibrium pressure at a given temperature of pure, coexisting liquid and vapor phases. The vapor pressure curve is a monotonic function of temperature from its minimum value (the triple point pressure) at the triple point temperature Tt, to its maximum value, Pc, at Tc. Liquid vapor pressure data over a limited temperature range can be correlated with the Antoine equation [Antoine, C., C.R., 107 (1888): 681, 836] In

P∗ B = A− T /K + C Pa

aτ + bτ1.5 + cτ 2.5 + d τ 5 1− τ

K = 0.0838

D = (0.0838)(7.0248 − 3.758) = 0.2738

C = 7.0248 − (42)(0.2738) = −4.4729

B = −(36)(0.2738) = −9.8552

A = −(35)(0.2738) = 9.5814

Calculation using Eq. (2-28) at each T (detailed calculation shown for T = 500 K): Tr = 500/632.35 = 0.7907

(2-25)

where τ ≡ 1 − Tr

ln Pr = 9.5814 −

or the Riedel equation [Riedel, L., Chem. Ing. Tech., 26 (1954): 679] ln

T T P∗ B = A+ + C ln + D    K Pa T /K K

aτ + bτ1.5 + cτ 2.5 + d τ5 + eτ 6 1− τ

Pr = exp(−1.7651) = 0.1712

(for alcohols)

(2-27)

B + C ln Tr + DTr6 Tr

(2-28)

is used with the constants for this equation determined from the following set of relationships: ψ = −35 + h = Tbr

36 + 42 ln Tbr − Tbr6 Tbr

ln ( Pc /1.01325 bar) 1 − Tbr

αc =

P = PrPc = (0.1712)(45.1911 bar) = 7.74 bar

(2-26)

Correlation of experimental data within a few tenths of a percent over the entire fluid range can usually be obtained with either the Wagner or Riedel equations. Two prediction methods are recommended for liquid vapor pressure. The first method is based on the Riedel equation; the second is a CS method. Both methods require Tc and Pc as input, but these can be estimated by the methods shown earlier if experimental values are unavailable. Recommended Method 1 Riedel method. Reference: Riedel, L., Chem. Ing. Tech., 26 (1954): 679. Classification: Empirical extension of theory and corresponding states. Expected uncertainty: Varies strongly depending upon relative T, but 1 percent or less above Tb is typical with uncertainties of 5 to 30 percent near the triple point. Applicability: Most organic compounds. Input data: Tb, Tc, Pc. Description: Equation (2-26) in reduced form ln Pr = A +

9.8552 − 4.4729 ln 0.7907 + (0.2738)(0.7907) 6 = −1.7651 0.7907

E

In its original form, E in Eq. (2-26) was assigned a value of 6, but other integer values of E from 1 to 6 have been found to be more effective for different families of chemicals in representing the vapor pressure over the whole liquid range. With the best value of E, either the Riedel or the Wagner equation can be used to correlate most fluids over the whole liquid range, but a fifth term is used in the Wagner equation for alcohols [Poling, B. E., Fluid Phase Equilib., 116 (1996): 102]: ln Pr∗ =

Tbr = 404.87/632.35 = 0.640

36 ψ = −35 + + 42 ln(0.640) − (0.640) 6 = 2.431 0.640 (3.758) (0.0838)(2.431) + ln (45.191/1.01325) = 7.0248 αc = (0.0838)(2.431) − ln (0.640)

(2-24)

Data from the triple point to the critical point can be correlated with either a modified form of the Wagner equation [Wagner, W., A New Correlation Method for Thermodynamic Data Applied to the Vapor-Pressure Curve of Argon, Nitrogen, and Water, J. T. R. Watson (trans. and ed.), IUPAC Thermodynamic Tables Project Centre, London, 1977; Ambrose, D., J. Chem. Thermodyn., 18 (1986): 45; Ambrose, D., and N. B. Ghiassee, J. Chem. Thermodyn., 19 (1987): 903, 911] ln Pr∗ =

Example Estimate the vapor pressure of chlorobenzene at 50 K intervals from 300 to 600 K. Input information: From the DIPPR 801 database, Tb = 404.87 K, Tc = 632.35 K, and Pc = 45.1911 bar. Auxiliary Quantities:

3.758 K ψ + ln(Pc /1.01325 bar) K ψ − ln Tbr

D = K (α c − 3.758) (2-28a)

T/K

Tr

ln Pr

P/bar

PDIPPR/bar

% Error

300 350 400 450 500 550 600

0.4744 0.5535 0.6326 0.7116 0.7907 0.8698 0.9488

−7.8532 −5.5704 −3.9323 −2.7101 −1.7651 −1.0067 −0.3705

0.0176 0.172 0.886 3.01 7.74 16.51 31.20

0.0175 0.172 0.880 2.98 7.67 16.39 31.11

0.3 0.1 0.6 0.9 0.9 0.8 0.3

Recommended Method 2 Ambrose-Walton method. References: Ambrose, D., and J. Walton, Pure & Appl. Chem., 61 (1989): 1395; Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510. Classification: Corresponding states. Expected uncertainty: Varies strongly with relative T, but less than 1 percent is typical above Tb if the acentric factor is known. Applicability: Most organic compounds. Input data: Tb, Tc, Pc, and w. Description: The acentric factor is used to interpolate within the simplefluid and deviation terms for ln P*. The f (i) terms have been obtained from correlations of the reference fluid vapor pressures with the Wagner vapor pressure equation ln Pr* = f (0) + ωf (1) + ω 2 f (2) −5.97616 τ + 1.29874 τ1.5 − 0.60394 τ 2.5 − 1.06841τ 5 1− τ −5.03365 τ + 1.11505 τ1.5 − 5.41217 τ 2.5 − 7.46628 τ 5 (1) f = 1− τ −0.64771τ + 2.41539 τ1.5 − 4.26979 τ 2.5 + 3.25259 τ 5 (2) f = 1− τ f (0) =

(2-29)

where t = 1 − Tr. Example Repeat the calculation of the liquid vapor pressure of chlorobenzene at 50-K intervals from 300 to 600 K using the Ambrose-Walton method. Input information: From the DIPPR 801 database, Tc = 632.35 K, Pc = 45.1911 bar, and w = 0.249857. Auxiliary quantities: Tr = 500/632.35 = 0.7907

t = 1 − 0.7907 = 0.2093

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES Simple-fluid and deviation vapor pressure terms at each T (shown for T = 500 K): ( − 5.97616)(0.2093) + (1.29874)(0.2093)1.5 − (0.60394)(0.2093) 2.5 − (1.06841)(0.2093)5 0.7907 = −1.4405

f (0) =

( − 5.03365)(0.2093) + (1.11505)(0.2093)1.5 − (5.41217)(0.2093) 2.5 − (7.46628)(0.2093)5 0.7907 = −1.3383

Applicability: Organic compounds for which group contributions have been regressed. Input data: Molecular structure. Description: GC values from Table 2-161 are directly additive for both enthalpy of formation and absolute third-law entropies: ∆H of

f (1) =

(−0.64771)(0.2093) + (2.41539)(0.2093)1.5 − (4.26979)(0.2093) 2.5 + (3.25259)(0.2093)5 0.7907 = 0.0145

f (2) =

Calculation using Eq. (2-29): *

ln Pr = −1.4405 + (0.249857)(−1.3383) + (0.249857)2(0.0145) = −1.774 P* = (45.1911 bar)[exp(−1.774)] = 7.667 bar

T

t

f (0)

300 350 400 450 500 550 600

0.5256 0.4465 0.3674 0.2884 0.2093 0.1302 0.0512

−5.9228 −4.3006 −3.1036 −2.1800 −1.4405 −0.8289 −0.3068

f (1) −7.5966 −5.0017 −3.3106 −2.1576 −1.3383 −0.7318 −0.2612

f (2) −0.3050 −0.1439 −0.0437 0.0043 0.0145 0.0036 −0.0081

ln P*r

P*/bar

P*DIPPR/ bar

% Error

−7.840 −5.559 −3.933 −2.719 −1.774 −1.012 −0.373

0.0178 0.174 0.885 2.98 7.67 16.43 31.14

0.0175 0.172 0.880 2.98 7.67 16.39 31.11

1.4 1.5 0.5 0.0 0.0 0.3 0.1

2-327

kJ/mol

N

= ∑ ni (∆H of )i i =1

N So = ∑ ni (S o )i −1 −1 J ⋅ mol K i =1

(2-31)

where ( ∆H of )i = enthalpy of formation GC value and (So)i = entropy GC value, both obtained from Table 2-161. Group values in Table 2-161 are defined by the central, nonhydrogen group and the atoms bonded to that group. Thus, C—(2H)(2C) represents a C atom to which 2 H and 2 C atoms are bonded. For example, propane (CH3—CH2—CH3) is composed of three groups: two C—(3H)(C) and one C—(2H)(2C). Example Estimate the standard and ideal gas enthalpies of formation of o-toluidine. Input information: Because the melting point (256.8 K) and boiling point (473.49 K) for o-toluidine bracket 298.15 K, the standard state phase at 298.15 K and 1 bar is liquid. Structure:

Group contributions:

Solids Below the triple point, the pressure at which the solid and vapor phases of a pure component are in equilibrium at any given temperature is the vapor pressure of the solid. It is a monotonic function of temperature with a maximum at the triple point. Solid vapor pressures can be correlated with the same equations used for liquids. Estimation of solid vapor pressure can be made from the integrated form of the Clausius-Clapeyron equation ln

P ∗ ∆H sub  Tt  = 1−  Pt∗ RTt  T 

Group

ni

Cb—(H)(2Cb) Cb—(C)(2Cb) Cb—(N)(2Cb) C—(3H)(C) N—(2H)(Cb)

4 1 1 1 1 Total

DH of gas

DH of liq.

So gas

Ss liq.

13.81 23.64 −1.30 −42.26 19.25 54.57

8.16 19.16 1.50 −47.61 −11.00 −5.31

48.31 −35.61 −43.53 127.32 126.90 368.32

28.87 −19.50 −24.43 83.30 71.71 226.56

(2-30)

where Tt = triple point temperature Pt* = triple point pressure DHsub = enthalpy of sublimation The liquid and solid vapor pressures are identical at the triple point. A good vapor pressure correlation that is valid at the triple point may be used to obtain the triple point pressure. Estimating solid vapor pressures by using Eq. (2-30) generally requires an estimation of DHsub, and so the illustrative example is combined with the example on enthalpy of sublimation in the section on latent enthalpy. THERMAL PROPERTIES Enthalpy of Formation The standard enthalpy (heat) of formation is the enthalpy change upon formation of 1 mole of the compound in its standard state from its constituent elements in their standard states. Two different standard enthalpies of formation are commonly defined based on the chosen standard state. The standard enthalpy of formation ∆H sf uses the naturally occurring phase at 298.15 K and 1 bar as the standard state while the ideal gas enthalpy (heat) of formation ∆H of uses the compound in the ideal gas state at 298.15 K and 1 bar as the standard state. In both cases, the standard state for the elements is their naturally occurring state of aggregation at 298.15 K and 1 atm. Sources for data include DIPPR, TRC, SWS, JANAF, and TDB. The Domalski-Hearing method is the most accurate general method for estimating either ∆H sf or ∆H of if the appropriate GC values are available, but a CC method is also as accurate for estimating ∆H of if an isodesmic reaction can be formulated and used. The Domalski-Hearing method also applies to entropies, and the entropy predictive equations are listed in this section for convenience because they are equivalent in form to the enthalpy equations. However, discussion and illustration of the estimation methods for entropy are delayed to the next subsection. Recommended Method Domalski-Hearing method. Reference: Domalski, E. S., and E. D. Hearing, J. Phys. Chem. Ref. Data, 22 (1993): 805. Classification: Group contributions. Expected uncertainty: 3 percent.

Calculation from Eq. (2-31):

∆H of kJ/mol

= 54.57

So = 368.32 J/(mol ⋅ K)

∆H Sf kJ/mol

= −5.31

Ss = 226.56 J/(mol ⋅ K) o

The recommended DIPPR 801 standard enthalpies of formation are ∆H f = 53.20 kJ/mol s and ∆H f = −4.72 kJ/mol. The estimated values are higher than the recommended values by 2.6 and 12.5 percent, respectively. The recommended DIPPR 801 standard entropies are So = 355.8 J/(mol ⋅ K) and Ss = 231.2 J/(mol ⋅ K). The estimated values differ from these by 3.5 and −2.0 percent, respectively.

Recommended Method Isodesmic reaction. Reference: Foresman, J. B., and A. Frisch, Exploring Chemistry with Electronic Structure Methods, 2d ed., Gaussian Inc., Pittsburgh, Pa., 1996. Classification: Computational chemistry. Expected uncertainty: 5 to 10 percent depending upon the level of theory and basis set size used. Applicability: Compounds for which an isodesmic reaction can be formulated. Input data: Experimental ∆H of values for all other participants in the isodesmic reaction. Description: While ab initio calculations of absolute enthalpies are not currently as accurate as GC methods, relative enthalpies of molecules calculated with the same level of theory and basis set can be very accurate, as in the case of isodesmic reactions. An isodesmic reaction is one in which the number and type of bonds are preserved during the reaction. For example, the reaction of acetaldehyde with ethane to form acetone and methane is

2-328

PHYSICAL AnD CHEMICAL DATA

TABLE 2-161

Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties

This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group

∆Hfo

So

∆Hfs liq.

S s liq.

∆Hfs solid

S s solid 56.69 23.01 −16.89 0.00 −33.19 0.00 0.00 0.00

21.75

CH Groups C}(3H)(C) C}(2H)(2C) C}(H)(3C) }CH3 corr (tertiary) C}(4C) }CH3 corr (quaternary) }CH3 corr (tert/quat) }CH3 corr (quat/quat) Cd}(2H) Cd}(H)(C) Cd}(2C) Cd}(H)(Cd) Cd}(C)(Cd) Cd}(Cd)(Cb) Cd}(H)(Cb) Cd}(C)(Cb) Cd}(H)(Ct) C}(4H), Methane Cd}(2Cb) C}(2H)(C)(Cd) C}(H)(2C)(Cd) }CH3 corr (tertiary) C}(3C)(Cd) }CH3 corr (quaternary) C}(H)(C)(2Cd) C}(2H)(2Cd) C}(2H)(Cd)(Cb) C}(H)(C)(Cd)(Cb) cis (unsat) corr tert}Butyl cis corr Ct}(H) Ct}(C) Ct}(Cd) Ct}(Cb) Ct}(Ct) C}(2H)(C)(Ct) C}(H)(2C)(Ct) }CH3 corr (tertiary) C}(3C)(Ct) }CH3 corr (quaternary) C}(2H)(2Ct) C}(2C)(2Ct) Ca Cb}(H)(2Cb) Cb}(C)(2Cb) Cb}(Cd)(2Cb) Cb}(Ct)(2Cb) Cb}(3Cb) C}(2C)(2Cb) C}(2H)(C)(Cb) C}(H)(2C)(Cb) C}(Cb)(3C) C}(2H)(2Cb) C}(H)(C)(2Cb) C}(H)(3Cb) C}(3Cb)(C) C}(4Cb) Cbf}(Cbf)(2Cb) Cbf}(Cb)(2Cbf) Cbf}(3Cbf) Cb}(2Cb)(Cbf) Cb}(Cb)(2Cbf) ortho corr, hydrocarbons meta corr, hydrocarbons Cyclopropane rsc (unsub) Cyclobutane rsc Cyclopentane rsc (unsub) Cyclohexane rsc (unsub) Cycloheptane rsc Cyclooctane rsc Cyclononane rsc Cyclodecane rsc

−42.26 −20.63 −1.17 −2.26 19.20 −4.56 −1.80 −0.64 26.32 36.32 44.14 28.28 36.78

127.32 39.16 −53.60 0.00 −149.49 0.00 0.00 0.00 115.52 33.05 −50.84 27.74 −61.33

−47.61 −25.73 −4.77 −2.18 17.99 −4.39 −1.77 −0.64 21.75 31.05 39.16 22.18 30.42

83.30 32.38 −23.89 0.00 −98.65 0.00 0.00 0.00 86.19 28.58 −29.83 13.30 −41.92

28.28 37.95 28.28 −74.48 32.88 −20.88 −1.63 −2.26 22.13 −4.56 −1.17 −18.92

27.74 −51.97 27.74 206.92

22.18 38.58 22.18

13.30

−46.74 −29.41 −5.98 −2.34 12.47 −4.35 −2.70 −2.24 22.43 25.48 32.97 17.53 27.91 56.07 17.53

13.30

17.53

38.20 −50.38 0.00 −150.23 0.00 −53.60 42.08

31.67 −28.07 0.00 −108.20 0.00 −23.89 19.32

49.91 −24.35 −6.49 −2.34 12.51 −4.35 −5.98 −21.60

4.85 17.24 113.50 115.10 121.42 120.76 120.76 −19.70 −3.16 −2.26

5.06 0.00 101.96 26.32 39.92 17.77 25.94 42.80 −45.69 0.00

0.00 0.00 67.57 14.25

5.73 17.57 110.34 101.66

32.36

103.28 103.28 −29.41

−4.56 −41.14

0.00

142.67 13.81 23.64 24.17 24.17 21.66

26.28 48.31 −35.61 −33.85 −33.85 −36.57

−21.34 −4.52 18.28 −46.43

42.59 −48.00 −147.19

30.83 −25.73 −5.02 −2.18 20.79 −4.39 −4.77 −24.43 −24.73 −6.90 5.27 17.48 104.47 107.15 114.77 119.00 104.80 −22.13 −2.18 22.83 −4.39 −39.08 20.67 134.68 8.16 19.16 19.12 19.12 17.21 −24.81 −5.82 18.70 −26.50 −21.47

0.00 0.00 14.39 28.87 −19.50 −9.04 −9.04 47.40 −13.90 −96.10 51.97 28.12

−6.86 27.04 20.10 16.00 3.59 22.46 1.26 −0.63 115.15 110.89 26.75 0.68 26.34 40.65 52.91 51.99

0.00

15.83 11.50 −0.90

−5.54

−2.50 0.00 134.86 126.04 116.22 78.18 73.97 70.78

3.26 0.00 111.58 106.64 22.84 −1.77 23.50 38.10 50.40 50.61

0.00 0.00 51.48 42.24 10.07 15.89 2.96

−2.34 26.38 −4.35 131.08 6.53 13.90 20.27 20.07 17.03 52.81 −22.10 −3.50 21.57 −21.44 16.40 34.48 116.25 64.89 14.10 12.00 1.94 −8.77 47.93 5.00 2.00 114.43 34.00 10.94

21.75 21.75

0.00 0.00 −16.89

0.00 0.00

0.00 0.00

22.75 −5.50 −10.00 −10.00 −6.00 26.90 22.85 −12.62 −6.00 2.00 7.00 0.00 0.00

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-161

2-329

Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued )

This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group

DHfo

DHfs liq.

So

S s liq.

DHfs solid

S s solid

CHO Groups CO}(2H), formaldehyde CO}(C)(CO) CO}(H)(CO) CO}(CO)(Cb) CO}(O)(CO) CO}(Cd)(O) CO}(C)(O) CO}(H)(O) CO}(2O) CO}(H)(Cd) CO}(2Cb) CO}(C)(Cb) CO}(H)(Cb) CO}(O)(Cb) CO}(2C) CO}(H)(C) CO}(C)(Cd) O}(2CO), aliphatic O}(2CO), aromatic O}(Cd)(CO) O}(C)(CO) O}(H)(CO) O}(Cb)(CO) O}(C)(O) O}(H)(O) O}(2Cd) O}(H)(Cd) O}(C)(Cd) O}(2Cb) O}(C)(Cb) O}(H)(Cb) O}(2C) O}(H)(C) Cd}(H)(CO) Cd}(C)(CO) Cd}(O)(Cd) Cd}(O)(C) Cd}(O)(H) Ct}(CO) Cb}(CO)(2Cb) Cb}(O)(2Cb) C}(2H)(2CO) C}(CO)(3C) C}(H)(CO)(2C) C}(2H)(CO)(C) C}(3H)(CO) C}(2H)(CO)(Cd) C}(2H)(CO)(Ct) C}(2H)(CO)(Cb) C}(H)(CO)(C)(Cb) C}(H)(O)(CO)(C) C}(4O) C}(H)(3O) C}(3O)(C) C}(2O)(2C) C}(H)(2O)(C) C}(2H)(2O) C}(2H)(O)(Cb) C}(2H)(O)(Cd) C}(H)(CO)(C)(Cb) C}(H)(CO)(2Cb) C}(O)(3Cb) C}(O)(3C) (ethers, esters) C}(H)(O)(2C) (ethers, esters) C}(O)(3C) (alcohols, peroxides) C}(H)(O)(2C) (alcohols, peroxides) C}(2H)(O)(C) C}(3H)(O) O}(CO)(O) C}(2C)(O)(Cb) C}(H)(C)(2O)

−108.60 −121.29 −105.98 −112.30 −123.75 −136.73 −137.24 −124.39 −111.88 −126.96 −110.00 −148.82 −121.35 −125.00 −132.67 −124.39

224.54

−214.50 −238.30 −198.03 −188.87 −254.30 −167.00 −20.75 −72.26 −139.29

34.16

−135.04

62.59 62.59 147.03

64.31 147.03

36.03 101.71

−123.30 −155.56 −149.37 −142.42 −122.00 −153.05 −119.00 −145.22 −138.12 −140.00 −152.76 −142.42 −230.50 −220.90 −201.42 −196.02 −285.64 −165.50 −23.50 −101.75 −137.32

−129.33 −77.66 −92.55 −160.30 −101.42 −159.33 32.30

121.50 29.33 121.50 35.19

−133.72 −85.27 −104.85 −191.75 −110.83 −191.50 26.61

36.78 44.14 36.32

−61.34 −50.84 33.05

30.42 39.08 31.05

15.50 −4.75 −30.74 23.93 −0.25 −21.84 −42.26 −16.95 −25.48 −16.20 126.63 −152.46 −113.97 −114.39 −53.56 −57.78 −62.22 −33.76 −27.49

9.50 −19.46 −13.50 −26.10 −32.90 −42.26 −88.00 15.30

−43.72

39.58 127.32

37.49

−141.92 −52.80 −144.60 −43.05 43.43 127.32

10.50 −5.61 −23.06 26.15 −3.89 −24.14 −47.61 −19.62 −26.61 −11.67 123.43 −133.34 −107.74 −99.54 −41.30 −51.42 −62.89 −29.17 −28.62

0.79 −21.00 −11.13 −27.60 −35.80 −47.61 −90.00 25.80

−140.75

32.72 94.68

33.81 93.55

−117.75 −120.81 −134.10 −153.60

32.90 32.13

−123.00

−42.92

−116.00 −143.70 −160.18 −145.00 −157.95

23.72 32.13

−235.00 −207.00 38.28 38.28

−210.60 −282.15 −170.00 −30.20 −105.30

12.09 21.78 45.32

23.31

−96.20 −122.87 −199.25 −119.00 −199.66 7.82

3.14

43.89 26.78 43.89

28.62 28.62 27.53

−85.98 −24.52 39.87 83.30

27.91 32.97 25.48 144.52 8.15 1.00 −19.10 24.02 −9.83 −27.90 −46.74

24.73 56.69

−46.71

14.81 −14.39

8.08

−41.92 −29.83 28.58 −10.59

0.08 1.59

23.85

−94.68 −25.31 −122.48 −29.83 32.59 83.30

−14.39 3.72 60.46 −0.50 −20.08 −12.25 −29.08 −33.00 −46.74 −80.50 29.30 −52.50

−14.77 6.95 24.73 56.69

(Continued )

2-330

PHYSICAL AnD CHEMICAL DATA

TABLE 2-161

Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued )

This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group

DHfo

So

DHfs liq.

S s liq.

DHfs solid

−47.61 −30.80 −14.65 −2.18 5.10 −4.39

83.30 32.38 −20.00 0.00 −87.99 0.00

−26.09 0.33 0.33 51.50 112.00 25.30 75.00 119.00

71.71 71.71 32.09 −38.62 60.58 22.05 −26.94

−46.74 −34.00 −13.90 −2.34 1.00 −4.35 −26.00 −33.31 −6.30 −46.00 47.80 101.00 18.97

S s solid

CHN and CHNO Groups C}(3H)(N) C}(2H)(C)(N) C}(H)(2C)(N) }CH3 corr (tertiary) C}(3C)(N) }CH3 corr (quaternary) C}(2H)(2N) C}(2H)(Cb)(N) N}(2H)(C) ( first, amino acids) N}(2H)(C) (second, amino acids) N}(H)(2C) N}(3C) N}(2H)(N) N}(H)(C)(N) N}(2C)(N) N}(2Cb)(N) N}(H)(Cb)(N) N}(2CO)(N) N}(H)(2Cd) N}(C)(2Cd) N}(2H)(Cb) N}(H)(C)(Cb) N}(2C)(Cb) N}(C)(2Cb) N}(H)(2Cb) N}(3Cb) NI}(C) NI}(Cb) NA}(C) NA}(Cb) NA}(oxide)(C) C}(2H)(C)(NA) C}(H)(2C)(NA) C}(3C)(NA) Cd}(H)(N) Cd}(C)(N) Cb}(N)(2Cb) Cb}(NO)(2Cb) Cb}(NO2)(2Cb) Cb}(CNO)(2Cb) Cb}(CN)(2Cb) Cb}(NA)(2Cb) Cb}(H)(2NI) CO}(H)(N) CO}(C)(N) CO}(Cb)(N) (amides) CO}(Cb)(N) (amino acids) CO}(Cd)(N) CO}(2N) N}(2H)(CO) (amides, ureas) N}(2H)(CO) (amino acids) N}(H)(C)(CO) (amides, ureas) N}(H)(C)(CO) (amino acids) N}(2C)(CO) N}(H)(Cb)(CO) N}(H)(2CO) N}(C)(2CO) N}(Cb)(2CO) N−(2Cb)(CO) N}(C)(Cb)(CO) C}(3H)(CN), acetonitrile C}(2H)(C)(CN) C}(H)(2C)(CN) C}(3C)(CN) C}(2C)(2CN) C}(2H)(Cd)(CN) Cd}(H)(CN) Ct}(CN) C}(3H)(NO2), nitromethane C}(2H)(2NO2), dinitromethane C}(H)(3NO2), trinitromethane C}(4NO2), tetranitromethane C}(2H)(C)(NO2)

−42.26 −28.30 −16.70 −2.26 0.29 −4.56 −30.00 −24.14 19.25 19.25 67.55 116.50 47.70 89.16 120.71

127.32 42.26 −63.55 0.00 −152.59 0.00 124.40 126.90 33.96 −61.71 122.18

87.50

73.40

83.55 120.64 19.25 59.00 126.40 120.44 83.55 123.15 81.46 69.00 109.50 109.50 40.80 −20.70 −2.66 11.50 −16.00 −5.74 −1.30 21.50 −1.45 −177.63 151.00 22.55 6.30 −124.39 −133.26

50.50 97.38 −11.00 26.25 109.40 97.38 50.50 121.80 73.68 54.50 104.85 104.85 22.65 −25.70 −5.42 15.50 −15.50 −5.62 1.50

−171.80 −111.00 −63.00 −63.00 −16.28 −16.28 45.00 −20.84 −91.00 −11.64 9.12 74.04 94.52 113.50 137.96 95.31 146.65 264.60 −74.86 −58.90 −0.30 82.30 −60.50

126.90

47.01

−43.53

71.71

36.40

−24.43

−28.30

79.95

122.38 20.08

64.75

147.03 56.70

−188.00 −185.00

93.55

96.00 88.25

−190.50 −63.90 −63.90 −17.10 −17.10 62.00 56.20

158.41 284.14

203.60

40.56 66.07 81.50 116.20 66.40 117.28 250.20 −112.60 −104.90 −32.80 38.30 −93.50

0.00 0.00 39.00 48.75

70.00

57.00 103.00 103.00 −29.41

85.25

252.60 167.25 67.86

137.35 66.90 73.62 45.40 88.92 −21.60 36.55 96.50 89.30 45.40 107.50

56.69 23.01

149.62 106.02 −17.91

10.50 −13.00 −3.95 9.75 23.00 −32.50 155.69 121.20 18.65 0.25

−37.57 110.46 50.45

−194.60 −177.75 −177.75

40.00

−203.10 −65.25 −59.75 −9.80 5.50 55.00 −3.50 −30.80 64.00

69.00 18.00 33.03

60.85 72.00 69.85 69.00 102.07

92.72 171.75 −48.00 −99.00

96.15 74.57

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-161

2-331

Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued )

This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group

DHfo

So

DHfs liq.

S s liq.

DHfs solid

S s solid

CHN and CHNO Groups C}(H)(2C)(NO2) C}(3C)(NO2) C}(2H)(Cb)(NO2) C}(H)(C)(2NO2) C}(2C)(2NO2) C}(H)(C)(CO)(N) C}(2H)(CO)(N) C}(H)(Cb)(CO)(N) O}(C)(NO) O}(C)(NO2) N}(H)(C)(NO2) N}(H)(Cb)(NO2) N}(H)(CO)(NO2) N}(C)(2NO2) N}(C)(Cb)(NO2) N}(2C)(NO) N}(2C)(NO2) C}(2H)(C)(N3) C}(H)(2C)(N3) C}(2H)(Cb)(N3) C}(3Cb)(N3) Cb}(N3)(2Cb)

−53.00 −36.65 −62.00 −36.80 −28.50 −18.70 −3.10

115.32

−24.23 −79.71

166.11 191.92

100.30 183.00 90.00 88.00

−82.50 −61.20 −82.76 −88.80 −77.20

−46.50 −108.96

−89.00 −76.55 −81.00 −91.50 −90.30 −11.65 −30.95 127.50

−124.00 16.50 −14.00

53.50 167.00 59.00 50.00 321.70 255.00 327.40

274.00 347.00 328.60 320.00

−4.00 24.00

150.50 55.00 40.00

346.50

303.50 CHS and CHSO Groups

C}(3H)(S) C}(2H)(C)(S) C}(H)(2C)(S) }CH3 corr (tertiary) C}(3C)(S) }CH3 corr (quaternary) }CH3 corr (tert/quat) }CH3 corr (quat/quat) C}(2H)(Cb)(S) C}(2H)(Cd)(S) C}(2H)(2S) Cb}(S)(2Cb) Cd}(H)(S) Cd}(C)(S) S}(C)(H) S}(Cb)(H) S}(2C) S}(H)(Cd) S}(C)(Cd) S}(2Cd) S}(Cb)(C) S}(C)(S) S}(Cb)(S) S}(2S) S}(2Cb) S}(H)(S) S}(H)(CO) CO}(C)(S) C}(3H)(SO) C}(2H)(C)(SO) C}(H)(2C)(SO) }CH3 corr (tertiary) C}(3C)(SO) }CH3 corr (quaternary) C}(2H)(Cd)(SO) cis correction Cb}(SO)(2Cb) O}(SO)(H) O}(C)(SO) SO}(2C) SO}(2Cb) SO}(2O) SO}(C)(Cb) C}(3H)(SO2) C}(2H)(C)(SO2) C}(H)(2C)(SO2) }CH3 corr (tertiary) C}(3C)(SO2) }CH3 corr (quaternary)

−42.26 −23.17 −5.88 −2.26 13.52 −4.56 −1.80 −0.64 −18.53 −25.93 −25.10 −4.75 36.32 45.73 18.64 48.10 46.99 25.52 54.39 102.60 76.21 27.62 57.45 12.59 102.60 7.95 −5.90 −132.67 −42.26 −29.16

127.32 41.87 −47.36 0.00 −145.38 0.00 0.00 0.00

−47.61 −26.77 −6.07 −2.18 16.69 −4.39 −1.77 −0.64 −23.82 −32.44

83.30 41.09 −16.61 0.00 −86.86 0.00 0.00 0.00

−46.74

56.69

−2.34

0.00

−4.35 −2.70 −2.24

0.00 0.00 0.00

43.72 33.05 −51.92 137.67 57.34 55.19

−5.61 31.05

−10.59 28.58

1.00 25.48

1.59

0.06 28.51 29.82

85.95 89.04 29.80

50.50

58.20 14.36

35.44 30.84

56.07 68.59

93.02

−2.26 4.56 −4.56 −27.56 4.11 15.48 −158.60 −92.60 −66.78 −62.26 −213.00 −72.00 −42.26 −27.03 −14.00 −2.26 1.52 −4.56

0.00

68.59

130.54 64.31 127.32

0.00 5.06

42.00 40.60

−152.76 −47.61 −36.88

33.81 83.30

−46.74

56.69

−2.18 0.97 −4.39 −32.63 5.27 25.44

0.00

−2.34

0.00

0.00

−4.35

0.00

0.00

5.73 7.55

0.00 0.08

75.73

−108.98

22.18

127.32

−47.61 −33.76

83.30

−46.74 −35.96

56.69

0.00

−2.18 2.00 −4.39

0.00

−2.34 3.78 −4.35

0.00

0.00

0.00

0.00 (Continued )

2-332

PHYSICAL AnD CHEMICAL DATA

TABLE 2-161

Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued )

This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group

DHfo

So

DHfs liq.

S s liq.

DHfs solid

S s solid

CHN and CHNO Groups }CH3 corr (quat/quat) C}(2H)(Cd)(SO2) C}(H)(C)(Cd)(SO2) C}(2H)(Cb)(SO2) C}(2H)(Ct)(SO2) Cb}(SO2)(2Cb) Cd}(H)(SO2) Cd}(C)(SO2) Ct}(SO2) SO2}(Cd)(Cb) SO2}(2Cd) SO2}(2C) SO2}(C)(Cb) SO2}(2Cb) SO2}(SO2)(Cb) SO2}(2O) SO2}(C)(Cd) SO2}(Ct)(Cb) O}(SO2)(H) O}(C)(SO2)

−0.64 −29.49 −71.99 −29.80 16.36 15.48 51.58 64.01 177.10 −291.55 −306.70 −288.58 −289.10 −287.76 −325.18 −417.30 −316.80 −296.30 −158.60 −91.40

C}(3H)(F), methyl fluoride C}(3H)(Cl), methyl chloride C}(3H)(Br), methyl bromide C}(3H)(I), methyl iodide C}(C)(3F) C}(2H)(C)(F) C}(H)(2C)(F) C}(3C)(F) C}(H)(C)(2F) C}(2C)(2F) C}(C)(Cl)(2F) C}(H)(C)(Cl)(F) C}(C)(3Cl) C}(H)(C)(2Cl) C}(2H)(C)(Cl) C}(2C)(2Cl) C}(H)(2C)(Cl) C}(3C)(Cl) C}(C)(3Br) C}(H)(C)(2Br) C}(2H)(C)(Br) C}(2C)(2Br) C}(H)(2C)(Br) C}(3C)(Br) C}(C)(3I) C}(H)(C)(2I) C}(2H)(C)(I) C}(2C)(2I) C}(H)(2C)(I) C}(3C)(I) C}(H)(C)(Br)(Cl) N}(C)(2F) C}(H)(C)(Cl)(O) C}(2H)(I)(O) C}(C)(2Cl)(F) C}(C)(Br)(2F) C}(C)(2Br)(F) C}(Br)(Cl)(F) Cd}(H)(F) Cd}(H)(Cl) Cd}(H)(Br) Cd}(H)(I) Cd}(C)(Cl) Cd}(2F) Cd}(2Cl) Cd}(2Br) Cd}(2I) Cd}(Cl)(F) Cd}(Br)(F) Cd}(Cl)(Br) Ct}(F)

−247.00 −81.90 −37.66 14.30 −673.81 −221.12 −204.46 −202.92 −454.74 −411.39 −462.70 −271.14 −81.98 −79.10 −69.45 −79.56 −55.61 −43.70

87.37

−0.64 −49.05

−2.24

25.44

7.55

0.08

−341.14

−356.62

32.10

−305.40 −361.75

CHX and CHXO Groups 231.93 243.60 254.94 263.14 178.22 146.80 55.76

−61.10 −11.70 −709.07

135.56

164.32 74.48 169.45

−487.23 −400.37 −466.00

138.31

202.14 183.28 159.24 95.41 71.34 −24.26 233.05

−112.93 −102.60 −86.90 −101.80 −71.17 −56.78

145.91 128.45 104.27

−21.78

173.31

−42.65

113.00

−10.75 7.26

84.69 −13.46

−27.31 −7.40

108.78 33.54

228.45 177.78

48.74 68.46 −18.45 −32.64 −90.37 15.90 −322.54 −394.55

88.10 −3.21 191.21

4.14

−343.87

−165.12 4.37 50.94 102.36 −5.06 −329.90 −11.51

137.24 147.85 159.91 169.45 62.76 155.63 175.41 199.16

−235.10

175.61 177.82 188.70

141.71 149.70

−12.67 −2.23 −32.08

−85.65

3.65

24.78 48.60

66.53 170.29

−428.77

115.35

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-161

2-333

Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued )

This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group

DHfs liq.

So

DHfo

S s liq.

DHfs solid

S s solid

−191.20 −32.20 19.90 73.70 0.00 −58.41 −55.11 −419.59 −696.66 −44.06 −7.24 −92.56 −225.29 −216.67 −175.49 −117.09 −35.46

54.19 55.47 74.85 61.08 0.00

−194.00 −32.00 13.50 70.40 0.00 −74.75

39.79 43.37 54.45

6.96 25.00 14.00 6.30 0.00 0.00 18.50 40.60 83.55 0.00 0.00 0.00 112.00 6.00 −6.00 8.00 8.00 6.00 10.00 8.50 0.00 34.43 23.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

CHX and CHXO Groups Ct}(Cl) 140.00 Ct}(Br) 151.30 Ct}(I) 35.53 Cb}(F)(2Cb) −181.26 67.52 Cb}(Cl)(2Cb) −17.03 77.08 Cb}(Br)(2Cb) 36.35 88.60 Cb}(I)(2Cb) 94.50 98.26 3.00 0.00 cis corr}(I)(I) C}(2H)(CO)(Cl) −44.26 C}(H)(CO)(2Cl) −40.40 CO}(C)(F) −379.84 C}(Cb)(3F) −691.79 179.08 C}(2H)(Cb)(Br) −29.49 C}(2H)(Cb)(I) 7.31 C}(2H)(Cb)(Cl) −73.79 CO}(C)(Cl) −200.54 176.66 CO}(Cb)(Cl) CO}(C)(Br) −148.54 CO}(C)(I) −83.94 C}(H)(C)(CO)(Cl) −39.88 C}(C)(CO)(2Cl) ortho corr}(I)(I) 7.56 0.00 ortho corr}(F)(F) 20.90 0.00 ortho corr}(Cl)(Cl) 9.50 0.00 ortho corr}(alkyl)(X) 2.51 0.00 cis corr}(Cl)(Cl) −4.00 0.00 cis corr}(CH3)(Br) −4.00 0.00 ortho corr}(F)(Cl) 13.50 0.00 ortho corr}(F)(Br) 37.25 0.00 ortho corr}(F)(I) 85.40 0.00 meta corr}(I)(I) 0.00 0.00 meta corr}(COCl)(COCl) 0.00 0.00 ortho corr}(COCl)(COCl) 0.00 0.00 ortho corr}(F)(CF3) 111.00 0.00 meta corr}(F)(CF3) 2.00 0.00 ortho corr}(F)(CH3) −3.30 0.00 ortho corr}(F)(F’) 8.00 0.00 ortho corr}(Cl)(Cl’) 8.00 0.00 meta corr}(F)(F) 0.00 0.00 meta corr}(Cl)(Cl) −5.00 0.00 ortho corr}(Cl)(CHO) −6.75 0.00 ortho corr}(F)(COOH) 20.00 0.00 ortho corr}(Cl)(COCl) 0.00 0.00 ortho corr}(F)(OH) 25.50 0.00 ortho corr}(Cl)(COOH) 0.00 0.00 ortho corr}(Br)(COOH) 0.00 0.00 ortho corr}(I)(COOH) 0.00 0.00 ortho corr}(NH2)(NH2) −10.00 0.00 meta corr}(NH2)(NH2) 0.00 0.00 ortho corr}(OH)(Cl) 7.50 0.00 cis corr}(CH3)(I) −4.00 0.00 *Domalski, E. S., and E. D. Hearing, J. Phys. Chem. Ref. Data, 22 (1993): 805.

isodesmic with 12 single bonds and 1 double bond in both reactants and products. To use this method, one devises an isodesmic reaction involving the compound for which ∆H of is to be determined with other compounds for which experimental ∆H of values are available. Ab initio calculations are performed on all the participating compounds, all at the same level of theory and basis set size, to obtain the enthalpy for each at 298.15 K. The enthalpy of reaction is then calculated from ∆H rxn = ∑ν i H i

(2-32)

where ni = stoichiometric coefficient of i (+ for products, − for reactants). The enthalpy of reaction is also related to DHfo by

0.00

−212.99

5.50 25.50 8.50 0.00 0.00 0.00 19.50 42.50 85.20 20.08 16.06

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 8.00 8.00 8.50 4.00 0.00 20.00 0.00 20.00 20.00 20.00 20.00 0.00 14.00 11.00 0.00

Input information: The isodesmic reaction shown above will be used. The recommended DHfo values from DIPPR 801 for the other three compounds are as follows: Acetone

Methane

Ethane

−215.70 kJ/mol

−74.52 kJ/mol

−83.82 kJ/mol

Ab initio calculations of enthalpy: With structures optimized using HF/6-31G(d) model chemistry and energies calculated with B3LYP/6-311+G(3df,2p), the following enthalpies are obtained (including the zero-point energy): Acetone

Methane

Ethane

Acetaldehyde

−5.071 × 105 kJ/mol −1.063 × 105 kJ/mol −2.095 × 105 kJ/mol −4.039 × 105 kJ/mol Calculation using Eq. (2-32): DHrxn = (−1.063 − 5.071 + 2.095 + 4.039) × 105 kJ/mol = − 41.67 kJ/mol

∆H rxn = ∑ν i (∆H of )i

(2-33)

Calculation using Eq. (2-33): ∆H of ,acetaldehyde = ∆H of ,acetone + ∆H of ,methane − ∆H of ,ethane − ∆H rxn

o f

With experimental values available for all ∆H except the desired compound, its value can be back-calculated from Eq. (2-33). Example Estimate the standard ideal gas enthalpy of formation of acetaldehyde.

∆H of ,acetaldehyde = ( − 215.70 − 74.52 + 83.82 + 41.67)

kJ kJ = −164.73 mol mol

The estimated value is 1.0 percent above the DIPPR 801 recommended value of −166.40 kJ/mol.

2-334

PHYSICAL AnD CHEMICAL DATA

Entropy Absolute or third-law entropies (relative to a perfectly ordered crystal at 0 K) of a compound in its standard state Ss or of an ideal gas So at 298.15 K and 1 bar can be found in various literature sources (DIPPR, JANAF, TRC, SWS, and TDB). Very good estimates for Ss or So can be obtained by using the Domalski-Hearing method. Excellent So values can also be obtained from statistical mechanics by using experimental vibrational frequencies or values of the frequencies generated from computational chemistry. The standard ∆S sf and ideal gas ∆S of entropies of formation at 298.15 K and 1 bar are related to the standard entropies by nA

s s ∆S sf = Scompound − ∑ν i Selement, i i =1

nA

o s ∆S of = Scompound − ∑ν i Selement, i

(2-34)

i =1

is the absolute entropy of element i in its standard state at where S 298.15 K and 1 bar. Recommended Method Domalski-Hearing method. Reference: Domalski, E. S., and E. D. Hearing, J. Phys. Chem. Ref. Data, 22 (1993): 805. Classification: Group contributions. Expected uncertainty: 3 percent. Applicability: Organic compounds for which group contributions have been regressed. Input data: Molecular structure. Description: See description given under Enthalpy of Formation above. s element,i

Example Calculate So for ammonia.

Structure: NH3. Input data: M = 17 kg/kmol. McQuarrie [McQuarrie, D. A., Statistical Mechanics, Harper & Row, New York, 1976] gives the following 3nA − 6 + d = 12 − 6 + 0 = 6 characteristic vibrational temperatures (in K): 1360, 2330, 2330, 4800, 4880, 4880. The characteristic rotational temperatures given by McQuarrie are QA = 13.6 K, QB = 13.6 K, and QC = 8.92 K. For NH3, s = 3. Vibrational contribution: The table below shows a spreadsheet calculation of the vibrational terms inside the summation sign in Eq. (2-35). Qj/K

Qj/(298.15 K)

1207.91 1850.16 1850.16 3688.19 3821.36 3821.36

4.051 6.205 6.205 12.370 12.817 12.817

Svib 0.08929 0.01457 0.01457 0.00006 0.00004 0.00004 Sum 0.1186

Rotational contribution: 1/2  1    (298.15 K)3π e 3 Sr = ln  ⋅    = 5.81593 R 3 (13.6 K)(13.6 K)(8.92 K)     

Calculation using Eq. (2-35):

Example Estimate the standard and ideal gas entropies of formation of o-toluidine. Standard state entropies: Estimation of Ss and So using the Domalski-Hearing method was illustrated above in the Enthalpy of Formation section. The standard entropies of formation can be obtained from the values determined in that example. Formula: C7H9N. The standard entropies of the elements from the DIPPR 801 database are as follows: Compound νi Sis/[J(kmol ⋅ K)]

N2

H2

C, graphite

1/2 1.9151 × 105

9/2 1.3057 × 105

7 5740

5 1 9   10 J ∆S sf =  2.2656 −   (1.9151) −   (1.3057) − (7)(0.0574)   2  2   kmol ⋅ K

J kmol ⋅ K 5 1 9   10 J ∆S of =  3.6832 −   (1.9151) −   (1.3057) − (7)(0.0574)      2 2  kmol ⋅ K  J = −3.552 ⋅10 5 kmol ⋅ K = −4.969 ⋅10 5

∆G of = ∆H of − T ∆S of

Recommended Method Statistical mechanics. Classification: Theory and computational chemistry. Expected uncertainty: 0.2 percent if vibrational frequencies (or their characteristic temperatures) are experimentally available; uncertainty depends upon model chemistry if frequencies are determined from computational chemistry, but generally within about 5 percent. Applicability: Ideal gases. Input data: M; σ (external symmetry number); characteristic rotational temperature(s) (ΘA for linear molecules; ΘA, ΘB, and ΘC for nonlinear molecules); and 3nA − 6 + d characteristic vibrational temperatures Qj. Description: For harmonic frequencies, the rigorous temperature dependence of So is given by So 3  M  Sr = ln 6175 + kg/kmol  R R 2  +

∑ j =1

 Θ j  Θ j /T −Θ /T  − 1)−1 − ln (1 − e j )   T  (e  

0 nonlinear where δ =  1 linear   1  πT 3e 3  1/2  ln     nonlinear S r   σ  Θ A Θ B ΘC   and =  R   Te   linear ln     σΘ A  

The calculated value differs from the DIPPR 801 recommended value of 1.927 × 105 J/(kmol ⋅ K) by 0.5 percent.

Gibbs Energy of Formation The standard Gibbs energy of formation is the Gibbs energy change upon formation of 1 mole of the compound in its standard state from its constituent elements in their standard states. The standard Gibbs energy of formation DGfs uses the naturally occurring phase at 298.15 K and 1 bar as the standard state, while the ideal gas Gibbs energy of formation DGfo uses the compound in the ideal gas state at 298.15 K and 1 bar as the standard state. In both cases, the standard state for the elements is their naturally occurring state of aggregation at 298.15 K and 1 bar. Sources for data include DIPPR, TRC, JANAF, and TDB. The Gibbs energies of formation are related to the corresponding enthalpies and entropies of formation by

Entropies of formation can be calculated from these values by using Eq. (2-34):

3 n A − 6+δ

o S 298 3 = ln (6175.17) + 5.81593 + 0.1186 = 23.277 R 2 J o = 1.935 × 10 5 S 298 kmol ⋅ K

(2-35)

and

∆G sf = ∆H sf − T ∆S sf

(2-36)

and predicted values of ∆G sf and ∆G of are obtained from Eq. (2-36) by estimating the enthalpies and entropies of formation as shown above. LATEnT EnTHALPY Enthalpy of Vaporization The enthalpy (heat) of vaporization DHυ is the difference between the molar enthalpies of the saturated vapor and saturated liquid at a temperature between the triple point and critical point (at the corresponding vapor pressure). Variable ∆Hυ is related to the vapor pressure P* by the thermodynamically exact Clapeyron equation ∆H υ = − R ∆Zυ

d ln P ∗ d ln P ∗ = RT 2 ∆Zυ dT d (1/T )

(2-37)

where ∆Zυ = ZG − ZL, ZG = Z of saturated vapor, and ZL = Z of saturated liquid. Experimental heats of vaporization can be effectively correlated with 2

∆H υ = A (1 − Tr ) B + CTr + DTr

+ ETr3

(2-38)

A simple method for obtaining DHυ at one temperature from a known value at a reference temperature, say at the normal boiling point, is to truncate Eq. (2-38) after the B term, set B = 0.38, and take a ratio of the ∆Hυ values at the two conditions to give the Watson [Thek, R. E., and L. I. Stiel, AIChE J., 12 (1966): 599; 13 (1967): 626] correlation  1 − Tr  ∆H υ = ∆H υ , ref    1 − Tr , ref 

0.38

(2-39)

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES If an accurate correlation for P* and accurate values for ZG and ZL are available, Eq. (2-37) is the preferred method for obtaining enthalpies of vaporization. Otherwise, the CS methods shown below should be used. Recommended Method 1 Vapor pressure correlation. Classification: Extension of theory. Expected uncertainty: The uncertainty varies significantly with temperature and with the quality and temperature range of the vapor pressure data used in the correlation. Applicability: Organic compounds for which group contributions have been regressed. Input data: Correlations for P*, ZG, and ZL. Description: An expression for DHυ can be obtained from Eq. (2-37) by using an appropriate vapor pressure correlation. If one differentiates the Riedel vapor pressure correlation, Eq. (2-26), in accordance with Eq. (2-37), one obtains the heat of vaporization as DHυ = R DZυ (−B + CT + DET E+1)

(2-40)

The ZG and ZL values can be evaluated using the methods given in the section on densities below. Example Calculate DHυ for anisole at 452 K. Input data: The vapor pressure coefficients in the DIPPR 801 database for Eq. (2-26) are A = 128.06

B = −9307.7

C = −16.693

D = 0.014919

E=1

The vapor pressure at 452 K is therefore  P∗  9307.7 − 16.693 ln ( 452 ) + 0.014919 (452)1 = 12.155 ln   = 128.06 −  Pa  452

2-335

Auxiliary quantities: From the previous example, the reduced temperature variables are Tr = 0.7

t = 1 − 0.7 = 0.3

Calculation using Eq. (2-41): ∆H υ = 7.08(0.3)0.354 + 10.95 (0.35017)(0.3)0.456 = 6.838 RTc J  kJ ∆H υ = (6.838)  8.314  (645.6 K) = 36.70  mol ⋅ K  mol ⋅ K This value is 2.2 percent below the DIPPR 801 recommended value of 37.51 kJ/(mol ⋅ K).

Enthalpy of Fusion The enthalpy (heat) of fusion DHfus is the difference between the molar enthalpies of the equilibrium liquid and solid at the melting temperature and 1.0 atm pressure. There is no generally applicable, high-accuracy estimation method for DHfus, but the GC method of Chickos can be used to obtain approximate results if the melting temperature is known. Recommended Method Chickos method. Reference: Chickos, J. S., C. M. Braton, D. G. Hesse, and J. R. Liebman, J. Org. Chem., 56 (1991): 927. Classification: QSPR and group contributions. Expected uncertainty: Considerable variation but generally less than 50 percent. Applicability: Only valid at the melting temperature. The method is based on the DSfus between a solid at 0 K and the liquid at the Tm so no solid-solid transitions are taken into account. Values of DHfus will be overestimated if there are solid-solid transitions for the actual material. Input data: Tm and molecular structure. Description:

P ∗ = exp (12.155) ⋅ Pa = 1.901 × 10 5 Pa Determine DZ: Required data from the DIPPR 801 database for this calculation are Tc = 645.6 K, Pc = 4.25 MPa, and w = 0.35017. These values are used to determine the reduced conditions, Tr =

452 = 0.7 645.6

Pr =

no nonaromatic rings  0 a= N N N 35.19 + 4.289( − 3 ) nonaromatic rings R CR R 

0.1901 = 0.045 4.25

and the values of ZG and ZL from the Lee-Kesler corresponding states method as discussed in the section on density. Interpolation of the Pr values in Tables 2-169 and 2-170 at a Tr of 0.7 gives ZG(0) = 0.9904 +

0.045 - 0.010 (0.9504 − 0.9904) = 0.9554 0.050 - 0.010

ZG(1) = − 0.0064 +

0.045 − 0.010 ( − 0.0507 + 0.0064) = −0.0452 0.050 − 0.010

ZG = ZG(0) + ω ZG(1) = 0.9554 + (0.35017)( − 0.0452) = 0.94 At this low pressure, ZL is very small compared to ZG and may be neglected; so DZV = ZG − ZL = 0.94 Calculation using Eq. (2-40): J  2 ∆H υ =  8.314  (0.94)[9307.7 − (16.693) (452) + (0.014919) (1)(452) ]  mol ⋅ K  = 37.59

kJ mol ⋅ K

This value is 0.2 percent higher than the value of 37.51 kJ/(mol ⋅ K) obtained from the DIPPR 801 database.

Recommended Method 2 Corresponding states correlation. Reference: [PGL5], p. 7.18. Classification: Corresponding states. Expected uncertainty: Less than about 6 percent. Applicability: Organic compounds. Input data: Tc, Pc, and w. Description: The following correlation is used: ∆H υ = 7.08τ 0.354 + 10.95ωτ 0.456 RTc

where τ = 1 − Tr

Example Repeat the above calculation for anisole’s DHυ at 452 K. Input data: Tc = 645.6 K, Pc = 4.25 MPa, and w = 0.35017.

∆H fus ∆S fus  Tm  =   = (Tm /K) (a + b) J/mol J/(mol ⋅ K)  K 

ng

ns

nf

i =1

j =1

k =1

b = ∑ Ng i ∆si + ∑ Ns jCs j ∆s j + ∑ Nf kCt k ∆s k

(2-42)

(2-43)

(2-44)

where  Ngi = number of C—H groups of type i bonded to other carbon atoms ng = number of different nonring or aromatic C—H groups bonded to other carbon atoms Nsj = number of C—H groups of type j bonded to at least one functional group or atom ns = number of different nonring or aromatic C—H groups bonded to at least one functional group or atom Nf k = number of functional groups of type k nf = number of different functional groups or atoms t = total number of functional groups or atoms with the exception that F atoms count as one regardless of number of occurrences Csj = value from Table 2-162 for C—H group j bonded to at least one functional group or atom Ctk = value from Table 2-163 for functional group k NR = number of nonaromatic rings NCR = number of —CH2— groups in nonaromatic ring(s) required to form cyclic paraffin of same ring size(s) Dsi = contribution from Table 2-162 for group i Dsk = contribution from Table 2-163 for group k Note that nonaromatic ring —CH2 groups are accounted for in the a term and are not included in the b term. Example Calculate DHfus at the melting point for (a) benzothiophene, (b) furfuryl alcohol, and (c) cis-crotonaldehyde. Structures:

(2-41)

2-336

PHYSICAL AnD CHEMICAL DATA

TABLE 2-162

Cs (C}H) Group Values for Chickos Estimation* of DHfus

Group

Description

Group

Ds

Cs

}CH3 methyl 1.0 >CH2 methylene 1.0 >CH} secondary C 0.69 >C< tertiary C 0.67 CH2= terminal alkene 1.0 }CH= alkene 3.23 >C= subst. alkene 1.0 ≡CH term. alkyne 1.0 ≡C} alkyne 1.0 *Chickos, J. S., et al., J. Org. Chem., 56 (1991): 927.

18.33 9.41 −16.91 −38.70 14.56 4.85 −11.38 10.88 2.18

}CHAr }CAr} }CAr} }CAr} >CrH} >Cr < }CrH= >Cr= ≡Cr} or =Cr=

Description aromatic C ar. C bonded to paraffinic C ar. C bonded to olefinic C or non-C group ar. C bonded to acetylinic C ring structure ring structure ring structure ring structure ring structure

(a) t = 1 (1 total “functional group”), so the C1 column in Table 2-163 is used. NR = 1 Group =CH} =C} =C} =CH} =CH} }S}

NCR = 5

a = 35.19 + (5 − 3)(4.289) = 43.77

Description

N

C

aromatic (Ng type) ring (Ng type) ring (Ns type) ring (Ng type) ring (Ns type) ring

4 1 1 1 1 1

1 1 0.86 1 0.62 1

Tm = 258.52 K

Cs

Ds

1.0 1.0 1.0 1.0 0.76 1.0 0.62 0.86 1.0

6.44 −10.33 −4.27 −2.51 −15.98 −32.97 −4.35 −11.72 −5.36

from DIPPR 801 database

DHfus = (Tm/K)(a + b) J/mol = (258.52)(43.77 + 3.51) J/mol = 12.22 kJ/mol

Ds

Total

6.44 −11.72 −11.72 −4.35 −4.35 2.18

25.76 −11.72 −10.08 −4.35 −2.70 2.18 Total −0.91

This value is 7 percent lower than the DIPPR 801 recommended value of 13.13 kJ/mol. (c) t = 1 a=0 NR = 0 Group

Description

N

C

Ds

Total

}CH3 =CH} =CH} }CHO

nonring (Ng type) nonring (Ng type) nonring (Ns type) aldehyde

1 1 1 1

1 1 3.23 1

18.33 4.85 4.85 19.66

18.33 4.85 15.67 19.66 Total

Tm = 304.5 K

from DIPPR 801 database DHfus = (Tm /K)(a + b) J/mol = (304.5)(43.77 − 0.91) J/mol = 13.05 kJ/mol This value is 10 percent higher than the DIPPR 801 recommended value of 11.83 kJ/mol. (b) t = 2 (2 total “functional groups”), so the C2 column in Table 2-163 is used. NR = 1 Group

NCR = 5

a = 35.19 + (5 − 3)(4.289) = 43.77

Description ring (Ng type) ring (Ns type) ring (Ns type) ring ether Ns type alcohol

=CH} =CH} =C< =O} }CH2} }OH

N

C

2 1 1 1 1 1

1 0.62 0.86 1 1 12.6

Total

−4.35 −4.35 −11.72 1.34 9.41 1.13

−8.70 −2.70 −10.08 1.34 9.41 14.24

Ct (Functional) Group Values for Chickos Estimation*

Group

Description

C1

C2

C3

C4

Ds

}OH }OH }O} }O} >C=O >C=O }CHO }COOH }COO} }NH2 }NH2 >NH >NH >N} >N} =N} =N} }CN }NO2 }CONH2 }CONH} }SH }S} }S} }SO2 }F }F }F }Cl }Br }I

alcohol phenol nonring ether ring ether nonring ketone ring ketone aldehyde acid ester aliphatic aromatic nonring ring nonring ring ring aromatic nitrile nitro primary amide secondary amide

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

12.6 1.0 1.0 1.0 1.0 1.0 1.0 1.83 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.4 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 2.0 1.0 1.0

18.9 1.0 1.0 1.0

26.4 1.0 1.0 1.0

1.13 16.57 1.09 1.34 3.14 −1.88 19.66 14.90 3.68 16.23 15.48 −2.18 1.84 −15.90 −17.07 1.67 7.32 9.62 17.36 26.19 −0.42 17.99 7.20 2.18 3.26 14.73 13.01 15.90 8.37 17.95 16.95

nonring ring nonring on aliph. C on olefinic C on ring C

*Chickos, J. S., et al., J. Org. Chem., 56 (1991): 927.

1.88 1.0

1.72 1.0

1.0 1.0

0.36 1.0 1.0 1.0 2.0 1.0

1.0 1.0 1.0 1.93 0.82

from DIPPR 801 database

DHfus = (Tm/K)(a + b) J/mol = (158.38)(0 + 58.51) J/mol = 9.27 kJ/mol This value is 5 percent higher than the DIPPR 801 recommended value of 8.86 kJ/mol.

Ds

Total 3.51

TABLE 2-163 of DH fus

Tm = 158.38 K

58.51

Enthalpy of Sublimation The enthalpy (heat) of sublimation DHsub is the difference between the molar enthalpies of the equilibrium vapor and solid along the sublimation curve below the triple point. The effects of pressure on DHsub and melting temperature are very small so that Tt and the normal melting point are nearly equal and DHsub(Tt) = DHυ (Tt) + DHfus(Tt)

(2-45)

Equation (2-45) can be used to estimate DHsub at the triple point if DHυ is accurately known at Tt. Because DHυ is usually obtained from Eq. (2-37), DHυ(T) correlations may be less accurate near Tt where P*(Tt) is very small and difficult to measure. In this case, it is better to estimate DHsub directly by using the following recommended method. DHsub is only a weak function of temperature and can generally be treated as a constant from the triple point temperature down to the first solid-solid phase transition. Recommended Method Goodman method. Reference: Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley, Int. J. Thermophys. 25 (2004): 337. Classification: QSPR and group contributions. Expected uncertainty: 6 percent. Applicability: Organic compounds for which group contributions have been regressed. Input data: Molecular structure and radius of gyration RG. Description: N N N R n ∆H sub (Tt ) = 698.04 + 3.83798 × 1012  G  + ∑ ni ai + ∑ ni2βi + ∑ i f i  m  i =1 RK n i =1 x i =1

(2-46)

where ai = GC values from Table 2-164 bi = nonlinear corrections for >CH2 and Ar—CH = groups fi = halogen corrections nx = total number of all halogen and hydrogen atoms attached to C and Si atoms Example Calculate DHsub and the solid vapor pressure for 1,2,3-trichlorobenzene

at 301.15 K. Structure:

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-164

Group Contributions and Corrections* for DHsub

Group

Description

736.5889 561.3543 111.0344 −800.517 572.6245 541.2918 117.9504 626.7621 348.8092 763.284 1317.056 911.2903 970.4474 3278.446 2402.093

Nonlinear terms

>C=O }COO} }COOH }NH2 }NH} >N} }NO2 }SH }S} }SS} }F }Cl }Br >Si< >Si(O})}

9.5553 −2.21614

Description

ai

ketone ester acid primary amine sec. amine tertiary amine nitro thiol/mercaptan sulfide disulfide fluoride chloride bromide silane siloxane

1816.093 2674.525 5006.188 2219.148 1561.222 325.9442 3661.233 1921.097 1930.84 2782.054 626.4494 1243.445 669.9302 −83.7034 −16.0597

Halogen correction terms

bi

methylene aromatic C

>CH2 Ar}CH=

Group

ai

methyl methylene secondary C tertiary C terminal alkene alkene substituted alkene aromatic C subst. aromatic C furan O pyridine N thiophene S ether alcohol aldehyde

}CH3 >CH2 >CH} >C< CH2= }CH= >C= Ar }CH= Ar >C= Ar }O} Ar }N= Ar }S} }O} }OH }COH

2-337

fi

F fraction Cl fraction Br fraction

}F }Cl }Br

−1397.4 −1543.66 5812.49

*Goodman, B., et al., Int. J. Thermophys., 25 (2004): 337.

Group contributions:

2

Linear groups

 A4 /T   A2 /T  C Po = A0 + A1    + A3   cosh(A4 /T )   sinh(A2 /T ) 

Nonlinear and correction terms

Group

ni

ai

Group

ni

bi

Ar}CH=

3

626.7621

Ar }CH=

3

−2.21614

Ar >C=

3

348.8092

}Cl

3

}Cl

3

nx

6

1243.445

(2-48)

fi −1543.66

and a polynomial form (generally fourth-order)

∑ ni ai = 6657.049

C Po =

4

∑ AT

i

(2-49)

i

i = 0

i

Input data: The value of RG from the DIPPR 801 database is 4.455 × 10−10 m. Calculation using Eq. (2-46): ∆H sub (Tt ) = 698.04 + (3.838 × 1012 )(4.455 × 10 −10 ) RK 3 + 6657.05 + (3 2 )(−2.21614) +   (−1543.66)  6  kJ  kJ = 68.78 ∆H sub (Tt ) = (8273 K)  0.008314 mol ⋅ K  mol  The estimated value is 5.6 percent above the DIPPR 801 recommended value of 65.11 kJ/mol. Estimate the solid vapor pressure at 301.15 K: The solid vapor pressure can be calculated from Eq. (2-30) by using the estimated DHsub and one additional solid vapor pressure point. In this example the triple point temperature and vapor pressure (Tt = 325.65 K; Pt* = 182.957 Pa) from the DIPPR 801 database are used in Eq. (2-30): ln

2

Ideal gas heat capacities may also be estimated from several techniques, of which two of the most accurate and commonly used are recommended here. Recommended Method 1 Statistical mechanics. Reference: Rowley, R. L., Statistical Mechanics for Thermophysical Property Calculations, Prentice-Hall, Englewood Cliffs, N.J., 1994. Classification: Theory and computational chemistry. Expected uncertainty: 0.2 percent if vibrational frequencies (or their characteristic temperatures) are experimentally available; accuracy depends upon model chemistry if frequencies are determined from computational chemistry, but generally within 3 percent. Applicability: Ideal gases. Input data: 3nA − 6 + d vibrational frequencies nj, or the corresponding characteristic vibrational temperatures Qj. The two are related by (2-50)

Qj = hnj /k

Description: For harmonic frequencies, the rigorous temperature dependence of C Po is given by

68.78 kJ/mol P∗  1 − 325.65  = −2.067 =   182.957 Pa [0.008314 kJ/(mol ⋅ K)](325.65 K)  301.15 

2

P* = (182.957 Pa) [exp(−2.067)] = 23.16 Pa The estimated value is 0.3 percent above the DIPPR 801 recommended value of 23.09 Pa.

HEAT CAPACITY

Θ /T  C Po 8 − δ 3 n A −6+δ  Θ j   e j = + ∑    Θ j /T 2    R 2 T − e ( 1) j =1  

0 δ = 1

nonlinear linear

(2-51)

Example Calculate the ideal gas heat capacity of ammonia at 300 K.

The isobaric heat capacity CP is defined as the energy required to change the temperature of a unit mass (specific heat) or mole (molar heat capacity) of the material by one degree at constant pressure. Typical units are J/(kg ⋅ K). Gases The isobaric heat capacity of a gas is related rigorously to the ideal gas value C Po by 2 P ∂ V  C P = C Po − T ∫  2  dP 0  ∂T  P

(2-47)

The second term, giving the deviation of the real fluid heat capacity from the ideal gas value, can be neglected at low to moderate pressures, or it can be calculated directly from an appropriate EoS. Ideal gas heat capacities are available from several sources (DIPPR, JANAF, TRC, and SWS). Two common correlating equations for C Po are the Aly-Lee equation [Aly, F. A., and L. L. Lee, Fluid Phase Equilib., 6 (1981): 169]

Structure:

Input data: McQuarrie (McQuarrie, D. A., Statistical Mechanics, Harper & Row, New York, 1976) gives the following 3nA − 6 + d = 12 − 6 + 0 = 6 characteristic vibrational temperatures (in K): 1360, 2330, 2330, 4800, 4880, and 4880. Alternatively, a computational chemistry package gives the following scaled frequencies for HF/6-31G+ model chemistry (1013 Hz): 3.24, 4.97, 4.97, 9.90, 10.26, and 10.26. Calculation: The table on the left uses the experimental Q values to determine the individual terms in the summation of Eq. (2-51). The table on the right uses the scaled frequencies from computational chemistry software and Eq. (2-50) to obtain Q values and the individual terms in Eq. (2-51).

2-338

PHYSICAL AnD CHEMICAL DATA HF/6-31G+ scaled frequencies*

Experimental frequencies Q/K 1360 2330 2330 4800 4880 4880

Q/(300 K) 4.533 7.767 7.767 16.000 16.267 16.267

Term

nscaled/10 Hz

Q/K

0.2256 0.0256 0.0256 0.0000 0.0000 0.0000

3.24 4.97 4.97 9.90 10.26 10.26

1555.0 2385.3 2385.3 4751.4 4924.2 4924.2

13

Q/(300 K) 5.183 7.951 7.951 15.838 16.414 16.414

Term 0.1524 0.0223 0.0223 0.0000 0.0000 0.0000

Sum: 0.2768 Sum: 0.1970 *Empirical scaling factors have been developed for each model chemistry to help correct theoretical frequencies for anharmonic effects [Scott, A. P., and L. Radom, J. Phys. Chem., 100 (1996): 16502].

Danner, AIChE J., 23 (1977): 944] and thermodynamic differentiation. The Ruzicka-Domalski method is generally accurate at low temperature, but the cubic behavior can overestimate the temperature rise at higher temperatures. The Lee-Kesler method is accurate for nonpolar and slightly polar fluids, but has less accuracy for strongly polar or associating fluids. Recommended Method 1 Ruzicka-Domalski. References: Ruzicka, V., and E. S. Domalski, J. Phys. Chem. Ref. Data, 22 (1993): 597, 619. Classification: Group contributions. Expected uncertainty: 4 percent. Applicability: Organic compounds for which group values are available. Input data: Molecular structure and Table 2-166 values. Description: Groups are summed to find the temperature coefficients for a cubic polynomial correlation:

From experimental frequencies:

 T   T  = A+ B   + D  100 K  R    100 K 

Cp

8 J  J C Po =  + 0.2768  R = (4.2768)  8.3143  = 35.56   2 mol ⋅ K  mol ⋅ K

N

A = ∑ ni ai

From computational chemistry frequencies:

i =1

8 J  J C Po =  + 0.197  R = (4.197)  8.3143  = 34.90   2 mol ⋅ K  mol ⋅ K The value calculated from experimental frequencies is 0.1 percent lower than the DIPPR 801 recommended value of 35.61 J/(mol ⋅ K); the value calculated from frequencies generated from computational chemistry software is 2.0 percent lower than the DIPPR 801 value.

Recommended Method 2 Benson method as implemented in CHETAH program. References: Benson, S. W., et al., Chem. Rev., 69 (1969): 279; CHETAH Version 8.0: The ASTM Computer Program for Chemical Thermodynamic and Energy Release Evaluation (NIST Special Database 16). Classification: Group contributions. Expected uncertainty: 4 percent. Applicability: Ideal gases of organic compounds. Input data: Table 2-165 group values at the seven specified temperatures. Description: Groups are summed at each individual temperature: N

C Po = ∑ ni ⋅ (C op )i

(2-52)

N

B = ∑ ni bi i =1

2

(2-53) N

D = ∑ ni di

(2-54)

i =1

where ni = number of occurrences of group i and ai, bi, di = individual group contributions. Example Estimate the liquid heat capacity for 2-methyl-2-propanol at 340 K. Structure:

Group contributions: Group

ni

C } (3C, O) (alcohol) O } (H)(C) C } (3H)(C)

1 1 3

ai −44.690 12.952 3.8452

Sum   −20.202

i =1

where ni = number of occurrences of group i and (C Po )i = individual group contribution. Either Eq. (2-48) or Eq. (2-49) can be used to interpolate between the discrete temperatures.

J  C p =  8.3143   mol ⋅ K  = 254.16

Example Calculate the ideal gas heat capacity of isoprene (2-methyl-1,3-butadiene)

at 400 K. Structure:

bi

di

31.769 −10.145 −0.33997

−4.8791 2.6261 0.19489

20.604

−1.668

2   304  − 1.668  340        −20.202 + 20.604     100  100 

J mol ⋅ K

This value is 0.7 percent higher than the DIPPR 801 recommended value of 252.40 J/(mol ⋅ K).

Group identification and values: Group

No.

Value, J/(mol ⋅ K)

Contribution, J/(mol ⋅ K)

=CH2

2

26.62

=C}(2C)

1

19.3

53.24 19.3

}CH3}(=C)

1

32.82

32.82

=CH}(C)

1

21.05

Recommended Method 2 Lee-Kesler. References: [PGL5] Classification: Corresponding states. Expected uncertainty: 4 percent. Applicability: Organic compounds other than those that are strongly polar or associate. Input data: Tc, w, and the ideal gas heat capacity at the same temperature. Description: The isobaric liquid heat capacity is calculated at the reduced temperature Tr using

21.05 Total

Cp

126.41

R

=

C op R

+ 1.586 +

 6.3(1 − Tr )1/3 0.4355  0.49 + ω  4.2775 + +  1 − Tr  1 − Tr Tr 

(2-55)

The value of 126.4 J/(mol ⋅ K) is 3.1 percent below the DIPPR 801 recommended value of 130.4 J/(mol ⋅ K).

Example Calculate the isobaric liquid heat capacity for 1,4-dioxane at 320 K.

Liquids Liquid isobaric heat capacity increases with increasing temperature, although a minimum occurs near the triple point for many compounds. Usually liquid heat capacity is correlated as a function of temperature with a polynomial equation; a third-order polynomial is usually adequate. Estimation of liquid heat capacity can be done by using a number of methods [Ruzicka, V., and E. S. Domalski, J. Phys. Chem. Ref. Data, 22 (1993): 597, 619; Chueh, C. F., and A. C. Swanson, Chem. Eng. Prog., 69, 7 (1973): 83; Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510; Tarakad, R. R., and R. P.

Auxiliary data: From the DIPPR 801 database: Tc = 597.0 K, w = 0.2793, and C /R = 11.94. The reduced temperature is therefore Tr = (320 K)/(597.0 K) = 0.536. From Eq. (2.55), o p

Cp R

= 11.94 + 1.586 +

1/3  0.49 6.3 (1 − 0.536 ) 0.4355  + (0.2793)  4.2775 + +  = 18.58 1 − 0.536 0.536 1 − 0.536  

and Cp = 154.5 J/(mol ∙ K). This is 4.6 percent below the DIPPR recommended value of 162.0 J/(mol ∙ K).

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-165

2-339

Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity

Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide; Nim = imino. Group

298 K

400 K

500 K

600 K

800 K

1000 K

1500 K

45.17 45.17 45.17 45.17 45.21 45.17 45.17 45.17 45.17 45.17 45.17 45.17 45.17 45.17

54.5 54.5 54.5 54.5 54.42 54.54 54.54 54.54 54.54 54.5 54.5 54.5 54.5 54.5

61.83 61.83 61.83 61.83 61.95 61.83 61.83 61.83 61.83 61.83 61.83 61.83 61.83 61.83

73.59 73.59 73.59 73.59 73.67 73.59 73.59 73.59 73.59 73.59

20.59 19.42 17.12 20.59 38.51 37.67 35.79 28.76 38.93 53.16

22.35 20.93 19.25 22.35 39.77 39.35 38.3 31.27 40.18 56.93

23.02 21.89 20.59 23.02 40.6 40.18 39.85 33.32 41.02 59.86

24.28 23.32 26.58 24.28

37.8 39.14 38.17 40.18 40.98 40.98 63.71 40.18 41.9 39.77 38.01 39.35 39.47 36.84 38.34 41.73 39.72 41.36 40.1 38.72 40.85

45.46 46.34 43.2 47.3 49.35 49.77 72.58 47.3 48.1 46.46 45.46 46.46 46.5 44.58 45.84 51.32 46.97 48.3 47.17 45.92 50.98

51.74 51.65 47.26 52.74 55.25 55.25 78.82 52.74 52.49 51.07 51.03 51.49 51.61 49.94 51.15 59.23 52.24 53.29 52.49 51.28 59.48

36.63 35.12 32.57 35.16 36.54 35.5 36.38 34.28 33.7 31.77

40.73 41.11 38.09 40.18 41.06 40.35 41.44 39.6 38.97 35.41

42.9 43.99 41.44 42.7 43.53 43.11 44.24 42.65 42.07 38.97

25.53 36.75 27.17 19.97 33.07 32.23 27.17 27.63 34.11 34.58 33.99

27.63 38.47 30.43 25.2 35.58 34.32 30.43 31.56 36.5 37.34 36.71

28.46 37.51 31.69 26.71 35.58 34.49 31.23 33.32 33.91 37.51 36.67

CH3 Groups CH3}(Cb) CH3}(CO) CH3}(Ct) CH3}(C) CH3}(N) CH3}(O) CH3}(PO) CH3}(P) CH3}(P=N) CH3}(Si) CH3}(SO2) CH3}(SO) CH3}(S) CH3}(=C)

25.91 25.91 25.91 25.91 25.95 25.91 25.91 25.91 25.91 25.91 25.91 25.91 25.91 25.91

32.82 32.82 32.82 32.82 32.65 32.82 32.82 32.82 32.82 32.82 32.82 32.82 32.82 32.82

39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35

73.59

Ct Groups Ct}(Cb) Ct}(Ct) Ct}(C) Ct}(=C) CtBr CtCl CtF CtH CtI Ct(CN)

10.76 14.82 13.1 10.76 34.74 33.07 28.55 22.06 35.16 43.11

14.82 16.99 14.57 14.82 36.42 35.16 31.65 25.07 36.84 47.3

14.65 18.42 15.95 14.65 37.67 36.42 33.99 27.17 38.09 50.65

41.77 37.04 64.04

CH2 Groups CH2}(2CO) CH2}(2C) CH2}(2O) CH2}(2=C) CH2}(Cb,O) CH2}(Cb,SO2) CH2}(Cb,S) CH2}(Cb,=C) CH2}(C,Cb) CH2}(C,CO) CH2}(C,Ct) CH2}(C,N) CH2}(C,O) CH2}(C,SO2) CH2}(C,SO) CH2}(C,S) CH2}(C,=C) CH2}(=C,O) CH2}(=C,SO2) CH2}(=C,SO) CH2}(=C,S)

16.03 23.02 11.85 19.67 15.53 15.53 38.09 19.67 24.45 25.95 20.72 21.77 20.89 17.12 19.05 22.52 21.43 19.51 20.34 18.42 22.23

26.66 29.09 21.18 28.46 26.26 27.5 49.02 28.46 31.85 32.23 27.46 28.88 28.67 24.99 26.87 29.64 28.71 29.18 28.51 26.62 28.59

CH}(2C,Cb) CH}(2C,CO) CH}(2C,Ct) CH}(2C,N) CH}(2C,O) CH}(2C,SO2) CH}(2C,S) CH}(2C,=C) CH}(3C) CH}(C,2O)

20.43 18.96 16.7 19.67 20.09 18.5 20.3 17.41 19 22.02

27.88 25.87 23.48 26.37 27.79 26.16 27.25 24.74 25.12 23.06

C}(2C,2O) C}(3C,Cb) C}(3C,CO) C}(3C,Ct) C}(3C,N) C}(3C,O) C}(3C,SO2) C}(3C,SO) C}(3C,S) C}(3C,=C) C}(4C)

19.25 19.72 9.71 0.33 18.42 18.12 9.71 12.81 19.13 16.7 18.29

19.25 28.42 18.33 7.33 25.95 25.91 18.33 19.17 26.25 25.28 25.66

32.15 34.53 31.48 35.16 34.66 34.66 57.43 35.16 37.59 36.42 33.19 34.74 34.74 31.56 33.28 36 34.83 36.21 34.95 29.05 34.45

59.65 60.28

60.28 57.6 59.44 61.11

60.11

CH Groups 33.07 30.89 28.67 31.81 33.91 31.65 32.57 30.72 30.01 27.67

44.7 46.55

47.22 46.76

C Groups 23.02 33.86 23.86 14.36 30.56 30.35 23.86 20.26 31.18 31.1 30.81

31.94

34.45 33.99 (Continued )

2-340

PHYSICAL AnD CHEMICAL DATA

TABLE 2-165

Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued )

Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide; Nim = imino. Group

298 K

400 K

500 K

600 K

800 K

1000 K

1500 K 25.32

Aromatic (Cb and Cp Groups) Cb}(Cb) Cb}(CO) Cb}(Ct) Cb}(C) Cb}(N) Cb}(O) Cb}(Si) Cb}(SO2) Cb}(SO) Cb}(S) Cb}(=C) Cb}(=Nim) CbBr CbCl CbF CbH CbI Cb(CHN2) Cb(CN) Cb(N3) Cb(NCO) Cb(NCS) Cb(NO2) Cb(SO2OH) Cp}(2Cb,Cp) Cp}(3Cp) Cp}(Cb,2Cp)

13.94 11.18 15.03 11.18 16.53 16.32 11.18 11.18 11.18 16.32 15.03 16.53 32.65 30.98 26.37 13.56 33.49 47.3 41.86 34.74 55.25 32.23 38.93 65.42 12.56 8.37 12.56

17.66 13.14 16.62 13.14 21.81 22.19 13.14 13.14 13.14 22.19 16.62 21.81 36.42 35.16 31.81 18.59 37.25

20.47 15.4 18.33 15.4 24.86 25.95 15.4 15.4 15.4 25.95 18.33 24.86 39.35 38.51 35.58 22.85 40.18

22.06 17.37 19.76 17.37 26.45 27.63 17.37 17.37 17.37 27.63 19.76 26.45 41.44 40.6 38.09 26.37 41.44

24.11 20.76 22.1 20.76 27.33 28.88 20.76 20.76 20.76 28.88 22.1 27.33 43.11 42.7 41.02 31.56 43.11

24.91 22.77 23.48 22.77 27.46 28.88 22.77 22.77 22.77 28.88 23.48 27.46 43.95 43.53 42.7 35.2 43.95

48.14

52.74

55.67

59.86

62.79

64.04

70.32

74.51

79.95

82.88

50.23 79.49 15.49 12.14 15.49

59.44 84.51 17.58 14.65 17.58

66.56 97.61 19.25 16.74 19.25

76.18 109.25 21.77 19.67 21.77

80.37 113.31 23.02 21.35 23.02

=C}(2C) =C}(CO,O) =C}(C,Cb) =C}(C,CO) =C}(C,O) =C}(C,SO2) =C}(C,S) =C}(C,=C) =CC}(=C,O) =CH}(Cb) =CH}(CO) =CH}(Ct) =CH}(C) =CH}(O) =CH}(SO2) =CH}(S) =CH}(=C) =CH2 =C=

17.16 23.4 18.42 22.94 17.16 15.49 14.65 18.42 18.42 18.67 31.73 18.67 17.41 17.41 12.72 17.41 18.67 21.35 16.32

19.3 29.3 22.48 29.22 19.3 26.04 14.94 22.48 22.9 24.24 37.04 24.24 21.05 21.05 19.55 21.05 24.24 26.62 18.42

22.02 32.44 25.87 31.98 22.02 38.51 17.12 25.87 26.29 31.06 40.31 31.06 27.21 27.21 28.63 27.21 31.06 35.58 20.93

24.28 33.57 27.21 33.53 24.28 44.62 18.46 27.21 27.21 34.95 43.45 34.95 32.02 32.02 32.94 32.02 34.95 42.15 22.19

25.45 34.03 27.71 34.32 25.45 47.47 20.93 27.71 27.71 37.63 46.21 37.63 35.37 35.37 36.29 35.37 37.63 47.17 23.02

O}(2C) O}(2O) O}(2=C) O}(Cb,CO) O}(CO,O) O}(C,Cb) O}(C,CO) O}(C,O) O}(C,=C) O}(=C,CO) OH}(Cb) OH}(CO) OH}(C) OH}(O) O(CN)}(Cb) O(CN)}(C) O(CN)}(=C) O(NO2)}(C) O(NO)}(C) (CO)Cl}(C) (CO)H}(Cb) (CO)H}(CO)

14.23 15.49 14.02 8.62 1.51 2.6 11.64 15.49 12.72 6.03 18 15.95 18.12 21.64 34.74 41.86 54.42 39.93 38.09 42.28 33.53 28.13

15.49 15.49 16.32 11.3 6.28 3.01 15.86 15.49 13.9 12.47 18.84 20.85 18.63 24.24

15.49 15.49 17.58 13.02 9.63 4.94 18.33 15.49 14.65 16.66 20.09 24.28 20.18 26.29

15.91 15.49 18.84 14.32 11.89 7.45 19.8 15.49 15.49 18.79 21.77 26.54 21.89 27.88

18.42 17.58 21.35 16.24 15.28 11.89 20.55 17.58 17.54 20.8 25.12 30.01 25.2 29.93

19.25 17.58 22.6 17.5 17.33 14.99 21.05 17.58 18.96 21.77 27.63 32.44 27.67 31.44

48.3 43.11 46.04 44.2 32.78

55.5 46.88 49.39 48.77 37.25

65.3 50.23 51.9 59.48 41.4

68.61 55.67 55.67 68.56 47.84

72.75 58.18 57.76 74.01 50.73

24.07 25.03 25.03

24.07

40.73

85.81

=C=,=C},=CH}Groups 20.89 31.31 24.82 31.02 20.89 33.32 16.03 24.82 24.82 28.25 38.8 28.25 24.32 24.32 24.82 24.32 28.25 31.44 19.67

26.62 28.13

28.13 41.77 41.77 40.27 40.27 41.77 55.21 23.86

Oxygen Groups 20.09

20.09

37.34 33.65 34.2

60.69

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-165

2-341

Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued )

Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide; Nim = imino. Group

298 K

400 K

500 K

600 K

800 K

1000 K

40.52 40.52 40.52 48.77 21.05

46.71 46.71 46.71 63.12 26.32

51.07 51.07 51.07 74.68 29.54

55.25 85.64 49.52 68.98 82.88 77.86 46.71 57.85 77.44 74.93 68.52 57.3 57.35 59.86 56.09 54.42 59.9 58.18 56.72 53.75 68.23 53.41 46.88 69.07 48.39 63.21 54.42 74.17 56.3 59.86 59.02 56.51 58.18 55.67 53.16 47.72 46.88 43.95 48.56

56.93 88.66 52.07 70.99 86.23 82.88 52.03 63.46 84.14 80.79 76.06 65.26 64.88 67.81 64.04 63.62 68.15 66.14 64.25 58.81 74.93 59.82

56.09 89.66 53.12 71.24 87.9 85.39 53.24 65.84 87.9 83.72 79.99 69.95 70.32 73.67 69.9 69.49 73.8 72 69.36 61.62 79.53 64.38

74.93 54.83 69.9 59.31 79.7 57.72 62.37 61.53 59.86 61.11 59.44 57.76 51.9 51.49 49.39 52.74

78.28 58.64 74.51 61.95 81.58 56.93 63.62 62.79 61.53 62.79 61.53 60.69 55.25 54.83 53.16 55.67

17.29 26.16 34.45 27.33 29.05 24.99 20.3 20.93 17.66 45.63 21.35 30.93 28.59 13.94 26.29 14.57 29.3 33.78 34.7 33.78 38.93 22.35 28.34

21.89 28.42 37.8 28.59 30.93 27.46 22.1 22.94 20.05 50.9 28.3 33.28 33.07 16.91 30.1 17.75 32.65 39.39 41.69 39.39 43.95 23.82 28.71

23.4 28.76 38.47 34.91 38.68 27.92 22.14 27.08 21.43 53.54 32.98 34.28 36.21 18.21 32.36 18.96 34.74 43.83 46.97 43.83 48.14 23.9 29.51

1500 K

Oxygen Groups (CO)H}(C) (CO)H}(N) (CO)H}(O) (CO)H}(=C) CO}(Cb)(O)

29.43 29.43 29.43 24.32 9.12

32.94 32.94 32.94 30.22 11.51

CBr}(3C) CBr3}(C) CCl}(3C) CCl2}(2C) CCl3}(C) CClF2}(C) CF}(3C) CF2}(2C) CF3}(Cb) CF3}(C) CF3}(S) CH2Br}(Cb) CH2Br}(C) CH2Br}(=C) CH2Cl}(C) CH2F}(C) CH2I}(Cb) CH2I}(C) CH2I}(O) CHBr}(2C) CHBrCl}(C) CHCl}(2C) CHCl}(C,O) CHCl2}(C) CHF}(2C) CHF2}(C) CHI}(2C) CHI2}(C) CI}(3C) =CBr2 =CBrCl =CBrF =CCl2 =CClF =CF2 =CHBr =CHCl =CHF =CHI

39.35 72.12 36.96 51.07 68.23 57.35 28.46 39.01 52.32 53.16 41.36 30.51 38.09 40.6 37.25 33.91 33.91 38.51 34.41 37.38 51.9 35.45 37.67 50.65 30.56 41.44 38.64 56.93 41.15 51.49 50.65 45.21 47.72 43.11 40.6 33.91 33.07 28.46 36.84

47.72 78.65 43.87 62.29 75.35 67.39 37.09 46.97 64.04 62.79 54.46 46.46 46.04 47.72 44.79 41.86 45.17 46.04 43.91 44.62 58.6 42.7 41.44 58.6 37.84 50.23 45.67 63.42 49.18 55.25 53.16 50.23 52.32 48.97 46.04 39.77 38.51 35.16 41.86

CH2(N3)}(C) =CH(N3) N}(2C,Cb) N}(2C,CO) N}(2C,SO2) N}(2C,SO) N}(2C,S) N}(3C) N}(Cb,2CO) N}(C,2CO) Nb pyrid}N NF2}(C) NH}(2Cb) NH}(2CO) NH}(2C) NH}(Cb,CO) NH}(C,Cb) NH}(C,CO) NH}(C,N) NH2}(Cb) NH2}(CO) NH2}(C) NH2}N =Naz}(C) =Naz}(N)

64.46 54.42 2.6 13.02 25.2 17.58 15.99 14.57 4.1 4.48 10.88 26.5 9.04 15.03 17.58 2.39 15.99 2.76 20.09 23.94 17.04 23.94 25.53 11.3 8.87

36.92 36.92 36.92 39.77 16.65 Halide Groups 52.74 82.92 47.72 66.76 79.95 73.25 42.7 53.24 72 68.65 62.08 52.2 52.74 54.42 51.49 50.23 53.7 54 51.19 50.06 63.3 48.89 43.95 64.46 43.83 57.35 50.9 69.61 54.08 58.18 56.51 53.58 55.67 52.74 50.23 44.37 43.11 39.77 45.63 Nitrogen Groups

8.46 19.17 26.58 24.61 21.64 19.09 12.81 12.99 13.48 34.58 13.06 23.19 21.81 6.32 20.47 6.49 24.28 27.25 24.03 27.25 30.98 17.16 17.5

13.69 23.52 31.56 25.62 25.99 22.73 17.71 18.04 15.95 40.9 17.29 28.05 25.66 9.96 23.9 10.3 27.21 30.64 29.85 30.64 35.16 20.59 23.06

27.21

39.97

37.67 51.4 51.4 55.25

(Continued )

2-342

PHYSICAL AnD CHEMICAL DATA

TABLE 2-165

Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued )

Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide; Nim = imino. Group

298 K

400 K

500 K

600 K

800 K

1000 K

1500 K

Nitrogen Groups =NazH =Nim}(Cb) =Nim}(C) =NimH

18.33 12.56 10.38 12.35

20.47

22.77

24.86

28.34

31.06

13.98 19.17

16.53 27

17.96 32.27

19.21 38.22

19.25 41.52

S}(2Cb) S}(2C) S}(2S) S}(2=C) S}(Cb,S) S}(C,Cb) S}(C,S) S}(C,=C) SH}(Cb) SH}(CO) SH}(C) SO}(2Cb) SO}(2C) SO2}(2Cb) SO2}(2C) SO2}(2=C) SO2}(Cb,SO2) SO2}(Cb,=C) SO2}(C,Cb) S(CN)}(Cb) S(CN)}(C) S(CN)}(=C)

8.37 20.89 19.67 20.05 12.1 12.64 21.89 17.66 21.43 31.94 24.53 23.94 37.17 34.99 48.22 48.22 41.06 41.4 41.61 39.77 46.88 59.44

8.41 20.76 20.93 23.36 14.19 14.19 22.69 21.26 22.02 33.86 25.95 38.05 41.98 46.17 50.1 50.1 48.14 48.14 48.14

11.47 21.22 21.77 26.33 17.37 16.91 23.06 24.15 25.24 34.2 28.38 47.93 45.17 62.54 59.77 59.77 61.66 61.16 60.74

15.91 22.65 22.19 33.24 20.01 19.34 22.52 24.57 29.26 35.58 30.56 47.97 45.96 66.39 64.38 64.38 65.76 65.8 65.38

19.72 23.98 22.6 40.73 21.35 20.93 21.43 24.57 32.82 34.49 32.27 47.09 46.76 66.81 66.47 66.47 67.1 66.64 66.64

113.23 −39.64

134.95

198.62

219.72

47.72 61.95 52.7 45.21 50.19 80.79 36.21 61.62 41.4 72.42 43.11 51.90 51.49 56.93

56.93

64.04

70.74

80.79

85.81

66.22 54 63.67 101.3 46.71 74.47 55.84

77.52 60.69 74.17 117.2 53.96 83.72 66.39

86.48 66.14 82.08 129.76 58.81 90.46 73.75

99.58 72 92.84 146.09 64.92 99.54 82.92

108.41 79.11 99.2 156.13 67.77 104.48 87.32

50.23

56.09

61.11

68.65

73.67

63.21 69.28

72.83 78.19

80.37 84.76

90.41 93.51

97.11 98.74

−11.05 −7.03 −7.95 −10.88 −12.64 −16.37 −14.56

−7.87 −6.2 −7.41 −9.63 18.09 −19.25 −10.88

−5.78 −5.57 −6.78 −8.63 24.35 −23.86 0.84

−10.97 −5.44 −5.99 −6.91 −15.91 −17.33 −12.56 −3.77 −16.74 −15.91 −2.89 −15.32 −15.32

−6.4 4.6 −1.21 −5.36 −11.72 −12.26 −10.88 9.21 −12.01 −11.3 3.6 −18.46 −18.46

−1.8 9.21 0.33 −4.35 −8.08 −9.46 −10.05 17.58 −9.08 −7.53 5.4 −23.32 −23.32

35.33

Sulfur Groups 9.38 21.01 21.35 23.15 15.57 15.53 23.06 23.27 23.32 33.99 27.25 40.6 43.95 56.72 55.88 55.88 56.59 55.88 56.3

Boron and Silicon Groups Si}(4C) SiH3}(C)

154.5

171.2

252.91

Monovalent Ligands CH2(CN)}(C) CH2(NCS)}(C) CH2(NO2)}(C) CH(CN)}(2C) CH(NO2)}(2C) CH(NO2)2}(C) C(CN)}(3C) C(CN)2}(2C) C(NO2)}(3C) =CH(CHN2) =CH(CN) =CH(NCS) =CH(NO2) =C(CN)2

105.9

3,4 Member Ring Corrections cyclobutane ring cyclobutene ring cyclopropane ring ethylene oxide ring ethylene sulfide ring thietane ring trimethylene oxide ring

−19.3 −10.59 −12.77 −8.37 −11.93 −19.21 −19.25

−16.28 −9.17 −10.59 −11.72 −10.84 −17.5 −20.93

1,4 dioxane ring cyclohexane ring cyclohexene ring cyclopentadiene ring cyclopentane ring cylopentene ring furan ring piperidine ring pyrrolidine ring tetrahydrofuran ring thiacyclohexane ring thiolane ring thiophene ring

−19.21 −24.28 −17.92 −14.44 −27.21 −25.03 −20.51 −24.7 −25.83 −25.12 −26.04 −20.51 −20.51

−20.8 −17.16 −12.72 −11.85 −23.02 −22.39 −18 −19.67 −23.36 −24.28 −17.83 −19.55 −19.55

−13.14 −7.91 −8.79 −12.56 −11.13 −16.37 −17.58

−2.8 −5.11 −6.36

5,6 Member Ring Corrections −15.91 −12.14 −8.29 −8.96 −18.84 −20.47 −15.07 −12.14 −20.09 −20.09 −9.38 −15.4 −15.4

13.81 3.39 −1.55 −4.52

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-165

2-343

Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued )

Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide; Nim = imino. Group

298 K

400 K

500 K

600 K

800 K

1000 K

−1.63 −1.63 −1.63 −1.63 −1.63 −1.26 2.93 3.68

−1.09 −1.09 −1.09 −1.09 −1.09

1500 K

7 and 8 Member Ring Corrections cycloheptane ring cyclooctane ring

−38.01 −44.16 Gauche and 1,5 Repulsion Corrections

but-2-ene structure C}C=C}C but-3-ene structure C}C}C=C cis- between 2 t-butyl groups cis- involving 1 t-butyl group cis-(not with t-butyl group) ortho- between Cl atoms ortho- between F atoms other ortho- (nonpolar-nonpolar)

−5.61 −5.61 −5.61 −5.61 −5.61 −2.09

−4.56 −4.56 −4.56 −4.56 −4.56 5.02 −0.84 5.65

4.69

−3.39 −3.39 −3.39 −3.39 −3.39 2.09 −0.42 5.44

−2.55 −2.55 −2.55 −2.55 −2.55 −2.51 1.26 4.9

2.76

−0.21

*Benson, S. W., et al., Chem. Rev., 69 (1969): 279. † CHETAH Version 8.0: The ASTM Computer Program for Chemical Thermodynamic and Energy Release Evaluation (NIST Special Database 16).

TABLE 2-166

Liquid Heat Capacity Group Parameters for Ruzicka-Domalski Method*

Table-specific nomenclature: Ct refers to a carbon atom with a triple bond; Cb refers to a carbon atom in benzene ring; =C refers to a carbon atom with a double bond; Cp refers to a carbon atom in a fused benzene ring; =C= refers to an allenic carbon atom. Group Definition

a

b

d

T range (K)

Group Definition

Hydrocarbon Groups C}(3H,C) C}(2H,2C) C}(H,3C) C}(4C) =C}(2H) =C}(H,C) =C}(2C) =C}(H,=C) =C}(C,=C) C}(3H,=C) C}(2H,C,=C) C}(H,2C,=C) C}(3C,=C) C}(2H,2=C) Ct}(H) Ct}(C) =C= Ct}(Cb) Cb}(H) Cb}(C) Cb}(=C) Cb}(Cb) C}(2H,C,Ct) C}(3H,Ct) C}(3H,Cb) C}(2H,C,Cb) C}(H,2C,Cb) C}(3C,Cb) C}(2H,2Cb) C}(H,3Cb) =C}(H,Cb) =C}(C,Cb) Cp}(Cp,2Cb) Cp}(2Cp,Cb) Cp}(3Cp)

3.8452 2.7972 −0.42867 −2.9353 4.1763 4.0749 1.9570 3.6968 1.0679 3.8452 2.0268 −0.87558 −4.8006 1.4973 9.1633 1.4822 3.0880 12.377 2.2609 1.5070 −5.7020 5.8685 2.0268 3.8452 3.8452 1.4142 −0.10495 1.2367 −18.583 −46.611 3.6968 1.0679 −3.5572 −11.635 26.164

−0.33997 −0.054967 0.93805 1.4255 −0.47392 −1.0735 −0.31938 −1.6037 −0.50952 −0.33997 −0.20137 0.82109 2.6004 −0.46017 −4.6695 1.0770 −0.62917 −7.5742 −0.2500 −0.13366 5.8271 −0.86054 −0.20137 −0.33997 −0.33997 0.56919 1.0141 −1.3997 11.344 24.987 −1.6037 −0.50952 2.8308 6.4068 −11.353

15.423 −8.9527 8.5430 10.880 9.6663 9.6663 −2.0600 6.3944 10.784 0.037620 13.532 7.2295 8.7956 7.1564 7.6646 9.3249

−9.2464 10.550 2.6966 −0.35391 −1.8601 −1.8601 5.3281 −0.10298 −2.4754 5.6204 −3.2794 0.41759 −0.19165 −0.84442 −2.0750 −1.2478

b

d

T range (K)

Halogen Groups 0.19489 0.10679 0.0029498 −0.085271 0.099928 0.21413 0.11911 0.55022 0.33607 0.19489 0.11624 0.18415 −0.040688 0.52861 1.1400 −0.19489 0.25779 1.3760 0.12592 0.011799 −1.2013 −0.063611 0.11624 0.19489 0.19489 0.0053465 −0.071918 0.41385 −1.4108 −3.0249 0.55022 0.33607 −0.39125 −0.78182 1.2756

80–490 80–490 85–385 145–395 90–355 90–355 140–315 130–305 130–305 80–490 90–355 110–300 165–295 130–300 150–275 150–285 140–315 230–550 180–670 180–670 230–550 295–670 90–355 80–490 80–490 180–470 180–670 220–295 300–420 375–595 130–305 130–305 250–510 370–510 385–480

=C}(Cl,F) Cb}(F) Cb}(Cl) Cb}(Br) Cb}(I) C}(Cb,3F) C}(2H,Cb,Cl)

7.8204 3.0794 4.5479 2.2857 2.9033 7.4477 16.752

C}(3H,N) C−(2H,C,N) C}(2H,Cb,N) C}(H,2C,N) C}(3C,N) N}(2H,C) N}(2H,Cb) N}(H,2C) N}(3C) N}(H,C,Cb) N}(2C,Cb) N}(C,2Cb) Cb}(N) N}(2H,N) N}(H,C,N) N}(2C,N) N}(H,Cb,N) C}(2H,C,CN) C}(3C,CN) =C}(H,CN) Cb}(CN) C}(2H,C,NO2) O}(C,NO2) Cb}(NO2) N}(H,2Cb) (pyrrole) Nb}(2Cb)

3.8452 2.4555 2.4555 2.6322 1.9630 8.2758 8.2758 −0.10987 4.5942 0.49631 −0.23640 4.5942 −0.78169 6.8050 1.1411 −1.0570 −0.74531 11.976 2.5774 9.0789 1.9389 18.520 −2.0181 15.277 −7.3662 0.84237

2.8647 −1.9986 −0.42564 0.08488 0.41360 0.41360 −0.82721 0.19403 0.33288 −0.92054 0.80145 0.15892 0.24596 0.27199 0.82003 0.44241

125–345 125–345 245–310 180–355 140–360 140–360 275–360 168–360 190–420 245–340 240–420 180–420 165–415 120–300 120–240 155–300

O}(H,C) O}(H,C) (diol) O}(H,Cb) (diol) O}(H,Cb) C–(3H,O) C–(2H,C,O) C–(2H,Cb,O) C–(2H,=C,O) C}(H,2C,O) (alcohol) C}(H,2C,O) (ether, ester) C}(3C,O) (alcohol) C}(3C,O) (ether, ester) O}(2C) O}(C,Cb) O}(2Cb) C}(2H,2O)

−0.69005 0.46959 0.22250 2.2573 2.9763 −0.92230 −6.7938

0.19165 −0.0055745 −0.0097873 −0.40942 −0.62960 0.39346 1.2520

120–240 210–365 230–460 245–370 250–320 210–365 245–345

0.19489 −0.24054 −0.24054 0.45109 0.31086 0.035272 0.035272 0.89325 0.55316 −0.57161 −2.5258 0.55316 −0.25287 0.15634 −0.69350 −0.71494 −0.53306 0.52358 −0.58466 0.32986 −0.47276 1.05080 −1.83980 0.71161 −0.68137 −0.20336

80−490 190–375 190–375 240–370 255–375 185–455 185–455 170–400 160–360 240–380 285–390 160–360 240–455 215–465 205–300 205–300 295–385 185–345 295–345 195–345 265–480 190–300 180–350 280–415 255–450 210–395

2.6261 0.54075 0.54075 −0.87263 0.19489 −0.27140 −4.9593 −4.9593 0.69508 −0.016124 −4.8791 −0.44354 0.37860 −1.44210 0.31655 −0.31693

155–505 195–475 195–475 285–400 80–490 135–505 260–460 260–460 185–460 130–170 200–355 170–310 130–350 320–350 300–535 170–310

Nitrogen Groups

Halogen Groups C}(C,3F) C}(2C,2F) C}(C,3Cl) C}(H,C,2Cl) C}(2H,C,Cl) C}(2H,=C,Cl) C}(H,2C,Cl) C}(2H,C,Br) C}(H,2C,Br) C}(2H,C,I) C}(C,2Cl,F) C}(C,Cl,2F) C}(C,Br,2F) =C}(H,Cl) =C}(2F) =C}(2Cl)

a

−0.33997 1.0431 1.0431 −2.0135 −1.7235 −0.18365 −0.18365 0.73024 −2.2134 3.4617 16.260 −2.2134 1.5059 −0.72563 3.5981 4.0038 3.6258 −2.4886 3.5218 −0.86929 3.0269 −5.4568 10.505 −4.4049 6.3622 1.25560

Oxygen Groups 12.952 5.2302 5.2302 −7.9768 3.8452 1.4596 −35.127 −35.127 2.2209 0.98790 −44.690 −3.3182 5.0312 −22.5240 −4.5788 1.0852

−10.145 −1.5124 −1.5124 8.10450 −0.33997 1.4657 28.409 28.409 −1.4350 0.39403 31.769 2.6317 −1.5718 13.1150 0.94150 1.5402

(Continued )

2-344

PHYSICAL AnD CHEMICAL DATA

TABLE 2-166

Liquid Heat Capacity Group Parameters for Ruzicka-Domalski Method* (Continued )

Table-specific nomenclature: Ct refers to a carbon atom with a triple bond; Cb refers to a carbon atom in benzene ring; =C refers to a carbon atom with a double bond; Cp refers to a carbon atom in a fused benzene ring; =C= refers to an allenic carbon atom. Group Definition

a

b

d

T range (K)

Group Definition

a

Oxygen Groups C}(2C,2O) Cb}(O) C}(3H,CO) C}(2H,C,CO) C}(H,2C,CO) C}(3C,CO) CO}(H,C) CO}(H,=C) CO}(H,Cb) CO}(2C) CO}(C,=C) CO}(C,Cb) CO}(H,O) CO}(C,O) CO}(=C,O) CO}(O,CO) O}(C,CO) O}(H,CO) =C}(H,CO) =C}(C,CO) Cb}(CO) CO}(Cb,O)

−12.955 −1.0686 3.8452 6.6782 3.92380 −2.2681 −3.82680 −8.00240 −8.00240 5.4375 41.507 −47.21100 13.11800 29.24600 41.61500 23.99000 −21.43400 −27.58700 −9.01080 −12.81800 12.15100 16.58600

9.10270 3.52210 −0.33997 −2.44730 −2.12100 1.75580 7.67190 3.63790 3.63790 0.72091 −32.632 24.36800 16.12000 3.42610 −12.78900 6.25730 −4.01640 −0.16485 15.14800 15.99700 −1.67050 5.44910

−1.53670 −0.79259 0.19489 0.47121 0.49646 −0.25674 −1.27110 −0.15377 −0.15377 −0.18312 6.0326 −2.82740 −5.12730 −2.89620 0.53631 −3.24270 3.05310 2.74830 −3.04360 −3.05670 −0.12758 −2.68490

275–335 285–530 80–490 180–465 185–375 225–360 180–430 220–430 220–430 185–380 275–355 300–465 280–340 180–445 195–350 320–345 175–440 230–500 195–355 195–430 175–500 175–500

0.19489 −0.08349 −0.31234 −0.72356 −0.75674 0.47368 0.47368 0.45625 0.45625 0.17938 0.45625 −0.06131

80–490 130–390 150–390 190–365 260–375 130–380 130–380 165–390 165–390 170–350 165–390 205–345

Sulfur Groups C}(3H,S) C}(2H,C,S) C}(H,2C,S) C}(3C,S) Cb}(S) S}(H,C) S}(H,Cb) S}(2C) S}(2Cb) S}(C,S) S}(Cb,S) S}(2Cb) (thiophene)

3.84520 1.54560 −1.64300 −5.38250 −4.45070 10.99400 10.99400 9.23060 9.23060 6.65900 9.23060 3.84610

−0.33997 0.88228 2.30700 4.50230 4.43240 −3.21130 −3.21130 −3.00870 −3.00870 −1.35570 −3.00870 0.36718

*Ruzicka, V., and E. S. Domalski, J. Phys. Chem. Ref. Data, 22 (1993): 597, 619.

Solids Solid heat capacity increases with increasing temperature and is proportional to T 3 near absolute zero. The heat capacity at a solid-solid phase transition becomes large, and there can be a substantial difference in the heat capacity of the two equilibrium solid phases that exist on either side of the transition temperature. The heat capacity generally rises steeply with increasing temperature near the triple point. For a quick estimation of solid heat capacity specifically at 298.15 K, the very simple modification of Kopp’s rule [Kopp, H., Ann. Chem. Pharm. (Liebig), 126 (1863): 362] by Hurst and Harrison [Hurst, J. E., and B. K. Harrison, Chem. Eng. Comm., 112 (1992): 21] can be used. At other temperatures and to obtain the temperature dependence of the solid heat capacity, the method given below by Goodman et al. should be used. Recommended Method 1 Goodman method. Reference: Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley, J. Chem. Eng. Data, 49 (2004): 24. Classification: Group contributions. Expected uncertainty: 10 percent. Applicability: Organic compounds for which group values are available. Input data: Molecular structure and Table 2-167 group values. Description: CP A T  =   J/(mol ⋅ K) 1000  K 

b

d

T range (K)

Ring Strain Contributions 4.4297 −4.3392 1.2313 −2.8988 −0.33642 −2.8663 0.21983 −1.5118 −2.0097 −0.72656 −11.460 4.9507 −4.1696 0.52991 5.9700 −3.7965 0.21433 −2.5214 −1.2086 −1.5041 −5.6817 1.5073 −14.885 7.4878 −8.9683 6.4959 −7.2890 3.1119 −8.7885 8.2530 −12.914 13.583 −6.1414 3.5709 −3.6501 2.4707 −6.3861 2.6257 −6.8984 0.66846 −3.9271 −0.29239 −19.687 8.8265 −0.67632 −1.4753 61.213 −30.927

1.0222 0.75099 0.70123 0.28172 0.14758 −0.74754 −0.018423 0.74612 0.63136 0.42863 −0.19810 −1.0879 −1.5272 −0.43040 −2.4573 −4.0230 −0.48620 −0.60531 −0.19578 −0.070012 0.048561 −1.4031 −0.13087 3.2269

155–240 140–300 180–300 135–365 145–485 270–300 295–320 175–310 140–300 160–320 220–300 260–330 170–300 205–320 200–310 275–330 170–395 280–375 250–320 235–485 210–425 315–485 315–485 310–485

15.281 12.703 25.681

−2.3360 1.3109 −7.0966

−0.13720 −1.18130 0.14304

195–330 170–400 265–370

6.8459 −7.0148 −2.3985 9.6704 3.2842 −13.017

−5.8759 7.3764 −0.48585 −2.8138 −5.8260 3.7416

1.2408 −2.1901 0.10253 0.11376 1.2681 −0.15622

135–325 185–300 175–300 190–305 160–320 295–325

−0.73127 −3.2899 −12.766

−1.3426 0.38399 5.2886

0.40114 0.089358 −0.59558

200–320 170–390 295–340

Example Estimate the solid heat capacity for p-cresol at 307.93 K. Structure:

Group contributions: Group

ni 1 4 2 1

}CH3 Ar }CH= Ar >C= }OH

ai 0.20184 0.082478 0.012958 0.10341

bi 0 −0.00033 0 0

From Eq. (2-57): A = exp [6.7796 + 0.20184 + (4) (0.082478) + (2)(0.012958) + 0.10341+ (4)2 (−0.00033)] = 1694.9 From Eq. (2-56):

0.79267

N N   A = exp  6.7796 + ∑ ni ai + ∑ ni2βi    i =1 i =1

Hydrocarbons (ring strain) cyclopropane cyclobutane cyclopentane (unsub) cyclopentane (sub) cyclohexane cycloheptane cyclooctane spiropentane cyclopentene cyclohexene cycloheptene cyclooctene cyclohexadiene cyclooctadiene cycloheptatriene cyclooctatetraene indan 1H-indene tetrahydronaphthalene decahydronaphthalene hexahydroindan dodecahydrofluorene tetradecahydrophenanthrene hexadecahydropyrene Nitrogen compounds ethyleneimine pyrrolidine piperidine Oxygen compounds ethylene oxide trimethylene oxide 1,3-dioxolane furan tetrahydrofuran tetrahydropyran Sulfur compounds thiacyclobutane thiacyclopentane thiacyclohexane

(2-56) CP =

(2-57)

where ni = number of occurrences of group i ai = individual group i contribution bi = nonlinear correction terms for chain and aromatic carbons

1694.9 J J = 159.1 (307.93) 0.79267 1000 mol ⋅ K mol ⋅ K

This value is 2.5 percent higher than the DIPPR 801 recommended value of 155.2 J/(mol ⋅ K).

Recommended Method 2 Modified Kopp’s rule. Reference: Kopp, H., Ann. Chem. Pharm. (Liebig), 126 (1863): 362; Hurst, J. E., and B. K. Harrison, Chem. Eng. Comm., 112 (1992): 21.

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES

2-345

TABLE 2-167 Group Values and nonlinear Correction Terms for Estimation of Solid Heat Capacity with the Goodman et al.* Method Group

Description

ai

}CH3 >CH2 >CH} >C< CH2= }CH= >C= =C= #CH #C} Ar }CH= Ar >C= Ar }O} Ar }N= Ar >N} Ar }NH} Ar }S} }O} }OH }COH >C=O }COO} }COOH }COOCO}

methyl methylene secondary C tertiary C terminal alkene alkene subst. alkene allene terminal alkyne alkyne arom. C subst. arom. C furan O pyridine N subst. pyrrole N pyrrole N thiophene S ether alcohol aldehyde ketone ester acid anhydride

0.20184 0.11644 0.030492 −0.04064 0.18511 0.11224 0.028794 0.053464 −0.02914 0.13298 0.082478 0.012958 0.066027 0.056641 0.008938 −0.05246 0.090926 0.064068 0.10341 0.15699 0.12939 0.13686 0.21019 0.33091

Group }CO3} }NH2 >NH >N} =NH #N }N=N} }NO2 }N=C=O }SH }S} }SS} =S >S=O }F }Cl }Br }I >Si< >Si(O})} cyc >Si(O})} P(=O)(O})3 >P} >P(=O)}

Description

ai

carbonate primary amine secondary amine tertiary amine double -bond NH nitrile diazide nitro isocyanate thiol/mercaptan sulfide disulfide sulfur double bond sulfoxide fluoride chloride bromide iodide silane linear siloxane cyclic siloxane phosphate phosphine phosphine oxide

0.2517 0.056138 −0.00717 −0.01661 0.17689 0.015355 0.3687 0.23327 0.2698 0.21123 0.14232 0.31457 0.13753 0.040002 0.15511 0.16995 0.19112 0.11318 0.12213 0.10125 0.063438 0.15016 0.069602 0.21875

Nonlinear Terms Groups

bi

Usage

>CH2 Ar=CH}

−0.00188 −0.00033

Methylene Aromatic carbon

*Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley, J. Chem. Eng. Data, 49 (2004): 24.

Classification: Group contributions. Expected uncertainty: 10 percent. Applicability: At 298.15 K; organic compounds that are solids at 298.15 K. Input data: Compound chemical formula and element contributions of Table 2-168. Description: N CP = ∑ nE ∆ E J/(mol ⋅ K) E = 1

C

C P , m = ∑ x iC P ,i

DEnSITY

Structure: C12H8S. Group values from Table 2-168:

DS = 12.36

Calculation using Eq. (2-54): CP = (12)(10.89) + (8)(7.56) + (1)(12.36) = 203.52 J/(mol ⋅ K)

TABLE 2-168 Element Contributions to Solid Heat Capacity for the Modified Kopp’s Rule*† Element

DE

Element

DE

Element

DE

C H O N S F Cl Br I Al B

10.89 7.56 13.42 18.74 12.36 26.16 24.69 25.36 25.29 18.07 10.10

Ba Be Ca Co Cu Fe Hg K Li Mg Mn

32.37 12.47 28.25 25.71 26.92 29.08 27.87 28.78 23.25 22.69 28.06

Mo Na Ni Pb Si Sr Ti V W Zr All others

29.44 26.19 25.46 31.60 17.00 28.41 27.24 29.36 30.87 26.82 26.63

*Kopp, H., Ann. Chem. Pharm. (Liebig), 126 (1863): 362. † Hurst, J. E., and B. K. Harrison, Chem. Eng. Comm., 112 (1992): 21.

(2-59)

i =1

This neglects the excess heat capacity, which, if available, can be added to the mole fraction average to improve the estimated value.

Example Estimate the solid heat capacity at 298.15 K for dibenzothiophene.

DH = 7.56

Mixtures The molar heat capacity of liquid and vapor mixtures can be estimated as a mole fraction average of the pure-component values

(2-58)

where N = number of different elements in compound nE = number of occurrences of element E in compound DE = contribution of element E from Table 2-168

DC = 10.89

This value is 2.5 percent higher than the DIPPR 801 recommended value of 198.45 J/(mol ⋅ K).

Density is defined as the mass of a substance per unit volume. Density is given in kg/m3 in SI units, but lbm/ft3 and g/cm3 are common AES and cgs units, respectively. Other commonly used forms of density include molar density (density divided by molecular weight) in kmol/m3, relative density (density relative to water at 15°C), and the older term specific gravity (density relative to water at 60°F). Often the inverse of density, specific volume, and the inverse of molar density, molar volume, are correlated and used to convey equivalent information. Gases Gases/vapors are compressible and their densities are strong functions of both temperature and pressure. Equations of state (EoS) are commonly used to correlate molar densities or molar volumes. The most accurate EoS are those developed for specific fluids with parameters regressed from all available data for that fluid. Super EoS are available for some of the most industrially important gases and may contain 50 or more constants specific to that chemical. Different predictive methods may be used for gas densities depending upon the conditions: 1. At very low densities (high temperatures, generally above the critical, and very low pressures, generally below a few bar), the ideal gas EoS Z ≡

PV =1 RT

(2-60)

may be applied. 2. At moderate densities (below 40 percent of the critical density), the virial equation truncated after the second virial coefficient Z =1+

B (T ) V

(2-61)

2-346

PHYSICAL AnD CHEMICAL DATA

may be used. Second virial coefficients B(T) are available in the DIPPR 801 database for many chemicals and can be estimated using the Tsonopoulos method. Recommended Method Tsonopoulos method. Reference: Tsonopoulos, C., AIChE J., 20 (1974): 263; 21 (1975): 827; 24 (1978): 1112. Classification: Corresponding states. Expected uncertainty: 8 percent for B(T). Applicability: Nonpolar organic compounds and some classes of polar compounds. Input data: Class of fluid, w, Pc, Tc, and m. Description: BPc = B (0) + ωB (1) + B (2) RTc

(2-62)

where B (0) = 0.1445 −

0.330 0.1385 0.0121 0.000607 − − − Tr3 Tr8 Tr Tr2

(2-63) (2-64)

a b − Tr6 Tr8

2

µ P T µ r =    c   c   D   bar   K 

3. For higher gas densities, the Lee-Kesler method described below provides excellent predictions for nonpolar and slightly polar fluids. Extended four-parameter corresponding-states methods are available for polar and slightly associating compounds. Recommended Method Lee-Kesler method. Reference: Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510. Classification: Corresponding states. Expected uncertainty: 1 percent except near the critical point where errors can be up to 30 percent. Applicability: Nonpolar and moderately polar compounds. An extended Lee-Kesler method, not described here, may be used for polar and slightly associating compounds [Wilding, W. V., and R. L. Rowley, Int. J. Thermophys., 8 (1986): 525]. Input data: Tc, Pc, w, Z(0), Z(1). Description: Z = Z(0) + wZ(1)

0.331 0.423 0.008 B = 0.0637 + 2 − 3 − 8 Tr Tr Tr (1)

B (2) =

r = V −1 = 0.86 kmol/m3 is much less than 40 percent of the critical density (the DIPPR 801 recommended value for the critical density is 13.8 kmol/m3).

(2-65)

where Z = compressibility factor Z(0) = compressibility factor of simple fluid obtained from Table 2-169 Z(1) = deviation from simple fluid obtained from Table 2-170 Analytical expressions for Z(0) and Z(1) can also be generated by using Z (0) = Z0

−2

(2-66)

and m = dipole moment. The values of a and b used in Eq. (2-65) depend upon the class of fluid, as given in the table below: Class

a

b

Nonpolar fluids Ketones, aldehydes, nitriles, ethers, esters, NH3, H2S, HCN Monoalkylhalides, mercaptans, sulfides 1-Alcohols except methanol Methanol

0 −21.4mr − 4.308 × 1019mr8

0 0

−2.188 × 1016mr4 − 7.831 × 1019mr8

0

0.0878 0.0878

0.00908 + 69.57mr 0.0525

Example Estimate the molar volume of ammonia at 430 K and 2.82 MPa.

Input properties: Recommended values from the DIPPR 801 database are Tc = 405.65 K, Pc = 11.28 MPa, m = 1.469 D, and w = 0.252608. Reduced conditions: Tr = (430 K)/(405.65 K) = 1.06 Pr = (2.82 MPa)/(11.28 MPa) = 0.25

Z (1) =

Z1 − Z0 0.3978

(2-68)

where Z0 and Z1 are determined from Zi =

PrVr B C D c γ −γ = 1 + + 2 + 5 + 3 4 2  β + 2  exp  2  Tr Vr Vr Vr Tr Vr  Vr   Vr 

b2 b3 b4 − − Tr Tr2 Tr3 c c C = c1 − 2 + 32 Tr Tr d D = d1 + 2 Tr B = b1 −

(2-69)

as applied to the simple reference fluid and to the acentric reference fluid (n-octane), respectively. The constants for Eq. (2-69) for the two reference fluids are given in Table 2-171. Example Estimate the molar volume of saturated n-decane vapor at 540.5 K.

Input properties: Recommended values from the DIPPR 801 database are Tc = 617.7 K, Pc = 2.11 MPa, P*(540.5 K) = 0.6799 MPa, and w = 0.492328. Reduced conditions:

mr = (1.469)2(112.8)/(405.65)2 = 0.0014793 Second virial coefficient from Eqs. (2-63) to (2-66):

(2-67)

Tr = (540.5 K)/(617.7 K) = 0.875 and Pr = (0.6799 MPa)/(2.11 MPa) = 0.322 LK compressiblity factor: Since vapor phase values are needed, the appropriate values from Tables 2-169 and 2-170 that can be used to double-interpolate are as follows:

B(0) = 0.1445 – 0.330/1.06 – 0.1385/(1.06)2 − 0.0121/(1.06)3 − 0.000607/(1.06)8 = −0.301 B(1) = 0.0637 + 0.331/(1.06)2 − 0.423/(1.06)3 − 0.008/(1.06)8 = −0.00189 a = (−21.4)(0.0014793) − (4.308 × 1019)(0.0014793)8 = −0.033 b=0 B(2) = (−0.033)/(1.06)6 = −0.023 From Eq. (2-62) : BPc/(RTc) = −0.301 − (0.252608)(0.00189) − 0.023 = −0.324 B = (−0.324)[0.008314 m3 ⋅ MPa/(kmol ⋅ K)](405.65 K)/(11.28 MPa) = −0.097 m3/kmol Molar volume from Eq. (2-61) : 3  m 3 ⋅ MPa  0.0083143 (430 K)  −0.097 m    kmol ⋅ K  RT  B   m3 kmol V= 1+  =  = 1.162 1+ P  V 2.82 M Pa V kmol    

Note that the ideal gas value, 1.268 m3/kmol, deviates by 9.1 percent from this more accurate value. The truncated virial EoS should be valid for this density since

Z(0) Tr\Pr 0.85 0.90

Z(1) 0.2 0.8810 0.9015

0.4

0.2

Tr\Pr

(0.7222) 0.7800

0.85 0.90

−0.0715 −0.0442

0.4 (−0.1503) −0.1118

Double linear interpolation within these values gives Z(0) = 0.8058 and Z(1) = −0.1025. From Eq. (2-67): Z = 0.8058 + (0.492328)(−0.1025) = 0.7553 Note: If the analytical form available in Eq. (2-69) is used, the following more accurate values are obtained: Z(0) = 0.8131, Z(1) = − 0.1067, and Z = 0.7606. Molar volume: ZRT = V= P

 m 3 ⋅ MPa  (0.7553)  0.0083143 (540.5 K)  kmol ⋅ K  0.6799 M Pa

= 4.992

m3 kmol

4. Cubic EoS can be used to obtain both vapor and liquid densities as an alternative method to those mentioned above.

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-169

2-347

Simple Fluid Compressibility Factors Z(0)

Values in parentheses are for the opposite phase and may be used to interpolate to or near the phase boundary [PGL4; Wilding, W. V., J. K. Johnson, and R. L. Rowley, Int. J. Thermophys., 8(1987):717]. Tr\Pr

0.010

0.050

0.100

0.200

0.400

0.600

0.800

1.000

1.200

1.500

2.000

3.000

5.000

7.000

10.000

0.30 0.35 0.40 0.45

0.0029 0.0026 0.0024 0.0022

0.0145 0.0130 0.0119 0.0110

0.0290 0.0261 0.0239 0.0221

0.0579 0.0522 0.0477 0.0442

0.1158 0.1043 0.0953 0.0882

0.1737 0.1564 0.1429 0.1322

0.2315 0.2084 0.1904 0.1762

0.2892 0.2604 0.2379 0.2200

0.3470 0.3123 0.2853 0.2638

0.4335 0.3901 0.3563 0.3294

0.5775 0.5195 0.4744 0.4384

0.8648 0.7775 0.7095 0.6551

1.4366 1.2902 1.1758 1.0841

2.0048 1.7987 1.6373 1.5077

2.8507 2.5539 2.3211 2.1338

0.50

0.0021

0.0103

0.0207

0.0413

0.0825

0.1236

0.1647

0.2056

0.2465

0.3077

0.4092

0.6110

1.0094

1.4017

1.9801

(0.9741)

(0.8699)

0.9804

0.0098

0.0195

0.0390

0.0778

0.1166

0.1553

0.1939

0.2323

0.2899

0.3853

0.5747

0.9475

1.3137

1.8520

(0.0020)

(0.9000)

(0.7995)

0.9849

0.0093

0.0186

0.0371

0.0741

0.1109

0.1476

0.1842

0.2207

0.2753

0.3657

0.5446

0.8959

1.2398

1.7440

(0.0019)

(0.9211)

(0.8405)

0.9881

0.9377

0.0178

0.0356

0.0710

0.1063

0.1415

0.1765

0.2113

0.2634

0.3495

0.5197

0.8526

1.1773

1.6519

(0.0018)

(0.0089)

(0.8707)

(0.7367)

0.9904

0.9504

0.8958

0.0344

0.0687

0.1027

0.1366

0.1703

0.2038

0.2538

0.3364

0.4991

0.8161

1.1241

1.5729

(0.0086)

(0.0172)

(0.7805)

0.9598

0.9165

0.0336

0.0670

0.1001

0.1330

0.1656

0.1981

0.2464

0.3260

0.4823

0.7854

1.0787

1.5047

(0.0085)

(0.0169)

(0.8181)

(0.6122)

0.9669

0.9319

0.8539

0.0661

0.0985

0.1307

0.1626

0.1942

0.2411

0.3182

0.4690

0.7598

1.0400

1.4456

(0.0168)

(0.0332)

(0.6659)

(0.4746)

0.9436

0.8810

0.0661

0.0983

0.1301

0.1614

0.1924

0.2382

0.3132

0.4591

0.7388

1.0071

1.3943

(0.0336)

(0.7222)

(0.5346)

0.9015

0.7800

0.1006

0.1321

0.1630

0.1935

0.2383

0.3114

0.4527

0.7220

0.9793

1.3496

(0.0364)

(0.0685)

(0.6040)

(0.4034)

0.9115

0.8059

0.6635

0.1359

0.1664

0.1963

0.2405

0.3122

0.4507

0.7138

0.9648

1.3257

(0.7350)

(0.1047)

(0.4499)

0.8206

0.6967

0.1410

0.1705

0.1998

0.2432

0.3138

0.4501

0.7092

0.9561

1.3108

(0.0822)

(0.1116)

0.4853)

0.8338

0.7240

0.5580

0.1779

0.2055

0.2474

0.3164

0.4504

0.7052

0.9480

1.2968

(0.1312)

(0.1532)

0.7360

0.5887

0.1844

0.2097

0.2503

0.3182

0.4508

0.7035

0.9442

1.2901

0.1959

0.2154

0.2538

0.3204

0.4514

0.7018

0.9406

1.2835

0.2901 0.4648 0.5146 0.6026 0.6880 0.7443 0.7858 0.8438 0.8827 0.9103 0.9308 0.9463 0.9583 0.9678 0.9754 0.9865 0.9941 0.9993 1.0031 1.0057 1.0097 1.0115

0.2237 0.2370 0.2629 0.4437 0.5984 0.6803 0.7363 0.8111 0.8595 0.8933 0.9180 0.9367 0.9511 0.9624 0.9715 0.9847 0.9936 0.9998 1.0042 1.0074 1.0120 1.0140

0.2583 0.2640 0.2715 0.3131 0.4580 0.5798 0.6605 0.7624 0.8256 0.8689 0.9000 0.9234 0.9413 0.9552 0.9664 0.9826 0.9935 1.0010 1.0063 1.0101 1.0156 1.0179

0.3229 0.3260 0.3297 0.3452 0.3953 0.4760 0.5605 0.6908 0.7753 0.8328 0.8738 0.9043 0.9275 0.9456 0.9599 0.9806 0.9945 1.0040 1.0106 1.0153 1.0221 1.0249

0.4522 0.4533 0.4547 0.4604 0.4770 0.5042 0.5425 0.6344 0.7202 0.7887 0.8410 0.8809 0.9118 0.9359 0.9550 0.9827 1.0011 1.0137 1.0223 1.0284 1.0368 1.0401

0.7004 0.6991 0.6980 0.6956 0.6950 0.6987 0.7069 0.7358 0.7761 0.8200 0.8617 0.8984 0.9297 0.9557 0.9772 1.0094 1.0313 1.0463 1.0565 1.0635 1.0723 1.0741

0.9372 0.9339 0.9307 0.9222 0.9110 0.9033 0.8990 0.8998 0.9112 0.9297 0.9518 0.9745 0.9961 1.0157 1.0328 1.0600 1.0793 1.0926 1.1016 1.1075 1.1138 1.1136

1.2772 1.2710 1.2650 1.2481 1.2232 1.2021 1.1844 1.1580 1.1419 1.1339 1.1320 1.1343 1.1391 1.1452 1.1516 1.1635 1.1728 1.1792 1.1830 1.1848 1.1834 1.1773

(0.9648)

0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.93 0.95 0.97 0.98

0.9922 0.9935 0.9946 0.9954 0.9959 0.9961 0.9963 0.9965

0.9725 0.9768 0.9790 0.9803 0.9815 0.9821

0.9528 0.9573 0.9600 0.9625 0.9637

0.9174 0.9227 0.9253

0.8398

(0.1703)

0.99

0.9966

0.9826

0.9648

0.9277

0.8455

0.7471

0.6138 (0.2324)

1.00 1.01 1.02 1.05 1.10 1.15 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.20 2.40 2.60 2.80 3.00 3.50 4.00

0.9967 0.9968 0.9969 0.9971 0.9975 0.9978 0.9981 0.9985 0.9988 0.9991 0.9993 0.9994 0.9995 0.9996 0.9997 0.9998 0.9999 1.0000 1.0000 1.0000 1.0001 1.0001

0.9832 0.9837 0.9842 0.9855 0.9874 0.9891 0.9904 0.9926 0.9942 0.9954 0.9964 0.9971 0.9977 0.9982 0.9986 0.9992 0.9996 0.9998 1.0000 1.0002 1.0004 1.0005

0.9659 0.9669 0.9679 0.9707 0.9747 0.9780 0.9808 0.9852 0.9884 0.9909 0.9928 0.9943 0.9955 0.9964 0.9972 0.9983 0.9991 0.9997 1.0001 1.0004 1.0008 1.0010

0.9300 0.9322 0.9343 0.9401 0.9485 0.9554 0.9611 0.9702 0.9768 0.9818 0.9856 0.9886 0.9910 0.9929 0.9944 0.9967 0.9983 0.9994 1.0002 1.0008 1.0017 1.0021

0.8509 0.8561 0.8610 0.8743 0.8930 0.9081 0.9205 0.9396 0.9534 0.9636 0.9714 0.9775 0.9823 0.9861 0.9892 0.9937 0.9969 0.9991 1.0007 1.0018 1.0035 1.0043

0.7574 0.7671 0.7761 0.8002 0.8323 0.8576 0.8779 0.9083 0.9298 0.9456 0.9575 0.9667 0.9739 0.9796 0.9842 0.9910 0.9957 0.9990 1.0013 1.0030 1.0055 1.0066

0.6353 0.6542 0.6710 0.7130 0.7649 0.8032 0.8330 0.8764 0.9062 0.9278 0.9439 0.9563 0.9659 0.9735 0.9796 0.9886 0.9948 0.9990 1.0021 1.0043 1.0075 1.0090

2-348

PHYSICAL AnD CHEMICAL DATA

TABLE 2−170

Acentric Deviations Z (1) from the Simple Fluid Compressibility Factor

Values in parentheses are for the opposite phase and may be used to interpolate to or near the phase boundary [PGL4; Wilding, W. V., J. K. Johnson, and R. L. Rowley, Int. J. Thermophys., 8(1987):717]. Tr\Pr

0.010

0.050

0.100

0.200

0.400

0.600

0.800

1.000

1.200

1.500

0.30 0.35 0.40 0.45

−0.0008 −0.0009 −0.0010 −0.0009

−0.0040 −0.0046 −0.0048 −0.0047

−0.0081 −0.0093 −0.0095 −0.0094

−0.0161 −0.0185 −0.0190 −0.0187

−0.0323 −0.0370 −0.0380 −0.0374

−0.0484 −0.0554 −0.0570 −0.0560

−0.0645 −0.0738 −0.0758 −0.0745

−0.0806 −0.0921 −0.0946 −0.0929

−0.0966 −0.1105 −0.1134 −0.1113

−0.1207 −0.1379 −0.1414 −0.1387

−0.0009

−0.0045

−0.0090

−0.0181

−0.0360

−0.0539

−0.0716

−0.0893

(−0.0457)

(−0.2270)

−0.0172

−0.0343

−0.0513

−0.0682

−0.0164

−0.0326

−0.0487

−0.0309

2.000

3.000

5.000

7.000

10.000

−0.2407 −0.2738 −0.2799 −0.2734

−0.3996 −0.4523 −0.4603 −0.4475

−0.5572 −0.6279 −0.6365 −0.6162

−0.7915 −0.8863 −0.8936 −0.8606

−0.1069 −0.1330

−0.1762 −0.2611

−0.4253

−0.5831

−0.8099

−0.0849

−0.1015 −0.1263

−0.1669 −0.2465

−0.3991

−0.5446

−0.7521

−0.0646

−0.0803

−0.0960 −0.1192

−0.1572 −0.2312

−0.3718

−0.5047

−0.6928

−0.0461

−0.0611

−0.0759

−0.0906 −0.1122

−0.1476 −0.2160

−0.3447

−0.4653

−0.6346

−0.0294

−0.0438

−0.0579

−0.0718

−0.0855 −0.1057

−0.1385 −0.2013

−0.3184

−0.4270

−0.5785

−0.0417

−0.0550

−0.0681

−0.0808 −0.0996

−0.1298 −0.1872

−0.2929

−0.3901

−0.5250

−0.0526

−0.0648

−0.0767 −0.0940

−0.1217 −0.1736

−0.2682

−0.3545

−0.4740

−0.0509

−0.0622

−0.0731 −0.0888

−0.1138 −0.1602

−0.2439

−0.3201

−0.4254

−0.0604

−0.0701 −0.0840

−0.1059 −0.1463

−0.2195

−0.2862

−0.3788

−0.0602

−0.0687 −0.0810

−0.1007 −0.1374

−0.2045

−0.2661

−0.3516

−0.0607

−0.0678 −0.0788

−0.0967 −0.1310

−0.1943

−0.2526

−0.3339

−0.0623

−0.0669 −0.0759

−0.0921 −0.1240

−0.1837

−0.2391

−0.3163

−0.0641

−0.0661 −0.0740

−0.0893 −0.1202

−0.1783

−0.2322

−0.3075

−0.0680

−0.0646 −0.0715

−0.0861 −0.1162

−0.1728

−0.2254

−0.2989

−0.0879 −0.0223 −0.0062 0.0220 0.0476 0.0625 0.0719 0.0819 0.0857 0.0864 0.0855 0.0838 0.0816 0.0792 0.0767 0.0719 0.0675 0.0634 0.0598 0.0565 0.0497 0.0443

−0.0609 −0.0678 −0.0473 −0.0621 0.0227 −0.0524 0.1059 0.0451 0.0897 0.1630 0.0943 0.1548 0.0991 0.1477 0.1048 0.1420 0.1063 0.1383 0.1055 0.1345 0.1035 0.1303 0.1008 0.1259 0.0978 0.1216 0.0947 0.1173 0.0916 0.1133 0.0857 0.1057 0.0803 0.0989 0.0754 0.0929 0.0711 0.0876 0.0672 0.0828 0.0591 0.0728 0.0527 0.0651

−0.0824 −0.0778 −0.0722 −0.0432 0.0698 0.1667 0.1990 0.1991 0.1894 0.1806 0.1729 0.1658 0.1593 0.1532 0.1476 0.1374 0.1285 0.1207 0.1138 0.1076 0.0949 0.0849

−0.1672 −0.1615 −0.1556 −0.1370 −0.1021 −0.0611 −0.0141 0.0875 0.1737 0.2309 0.2631 0.2788 0.2846 0.2848 0.2819 0.2720 0.2602 0.2484 0.2372 0.2268 0.2042 0.1857

−0.2185 −0.2116 −0.2047 −0.1835 −0.1469 −0.1084 −0.0678 0.0176 0.1008 0.1717 0.2255 0.2628 0.2871 0.3017 0.3097 0.3135 0.3089 0.3009 0.2915 0.2817 0.2584 0.2378

−0.2902 −0.2816 −0.2731 −0.2476 −0.2056 −0.1642 −0.1231 −0.0423 0.0350 0.1058 0.1673 0.2179 0.2576 0.2876 0.3096 0.3355 0.3459 0.3475 0.3443 0.3385 0.3194 0.2994

−0.1608 −0.1834 −0.1879 −0.1840

(−0.0740)

0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.93 0.95 0.97 0.98

−0.0314

−0.0043

−0.0086

(−0.0009)

(−0.1438)

(−0.2864)

−0.0205

−0.0041

−0.0082

(0.0008)

(0.0949)

(−0.1857)

−0.0137

−0.0772

−0.0078

−0.0156

(−0.0008)

(0.0039)

(−0.1262)

(−0.2424)

−0.0093 −0.0064 −0.0044 −0.0029 −0.0019 −0.0015 −0.0012 −0.0010 −0.0009

−0.0507

−0.1161

−0.0148

(−0.0038)

(−0.0075)

(−0.1685)

−0.0339

−0.0744

−0.0143

−0.0282

(−0.0037)

(−0.0072)

(−0.1298)

(−0.2203)

−0.0228 −0.0152 −0.0099 −0.0075 −0.0062 −0.0050 −0.0044

−0.0487

−0.1160

−0.0272

−0.0401

(−0.0073)

(−0.0139)

(−0.1682)

(−0.2185)

−0.0319 −0.0205 −0.0154 −0.0126 −0.0101 −0.0090

−0.0715

−0.0268

−0.0391

(−0.0144)

(−0.1503)

(−0.1692)

−0.0442

−0.1118

−0.0396

−0.0503

(−0.0179)

(−0.0286)

(−0.1580)

(−0.1464)

−0.0326 −0.0262 −0.0208 −0.0184

−0.0763

−0.1662

−0.0514

(−0.0340)

(−0.0424)

(−0.1418)

−0.0589

−0.1110

−0.0540

(−0.0444)

(−0.0490)

(−0.1532)

−0.0450 −0.0390

−0.0770

−0.1647

(−0.0714)

(−0.0643)

−0.0641

−0.1100 (−0.0828)

0.99

−0.0008

−0.0039

−0.0079

−0.0161

−0.0335

−0.0531

−0.0796 (−0.1621)

1.00 1.01 1.02 1.05 1.10 1.15 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.20 2.40 2.60 2.80 3.00 3.50 4.00

−0.0007 −0.0006 −0.0005 −0.0003 0.0000 0.0002 0.0004 0.0006 0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 0.0007 0.0006 0.0006 0.0005 0.0005

−0.0034 −0.0030 −0.0026 −0.0015 0.0000 0.0011 0.0019 0.0030 0.0036 0.0039 0.0040 0.0040 0.0040 0.0040 0.0039 0.0037 0.0035 0.0033 0.0031 0.0029 0.0026 0.0023

−0.0069 −0.0060 −0.0051 −0.0029 0.0001 0.0023 0.0039 0.0061 0.0072 0.0078 0.0080 0.0081 0.0081 0.0079 0.0078 0.0074 0.0070 0.0066 0.0062 0.0059 0.0052 0.0046

−0.0140 −0.0120 −0.0102 −0.0054 0.0007 0.0052 0.0084 0.0125 0.0147 0.0158 0.0162 0.0163 0.0162 0.0159 0.0155 0.0147 0.0139 0.0131 0.0124 0.0117 0.0103 0.0091

−0.0285 −0.0240 −0.0198 −0.0092 0.0038 0.0127 0.0190 0.0267 0.0306 0.0323 0.0330 0.0329 0.0325 0.0318 0.0310 0.0293 0.0276 0.0260 0.0245 0.0232 0.0204 0.0182

−0.0435 −0.0351 −0.0277 −0.0097 0.0106 0.0237 0.0326 0.0429 0.0477 0.0497 0.0501 0.0497 0.0488 0.0477 0.0464 0.0437 0.0411 0.0387 0.0365 0.0345 0.0303 0.0270

−0.0588 −0.0429 −0.0303 −0.0032 0.0236 0.0396 0.0499 0.0612 0.0661 0.0677 0.0677 0.0667 0.0652 0.0635 0.0617 0.0579 0.0544 0.0512 0.0483 0.0456 0.0401 0.0357

−0.1118 −0.1072 −0.1021 −0.0838 −0.0373 0.0332 0.1095 0.2079 0.2397 0.2433 0.2381 0.2305 0.2224 0.2144 0.2069 0.1932 0.1812 0.1706 0.1613 0.1529 0.1356 0.1219

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-171 Constants for the Two Reference Fluids Used in Lee-Kesler Method* Constant b1 b2 b3 b4 c1 c2 c3 c4 d1 × 104 d2 × 104 b g

2-349

Tr = (353.15 K)/(405.65 K) = 0.871

Simple reference fluid

Acentric reference fluid

0.1181193 0.265728 0.154790 0.030323 0.0236744 0.0186984 0.0 0.042724 0.155488 0.623689 0.65392 0.060167

0.2026579 0.331511 0.027655 0.203488 0.0313385 0.0503618 0.016901 0.041577 0.48736 0.0740336 1.226 0.03754

α = {1 + [0.48 + (1.574) (0.252608) − (0.176) (0.252608)2] [1 − (0.871)0.5]}2 = 1.119 Rearrange and solve Eq. (2-70) for V: P=

RT aα − V − b V (V + b)

PV 3 − RTV 2 + (aα − bRT − Pb2)V − abα = 0

or 3

m3   V   V   − 0.029 41.352  3    m /mol   mol   m 3 /mol 

2

 m6   V  −10 +  4.037 × 10 −6  − 1.25 × 10 = 0   mol 2   m 3 /mol  Vapor root (initial guess of V = 7.1 × 10−7 m3/mol from ideal gas equation):

*Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510.

Vvap = 5.395 × 10−4 m3/mol

and rvap = 1/Vvap = 1.854 kmol/m3

Liquid root (initial guess of V = 2.72 × 10−5 m3/mol from 1.05b):

Recommended Method Cubic EoS. Classification: Empirical extension of theory. Expected uncertainty: Varies depending upon compound and conditions, but a general expectation is 10 to 20 percent. Applicability: Nonpolar and moderately polar compounds. Input data: Tc, Pc, w. Description: The more common cubic EoS can be written in the form a α (Tr ) V V − Z= V − b V 2 + δV + ε RT

Vliq = 4.441 × 10−5 m3/mol

The corresponding values and equation for the Peng-Robinson EoS are a = 4.611 × 106 cm6 ⋅ bar/mol2 P= or

(2-70)

353.15 K, using the Soave and Peng-Robinson EoS. Required properties: Recommended values in the DIPPR 801 database are Tc = 405.65 K            Pc = 112.8 bar               w = 0.252608 P*(353.15 K) = 41.352 bar (vapor pressure at 353.15 K) EoS parameters (shown for Soave EoS): 2

  bar ⋅ cm 3  0.42748  83.145 (405.65 K)  6  mol ⋅ K  0.42748 (RTc )   = 4.311 × 10 6 cm ⋅ bar = a= 112.8 bar Pc mol 2 2

 bar ⋅ cm 3  0.08664  83.145 (405.65 K)  mol ⋅ K  cm 3 = 25.906 112.8 bar mol

EoS

RT aα − V − b V 2 + 2bV − b 2

PV 3 + (bP − RT)V 2 + (aα − 2bRT − 3Pb2)V + (bP 3 + RTb2 − abα) = 0 m3   V   V   − 0.0284 41.352  3    m /mol   mol   m 3 /mol 

2

 m6   V  −10 +  3.651 × 10 −6  − 1.018 × 10 = 0   mol 2   m 3 /mol  Solve for the two physical roots of this equation: Vvap = 5.286 × 10−4 m3/mol and rvap = 1.892 kmol/m3 Vliq = 3.914 × 10−5 m3/mol and rliq = 25.55 kmol/m3 The liquid density calculated from the Soave EoS is 24.2 percent below the DIPPR 801 recommended value of 29.69 kmol/m3; that calculated from the Peng-Robinson EoS is 13.9 percent below the recommended value.

Liquids For most liquids, the saturated molar liquid density r can be effectively correlated with ρ=

Example Estimate the molar density of liquid and vapor saturated ammonia at

TABLE 2-172

b = 23.262 cm3/mol α = 1.103

3

where a, b, d, and e are constants that depend upon the model EoS chosen, as does the temperature dependence of the function α(Tr). Definitions of these constants and α(Tr) for some of the more commonly used EoS models are shown in Table 2-172. The corresponding relations for many other EoS models in this same form are available [Soave, G., Chem. Eng. Sci., 27 (1972): 1197]. The independent parameters a and b in these models can be regressed from experimental data to correlate densities or can be obtained from known critical constants to predict density data. Of the cubic EoS given in Table 2-172, the Soave and Peng-Robinson are the most accurate, but there is no general rule for which EoS produces the best estimated volumes for specific fluids or conditions. The Peng-Robinson equation has been better tuned to liquid densities, while the Soave equation has been better tuned to vapor-liquid equilibrium and vapor densities. In solving the cubic equation for volume, a convenient initial guess to find the vapor root is the ideal gas value, while an initial value of 1.05b is convenient to locate the liquid root.

0.08664 (RTc ) b= = Pc

rliq = 1/Vliq = 22.516 kmol/m3

and

A D B [1+(1−T /C ) ]

(2-71)

adapted from the Rackett prediction equation [Rackett, H. G., J. Chem. Eng. Data, 15 (1970): 514]. The regression constants A, B, and D are determined from the nonlinear regression of available data, while C is usually taken as the critical temperature. The liquid density decreases approximately linearly from the triple point to the normal boiling point and then nonlinearly to the critical density (the reciprocal of the critical volume). A few compounds such as water cannot be fit with this equation over the entire range of temperature. The recommended method for estimation of saturated liquid density for pure organic compounds is the Rackett prediction method. Recommended Method Rackett method. Reference: Rackett, H. G., J. Chem. Eng. Data, 15 (1970): 514. Classification: Corresponding states. Expected uncertainty: 15 percent as purely predictive equation; 2 percent if a liquid density value is available.

Relationships for Eq. (2-70) for Common Cubic EoS d

e

α(Tr)

van der Waals* 0 0 1 Relich-Kwong† 0 0 Tr−0.5 Soave‡ b 0 [1 + (0.48 + 1.574w − 0.176w2)(1 − Tr0.5)]2 Peng-Robinson§ 2b −b2 [1 + (0.37464 + 1.54226w − 0.2699w2)(1 − Tr0.5)]2 *van der Waal, J. H., Z. Phys. Chem., 5 (1890): 133. † Redlich, O., and J. N. S. Kwong, Chem. Rev., 44 (1949): 233. ‡ Soave, G., Chem. Eng. Sci., 27 (1972): 1197. § Peng, D. Y., and D. B. Robinson, Ind. Eng. Chem. Fundam., 15 (1976): 59.

aPc/(RTc)2

bPc/(RTc)

0.42188 0.42748 0.42748 0.45724

0.125 0.08664 0.08664 0.0778

2-350

PHYSICAL AnD CHEMICAL DATA

Applicability: Saturated liquid densities of organic compounds. Input data: Tc, Pc, and Zc (or, equivalently, Vc). Description: A predictive form of the equation is given by  RT  1 = V =  c  Zcq ρ  Pc 

Example Estimate the density of solid naphthalene at 281.46 K. Required properties: The recommended values from the DIPPR 801 database for Tt and the liquid density at Tt are

where q = 1 + (1 − Tr )

(2-72)

When one or more liquid density data points are available, Zc in Eq. (2-72) can be replaced with an adjustable parameter fitted from the data (ZRA in the notation of Spencer and Danner [Spencer, C. F., and R. P. Danner, J. Chem. Eng. Data 17 (1972): 236]). This produces densities in good agreement with experiment and permits accurate interpolation of the densities over most of the liquid temperature range, but it does not give the correct critical density unless ZRA = Zc. Example Estimate the saturated liquid density of acetonitrile at 376.69 K.

Required properties: The recommended values from the DIPPR 801 database are Tc = 545.5 K

rL(Tt) = 7.6326 kmol/m3

Tt = 353.43 K 2/7

Pc = 4.83 MPa

Zc = 0.184

Calculate supporting quantities:

From Eq. (2-73):  281.46 K   kmol kmol  ρs =  1.28 − 0.16  7.6326 3  = 8.797 3 m m 353.43 K    The estimated value is 4.3 percent lower than the DIPPR 801 recommended value of 9.1905 kmol/m3.

Mixtures Both liquid and vapor densities can be estimated using purecomponent CS and EoS methods by treating the fluid as a pseudo-pure component with effective parameters calculated from the pure-component parameters using ad hoc mixing rules. To apply the Lee-Kesler CS method to mixtures, pseudo-pure fluid constants are required. One of the simplest set of mixing rules for these quantities is [Prausnitz, J. M., and R. D. Gunn, AIChE J., 4 (1958): 430, 494; Joffe, J., Ind. Eng. Chem. Fundam., 10 (1971): 532]:

Tr = (376.69 K)/(545.5 K) = 0.691

C

Tc = ∑ x iTc ,i

q = 1 + (1 − 0.691)2/7 = 1.715 Calculate saturated liquid density from Eq. (2-72):

C

∑x Z i

Pc =

    4.83 × 10 6 Pa   (0.184)− 1.715 = 19.42 kmol ρ=   m3 Pa ⋅ m 3  (545.5 K) 8.314     mol ⋅ K   

RTc

(2-75)

i =1

ω = ∑ xiωi

1/1.798

(2-76)

i =1

The procedures are identical to those for pure components with the replacement of Tc, Pc, and w with the effective mixture values obtained from the above equations. To use a cubic EoS for a mixture, mixing rules are used to calculate effective mixture parameters in terms of the pure-component values. Although more complex mixing rules may improve prediction accuracy, the simple forms recommended here provide reasonable accuracy without adjustable parameters:

= 0.202

C

b = ∑ x i bi

(2-77)

i =1

    6 × 4.83 10 Pa  (0.202)−1.715 = 16.577 kmol ρ=    m3 Pa ⋅ m 3  (545.5 K)    8.314 mol ⋅ K   

2

The value obtained by the modified Rackett method is 0.9 percent below the DIPPR 801 recommended value. Note, however, that with ZRA = 0.202 instead of Zc, Eq. (2-72) gives rc = 5.28 kmol/m3 instead of rc = Pc/(ZcRTc) = 5.79 kmol/m3.

Solids Solid density data are sparse and usually available only within a narrow temperature range. For most solids, density decreases approximately linearly with increasing temperature. No accurate method for prediction of solid densities is available, but an approximate correlation has been found between the density of the liquid phase at the triple point and the solid that is stable at the triple point conditions. Recommended Method Goodman method. Reference: Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley, J. Chem. Eng. Data, 49 (2004): 1512. Classification: Empirical correlation. Expected uncertainty: 6 percent. Applicability: Organic compounds; applicable to the stable solid phase at the triple point temperature Tt; applicable T range is from Tt down to either the first solid-phase transition temperature or to approximately 0.3Tt. Input data: Liquid density at the triple point. Description: The density for the solid phase that is stable at the triple point has been correlated as a function of temperature and the liquid density at Tt as  T ρs =  1.28 − 0.16  ρL (Tt ) Tt  

∑x V C

q = 1 + (1 – 0.546)2/7 = 1.798

    4.83 × 10 6 Pa   Z RA =  kmol   Pa ⋅ m 3   (545.5 K) 18.919     8.314   m3   kmol ⋅ K  

c ,i

i =1 C

i c ,i

The estimated density is 16 percent above the DIPPR 801 value of 16.73 kmol/m3. Calculate rsat from Eq. (2-72) with a known liquid density: Kratzke and Muller [Kratzke, H., and S. Muller, J. Chem. Thermo., 17 (1985): 151] reported an experimental density of 18.919 kmol/m3 at 298.08 K. Use of this experimental value in Eq. (2-72) to calculate ZRA gives Tr = (298.08 K)/(545.5 K) = 0.546

(2-74)

i =1

(2-73)

C  (2-78) aα =  ∑ x i (ai α i )1/2   i =1  Mixture calculations are then identical to the pure-component calculations using these effective mixture parameters for the pure-component aα and b values. The modified Rackett method has also been extended to liquid mixtures [Spencer, C. F., and R. P. Danner, J. Chem. Eng. Data, 17 (1972): 236] using the following combining and mixing rules as modified by Li [Li, C. C., Can. J. Chem. Eng., 19 (1971): 709]: Tc ,ij = Tc ,iTc , j

φi =

x iVc ,i C

∑x V

j c, j

C

C

Tc = ∑ ∑ φi φ jTc ,ij

(2-79)

i =1 j =1

j =1

Recommended Method Spencer-Danner-Li mixing rules with Rackett equation. References: Spencer, C. F., and R. P. Danner, J. Chem. Eng. Data, 17 (1972): 236; Li, C. C., Can. J. Chem. Eng., 19 (1971): 709. Classification: Corresponding states. Expected uncertainty: About 7 percent on average; higher near the Tc of any of the components. Applicability: Saturated (at the bubble point) liquid mixtures. Input data: Tc, Vc, and xi. Description: The predictive form of the equation is given by  C xT  q 1 = V = R  ∑ i c ,i  Z RA ρ  i =1 Pc ,i 

q = 1.0 + (1.0 − Tr )2/7

(2-80)

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES where C

Z RA = 0.29056 − 0.08775 ∑ x i ω i

and

Tr =

i =1

T Tc

(2-81)

2-351

Input data: Tc, Pc, and M. Description: The correlation for viscosity as a function of reduced temperature is 46.1Tr0.618 - 20.4 exp( - 0.449Tr ) + 19.4 exp( − 4.058 Tr ) + 1 ηo = 2.173424 × 1011 (Tc /K)1/6 (M /g ⋅ mol −1 )−1/2 (Pc / Pa)−2/3 Pa ⋅ s

Example Estimate the saturated liquid density of a liquid mixture of 50 mol% ethane(1) and 50 mol% n-decane(2) at 377.6 K. Required properties: The recommended values from the DIPPR 801 database for the required properties are as follows:

Example Estimate the low-pressure vapor viscosity of propane at 353 K. Required constants: The DIPPR 801 database recommends the following values: Tc = 369.83 K

Tc/K

Vc /(m3 ⋅ kmol−1)

Pc /bar

w

Ethane

305.32

0.1455

48.72

0.0995

Decane

617.7

0.617

21.1

0.4923

(2-83)

Pc = 4.248 MPa

M = 44.0956 g/mol

Reduced temperature: Tr = (353 K)/(369.83 K) = 0.9545 Calculation using Eq. (2-83):

Auxiliary quantities from Eq. (2-79): φ1 =

(0.5) (0.1455) = 0.191; (0.5)(0.1455) + (0.5)(0.617)

(46.1) (0.9545)0.618 − 20.4 exp[ − (0.449) (0.9545)] + 19.4 exp[ − 4.058(0.9545)] + 1 ηo = Pa ⋅ s (2.173424 × 1011 ) (369.83) −1/6 (44.0956) −1/2 (4.248 × 10 6 )−2/3 = 9.84 × 10 −6

φ2 = 0.809

This value is 1.5 percent higher than the DIPPR 801 recommended value of 9.70 × 10−6 Pa ⋅ s.

Tc ,12 = (305.32 K) (617.7 K) = 434.3 K Tc = φ12Tc ,1 + 2φ1φ2Tc ,12 + φ22Tc ,2 K = (0.191)2 (305.32) + (2)(0.191)(0.809)(434.3) + (0.809)2 (617.7)

Recommended Method 2 Reichenberg method. Reference: Reichenberg, D., AIChE J., 21 (1975): 181. Classification: Group contributions and corresponding states. Expected uncertainty: 5 percent. Applicability: Nonpolar and polar organic and inorganic vapors. Input data: Tc, Pc, M, m, and molecular structure. Description: The temperature dependence of the viscosity is given by

Tc = 549.68 K Calculations from Eqs. (2-80) and (2-81): Tr = (377.6 K)/(549.63 K) = 0.687 q = 1 + (1 − 0.687)2/7 = 1.718

 1 + 270(µ ∗r ) 4  ATr2 ηo =   Pa ⋅ s [1 + 0.36 Tr (Tr − 1)]1/6  Tr + 270(µ ∗r ) 4 

ZRA = 0.29056 − 0.08775[(0.5)(0.0995) + (0.5)(0.4923)] = 0.2646  m 3 ⋅ bar   (0.5)(305.32 K) (0.5) (617.7 K)  m3 1.718 + V =  0.08314   (0.2646) = 0.151   K ⋅ kmol   48.72 bar 21.1 bar  kmol

The experimental value [Reamer, H. H., and B. H. Sage, J. Chem. Eng. Data, 7 (1962): 161] is 0.149 m3/kmol, and the error in the estimated value is 1.3 percent.

where the parameter A is determined from group contributions and the modified reduced dipole µ∗r is found from µ∗r = 52.46mr

ηo =

AT B 1 + C /T + D /T 2

(2-82)

Over smaller temperature ranges, parameters C and D may not be necessary as ln(h) is often reasonably linear with ln(T). Care should be taken in extrapolating using Eq. (2-82) as there can be unintended mathematical poles where the denominator approaches zero. Numerous methods have been developed for estimation of vapor viscosity. For nonpolar vapors, the Yoon-Thodos CS method works well, but for polar fluids the Reichenberg method is preferred. Both methods are illustrated below. Recommended Method 1 Yoon-Thodos method. Reference: Yoon, P., and G. Thodos, AIChE J., 16 (1970): 300. Classification: Corresponding states. Expected uncertainty: 5 percent. Applicability: Nonpolar and slightly polar organic vapors.

(2-85)

and Eq. (2-66). For organic compounds, A is found from the group values Ci, listed in Table 2-173, using

VISCOSITY Viscosity is defined as the shear stress per unit area at any point in a confined fluid, divided by the velocity gradient in the direction perpendicular to the direction of flow. The absolute viscosity h is the shear stress at a point, divided by the velocity gradient at that point. The SI unit of viscosity is Pa ⋅ s [1 kg/(m ⋅ s)], but the cgs units of poise (P) [1 g/(cm ⋅ s)] and centipoise (cP = 0.01 P) are also frequently used (1 cP = 1 mPa ⋅ s). The kinematic viscosity n is defined as the ratio of the absolute viscosity to density at the same temperature and pressure. The SI unit for n is m2/s, but again cgs units are very common and n is often given in stokes (1 St = 1 cm2/s) or centistokes (1 cSt = 0.01 cm2/s). Gases Experimental data for gases and vapors at low density are often correlated with

(2-84)

A = 10

 M    −7  kg/kmol 

1/2

(Tc /K) (2-86)

N

∑n C i

i

i =1

For inorganic gases, A is obtained from  M  1/2  P  2/3  T  −1/6  c c A = 1.6104 × 10 −10         g/mol   Pa   K  

TABLE 2-173 Group

(2-87)

Reichenberg* Group Contribution Values Ci

Group

}CH3 9.04 }F >CH2 6.47 }Cl >CH} 2.67 }Br >C< −1.53 }OH alcohol =CH2 7.68 >O =CH} 5.53 >C=O >C= 1.78 }CHO ≡CH 7.41 }COOH ≡C} 5.24 }COO} or HCOO} >CH2 ring 6.91 }NH2 >CH} ring 1.16 >NH >C< ring 0.23 =N} ring =CH} ring 5.90 }CN >C= ring 3.59 >S ring *Reichenberg, D., AIChE J., 21 (1975): 181.

Ci 4.46 10.06 12.83 7.96 3.59 12.02 14.02 18.65 13.41 9.71 3.68 4.97 18.13 8.86

2-352

PHYSICAL AnD CHEMICAL DATA

Example Estimate the low-pressure vapor viscosity of ethyl acetate at 401.25 K. Required constants: The DIPPR 801 database recommends the following values: M = 88.1051 g/mol      Tc = 523.3 K

Pc = 3.88 MPa

where rc = Pc /(ZcRTc) and

m = 1.78 D

T ξ = 2173.4  c   K

Supporting quantities: Structural groups:

 M   kg/kmol 

−1/2

 Pc    MPa 

−2/3

(2-93)

Example Estimate the vapor viscosity of CO2 at 350 K and 20 MPa if h° = 0.0174 mPa ⋅ s and Z = 0.4983 (estimated from Lee-Kesler method, see section on density). Required properties: From the DIPPR 801 database, M = 44.01 kg/kmol

Group

ni

Ci

Contribution 18.08

—CH3

2

9.04

>CH2

1

6.47

6.47

—COO—

1

13.41

13.41 Total

Zc = 0.274 Auxiliary quantities:

ρc =

37.96 ρr =

From Eqs. (2-66) and (2-85): µ∗r = 52.46

Tc = 304.21 K

Pc = 7.383 MPa

m = 0 D (nonpolar)

x = (2173.4)(304.21)1/6 (44.01)−1/2(7.383)−2/3 = 224.1

Tr = (401.25 K)/(523.3 K) = 0.767

7.383 MPa kmol = 10.654 3 0.274 [0.008314 m 3 MPa/(K ⋅ kmol)](304.21 K) m

20 MPa ρ P = = = 1.295 ρc ZRT ρc 0.4983[0.008314m 3 ⋅ MPa/(K ⋅ kmol)](350 K) (10.654 m 3 ⋅ kmol)

Calculation using Eq. (2-88) for nonpolar fluids:

(1.78)2 (38.8) = 0.024 (523.3) 2

1/4

  η− ηo   + 1  224.1   mPa ⋅ s   

From Eq. (2-86):

= 1.0230 + 0.23364(1.295) + 0.58533(1.295) 2

− 0.40758(1.295) 3 + 0.093324(1.295) 4 = 1.684

(88.1051)1/2 (523.3) A = 10 = 1.294 × 10 −5 37.96 −7

η=

Calculation using Eq. (2-84):

1.684 4 − 1 mPa ⋅ s + 0.0174 mPa ⋅ s = 0.0489 mPa ⋅ s 224.1

This differs from the experimental value of 0.0473 mPa ⋅ s by 3.4 percent.

(1.294 × 10 −5 ) (0.767) 2 1 + (270) (0.024) 4 ηo = = 1.003 × 10 −5 1/6 Pa ⋅ s [1 + (0.36) (0.767) (0.767 − 1)] 0.767 + (270) (0.024) 4 The estimated value is 1.5 percent lower than the DIPPR 801 recommended value of 1.018 × 10−5 Pa ⋅ s. The dependence of viscosity upon pressure is principally a density effect. Estimation of vapor viscosity at elevated pressures is commonly done by correlating density deviations from the low-pressure values estimated. Several methods are available, but the method developed by Jossi et al. and extended to polar fluids by Stiel and Thodos is relatively accurate and easy to apply.

Recommended Method Jossi-Stiel-Thodos method. References: Stiel, L. I., and G. Thodos, AIChE J., 10 (1964): 26; Jossi, J. A., L. I. Stiel, and G. Thodos, AIChE J., 8 (1962): 59. Classification: Empirical correlation and corresponding states. Expected uncertainty: 9 percent—often less for nonpolar gases, larger for polar gases. Applicability: Nonassociating gases; rr < 2.6. Input data: M, Tc, Pc, Zc, m, ho (low-pressure viscosity at same T may be estimated by using methods given above), and r (may be calculated from T and P by using density methods given above). Description: Deviation of h from the low-pressure value ho is given by one of the following correlations depending upon its polarity and reduced density range: For nonpolar gases, 0.1 < rr < 3.0:   η− ηo    ξ + 1   mPa ⋅ s 

1/6

1/4

= 1.0230 + 0.23364 ρr + 0.58533ρr2 − 0.40758ρ3r + 0.093324 ρr4

(2-88)

Liquids Liquid viscosity can be correlated as a function of temperature for low pressures. Usually the correlation is based on the Andrade equation [Andrade, E. N. da C., Nature, 125 (1930): 309] ln ( η) = A +

(2-94)

or an extension of it. For example, the DIPPR 801 database uses the equation ln ( η) = A +

B + C ln T + DT E T

(2-95)

which is analogous to the Riedel [Riedel, L., Chem. Ing. Tech., 26 (1954): 83] vapor pressure equation. Currently the most accurate method for predicting pure liquid viscosity is the GC method by Hsu et al. It has been found that most liquids have a viscosity between 0.15 mPa ⋅ s (or cP) and 0.55 mPa ⋅ s at the normal boiling point, and this “rule” can be used as a valuable criterion to validate estimated viscosities as a function of temperature. Recommended Method Hsu method. Reference: Hsu, H.-C., Y.-W. Sheu, and C.-H. Tu, Chem. Eng. J., 88 (2002): 27. Classification: Group contributions. Expected uncertainty: 20 percent. Applicability: Organic liquids; Tr < 0.75. Input data: Pc and molecular structure. Description: The temperature dependence of the liquid viscosity is given by N

∑ ci  N  N P η  N ln  = ∑ ai + T ∑ bi + i =1 2 +  ∑ di  ln  c    mPa ⋅ s  i =1 T  i =1   bar  i =1

For polar gases, rr ≤ 0.1:  η− η  1.111  mPa ⋅ s  ξ = 1.656ρr

B T

o

(2-89)

(2-96)

where Pc is critical pressure and ai, bi, ci, and di are the group contributions obtained from Table 2-174.

For polar gases, 0.1 < rr ≤ 0.9:  η− ηo  1.739  mPa ⋅ s  ξ = 0.0607 (9.045ρr + 0.63)

(2-90)

Example Estimate the liquid viscosity of benzotrifluoride at 303.15 K. Structural information:

For polar gases, 0.9 < rr ≤ 2.2:  η− ηo     log  4 − log   ξ   = 0.6439 − 0.1005ρr  mPa ⋅ s    

(2-91)

For polar gases, 2.2 < rr ≤ 2.6:  η− ηo     3 2 log  4 − log   ξ   = 0.6439 − 0.1005ρr − 0.000475(ρr − 10.65)  mPa ⋅ s    

(2-92)

Group >C< (=CH})A (=CCH} >C< =CH2 =CH} =C< ≡CH ≡C} (}CH2})R (>CH})R (=CH})R cycloalkene (>CCH2 (n = 1–11) CH3

1 1 1 1

43.64 28.64 39.92 55.25

43.64 28.64 39.92 55.25 Total 167.45

Calculation using Eq. (2-114): (0.525) (0.475) (2) (0.1383) (0.2069)  W  k = (0.525)2 (0.1383) + 2 ⋅ + (0.475)2 (0.2069)  0.1383 + 0.2069  m⋅K  = 0.167 W/(m ⋅ K) The Filippov value is 7.5 percent lower than the experimental value of 0.173 W/(m ⋅ K) [Jamieson, D. T., and B. K. Hastings, Thermal Conductivity, Proceedings of the Eighth Conference, C. Y. Ho and R. E. Taylor, eds., Plenum Press, New York, 1969]; the Li value is 3.5 percent lower than the experimental value.

SURFACE TEnSIOn The surface at a vapor-liquid interface is in tension due to the difference in attractive forces experienced by molecules at the interface between the dense liquid phase and the low-density gas phase. This causes the liquid to contract to minimize the surface area. Surface tension is defined as the force in the surface plane per unit length. Jasper [Jasper, J. J., J. Phys. Chem. Ref. Data, 1 (1972): 841] has made a critical evaluation of experimental surface tension data for approximately 2200 pure chemicals and correlated surface tension s (mN/m = dyn/cm) with temperature as

4

N 13.2573   mN  = 0.02429 σ = (167.45)   1000   m m  The estimated value is 0.9 percent above the DIPPR 801 recommended value of 0.02407 N/m.

Recommended Method 2 Brock-Bird method. Reference: Brock, J. R., and R. B. Bird, AIChE J., 1 (1955): 174; Miller, D. G., Ind. Eng. Chem. Fundam., 2 (1963): 78. Classification: Corresponding states. Expected uncertainty: 5 percent. Applicability: Nonpolar and moderately polar organic compounds. Input data: Tc, Pc, and Tb. Description: P σ = (5.553 × 10 −5 )  c   Pa  mN/m

Jasper’s evaluation also includes values of A and B for most of the tabulated chemicals. Surface tension decreases with increasing temperature and increasing pressure. Pure Liquids An approach suggested by Macleod [Macleod, D. B., Trans. Faraday Soc., 19 (1923): 38] and modified by Sugden [Sugden, S. J., Chem. Soc., 125 (1924): 32] relates s to the liquid and vapor molar densities and a temperature-independent parameter called the Parachor P 4

(2-116)

2/3

 Tc    K

1/3

F (1 − Tr )11/9

(2-118)

where

(2-115)

s = A − BT

σ   ρL − ρv   = P ⋅  mN/m   10 3 kmol/m3  

Required properties: The DIPPR 801 database gives rL = 13.2573 kmol/m3 at 237.45 K. Calculation using Eq. (2-116):

F=

Tbr [ln(Pc /Pa) − 11.5261] − 1.3281 1 − Tbr

(2-119)

Example Estimate the surface tension for ethyl mercaptan at 303.15 K. Required properties from DIPPR 801: Tc = 499.15 K

Pc = 5.49 × 106 Pa

Tb = 308.15 K

Supporting quantities: Tr = (303.15 K)/(499.15 K) = 0.6073 Tbr = (308.15 K)/(499.15 K) = 0.6173 F = {0.6173[ln (5.49 × 106) − 11.5261]/(1 − 0.6173)} − 1.3281 = 5.113 [ from Eq. (2-119)] From Eq. (2-118):

where rL and rV are the saturated molar liquid and vapor densities, respectively. At low temperatures, where rL >> rV, the vapor density can be neglected, but at higher temperatures the density of both phases must be calculated. The surface tension is zero at the critical point where rL = rV. Quayle [Quayle, O. R., Chem. Rev., 53 (1953): 439] proposed a group contribution method for estimating P that has been improved in recent years by Knotts et al. [Knotts, T. A., et. al., J. Chem. Eng. Data, 46 (2001): 1007]. This method using P is recommended when groups are available; otherwise, the Brock-Bird [Brock, J. R., and R. B. Bird, AIChE J., 1 (1955): 174] corresponding-states method as modified by Miller [Miller, D. G., Ind. Eng. Chem. Fundam., 2 (1963): 78] may be used to estimate surface tension for compounds that are not strongly polar or associating. Recommended Method 1 Parachor method. References: Macleod, D. B., Trans. Faraday Soc., 19 (1923): 38; Sugden, S. J., Chem. Soc., 125 (1924): 32; Knotts, T. A., W. V. Wilding, J. L. Oscarson, and R. L. Rowley, J. Chem. Eng. Data, 46 (2001): 1007. Classification: Group contributions and QSPR. Expected uncertainty: 4 percent. Applicability: Organic compounds for which group values are available. Input data: rL, molecular structure, and Table 2-177. Description: Equation (2-116) is used with P calculated from N

P = ∑ ni ∆Pi i =1

Group values for the Parachor are given in Table 2-177.

(2-117)

s = (5.553 × 10−5) (5.49 × 106)2/3(499.15)1/3(5.113) (1 − 0.6073)11/9 mN/m = 22.36 mN/m The estimated value is 1.4 percent lower than the DIPPR 801 value of 22.68 mN/m.

Liquid Mixtures Compositions at the liquid-vapor interface are not the same as in the bulk liquid, and so simple (bulk) compositionweighted averages of the pure-fluid values do not provide quantitative estimates of the surface tension at the vapor-liquid interface of a mixture. The behavior of aqueous mixtures is more difficult to correlate and estimate than that of nonpolar mixtures because small amounts of organic material can have a pronounced effect upon the surface concentrations and the resultant surface tension. These effects are usually modeled with thermodynamic methods that account for the activity coefficients. For example, a UNIFAC method [Suarez, J. T., C. Torres-Marchal, and P. Rasmussen, Chem. Eng. Sci., 44 (1989): 782] is recommended and illustrated in [PGL5]. For nonaqueous systems the extension of the Parachor method, used above for pure fluids, is a simple and reasonably effective method for estimating s for mixtures. Recommended Method Parachor correlation. Reference: Hugill, J. A., and A. J. van Welsenes, Fluid Phase Equilib., 29 (1986): 383; Macleod, D. B., Trans. Faraday Soc., 19 (1923): 38; Sugden, S. J., Chem. Soc., 125 (1924). Classification: Corresponding states. Expected uncertainty: 3 to 10 percent. Applicability: Nonaqueous mixtures.

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-177

Knotts* Group Contributions for the Parachor in Estimating Surface Tension

Group

Group

DPi

(a) Nonring C }CH3 55.25 >CH2 (n = 1–11) 39.92 >CH2 (n = 12–20) 40.11 >CH2 (n > 20) 40.51 >CH} 28.90 >C< 15.76 =CH2 49.76 =CH} 34.57 =C< 24.50 =C= 24.76 ≡CH 43.64 ≡C} 28.64 Branch corrections Per branch −6.02 sec-sec adjacency −2.73 sec-tert adjacency −3.61 tert-tert adjacency −6.10 (b) Nonaromatic ring C }CH2} 39.21 >CH} 23.94 >C< 7.19 =CH} 34.07 =C< 18.85 >CH} ( fused ring) 22.05 Ring corrections Three-member ring 12.67 Four-member ring 15.76 Five-member ring 7.04 Six-member ring 5.19 Seven-member ring 3.00 (c) Aromatic ring C >CH 34.36 >C} 16.07 }C} ( fused arom/arom) 19.73 }C} ( fused arom/aliph) 14.41 Arom ring corr ortho −0.60 para 3.40 meta 2.24 subst. naphthalene corr −7.07 (d) Oxygen groups }OH (alc, primary) 31.42 }OH (alc, sec) 22.68 }OH (alc, tertiary) 20.66 }OH (phenol) 30.32 }O} (nonring) 20.61 }O} (ring) 21.67 }O} (aromatic) 23.54 >C=O (nonring) 47.02 >C=O (ring) 50.04 O=CH} (aldehyde) 66.06 CHOOH ( formic) 94.01 }COOH (acid) 74.57 }OCHO ( formate) 82.29 }COO} (ester) 64.97 }COOCO} (acid anhyd) 115.07 }OC(=O)O} (ring) 84.05 *Knotts, T. A., et al., J. Chem. Eng. Data, 46 (2001): 1007.

Input data: Liquid and vapor r at mixture T; Parachors of pure components; xi. Description: ρ ρ σm   =  PL ,m 3 L ,m 3 − Pv ,m 3 V ,m 3  mN/m  10 kmol/m 10 kmol/m 

4

(2-120)

where sm = surface tension of the mixture PL,m, PV,m = Parachor of liquid and vapor mixtures, respectively rL,m, rV,m = mixture molar density of liquid and vapor, respectively

PL ,m =

C

1 ∑ ∑ x i x j (Pi + Pj ) 2 i =1 j=1

C

PV ,m =

44.98 44.63 46.44 46.53 29.04 31.97 33.92 10.77 15.71 23.24 26.49 80.94 65.23 67.54 93.43 73.64 57.05 91.69 77.12 64.32 73.86 75.05 66.89 63.34 65.33 68.30 51.37 51.75 51.47 72.21 93.20 90.13 21.81 26.24 51.16 54.56 66.30 70.39 90.84 92.04 105.11 54.50 44.93 28.64 115.59 48.84 22.65 25.06 106.03

Note that rV is generally very small compared to rL at temperatures substantially lower than Tc and can often be neglected. Example Estimate the surface tension for a 16.06 mol% n-pentane(1) + 83.94 mol% dichloromethane(2) mixture at 298.15 K. Required properties from DIPPR 801: P

C

1 ∑ ∑ y i y j (Pi + Pj ) 2 i =1 j=1

DPi

(e) Nitrogen groups R}NH2 (primary R) R}NH2 (sec R) R}NH2 (tert R) A}NH2 (attached to arom ring) >NH (nonring) >NH (ring) >NH (in arom ring) >N- (nonring) >N- (ring) }N= (nonring) >N (aromatic) HC≡N (hyd cyanide) }C≡N }C≡N (aromatic) ( f) Nitrogen and oxygen groups }C=ONH2 (amides) }C=ONH- (amides) }C=ON< (amides) }NHCHO >NCHO }N=O }NO2 }NO2 (aromatic) (g) Sulfur groups R-SH (primary R) R-SH (sec R) R-SH (tert R) }SH (aromatic) }S} (nonring) }S} (ring) }S} (aromatic) >S=O (nonring) >SO2 (nonring) >SO2 (ring) (h) Halogen groups }F }Cl }Br }I }F (aromatic) }Cl (aromatic) }Br (aromatic) }I (aromatic) (i) Si groups SiH4 >SiH} >Si< >Si< (ring) (j) Other inorganic groups }PO4 >P} >B} >Al} }ClO3

n-Pentane Dichloromethane

The following definitions are used for the liquid and vapor mixture Parachors: C

2-359

(2-121)

8.6173 15.5211

Mixture Parachor from Eq. (2-121) and mixture density: PL,m = (0.1606)2(231.1) + (0.1606)(0.8394)(231.1 + 146.6) + (0.8394)2(146.6) = 160.17 −1

where xi is the mole fraction of component i in the liquid and yi is the mole fraction of component i in the vapor.

rL/(kmol ⋅ m−3) at 298.15 K

231.1 146.6

−1  C x  0.1606 0.8394  kmol kmol ρL ,m =  ∑ i  =  = 13.752 3 +   8.6173 15.5211 m3 m  i =1 ρi 

2-360

PHYSICAL AnD CHEMICAL DATA

Calculation using Eq. (2-120): Because the temperature is low, the density of the vapor can be neglected, and mN σm = [(160.17) (0.013752)]4 = 23.54 m mN/m The estimated value is 2.9 percent below the experimental value of 24.24 mN/m reported by De Soria [De Soria, M. L. G., et al., J. Colloid Interface Sci., 103 (1985): 354].

FLAMMABILITY PROPERTIES Flash Point The flash point is the lowest temperature at which a liquid gives off sufficient vapor to form an ignitable mixture with air near the surface of the liquid or within the vessel used. ASTM test methods include procedures using a closed-cup apparatus (ASTM D 56, ASTM D 93, and ASTM D 3828), which is preferred, and an open-cup apparatus (ASTM D 92 and ASTM D 1310). Closed-cup values are typically lower than open-cup values. Estimation methods cannot take into account the apparatus and procedural influences on the observed flash point. Recommended Method Leslie-Geniesse method. Reference: Leslie, E. H., and J. C. Geniesse, International Critical Tables, vol. 2, McGraw-Hill, New York, 1927, p. 161. Classification: GC (element contributions). Expected uncertainty: ∼4 K or about 1.5 percent. Applicability: Organic compounds. Input data: Chemical structure and vapor pressure correlation. Description: The flash point TFP is obtained from the moles of oxygen required for stoichiometric combustion β, by back-solving from the vapor pressure correlation using P ∗ (TFP ) 1 = atm 8β

(2-122)

Recommended Method Rowley method. Reference: Rowley, J. R., R. L. Rowley, and W. V. Wilding, J. Hazard. Materials, 186 (2011): 551; Rowley, J. R., “Flammability Limits, Flash Points, and Their Consanguinity: Critical Analysis, Experimental Exploration, and Prediction,” Ph.D. Dissertation, Brigham Young University, 2010. Classification: GC and extended theory. Expected uncertainty: 10 percent for the lower limit; 25 percent for the upper limit. Applicability: Organic compounds. Input data: Group contributions from Tables 2-178, ∆Hfo, and the thermal properties (ideal gas heat of formation and average isobaric heat capacity) of the combustion products. These latter quantities are given in Table 2-179. A vapor pressure correlation is also required to obtain the corresponding flammability limit temperature. Description: A GC method is used to obtain the adiabatic flame temperature (Tad) of a lower-limit fuel-air mixture using the ΔTad, j contributions shown in Table 2-178:

∑n ⋅∆T j

o C p ,i H i (Tad ) ∆H f ,i (Tad − 298)K = + kJ/mol kJ/mol (kJ/mol ⋅ K)

NC, NSi, NS, NH, NX, NO = number of carbon, silicon, sulfur, hydrogen, halogen, and oxygen atoms in the molecule, respectively Example Estimate the flash point of phenol.

(2-125)

The lower flammability limit in volume percent is then calculated from

where P = vapor pressure at the flash point (2-123)

(2-124)

N

where N is the total number of groups in the molecule. The ideal gas enthalpies Hi of the combustion products and oxygen at Tad are then calculated from the ideal gas enthalpies of formation at 298 K and the average isobaric heat capacities (given in Table 2-179) with Eq. (2-125):

*

N - N X - 2NO β = N C + N Si + N S + H 4

ad,j

j

Tad =

100% LFL = ν= 1+ ν

∆H of ,fuel −

∑

products

ni H i (Tad ) + βH O2 (Tad )

C p ,air (Tad − 298) K

(2-126)

where β is defined in Eq. (2-123). The upper flammability limit in volume percent is obtained from the UFL group values given in Table 2-178 and

Structure:

 ∑n j ⋅ UFL j  UFL  j =  4.30C st0.72 +  % N    

(2-127)

where Cst is the fuel concentration required for stoichiometric combustion given by

Atomic contributions: Atom type

Number

C H O

6 6 1

β = 6 + (6 − 2∙1)/4 = 7 From Eq. (2-123), The DIPPR 801 correlation for the vapor pressure of phenol is

C st =

100 1 + 4.773β

(2-128)

Example Estimate the lower and upper flammability limits of toluene. Structure:

6  10,113 K P∗ T T  = exp  95.444 − − 10.09 In   + 6.7603 × 10 −18        T Pa K K  

When this expression is used in Eq. (2-122) and solved for temperature, one obtains TFP = 350.84 K, which is 0.4 percent below the DIPRR recommended value of 352.15 K.

Flammability Limits The lower flammability limit (LFL) is the equilibrium-mixture boundary-line volume percent of vapor or gas in air which if ignited will just propagate a flame away from the ignition source. Similarly, the upper flammability limit (UFL) is the upper volume percent boundary at which a flame can propagate in an ignited fuel/air equilibrium mixture. Each of these limits has a temperature at which the corresponding volumetric percent is reached. The lower flammability limit temperature corresponds approximately to the flash point, but since the flash point is determined with downward flame propagation and nonuniform mixtures and the lower flammability temperature is determined with upward flame propagation and uniform vapor mixtures, the measured lower flammability temperature is generally slightly lower than the flash point.

Group contributions: Group CH3—c c— c—H

nj

∆Tad

1 1 5

1862.04 1719.69 1731.92

UFLj −4.49 5.50 −1.25

Auxiliary calculations: Tad = [1862.04 + 1719.69 + (5)(1731.92)]/7 = 1748.8 β = 7 + 8/4 = 9

PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES

2-361

TABLE 2-178 Group Contributions for Quantities Used to Estimate Flammability Limits by Rowley et al.* Method for Organic Compounds (special notation: lower case indicates aromatic atom; # = triple bond; R = ring) Example

DTad,i

UFLi

#C}

vinyl acetate

991.44

−8.65

n

pyridine

2622.13

4.46

#CH

acetylene

1237.85

61.25

n

piperazine

2124.88

13.32

=C
NH

n-pentylamine

1566.76

−0.78

=CH

trans-2-butene

1751.82

0.30

>N}(c)

N-ethylaniline

2695.31

−7.25

=CH2

1-hexene

1558.49

3.06

N#C

benzonitrile

939.73

−9.72

=CH}(c)

styrene

−76.72

−11.24

N=C=O

methyl isocyanate

1147.48

4.95

=C}(c)

α-methylstyrene

2091.10

−5.13

}NO2

nitroethane

1777.58

−11.46

>C
N} −24.38 *Rowley, J. R., R. L. Rowley, and W. V. Wilding, J. Hazard. Materials, 186 (2011): 551; Rowley, J. R., “Flammability Limits, Flash Points, and Their Consanguinity: Critical Analysis, Experimental Exploration, and Prediction,” Ph.D. Dissertation, Brigham Young University, 2010.

Calculation of H(Tad ) from Eq. (2-125) and Table 2-179: Species

H°(298 K)/(kJ/mol)

Toluene CO2 H2O O2 Air

Cp/[kJ/(mol ⋅ K)]

50.17 −393.51 −241.81 0 0

— 0.0372433 0.0335780 0.0293468 0.0289937

LFL = H(Tad)/(kJ/mol) — −339.48 −193.10 42.58 —

From Eq. (2-126) and the stoichiometry of the combustion reaction, C7H8 + 9O2 = 7CO2 + 4H2O:  50.17 − [(7)(−339.48) + (4)(−193.10)] + (9)(42.58)  ν=  = 85.148 (0.0289937)(1749 − 298)  

TABLE 2-179 Ideal Gas Enthalpies of Formation and Average Heat Capacities of Combustion Gases for Use in Eq. (2-125) Species Air O2 N2 CO2 H2O SO2 SiO2 HF HCl HBr HI

H°/(kJ/mol) 0 0 0 −393.51 −241.81 −296.84 −305.43 −273.30 −92.31 −36.29 −26.50

100% = 1.16% 1 + 85.148

The UFL is found from Eqs. (2-127) and (2-128):

  100 UFL = (4.30)    1 + (4.773)(9) 

0.72

+

−4.49 + 5.50 + (5)(−1.25) = 7.02% 7

These values agree well with the DIPPR 801 recommended values of 1.2 and 7.1 percent, respectively. Flammability limit temperatures are found by determining the temperature at which the vapor pressure equals the partial pressure corresponding to the LFL or UFL. The vapor pressure correlation for toluene from DIPPR 801 is 2  6729.8 K P∗ T T  = exp 76.945 − − 8.179ln   + 5.3017 × 10 −6        T Pa K K  

Cp/[J/(mol ⋅ K)] 28.9937 29.3468 29.1260 37.2433 33.5780 39.8980 44.0254 29.1361 29.1436 29.1327 29.1583

Back-solving for T using the partial pressures of 0.0116 atm for LFL and 0.0702 atm for UFL gives TLFL = 277 K and TUFL = 311 K

Autoignition Temperature The autoignition temperature (AIT) is the minimum temperature for a substance to initiate self-combustion in air in the absence of an ignition source. Methods to estimate AIT are in general rather approximate. The method illustrated here may provide reasonable estimates, but significant errors can also result. Estimated values should not be assumed to be reliable for design and safety purposes.

2-362

PHYSICAL AnD CHEMICAL DATA TABLE 2-180 Group Contributions for Pintar* Autoignition Temperature Method for Organic Compounds Group

bi

Group

bi

Group

bi

}CH3 301.91 }Cl3 1073.47 }SO3} — >CH2 −10.86 }F 360.60 }SO4} −31.71 >CH} −275.17 }F2 755.54 }CO3} 442.26 >C< −570.43 }F3 1082.00 }P= −334.91 }H 391.48 }Br 420.96 }PO} −549.59 }OH 324.10 }Br2 607.69 }OPO2} — }O} −18.60 }Br3 1260.00 }PO4= −329.45 † }O}O} −397.61 }I 310.53 Si}C −147.69 =C=O 57.65 }I2 — Si}O† −136.99 † }CHO 195.20 }I3 — Si}H −310.52 }COOH 370.75 }NH2 354.11 Si}Cl† −200.88 }COO} 43.90 >NH 9.88 Si}N† — }CO}O}CO} 46.11 }N= −249.91 Si}Si — }C6H5 380.27 }CN 469.67 Al — m}C6H4 153.15 =C=N} −273.70 B — o}C6H4 77.48 =N}NH2 378.27 Cr — p}C6H4 99.87 >N}NH2 −215.02 Na 534.29 Aromatic ring −1339.65 }NO2 292.57 cis −29.19 = 578.72 }SH 273.84 trans −38.31 ≡ 1116.50 }S} −60.75 Nonarom.ring 605.97 }Cl 347.39 }SO} −91.10 Add’l.ring 565.11 }Cl2 726.03 }SO2} — Zn 349.02 *Pintar, A. J., Estimation of Autoignition Temperature, Technical Support Document DIPPR Project 912, Michigan Technological University, Houghton, 1996. † Does not include contribution of atoms attached to silicon.

Recommended Method Pintar method. Reference: Pintar, A. J., Estimation of Autoignition Temperature, Technical Support Document DIPPR Project 912, Michigan Technological University, Houghton, 1996. Classification: Group contributions. Expected uncertainty: 25 percent. Applicability: Organic compounds. Input data: Group contributions from Table 2-180. Description: A simple GC method with first-order contributions is given by N

AIT = ∑ ni bi

(2-129)

Example Estimate the autoignition temperature of 2,3-dimethylpentane. Structure and group information:

Group

ni

bi

}CH3 >CH2 >CH}

4 1 2

301.91 −10.86 −275.17

i =1

where ni is the number of groups of type i in the molecule and bi is the contribution of group i to the autoignition temperature. A more accurate but somewhat more complicated logarithmic GC method was also developed by Pintar in the same reference cited here.

Calculation using Eq. (2-129): AIT = 4(301.91) − 10.86 + 2(−275.17) = 646.4 K The estimated value is 6.3 percent above the DIPPR 801 recommended value of 608.15 K.

Section 3

Mathematics

Bruce A. Finlayson, Ph.D. Rehnberg Professor Emeritus, Department of Chemical Engineering, University of Washington; Member, National Academy of Engineering (Section Editor, numerical methods and all general material) Lorenz T. Biegler, Ph.D. Bayer Professor of Chemical Engineering, Carnegie Mellon University; Member, National Academy of Engineering (Optimization)

GEnERAL REFEREnCES MATHEMATICS General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Miscellaneous Mathematical Constants and Formulas . . . . . . . . . . . . . . . . . . . . . . . Integral Exponents (Powers and Roots) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Algebraic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arithmetic-Geometric Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Carleman’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cauchy-Schwarz Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minkowski’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hölder’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lagrange’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-4 3-5 3-5 3-6 3-6 3-6 3-6 3-6 3-6 3-6 3-6

MEnSURATIOn FORMULAS Plane Geometric Figures with Straight Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rectangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parallelogram (opposite sides parallel) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rhombus (equilateral parallelogram). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trapezoid ( four sides, two parallel) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quadrilateral ( four-sided) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Regular Polygon of n Sides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plane Geometric Figures with Curved Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ellipse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parabola . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Catenary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solid Geometric Figures with Plane Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rectangular Parallelepiped . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pyramid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Frustum of Pyramid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Volume and Surface Area of Regular Polyhedra with Edge l. . . . . . . . . . . . . . . . . Solids Bounded by Curved Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ellipsoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Torus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prolate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-6 3-6 3-6 3-6 3-6 3-6 3-6 3-6 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-8

Oblate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hemisphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ellipsoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Miscellaneous Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Volume of a Solid Revolution (the solid generated by rotating a plane area about the x axis) . . . . . . . . . . . . Area of a Surface of Revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Area Bounded by f (x), the x Axis, and the Lines x = a, x = b . . . . . . . . . . . . . . . . . Length of Arc of a Plane Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Irregular Areas and Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Irregular Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Irregular Volumes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-9

ELEMEnTARY ALGEBRA Operations on Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operations with Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fractional Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Factoring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laws of Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Progressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Permutations, Combinations, and Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cubic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quartic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Polynomials of the nth Degree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-9 3-9 3-9 3-9 3-9 3-9 3-9 3-9 3-9 3-9 3-10 3-10 3-10 3-10 3-10 3-10 3-10 3-10

AnALYTIC GEOMETRY Plane Analytic Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Straight Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Asymptotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conic Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parametric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solid Analytic Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lines and Planes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-11 3-11 3-11 3-11 3-11 3-12 3-12 3-12 3-12 3-1

3-2

MATHEMATICS

Space Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-13 3-13

PLAnE TRIGOnOMETRY Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Functions of Circular Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plane Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Values of the Trigonometric Functions for Common Angles . . . . . . . . . . . . . . . . Relations between Functions of a Single Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Functions of Negative Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relations between Angles and Sides of Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solutions of Triangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Law of Sines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Law of Tangents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Law of Cosines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Right Triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hyperbolic Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inverse Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnitude of the Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Approximations for Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-14 3-14 3-14 3-15 3-15 3-15 3-15 3-15 3-15 3-15 3-15 3-15 3-15 3-15 3-16 3-16 3-16 3-16 3-16

DIFFEREnTIAL AnD InTEGRAL CALCULUS Differential Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indeterminate Forms: L’Hôpital’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multivariable Calculus Applied to Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . State Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermodynamic State Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Derivatives of Intensive Thermodynamic Functions . . . . . . . . . . . . . . . . Integral Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indefinite Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods of Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definite Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods of Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-16 3-16 3-16 3-16 3-17 3-17 3-18 3-18 3-18 3-19 3-20 3-20 3-20 3-21 3-21 3-21 3-21

InFInITE SERIES Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operations with Infinite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tests for Convergence and Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Series Summation and Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sums for the First n Numbers to Integer Powers . . . . . . . . . . . . . . . . . . . . . . . . . . . Arithmetic Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geometric Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Harmonic Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Binomial Series (See Also Elementary Algebra) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Taylor’s Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maclaurin’s Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exponential Series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logarithmic Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trigonometric Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Taylor Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Sums of Infinite Series, and How They Grow. . . . . . . . . . . . . . . . . . . . . . . .

3-22 3-22 3-22 3-22 3-22 3-23 3-23 3-23 3-23 3-23 3-23 3-23 3-23 3-23 3-23 3-23

COMPLEX VARIABLES Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Special Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trigonometric Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Powers and Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elementary Complex Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Complex Functions (Analytic) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Functions of a Complex Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Singular Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Harmonic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conformal Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-23 3-23 3-23 3-23 3-23 3-23 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-25 3-25 3-25 3-25

DIFFEREnTIAL EQUATIOnS Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ordinary Differential Equations of the First Order. . . . . . . . . . . . . . . . . . . . . . . . . . . . Equations with Separable Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ordinary Differential Equations of Higher Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linear Differential Equations with Constant Coefficients and Right-Hand Member of Zero (Homogeneous) . . . . . . . . . . . . . . . . . . . . . . . . Linear Nonhomogeneous Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . Perturbation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Special Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Euler’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bessel’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Legendre’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laguerre’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hermite’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chebyshev’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Differential Equations of Second and Higher Order . . . . . . . . . . . . . . . . . Group Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Separation of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integral-Transform Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matched-Asymptotic Expansions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-25 3-26 3-26 3-26 3-26 3-27 3-27 3-27 3-27 3-27 3-27 3-27 3-27 3-27 3-27 3-28 3-28 3-29 3-29 3-30

DIFFEREnCE EQUATIOnS Nonlinear Difference Equations: Riccati Difference Equation . . . . . . . . . . . . . .

3-30

InTEGRAL EQUATIOnS Classification of Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-31

InTEGRAL TRAnSFORMS (OPERATIOnAL METHODS) Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sufficient Conditions for the Existence of the Laplace Transform . . . . . . . . . . Properties of the Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convolution Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of the Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fourier Cosine Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-32 3-32 3-32 3-33 3-33 3-33 3-33

MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS Matrix Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matrix Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vector and Matrix Norms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matrix Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LU Factorization of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solution of Ax = b by Using LU Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . QR Factorization of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Singular-Value Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Principal Component Analysis (PCA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-33 3-33 3-34 3-34 3-34 3-34 3-34 3-35 3-35 3-36

nUMERICAL APPROXIMATIOnS TO SOME EXPRESSIOnS Approximation Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-36

nUMERICAL AnALYSIS AnD APPROXIMATE METHODS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Solution of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Solution of Nonlinear Equations in One Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods for Nonlinear Equations in One Variable . . . . . . . . . . . . . . . . . . . . . . . . . Methods for Multiple Nonlinear Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Method of Successive Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Newton-Raphson Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lagrange Interpolation Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthogonal Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linear Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equally Spaced Forward Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equally Spaced Backward Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Central Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spline Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Use of Interpolation Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Smoothing Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Integration (Quadrature) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Newton-Cotes Integration Formulas (Equally Spaced Ordinates) for Functions of One Variable. . . . . . . . . . . . . . . . . Gaussian Quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Romberg’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthogonal Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cubic Splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-36 3-37 3-37 3-37 3-37 3-37 3-37 3-37 3-37 3-38 3-38 3-38 3-38 3-38 3-39 3-39 3-39 3-39 3-39 3-39 3-39 3-39 3-40 3-40 3-40 3-40

MATHEMATICS Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Dimensional Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gaussian Quadrature Points and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-40 3-40 3-40

nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS Implicit Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differential-Algebraic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computer Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability, Bifurcations, and Limit Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molecular Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ordinary Differential Equations—Boundary-Value Problems . . . . . . . . . . . . . . . . . Finite Difference Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finite Difference Methods Solved with Spreadsheets. . . . . . . . . . . . . . . . . . . . . . . Orthogonal Collocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Galerkin Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adaptive Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Singular Problems and Infinite Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Solution of Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Solution of Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . Parabolic Equations in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elliptic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hyperbolic Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finite Volume Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parabolic Equations in Two or Three Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . Computer Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-42 3-42 3-42 3-42 3-42 3-43 3-43 3-43 3-43 3-44 3-45 3-45 3-45 3-45 3-46 3-46 3-46 3-46 3-47 3-48 3-49 3-49 3-49 3-49

OPTIMIZATIOn Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gradient-Based Nonlinear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Local Optimality Conditions: A Kinematic Interpretation . . . . . . . . . . . . . . . . . . Convex Cases of NLP Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solving the General NLP Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Gradient-Based NLP Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Algorithmic Details for NLP Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimization Methods without Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classical Direct Search Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Derivative-Free Optimization (DFO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Global Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixed Integer Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixed Integer Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixed Integer Nonlinear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Development of Optimization Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-50 3-51 3-51 3-52 3-52 3-53 3-54 3-54 3-54 3-54 3-54 3-55 3-55 3-55 3-55 3-56 3-57

STATISTICS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Type of Data Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-58 3-58 3-58 3-58 3-58

Sample Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characterization of Chance Occurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enumeration Data and Probability Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Binomial Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geometric Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Poisson Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hypergeometric Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement Data and Sampling Densities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t Distribution of Averages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t Distribution for the Difference in Two Sample Means with Equal Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t Distribution for the Difference in Two Sample Means with Unequal Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chi-Square Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Confidence Interval for a Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Confidence Interval for the Difference in Two Population Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Confidence Interval for a Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tests of Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Nature of Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for a Mean Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Population Test of Hypothesis for Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for Paired Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for Matched Pairs: Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for a Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for a Proportion: Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for Two Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for Two Proportions: Procedure . . . . . . . . . . . . . . . . . . . . . . . . Goodness-of-Fit Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Goodness-of-Fit Test: Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Way Test for Independence for Count Data . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Way Test for Independence for Count Data: Procedure. . . . . . . . . . . . . . . . Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linear Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polynomial Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiple Nonlinear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Error Analysis of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis of Variance (ANOVA) and Factorial Design of Experiments . . . . . . . . . . ANOVA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis of Variance: Estimating the Variance of Four Treatments . . . . . . . . . . Factorial Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Level Factorial Design with Three Variables . . . . . . . . . . . . . . . . . . . . . . . . . .

3-3 3-59 3-59 3-59 3-59 3-59 3-59 3-60 3-60 3-60 3-61 3-61 3-62 3-62 3-62 3-63 3-63 3-63 3-63 3-64 3-64 3-64 3-64 3-65 3-65 3-66 3-66 3-67 3-67 3-67 3-68 3-68 3-69 3-69 3-69 3-70 3-70 3-70 3-70 3-70 3-71 3-71 3-71 3-72 3-72

DIMEnSIOnAL AnALYSIS PROCESS SIMULATIOn Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Modules or Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Commercial Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-73 3-74 3-74 3-74 3-75

GEnERAL REFEREnCES Courant, R., and D. Hilbert, Methods of Mathematical Physics, vol. I, Interscience, New York, 1953; Finlayson, B. A., Nonlinear Analysis in Chemical Engineering, McGraw-Hill, New York, 1980; Finlayson, B. A., L. T. Biegler, and I. E. Grossmann, Mathematics in Chemical Engineering, Ullmann’s Encyclopedia of Industrial Chemistry, Published Online: 15 DEC 2006, DOI: 10.1002/14356007.b01_01.pub2, Wiley, New York, 2006; Jeffrey, A., Mathematics for Engineers and Scientists, 6th ed., Chapman & Hall/CRC, New York, 2004; Kaplan, W., Advanced Calculus, 5th ed., Addison-Wesley, Redwood City, Calif., 2003; Lipschultz, S., M. Spiegel, and J. Liu, Schaum’s Outline of Mathematical Handbook of Formulas and Tables, 4th ed., McGraw-Hill Education, New York, 2012; Logan, J. D., and W. R. Wolesensky, Mathematical Methods in Biology, Wiley, New York, 2009; Olver, F. W. J., D. W. Lozier, R. F. Boisvert, and C. W. Clark, eds., NIST Handbook of Mathematical Functions, Cambridge University

Press, London, 2010; see also http://dlmf.nist.gov; Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Plannery, Numerical Recipes, 3d ed., Cambridge University Press, London, 2007; Rice, R. G., and D. D. Do, Applied Mathematics and Modeling for Chemical Engineers, 2d ed., Wiley, New York, 2012; Stroud, K. A., and D. J. Booth, Engineering Mathematics, 7th ed., Industrial Press, South Norwick, Conn., 2013; Thompson, W. J., Atlas for Computing Mathematical Functions, Wiley, New York, 1997; Varma, A., and M. Morbidelli, Mathematical Methods in Chemical Engineering, Oxford Press, New York, 1997; Weisstein, E. W., CRC Concise Encyclopedia of Mathematics, 3d ed., CRC Press, New York, 2009; Wrede, R. C., and M. R. Spiegel, Schaum’s Outline of Theory and Problems of Advanced Calculus, 3d ed., McGraw-Hill, New York, 2010.

MATHEMATICS GEnERAL The basic problems of the sciences and engineering fall broadly into three categories: 1. Steady-state problems. In such problems the configuration of the system is to be determined. This solution does not change with time but continues indefinitely in the same pattern, hence the name steady state. Typical chemical engineering examples include steady temperature distributions in heat conduction, equilibrium in chemical reactions, and steady diffusion problems. 2. Eigenvalue problems. These are extensions of equilibrium problems in which critical values of certain parameters are to be determined in addition to the corresponding steady-state configurations. The determination of eigenvalues may also arise in propagation problems and stability problems. Typical chemical engineering problems include those in heat transfer and resonance in which certain boundary conditions are prescribed. 3. Propagation problems. These problems are concerned with predicting the subsequent behavior of a system from a knowledge of the initial state. For this reason they are often called the transient (time-varying) or unsteady-state phenomena. Chemical engineering examples include the transient state of chemical reactions (kinetics), the propagation of pressure waves in a fluid, transient behavior of an adsorption column, and the rate of approach to equilibrium of a packed distillation column. The mathematical treatment of engineering problems involves four basic steps: 1. Formulation. This involves the expression of the problem in mathematical language. That translation is based on the appropriate physical laws governing the process. 2. Solution. Appropriate mathematical and numerical operations are carried out so that logical deductions may be drawn from the mathematical model. 3. Interpretation. This process develops relations between the mathematical results and their meaning in the physical world. 4. Refinement. The procedure is recycled to obtain better predictions, as indicated by experimental checks. Steps 1 and 2 are of primary interest here. The actual details are left to the various subsections, and only general approaches will be discussed. The formulation step may result in algebraic equations, difference equations, differential equations, integral equations, or combinations of these. In any event these mathematical models usually arise from statements of physical laws such as the laws of mass and energy conservation in the form Input of x - output of x + production of x = accumulation of x

Many general laws of the physical universe are expressible by differential equations. Specific phenomena are then singled out from the infinity of solutions of these equations by assigning the individual initial or boundary conditions which characterize the given problem. For steady-state or boundary-value problems (Fig. 3-1), the solution must satisfy the differential equation inside the region and the prescribed conditions on the boundary.

FIG. 3-1 Boundary conditions.

In mathematical language, the propagation problem is known as an initialvalue problem (Fig. 3-2). Schematically, the problem is characterized by a differential equation plus an open region in which the equation holds. The solution of the differential equation must satisfy the initial conditions plus any “side” boundary conditions.

FIG. 3-2 Propagation problem.

The description of phenomena in a continuous medium such as a gas or a fluid often leads to partial differential equations. In particular, phenomena of “wave” propagation are described by a class of partial differential equations called hyperbolic, and these are essentially different in their properties from other classes such as those that describe equilibrium (elliptic) or diffusion and heat transfer (parabolic). Prototypes are as follows: 1. Elliptic. Laplace’s equation ∂2 u ∂2 u + =0 ∂x 2 ∂ y 2

or Rate of input of x - rate of output of x + rate of production of x = rate of accumulation of x where x = mass, energy, etc. These statements may be abbreviated by the statement Input - output + production = accumulation 3-4

Poisson’s equation ∂2 u ∂2 u + = g (x , y ) ∂x 2 ∂ y 2 These do not contain the variable t (time) explicitly; accordingly, their solutions represent equilibrium configurations. Laplace’s equation corresponds to a “natural” equilibrium, while Poisson’s equation corresponds to an

MATHEMATICS equilibrium under the influence of g(x, y). Steady heat-transfer and masstransfer problems are elliptic. 2. Parabolic. The heat equation ∂u ∂2 u ∂2 u = + ∂t ∂ x 2 ∂ y 2 describes unsteady or propagation states of diffusion as well as heat transfer. 3. Hyperbolic. The wave equation ∂2 u ∂2 u ∂2 u = + ∂t 2 ∂ x 2 ∂ y 2 describes wave propagation of all types when the assumption is made that the wave amplitude is small and that interactions are linear. The solution phase has been characterized in the past by a concentration on methods to obtain analytic solutions to the mathematical equations. These efforts have been most fruitful in the area of linear equations such as those just given. However, many natural phenomena are nonlinear. While there are a few nonlinear problems that can be solved analytically, most cannot. In those cases, numerical methods are used. Due to the widespread availability of software for computers, the engineer has quite good tools available. Numerical methods almost never fail to provide an answer to any particular situation, but they can never furnish a general solution of any problem. The mathematical details outlined here include both analytic and numeric techniques useful in obtaining solutions to problems. Our discussion to this point has been confined to those areas in which the governing laws are well known. However, in many areas, information on the governing laws is lacking and statistical methods are used. Broadly speaking, statistical methods may be of use whenever conclusions are to be drawn or decisions made on the basis of experimental evidence. Since statistics could be defined as the technology of the scientific method, it is primarily concerned with the first two aspects of the method, namely, the performance of experiments and the drawing of conclusions from experiments. Traditionally the field is divided into two areas: 1. Design of experiments. When conclusions are to be drawn or decisions made on the basis of experimental evidence, statistical techniques are most useful when experimental data are subject to errors. First, the design of experiments may be carried out in such a fashion as to avoid some of the sources of experimental error and make the necessary allowances for that portion which is unavoidable. Second, the results can be presented in terms of probability statements which express the reliability of the results. Third, a statistical approach frequently forces a more thorough evaluation of the experimental aims and leads to a more definitive experiment than would otherwise have been performed. 2. Statistical inference. The broad problem of statistical inference is to provide measures of the uncertainty of conclusions drawn from experimental data. This area uses the theory of probability, enabling scientists to assess the reliability of their conclusions in terms of probability statements. Both of these areas, the mathematical and the statistical, are intimately intertwined when applied to any given situation. The methods of one are often combined with those of the other. And both, in order to be successfully used, must result in the numerical answer to a problem, that is, they constitute the means to an end. Increasingly the numerical answer is being obtained from the mathematics with the aid of computers. The mathematical notation is given in Table 3-1. MISCELLAnEOUS MATHEMATICAL COnSTAnTS AnD FORMULAS Numerical values of the constants that follow are approximate to the number of significant digits given. π = 3.1415926536 e = 2.7182818285 γ = 0.5772156649 Radian = 57.2957795131°

Pi Napierian (natural) logarithm base Euler’s constant

Integral Exponents (Powers and Roots) If m and n are positive integers and a and b are numbers or functions, then the following properties hold: a −n = 1/a n a≠0 (ab)n = a n b n a n a m = a n+m (a n )m = a nm n a = a 1/n if a 0 = 1 (a ≠ 0) 0 a = 0 (a ≠ 0)

a>0

3-5

TABLE 3-1 Mathematical Signs, Symbols, and Abbreviations ∓ (±)

plus or minus (minus or plus)

∶

divided by, ratio sign

∷

proportional sign




greater than

≯

not greater than

≅

approximately equals, congruent to

∼

similar to

≎ ≠

equivalent to

≐

not equal to approaches, is approximately equal to

∝

varies as

∞

infinity

∴

therefore

∩

intersection square root cube root

3 n

nth root

∠

angle

⊥

perpendicular to

∙ x log (or log10) ln (or loge) e a° a′ a″ sin cos tan cot (or ctn) sec csc sin–1 sinh cosh tanh sinh–1 f (x) or f(x) Δx Σ dx dy/dx or y ′ d 2y/dx 2 or y″ d ny/dx n ∂y/∂x ∂ny/∂xn ∂n z ∂x ∂ y

parallel to

∫ ∫

numerical value of x common logarithm or Briggsian logarithm natural logarithm or hyperbolic logarithm or Napierian logarithm base (2.718) of natural system of logarithms an angle a degrees a prime, an angle a minutes a double prime, an angle a seconds, a second sine cosine tangent cotangent secant cosecant inverse sin, anti-sine, or angle whose sine is hyperbolic sine hyperbolic cosine hyperbolic tangent anti-hyperbolic sine or angle whose hyperbolic sine is function of x increment of x, delta x summation of differential of x derivative of y with respect to x second derivative of y with respect to x nth derivative of y with respect to x partial derivative of y with respect to x nth partial derivative of y with respect to x nth partial derivative with respect to x and y integral of

b a .

y ÿ

Δ or ∇2 d ∮

integral between the limits a and b first derivative of y with respect to time second derivative of y with respect to time  ∂2 ∂2 ∂2  laplacian  2 + 2 + 2   ∂x ∂ y ∂z  sign of a variation sign for integration around a closed path

3-6

MATHEMATICS The equality holds if, and only if, the sequences |a1|p, |a2|p, …, |an|p and |b1|q, |b2|q, …, |bn|q are proportional and the argument (angle) of the complex numbers ak bk is independent of k. This last condition is of course automatically satisfied if a1, …, an and b1, …, bn are positive numbers. Lagrange’s Inequality Let a1, a2, …, an and b1, b2, …, bn be real numbers. Then

Logarithms log ab = log a + log b , a > 0, b > 0 log a n = n log a log (a /b) = log a − log b

2

log n a = (1/n ) log a The common logarithm (base 10) is denoted log a (or log10 a in some texts). The natural logarithm (base e) is denoted ln a (or in some texts loge a). If the text is ambiguous (perhaps using log x for ln x), test the formula by evaluating it. ALGEBRAIC InEQUALITIES Arithmetic-Geometric Inequality Let An and Gn denote, respectively, the arithmetic and the geometric means of a set of positive numbers a1, a2, …, an. Then An ≥ Gn, that is,

  n  n  n  ∑ ak bk  =  ∑ a k2  ∑ bk2  − ∑ (a k b j − a j bk )2        k =1   k =1  1 ≤ k ≤ j ≤ n  k =1 Example Two chemical engineers, Mary and John, purchase stock in the same company at times t1, t2, …, tn, when the price per share is, respectively, p1, p2, …, pn. Their methods of investment are different, however: John purchases x shares each time, whereas Mary invests P dollars each time ( fractional shares can be purchased). Who is doing better? While one can argue intuitively that the average cost per share for Mary does not exceed that for John, we illustrate a mathematical proof using inequalities. The average cost per share for John is equal to n

a1 + a2 +  + an ≥ (a1a2  an )1/n n

x ∑ pi

The equality holds only if all the numbers ai are equal. Carleman’s Inequality The arithmetic and geometric means just defined satisfy the inequality

Total money invested i =1 = Number of shares purchased nx

1 2

nP n = n 1 P ∑p ∑p i =1 i i =1 i

 ar )1/r ≤ neAn

n

r =1

where e is the best possible constant in this inequality. Cauchy-Schwarz Inequality Let a = (a1, a2, …, an) and b = (b1, b2, …, bn), where the ai and bi are real or complex numbers. Then 2

n

∑ (a b ) k k

k =1

  n n ≤  ∑| a k |2  ∑| bk |2     k =1  k =1

The equality holds if, and only if, the vectors a and b are linearly dependent (i.e., one vector is a scalar times the other vector). Minkowski’s Inequality Let a1, a2, …, an and b1, b2, …, bn be any two sets of complex numbers. Then for any real number p > 1,  n  ∑| ak + bk | p      k =1

1/p

 n ≤ ∑| a k | p    k =1

1/p

 n + ∑| bk | p    k =1

 n ∑ akbk ≤ ∑| ak | p  k =1   k =1

1/ p

 n ∑| bk |q      k =1

Thus the average cost per share for John is the arithmetic mean of p1, p2, …, pn, whereas that for Mary is the harmonic mean of these n numbers. Since the harmonic mean is less than or equal to the arithmetic mean for any set of positive numbers and the two means are equal only if p1 = p2 = … = pn, we conclude that the average cost per share for Mary is less than that for John if two of the prices pi are distinct. One can also give a proof based on the Cauchy-Schwarz inequality. To this end, define the vectors a = ( p1−1/2 , p2−1/2 ,  , pn−1/2 ) b = ( p11/2 , p21/2 ,  , pn1/2 ) Then a · b = 1 + … + 1 = n, and so by the Cauchy-Schwarz inequality

1/p

Hölder’s Inequality Let a1, a2, …, an and b1, b2, …, bn be any two sets of complex numbers, and let p and q be positive numbers with 1/p + 1/q = 1. Then n

1 n ∑ pi n i =1

The average cost per share for Mary is

n

∑(a a

=

n

n

1 pi

(a ⋅ b ) 2 = n 2 ≤ ∑ i =1

∑p

j

j =1

with the equality holding only if p1 = p2 = … = pn. Therefore n

∑p

i

n

1/q n

∑ i =1

1 pi

≤

i =1

n

MEnSURATIOn FORMULAS Reference: http://mathworld.wolfram.com/SphericalSector.html, etc.

PLAnE GEOMETRIC FIGURES WITH STRAIGHT BOUnDARIES Let A denote area and V volume in the following. Triangles (see also “Plane Trigonometry”) A = ½bh where b = base, h = altitude. Rectangle A = ab where a and b are the lengths of the sides. Parallelogram (opposite sides parallel) A = ah = ab sin α where a and b are the lengths of the sides, h is the height, and α is the angle between the sides. See Fig. 3-3. Rhombus (equilateral parallelogram) A = ½ab where a and b are the lengths of the diagonals. Trapezoid (four sides, two parallel) A = ½(a + b)h where the lengths of the parallel sides are a and b and h = height. Quadrilateral (four-sided) A = ½ab sin q where a and b are the lengths of the diagonals and the acute angle between them is q.

Regular Polygon of n Sides

See Fig. 3-4.

1 180° A = nl 2 cot where l = length of each side 4 n

FIG. 3-3 Parallelogram.

FIG. 3-4 Regular polygon.

MEnSURATIOn FORMULAS l 180° R = csc 2 n

where R is the radius of the circumscribed circle

l 180° r = cot 2 n

where r is the radius of the inscribed circle

3-7

Radius r of Circle Inscribed in Triangle with Sides a, b, c r=

( s − a )( s − b)( s − c ) where s = 1 2 (a + b + c ) s

FIG. 3-7 Parabola .

FIG. 3-6 Ellipse .

Radius R of Circumscribed Circle R=

abc 4 s ( s − a )( s − b)( s − c )

Ellipse (Fig. 3-6)

Let the semiaxes of the ellipse be a and b. A = πab

Area of Regular Polygon of n Sides Inscribed in a Circle of Radius r A = (nr /2) sin (360°/n) 2

C = 4aE(e) where e2 = 1 - b2/a2 and E(e) is the complete elliptic integral of the second kind

Perimeter of Inscribed Regular Polygon

2  π  1 E (e ) = 1 −   e 2 +  2  2 

P = 2nr sin (180°/n) Area of Regular Polygon Circumscribed about a Circle of Radius r A = nr2 tan (180°/n) Perimeter of Circumscribed Regular Polygon P = 2nr tan

180° n

PLAnE GEOMETRIC FIGURES WITH CURVED BOUnDARIES Circle (see Fig. 3-5). Let C = circumference r = radius D = diameter A = area S = arc length subtended by q l = chord length subtended by q H = maximum rise of arc above chord, r - H = d q = central angle (rad) subtended by arc S C = 2πr = πD (π = 3.14159 …) S = rq = ½ Dq l = 2 r 2 − d 2 = 2 r sin (θ/2) = 2 d tan (θ/2) 1 1 θ 4 r 2 − l 2 = l cot 2 2 2 S d l θ = = 2 cos−1 = 2 sin −1 r r D

d=

A (circle) = πr2 = ¼πD2 A (sector) = ½rS = ½r2q A (segment) = A (sector) - A (triangle) = ½r2(q - sin q) Ring (area between two circles of radii r1 and r 2) The circles need not be concentric, but one of the circles must enclose the other. A = π(r1 + r2)(r1 - r2)

FIG. 3-5 Circle .

r1 > r2

[an approximation for the circumference C = 2 π (a 2 + b 2 )/ 2)]. Parabola

(Fig. 3-7)

Length of arc EFG =

4x2 + y 2 +

Area of section EFG =

4 xy 3

y 2 2x + 4x 2 + y 2 ln 2x y

Catenary (the curve formed by a cord of uniform weight suspended freely between two points A and B; Fig. 3-8) y = a cosh (x/a) The length of arc between points A and B is equal to 2a sinh (L/a). The sag of the cord is D = a cosh (L/a) - a. SOLID GEOMETRIC FIGURES WITH PLAnE BOUnDARIES Cube Volume = a3; total surface area = 6a2; diagonal = a 3 , where a = length of one side of the cube. Rectangular Parallelepiped Volume = abc; surface area = 2(ab + ac + bc); diagonal = a 2 + b 2 + c 2 , where a, b, and c are the lengths of the sides. Prism Volume = (area of base) × (altitude); lateral surface area = (perimeter of right section) × (lateral edge). Pyramid Volume = ⅓ (area of base) × (altitude); lateral area of regular pyramid = ½ (perimeter of base) × (slant height) = ½ (number of sides) (length of one side) (slant height) . Frustum of Pyramid It is formed from the pyramid by cutting off the top with a plane V = 1 3 ( A1 + A2 + A1 ⋅ A2 )h where h = altitude and A1 and A2 are the areas of the base; lateral area of a regular figure = ½ (sum of the perimeters of base) × (slant height) .

FIG. 3-8 Catenary .

3-8

MATHEMATICS

Volume and Surface Area of Regular Polyhedra with Edge l Type of surface 4 equilateral triangles 6 squares 8 equilateral triangles 12 pentagons 20 equilateral triangles

Name Tetrahedron Hexahedron (cube) Octahedron Dodecahedron Icosahedron

Volume 0.1179l3 1.0000l3 0.4714l3 7.6631l3 2.1817l3

Surface area 1.7321l2 6.0000l2 3.4641l2 20.6458l2 8.6603l2

SOLIDS BOUnDED BY CURVED SURFACES Cylinders (Fig. 3-9) V = (area of base) × (altitude); lateral surface area = (perimeter of right section) × (lateral edge). Right Circular Cylinder V = π (radius)2 × (altitude); lateral surface area = 2π (radius) × (altitude). Truncated Right Circular Cylinder V = πr2h

lateral area = 2πrh

h = ½ (h1 + h2) Hollow Cylinders Volume = πh(R2 - r2), where r and R are the internal and external radii, respectively, and h is the height of the cylinder. Sphere See Fig. 3-10. V (sphere) = 4∕3πR3 = 1∕6πD3 V (spherical sector) = ⅔πR2h1 V (spherical segment of one base) = 1∕6πh1(3 r 22 + h 21) V (spherical segment of two bases) = 1∕6πh2(3 r 21+ 3 r 22 + h 22 ) A (sphere) = 4πR2 = πD2 A (zone) = 2πRh = πDh A (lune on surface included between two great circles, with inclination of q radians) = 2R2q . Cone V = ⅓ (area of base) × (altitude) . Right Circular Cone V = (π/3)r2h, where h is the altitude and r is the radius of the base; curved surface area = πr r 2 + h 2 , curved surface of the frustum of a right cone = π(r1 + r2 ) h 2 + (r1 − r2 )2 , where r1 and r2 are the radii of the base and top, respectively, and h is the altitude; volume of the the frustum of a right cone = π(h/3) (r 21 + r1r2 + r 22) = h/3 ( A1 + A2 + A1 A2 ), where A1 = area of base and A2 = area of top . Ellipsoid V = (4∕3)πabc, where a, b, and c are the lengths of the semiaxes . Torus (obtained by rotating a circle of radius r about a line whose distance is R > r from the center of the circle) V = 2π2Rr2

Surface area = 4π2Rr

Prolate Spheroid ( formed by rotating an ellipse about its major axis 2a) Surface area = 2πb2 + 2π(ab/e) sin-1 e

b2 1 + e ln 1−e e

Hemisphere V =

V = 4∕3πa2b

π 3 D 12

π A = D2 2

For a hemisphere (concave up) partially filled to a depth h1, use the formulas for spherical segment with one base, which simplify to V = πh 21(R - h1/3) = πh 21 (D/2 - h1/3) A = 2πRh1 = πDh1 For a hemisphere (concave down) partially filled from the bottom, use the formulas for a spherical segment of two bases, one of which is a plane through the center, where h = distance from the center plane to the surface of the partially filled hemisphere . V = πh(R2 - h2/3) = πh(D2/4 - h2/3) A = 2πRh = πDh Cone For a cone partially filled, use the same formulas as for right circular cones, but use r and h for the region filled . Ellipsoid If the base of a vessel is one-half of an oblate spheroid (the cross section fitting to a cylinder is a circle with radius of D/2 and the minor axis is smaller), then use the formulas for one-half of an oblate spheroid . V = 0 .1745D3 V = 0 .1309D3

S = 1 .236D2 S = 1 .084D2

minor axis = D/3 minor axis = D/4

MISCELLAnEOUS FORMULAS See also “Differential and Integral Calculus .” Volume of a Solid Revolution (the solid generated by rotating a plane area about the x axis) V = π ∫ [ f ( x )]2 dx b

a

where y = f (x) is the equation of the plane curve and a ≤ x ≤ b. Area of a Surface of Revolution S = 2 π ∫ y ds b

a

where ds = 1 + (dy /dx )2 dx and y = f ( x ) is the equation of the plane curve rotated about the x axis to generate the surface . Area Bounded by f (x), the x Axis, and the Lines x = a, x = b A=

∫

b a

f ( x ) dx

[ f ( x ) ≥ 0]

Length of Arc of a Plane Curve If y = f (x), Length of arc s =

V = 4∕3πab2

where a and b are the major and minor axes and e = eccentricity (e < 1) . Oblate Spheroid ( formed by the rotation of an ellipse about its minor axis 2b) Surface area = 2 πa 2 + π

For process vessels, the formulas reduce to the following:

∫

b a

2

 dy  1 +   dx  dx 

If x = f (t), y = g(t), Length of arc s =

∫

t1 t0

2

2

 dx   dy    +   dt  dt   dt 

In general, (ds)2 = (dx)2 + (dy)2 . IRREGULAR AREAS AnD VOLUMES Irregular Areas Let y0, y1, …, yn be the lengths of a series of equally spaced parallel chords and h be their distance apart (Fig . 3-11) . The area of the figure is given approximately by any of the following:

FIG. 3-9 Cylinder .

FIG. 3-10 Sphere .

FIG. 3-11 Irregular area .

ELEMEnTARY ALGEBRA AT = (h/2)[(y0 + yn) + 2(y1 + y2 +  + yn-1)] As = (h/3)[(y0 + yn) + 4(y1 + y3 + y5 +  + yn-1) + 2(y2 + y4 +  + yn-2)]

(trapezoidal rule) (n even, Simpson’s rule)

3-9

The greater the value of n, the greater the accuracy of the approximation. Irregular Volumes To find the volume, replace the y’s by cross-sectional areas Aj and use the results in the preceding equations.

ELEMEnTARY ALGEBRA References: Stillwell, J., Elements of Algebra, Springer-Verlag, New York, 2010; Rich, B., and P. Schmidt, Schaum’s Outline of Elementary Algebra, 3d ed., McGraw-Hill Education, New York, 2009.

OPERATIOnS On ALGEBRAIC EXPRESSIOnS An algebraic expression will be denoted here as a combination of letters and numbers such as 3ax - 3xy + 7x2 + 7x3/2 - 2.8xy Addition and Subtraction Only like terms can be added or subtracted in two algebraic expressions. Example (3x + 4xy - x2) + (3x2 + 2x - 8xy) = 5x - 4xy + 2x2. Multiplication Multiplication of algebraic expressions is term by term, and corresponding terms are combined. Example (2x + 3y - 2xy)(3 + 3y) = 6x + 9y + 9y2 - 6xy2. Division This operation is analogous to that in arithmetic. Example Divide 3e2x + ex + 1 by ex + 1.

Divisor e x + 1

Dividend | 3e 2x + e x + 1

n n! where   = = number of combination of n things taken j at a time  j  j !(n − j )! and n! = 1 ⋅ 2 ⋅ 3 ⋅ 4 … n, 0! = 1. Example ( x + y ) 4 = x 4 + 4 x 3 y + 6 x 2 y 2 + 4 xy 3 + y 4. If n is not a positive integer, the sum formula no longer applies and an infinite series results for (a + b)n. Example (1 + x)1/2 = 1 + ½x - ½ ⋅ ¼x2 + ½ ⋅ ¼ ⋅ 3∕6 x3 … (convergent for x2 < 1) . Additional discussion can be found under “Infinite Series .” PROGRESSIOnS An arithmetic progression is a succession of terms such that each term, except the first, is derivable from the preceding by the addition of a quantity d, called the common difference . All arithmetic progressions have the form a, a + d, a + 2d, a + 3d, … . With a = first term, l = last term, d = common difference, n = number of terms, and s = sum of the terms, the following relations hold: s n −1 l = a + (n − 1)d = + d n 2 n n n s = [2 a + (n − 1)d ] = (a + l ) = [2 l − (n − 1)d ] 2 2 2 s (n − 1)d 2 s = −l a = l − (n − 1)d = − 2 n n l − a 2( s − an ) 2(nl − s ) = = d= n − 1 n (n − 1) n (n − 1) l −a 2s +1= n= d l +a

3e x − 2 quotient

3e 2x + 3e x − 2e x + 1 −2 e x − 2 + 3 (remainder) Therefore, 3e2x + ex + 1 = (ex + 1)(3ex - 2) + 3. Operations with Zero All numerical computations (except division) can be done with zero. Both a/0 and 0/0 have no meaning. Fractional Operations  −x  x −x x x −x x ax if a ≠ 0 − = −  = = = = y y −y y ay −y  −y y  x   z  xz x z x±z x /y  x   t  xt ± = =   =    =   y y y y t yt z /t  y   z  yz   Factoring It is that process of analysis consisting of reducing a given expression to the product of two or more simpler expressions, called factors. Some of the more common expressions are factored here: (1) x2 - y2 = (x - y)(x + y) (2) x2 + 2xy + y2 = (x + y)2 (3) x3 - y3 = (x - y)(x2 + xy + y2) (4) x3 + y3 = (x + y)(x2 - xy + y2) (5) x4 - y4 = (x - y)(x + y)(x2 + y2) (6) x5 + y5 = (x + y)(x4 - x3y + x2y2 - xy3 + y4) (7) xn - yn = (x - y)(xn -1 + xn -2y + xn -3y2 + … + yn -1) Laws of Exponents (a n )m = a nm ; a n + m = a n ⋅ a m ; a n/m = (a n )1/m ; a n − m = a n /a m ; a 1/m = m a ; a 1/2 = a ; x 2 = | x | (absolute value of x ). For x > 0, y > 0, xy = x y ;

The arithmetic mean or average of two numbers a and b is (a + b)/2 and of n numbers a1, …, an is (a1 + a2 + … + an)/n. A geometric progression is a succession of terms such that each term, except the first, is derivable from the preceding by the multiplication of a quantity r called the common ratio . All such progressions have the form a, ar, ar2, …, ar n-1 . With a = first term, l = last term, r = ratio, n = number of terms, and s = sum of the terms, the following relations hold: l = ar n −1 = s=

a (r n − 1) a (1 − r n ) rl − a lr n − l = = = r −1 r − 1 r n − r n −1 1− r

a=

s−a (r − 1) s log l − log a l = ,r = , log r = n −1 rn−l rn −1 s−l

n=

log[ a + (r − 1) s ] − log a log l − log a +1 = log r log r

The geometric mean of two nonnegative numbers a and b is ab ; of n numbers is (a1a2 … an)1/n . The geometric mean of a set of positive numbers is less than or equal to the arithmetic mean . Example Find the sum of 1 + ½ + ¼ + … + 1∕64 . Here a = 1, r = ½, n = 7 . Thus

for x > 0 n x m = x m/n ; n 1/x = 1/ n x s=

BInOMIAL THEOREM

+

1

2

( 1 64 ) − 1 = 127/64 1 −1 2

s = a + ar + ar 2 +  + ar n −1 =

If n is a positive integer, then (a + b)n = a n + na n−1b +

a + (r − 1) s (r − 1) sr n − 1 = r rn −1

n (n − 1) n−2 2 a b 2!

n  n  n− j j n (n − 1) (n − 2) n−3 3 a b a b +  + b n = ∑  j  3! j = 0

If | r | < 1,

then

lim s =

n →∞

a ar n − 1− r 1− r

a 1−r

which is called the sum of the infinite geometric progression .

3-10

MATHEMATICS

Example The present worth (PW) of a series of cash flows Ck at the end of year k is n

PW = ∑ k =1

Ck (1 + i ) k

where i is an assumed interest rate. (Thus the present worth always requires specification of an interest rate.) If all the payments are the same, Ck = R, then the present worth is n

PW = R ∑ k =1

1 (1 + i ) k

This can be rewritten as PW =

R 1+ i

n

1

∑ (1 + i ) k =1

k -1

=

R 1+ i

n -1

1

∑ (1 + i ) j =0

j

This is a geometric series with r = 1/(1 + i) and a = R/(1 + i). The formulas above give PW (= s ) =

R (1 + i )n − 1 i (1 + i )n

The same formula applies to the value of an annuity (PW) now, to provide for equal payments R at the end of each of n years, with interest rate i. A progression of the form a, (a + d)r, (a + 2d)r2, (a + 3d)r3, etc., is a combined arithmetic and geometric progression. The sum of n such terms is s=

a − [ a + (n − 1)d ]r n rd (1 − r n − 1 ) + 2 1− r (1 − r )

a + rd /(1 − r )2 . 1− r The nonzero numbers a, b, c, etc., form a harmonic progression if their reciprocals 1/a, 1/b, 1/c, etc., form an arithmetic progression. Example The progression 1, ⅓, 1∕5, 1∕7, …, 1∕31 is harmonic since 1, 3, 5, 7, …, 31 form an arithmetic progression . The harmonic mean of two numbers a and b is 2ab/(a + b) .

Quadratic Equations Every quadratic equation in one variable is expressible in the form ax2 + bx + c = 0, a ≠ 0 . This equation has two solutions, say, x1 and x2, given by x 1  −b ± b 2 − 4 ac = x 2  2a If a, b, and c are real, the discriminant b2 - 4ac gives the character of the roots . If b2 - 4ac > 0, the roots are real and unequal . If b2 - 4ac < 0, the roots are complex conjugates . If b2 - 4ac = 0, the roots are real and equal. Two quadratic equations in two variables in general can be solved only by numerical methods (see Numerical Analysis and Approximate Methods) . Cubic Equations A cubic equation in one variable has the form x3 + bx2 + cx + d = 0 . Every cubic equation having complex coefficients has three complex roots . If the coefficients are real numbers, then at least one of the roots must be real . The cubic equation x3 + bx2 + cx + d = 0 may be reduced by the substitution x = y - b/3 to the form y3 + py + q = 0, where p = ⅓(3c - b2) and q = 1∕27(27d - 9bc + 2b3) . This reduced equation has the solutions y 1 = A + B , y 2 = − 1 2 ( A + B ) + (i 3/2) ( A − B ), y 3 = − 1 2 ( A + B ) − (i 3/2) ( A − B ), where i 2 = − 1, A = 3 − q /2 + R , B = 3 − q /2 − R , and R = ( p /3)3 + (q /2)2 . If b, c, and d are all real and if R > 0, there are one real root and two conjugate complex roots; if R = 0, there are three real roots, of which at least two are equal; if R < 0, there are three real unequal roots . If R < 0, which requires p < 0, these formulas are impractical . In this case, the roots are given by y k =  2 − p /3 cos[(ϕ/3) + 120 k ], k = 0, 1, 2 , where

If | r | < 1, lim s = n →∞

PERMUTATIOnS, COMBInATIOnS, AnD PROBABILITY Each separate arrangement of all or a part of a set of things is called a permutation . The number of permutations of n things taken r at a time is written P (n , r ) =

n! = n (n − 1) (n − 2)  (n − r + 1) (n − r )!

Each separate selection of objects that is possible irrespective of the order in which they are arranged is called a combination . The number of combinations of n things taken r at a time is written C(n, r) = n!/[r!(n - r)!] . An important relation is r!C(n, r) = P(n, r) . If an event can occur in p ways and can fail to occur in q ways, with all ways being equally likely, the probability of its occurrence is p/(p + q), and that of its failure is q/(p + q) . Example Two dice may be thrown in 36 separate ways . What is the probability of throwing such that their sum is 7? The number 7 may arise in 6 ways: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1 . The probability of shooting a 7 is 1⁄6 . THEORY OF EQUATIOnS Linear Equations A linear equation is one of the first degree (i .e ., only the first powers of the variables are involved), and the process of obtaining definite values for the unknown is called solving the equation . Every linear equation in one variable is written Ax + B = 0 or x = -B/A. Linear equations in n variables have the form a11x1 + a12x2 +  + a1nxn = b1 a21x1 + a22x2 +  + a2nxn = b2    am1x1 + am2x2 +  + amnxn = bm The solution of the system may then be found by elimination or matrix methods if a solution exists (see Matrix Algebra and Matrix Computations) .

φ = cos−1

q 2 /4 − p 3 /27

and the negative sign applies if q > 0, and the positive sign applies if q < 0 . Example Many equations of state involve solving cubic equations for the compressibility factor Z . For example, the Soave-Redlich-Kwong equation of state requires solving Z3 - Z2 + cZ + d = 0

d 0, are desired . Quartic Equations See Olver et al . (2010) in General References . General Polynomials of the nth Degree If n > 4, there is no formula that gives the roots of the general equation . The roots can be found numerically (see “Numerical Analysis and Approximate Methods”) . Fundamental Theorem of Algebra Every polynomial of degree n has exactly n real or complex roots, counting multiplicities . Determinants Consider the system of two linear equations a11x1 + a12x2 = b1 a21x1 + a22x2 = b2 If the first equation is multiplied by a22 and the second by -a12 and the results are added, we obtain (a11a22 - a21a12)x1 = b1a22 - b2a12 The expression a11a22 - a21a12 may be represented by the symbol a11 a21

a12 = a11a22 − a21a12 a22

This symbol is called a determinant of second order . The value of the square array of n2 quantities aij, where i = 1, …, n, is the row index, j = 1, …, n. The column index, written in the form a11

a12

a13 ⋯ a1n

a | A | = 21 ⋮ an 1

a22

⋯⋯a2 n

an 2

an 3 ⋯ ann

AnALYTIC GEOMETRY is called a determinant. The n2 quantities aij are called the elements of the determinant. In the determinant |A|, let the ith row and jth column be deleted and a new determinant be formed having n - 1 rows and columns. This new determinant is called the minor of aij, denoted Mij. Example

a11 a21 a31

a12 a22 a32

a13 a11 a23 The minor of a23 is M 23 = a31 a33

The cofactor Aij of the element aij is the signed minor of aij determined by the rule Aij = (-1)i+ jMij. The value of |A| is obtained by forming any of the n n equivalent expressions ∑ j = 1 aij Aij, ∑ i = 1 aijAij, where the elements aij must be taken from a single row or a single column of A. Example a11 a21 a31

a12 a22 a32

a13 a23 = a31 A31 + a32 A32 + a33 A33 a33 = a31

a12 a22

a13 a11 − a32 a23 a21

In general, Aij will be determinants of order n - 1, but they may in turn be expanded by the rule. Also, n

∑a j =1

a12 a32

a13 a11 + a33 a23 a21

a12 a22

3-11

ji

 | A | i = k n A jk = ∑ aij A jk =   0 i ≠ k j =1

Fundamental Properties of Determinants 1. The value of a determinant |A| is not changed if the rows and columns are interchanged. 2. If the elements of one row (or one column) of a determinant are all zero, the value of |A| is zero. 3. If the elements of one row (or column) of a determinant are multiplied by the same constant factor, the value of the determinant is multiplied by this factor. 4. If one determinant is obtained from another by interchanging any two rows (or columns), the value of either is the negative of the value of the other. 5. If two rows (or columns) of a determinant are identical, the value of the determinant is zero. 6. If two determinants are identical except for one row (or column), the sum of their values is given by a single determinant obtained by adding corresponding elements of dissimilar rows (or columns) and leaving unchanged the remaining elements. 7. The value of a determinant is not changed if one row (or column) is multiplied by a constant and added to another row (or column).

AnALYTIC GEOMETRY References: Gersting, J. L., Technical Calculus with Analytic Geometry, Dover, Mineola, N.Y., 2010.

Analytic geometry uses algebraic equations and methods to study geometric problems. It also permits one to visualize algebraic equations in terms of geometric curves, which frequently clarifies abstract concepts. PLAnE AnALYTIC GEOMETRY Coordinate Systems The basic concept of analytic geometry is the establishment of a one-to-one correspondence between the points of the plane and number pairs (x, y). This correspondence may be done in a number of ways. The rectangular or cartesian coordinate system consists of two straight lines intersecting at right angles (Fig. 3-12). A point is designated by (x, y). Another common coordinate system is the polar coordinate system (Fig. 3-13). In this system the position of a point is designated by the pair (r, q), with r = x 2 + y 2 being the distance to the origin O(0, 0) and q being the angle the line r makes with the positive x axis (polar axis). To change from polar to rectangular coordinates, use x = r cos q and y = r sin q. To change from rectangular to polar coordinates, use r = x 2 + y 2 and q = tan-1 (y/x) if x ≠ 0; q = π/2 if x = 0. The distance between two points (x1, y1) and (x2, y2) is defined by d = ( x 1 − x 2 )2 + ( y 1 − y 2 )2 in rectangular coordinates or by d = r 21 + r 22 − 2 r1r2 cos (θ1 − θ2 ) in polar coordinates. Other coordinate systems are sometimes used. For example, on the surface of a sphere, latitude and longitude prove useful. Straight Line See Fig. 3-14. The slope m of a straight line is the tangent of the inclination angle q made with the positive x axis. If (x1, y1) and (x2, y2) are any two points on the line, then slope = m = (y2 - y1)/(x2 - x1). The slope of a line parallel to the x axis is zero; the slope of a line parallel to the y axis is undefined. Two lines are parallel if and only if they have the same slope. Two lines are perpendicular if and only if the product of their slopes is -1 (the exception being that case when the lines are parallel to the coordinate axes). Every equation of the type Ax + By + C = 0 represents a straight line, and every straight line has an equation of this form. A straight line is determined by a variety of conditions:

FIG. 3-14 Straight line.

Given conditions

Equation of line

1. Parallel to x axis 2. Parallel to y axis 3. Point (x1, y1) and slope m 4. Intercept on y axis (0, b), m 5. Intercept on x axis (a, 0), m 6. Two points (x1, y1), (x2, y2) 7. Two intercepts (a, 0), (0, b)

y = constant x = constant y - y1 = m(x - x1) y = mx + b y = m(x - a) y −y y − y 1 = 2 1 ( x − x1 ) x 2 − x1 x/a + y/b = 1

The angle b that a line with slope m1 makes with a line having slope m2 is given by tan b = (m2 - m1)/(m1m2 + 1). The distance from a point (x1, y1) to a line with equation Ax + By + C = 0 is d=

| Ax 1 + By 1 + C | A2 + B 2

Occasionally some nonlinear algebraic equations can be reduced to linear equations under suitable substitutions or changes of variables. Example Consider y = bxn and B = log b. Taking logarithms gives log y = n log x + log b. Let Y = log y, X = log x, and B = log b. The equation then has the form Y = nX + B, which is a linear equation. Consider k = k0 exp (-E/RT); taking logarithms gives ln k = ln k0 - E/(RT). Let Y = ln k, B = ln k0, m = -E/R, and X = 1/T, and the result is Y = mX + B.

II

I

III

IV

FIG. 3-12

Rectangular coordinates.

FIG. 3-13 Polar coordinates.

Asymptotes The limiting position of the tangent to a curve, as the point of contact tends to an infinite distance from the origin, is called an asymptote. Conic Sections The curves included in this group are obtained from plane sections of the cone. They include the circle, ellipse, parabola, hyperbola, and degeneratively the point and straight line. A conic is the locus of a point whose distance from a fixed point called the focus is in a constant

3-12

MATHEMATICS

ratio to its distance from a fixed line, called the directrix. This ratio is the eccentricity e. If e = 0, the conic is a circle; if 0 < e < 1, the conic is an ellipse; if e = 1, the conic is a parabola; if e > 1, the conic is a hyperbola. Every conic section is representable by an equation of second degree. Conversely, every equation of second degree in two variables represents a conic. The general equation of the second degree is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. Let Δ be defined as the determinant 2A B ∆ = B 2C D E

Δ≠0

Δ=0

AΔ < 0, A ≠ C, an ellipse AΔ < 0, A = C, a circle AΔ > 0, no locus

4

3

4 −4 −2 3

−2

= −596 ≠ 0, B 2 − 4 AC = 40 > 0

14

Polar equation

B2 - 4AC = 0

B2 - 4AC > 0

Parabola

Hyperbola

Two parallel lines if Q = D2 + E2 - 4(A + C)F > 0 One straight line if Q = 0 no locus if Q < 0

Point

6 ∆=

The curve is therefore a hyperbola.

D E 2F

The table characterizes the curve represented by the equation. B2 - 4AC < 0

Example 3x2 + 4xy - 2y2 + 3x - 2y + 7 = 0.

Two intersecting straight lines

Type of curve

(1) r = a (2) r = 2a cos q (3) r = 2a sin q (4) r2 - 2br cos (q - b) + b2 - a2 = 0 (5) r =

ke 1 − e cos θ

Circle, Fig. 3-20 Circle, Fig. 3-21 Circle, Fig. 3-22 Circle at (b, b), radius a e = 1 parabola, Fig. 3-17 0 < e 1 hyperbola, Fig. 3-18

Parametric Equations It is frequently useful to write the equations of a curve in terms of a parameter. For example, a circle of radius a, center at (0, 0), can be written in the equivalent form x = a cos f, y = a sin f, where f is the parameter. Similarly, x = a cos f and y = b sin f are the parametric equations of the ellipse x2/a2 + y2/b2 = 1 with parameter f. SOLID AnALYTIC GEOMETRY

(1) ( x − h)2 + ( y − k )2 − a 2

x = h + acos θ y = k + asin θ

(2)

( x − h)2 ( y − k )2 + =1 a2 b2

x = h + a cos φ y = k + a sin φ  −at  x = 2 t +1  y = a  t 2 +1

(3) x 2 + y 2 = a 2

Circle (Fig. 3-15) parameter is angle q Ellipse (Fig. 3-16) parameter is angle q

dy = dx slope of tangent at (x, y)

Circle parameter is t =

(4) x 2 = y + k

Parabola (Fig. 3-17)

x2 y2 (5) 2 − 2 = 1 a b x (6) y = a cosh a

Hyperbola with the origin at the center (Fig. 3-18)  s  x = a sinh−1 a  2 2  2 y =a +s  x = a (φ − sin φ)   y = a (1 − cos φ)

(7) Cycloid

FIG. 3-15

Catenary (such as hanging cable under gravity) Parameter s = arc length from (0, a) to (x, y) (Fig. 3-19)

FIG. 3-16 Ellipse, 0 < e < 1.

Circle.

FIG. 3-19 Cycloid.

Coordinate Systems There are three commonly used coordinate systems. Others may be used in specific problems (see Morse, P. M., and H. Feshbach, Methods of Theoretical Physics, vols. 1 and I2, McGraw-Hill, New York, 1953). The rectangular (cartesian) system (Fig. 3-23) consists of mutually orthogonal axes x, y, and z. A triple of numbers (x, y, z) is used to represent each point. The cylindrical coordinate system (r, q, z; Fig. 3-24) is frequently used to locate a point in space. These are essentially the polar coordinates (r, q) coupled with the z coordinate. As before, x = r cos q, y = r sin q, z = z and r2 = x2 + y2, y/x = tan q. If r is held constant and q and z are allowed to vary, the locus of (r, q, z) is a right circular cylinder of radius r along the z axis. The locus of r = C is a circle, and q = constant is a plane containing the z axis and making an angle q with the xz plane. Cylindrical coordinates are convenient to use when the problem has an axis of symmetry. The spherical coordinate system is convenient if there is a point of symmetry in the system. This point is taken as the origin and the coordinates (r, f, q) are illustrated in Fig. 3-25. The relations are x = r sin f cos q, y = r sin f sin q, z = r cos f, and r = r sin f. Also q = constant is a plane containing the z axis and making an angle q with the xz plane; f = constant is a cone with vertex at 0; r = constant is the surface of a sphere of radius r, center at the origin 0. Every point in the space may be given spherical coordinates restricted to the ranges 0 ≤ f ≤ π, r ≥ 0, 0 ≤ q < 2π. Lines and Planes The distance between two points ( x 1 , y 1 , z1 ), (x2, y2, z2) is d = ( x 1 − x 2 )2 + ( y 1 − y 2 )2 + ( z1 − z 2 )2 . There is nothing in the geometry of three dimensions quite analogous to the slope of a line in

FIG. 3-17 Parabola, e = 1.

FIG. 3-20 Circle center (0, 0), r = a.

FIG. 3-18 Hyperbola, e > 1.

FIG. 3-21 Circle center (a, 0), r = 2a cos q.

AnALYTIC GEOMETRY

FIG. 3-22

Circle center (0, a), r = 2a sin θ.

3-13

Space Curves Space curves are usually specified as the set of points whose coordinates are given parametrically by a system of equations x = f (t), y = g(t), z = h(t) in the parameter t. Example The equation of a straight line in space is (x - x1)/a = (y - y1)/b = (z - z1)/c. Since all these quantities must be equal (say, to t), we may write x = x1 + at, y = y1 + bt, and z = z1 + ct, which represent the parametric equations of the line. Example The equations z = a cos βt, y = a sin βt, and z = bt, with a, β, and b positive constants, represent a circular helix. Surfaces The locus of points (x, y, z) satisfying f (x, y, z) = 0, broadly speaking, may be interpreted as a surface. The simplest surface is the plane. The next simplest is a cylinder. Example The parabolic cylinder y = x2 (Fig. 3-26) is generated by a straight line parallel to the z axis passing through y = x2 in the plane z = 0. A surface whose equation is a quadratic in the variables x, y, and z is called a quadric surface. Some of the more common such surfaces are tabulated and pictured in Figs. 3-26 to 3-34.

FIG. 3-23 Cartesian coordinates.

FIG. 3-27 Ellipsoid.

FIG. 3-24 Cylindrical coordinates.

FIG. 3-25

FIG. 3-26

Parabolic cylinder.

FIG. 3-28

Hyperboloid of one sheet.

x 2 y 2 z2 + + = 1 (sphere if a = b = c ) a 2 b2 c 2

Spherical coordinates.

the plane. Instead of specifying the direction of a line by a trigonometric function evaluated for one angle, a trigonometric function evaluated for three angles is used. The angles α, β, and γ that a line segment makes with the positive x, y, and z axes, respectively, are called the direction angles of the line, and cos α, cos β, and cos γ are called the direction cosines. Let (x1, y1, z1) and (x2, y2, z2) be on the line. Then cos α = (x2 - x1)/d, cos β = (y2 - y1)/d, and cos γ = (z2 - z1)/d, where d = the distance between the two points. Clearly cos2 α + cos2 β + cos2 γ = 1. If two lines are specified by the direction cosines (cos α1, cos β1, cos γ1) and (cos α2, cos β2, cos γ2), then the angle θ between the lines is cos θ = cos α1 cos α2 + cos β1 cos β2 + cos γ1 cos γ2. Thus the lines are perpendicular if and only if θ = 90° or cos α1 cos α2 + cos β1 cos β2 + cos γ1 cos γ2 = 0. The equation of a line with direction cosines (cos α, cos β, cos γ) passing through (x1, y1, z1) is (x - x1)/cos α = (y - y1)/cos β = (z - z1)/cos γ. The equation of every plane is of the form Ax + By + Cz + D = 0. The numbers A B C , , A2 + B 2 + C 2 A2 + B 2 + C 2 A2 + B 2 +C 2

x 2 y 2 z2 + − =1 a 2 b2 c 2

FIG. 3-29

Hyperboloid of two sheets. x 2 y 2 z2 + − = −1 a 2 b2 c 2

are direction cosines of the normal lines to the plane. The plane through the point (x1, y1, z1) whose normals have these as direction cosines is A(x - x1) + B(y - y1) + C(z - z1) = 0. Example Find the equation of the plane through (1, 5, -2) perpendicular to the line (x + 9)/7 = (y - 3)/(-1) = z/8. The numbers (7, -1, 8) are called direction numbers. They are a constant multiple of the direction cosines cos α = 7/114, cos β = -1/114, and cos γ = 8/114. The plane has the equation 7(x - 1) - 1(y - 5) + 8(z + 2) = 0 or 7x - y + 8z + 14 = 0. The distance from the point (x1, y1, z1) to the plane Ax + By + Cz + D = 0 is d=

| Ax 1 + By 1 + Cz1 + D | A2 + B 2 + C 2

FIG. 3-31 Elliptic paraboloid.

x 2 y 2 z2 FIG. 3-30 Cone. 2 + 2 + 2 = 0 a b c

x2 y2 + + cz = 0 a2 b2

3-14

MATHEMATICS

FIG. 3-32 Hyperbolic paraboloid .

x2 y2 − + cz = 0 a 2 b2

FIG. 3-33

Elliptic cylinder .

x2 y2 + =1 a 2 b2

PLAnE TRIGOnOMETRY References: Gelfand, I. M., and M. Saul, Trigonometry, Birkhäuser, Boston, 2001; Heineman, E. Richard, and J. Dalton Tarwater, Plane Trigonometry, 7th ed., McGraw-Hill, New York, 1993.

AnGLES An angle is generated by the rotation of a line about a fixed center from some initial position to some terminal position. If the rotation is clockwise, the angle is negative; if it is counterclockwise, the angle is positive. Angle size is unlimited. If α and b are two angles such that α + b = 90°, they are complementary; they are supplementary if α + b = 180°. Angles are most commonly measured in the sexagesimal system or by radian measure. In the first system there are 360° in 1 complete revolution (1 r); 1° = 1∕90 of a right angle . The degree is subdivided into 60 minutes; the minute is subdivided into 60 seconds . In the radian system, 1 radian (1 rad) is the angle at the center of a circle subtended by an arc whose length is equal to the radius of the circle . Thus 2π rad = 360°; 1 rad = 57 .29578°; 1° = 0 .01745 rad; 1 min = 0 .00029089 rad . The advantage of radian measure is that it is dimensionless. The quadrants are conventionally labeled, as Fig . 3-35 shows .

FIG. 3-36 Triangles .

FUnCTIOnS OF CIRCULAR TRIGOnOMETRY The trigonometric functions of angles are the ratios between the various sides of the reference triangles shown in Fig . 3-36 for the various quadrants . Clearly r = x 2 + y 2 ≥ 0. The fundamental functions (see Figs . 3-37, 3-38, 3-39) are as follows: Plane Trigonometry Sine of q = sin q = y/r Cosine of q = cos q = x/r Tangent of q = tan q = y/x

FIG. 3-37 Graph of y = sin x.

Secant of q = sec q = r/x Cosecant of q = csc q = r/y Cotangent of q = cot q = x/y

FIG. 3-38 Graph of y = cos x.

II

I

III

IV

FIG. 3-35 Quadrants .

FIG. 3-39 Graph of y = tan x.

FIG. 3-34

Hyperbolic cylinder .

x2 y2 − =1 a 2 b2

PLAnE TRIGOnOMETRY Values of the Trigonometric Functions for Common Angles

1− x2 x = cot −1 2 x 1− x

sin −1 x = cos−1 1 − x 2 = tan −1 q°

q, rad

sin q

0 30

0 π/6

45

π/4

2/2

60

π/3

3/2

90

π/2

0 1/2

1

cos q

tan q

1

0 3/2

= sec−1

3/3

0

Given a > 0

Required angles are

sin q0 = a cos q0 = a tan q0 = a sin q0 = a cos q0 = a tan q0 = a

q0 and 180° - q0 q0 and 360° - q0 q0 and 180° + q0 180° + q0 and 360° - q0 180° - q0 and 180° + q0 180° - q0 and 360° - q0

x

= cot −1

x 1 = sec−1 x 1− x2

= csc−1

π 1 = − sin −1 x 1− x 2 2

tan −1 x = sin −1 = cot −1

Find an acute angle q0 such that

1− x2

cos−1 x = sin −1 1 − x 2 = tan −1

3 +∞

If 90° ≤ q ≤ 180°, sin q = sin (180° - q); cos q = -cos (180° - q); tan q = -tan (180° - q). If 180° ≤ q ≤ 270°, sin q = -sin (270° - q); cos q = -cos (270° - q); tan q = tan (270° - q). If 270° ≤ q ≤ 360°, sin q = -sin (360° - q); cos q = cos (360° - q); tan q = -tan (360° - q). The reciprocal properties may be used to find the values of the other functions. If it is desired to find the angle when a function of it is given, the procedure is as follows: There will in general be two angles between 0° and 360° corresponding to the given value of the function.

sin q = +a cos q = +a tan q = +a sin q = -a cos q = -a tan q = -a

1 π 1 = csc−1 = − cos−1 x x 2 1− x2

1

2/2 1/2

3-15

x 1 = cos−1 1+ x 2 1− x2 1+ x 2 1 = sec−1 1 + x 2 = csc−1 x x

RELATIOnS BETWEEn AnGLES AnD SIDES OF TRIAnGLES

Relations between Functions of a Single Angle sec q = 1/cos q; csc q = 1/sin q, tan q = sin q/cos q = sec q/csc q = 1/cot q; sin2 q + cos2 q = 1; 1 + tan2 q = sec2 q; 1 + cot2 q = csc2 q. For 0 ≤ q ≤ 90° the following results hold:

Solutions of Triangles (Fig. 3-40) Let a, b, and c denote the sides and α, b, and γ the angles opposite the sides in the triangle. Let 2s = a + b + c, A = area, r = radius of the inscribed circle, R = radius of the circumscribed circle, and h = altitude. In any triangle α + b + γ = 180°. Law of Sines sin α/a = sin b/b = sin γ/c = 1/(2R). Law of Tangents

θ θ sin θ = 2 sin   cos   2 2

a + b tan 1 2 (α + β) b + c tan 1 2 (β + γ) a + c tan 1 2 (α + γ) = = = ; ; a − b tan 1 2 (α − β) b − c tan 1 2 (β − γ) a − c tan 1 2 (α − γ)

and

θ θ cos θ = cos 2   − sin 2   2 2

The cofunction property is very important. cos q = sin (90° - q), sin q = cos (90° - q), tan q = cot (90° - q), cot q = tan (90° - q), etc. Functions of Negative Angles sin (-q) = -sin q, cos (-q) = cos q, tan (-q) = -tan q, sec (-q) = sec q, csc (-q) = -csc q, cot (-q) = -cot q. Identities Sum and Difference Formulas Let x, y be two angles. sin (x ± y) = sin x cos y ± cos x sin y; cos (x ± y) = cos x cos y ∓ sin x sin y ; tan (x ± y) = (tan x ± tan y)/(1 ∓ tan x tan y); sin x ± sin y = 2 sin ½(x ± y) cos ½(x ∓ y); cos x + cos y = 2 cos ½(x + y) cos ½(x - y); cos x - cos y = -2 sin ½(x + y) sin ½(x - y); tan x ± tan y = [sin (x ± y)]/(cos x cos y); sin2 x - sin2 y = cos2 y - cos2 x = sin (x + y) sin (x - y); cos2 x - sin2 y = cos2 y - sin2 x = cos (x + y) × cos (x - y); sin (45° + x) = cos (45° - x); sin (45° - x) = cos (45° + x); tan (45° ± x) = cot (45° ∓ x). Multiple and Half-Angle Identities Let x = angle, sin 2x = 2 sin x cos x; sin x = 2 sin ½x × cos ½x; cos 2x = cos2 x - sin2x = 1 - 2 sin2 x = 2 cos2 x - 1. tan 2x = (2 tan x)/(1 - tan2 x); sin 3x = 3 sin x - 4 sin3x; cos 3x = 4 cos3 x - 3 cos x. tan 3x = (3 tan x - tan3 x)/(1 - 3 tan2 x); sin 4x = 4 sin x cos x - 8 sin3 x cos x; cos 4x = 8 cos4 x - 8 cos2 x + 1. x sin   = 2 x cos   = 2

1

2

1

2

(1 − cos x ) (1 + cos x )

1 − cos x sin x 1 − cos x x tan   = = = 2 1 + cos x 1 + cos x sin x

Law of Cosines a2 = b2 + c2 - 2bc cos α; b2 = a2 + c2 - 2ac cos b; c2 = a2 + b2 - 2ab cos γ. More formulas can be generated by replacing a by b, b by c, c by a, α by b, b by γ, and γ by α. 1 1 A = bh = ab sin γ = s ( s − a ) ( s − b) ( s − c ) = rs 2 2 where

r=

( s − a ) ( s − b) ( s − c ) s

R = a/(2 sin α) = abc/4A

h = c sin α = a sin γ = 2rs/b

Right Triangle (Fig. 3-41) Given one side and any acute angle α or any two sides, the remaining parts can be obtained from the following formulas: a = (c + b) (c − b) = c sin α = b tan α b = (c + a ) (c − a ) = c cos α = a cot α c = a 2 + b2

sin α =

a c

cos α =

b c

tan α =

a b

β = 90° − α

b 2 tan α c 2 sin 2α 1 a2 = = A = ab = 2 2 tan α 2 4

InVERSE TRIGOnOMETRIC FUnCTIOnS Note that y = sin -1 x = arcsin x is the angle y whose sine is x. Example y = sin-1 (½), y is 30°. The complete solution of the equation x = sin y is y = (-1)n sin-1 x + n(180°), -π/2 ≤ sin-1 x ≤ π/2 where sin-1 x is the principal value of the angle whose sine is x. The range of principal values of cos-1 x is 0 ≤ cos-1 x ≤ π and -π/2 ≤ tan-1 x ≤ π/2. If these restrictions are allowed to hold, the following formulas result:

FIG. 3-40

Triangle.

FIG. 3-41 Right triangle.

3-16

MATHEMATICS

HYPERBOLIC TRIGOnOMETRY The hyperbolic functions are certain combinations of exponentials ex and e-x.

Inverse Hyperbolic Functions If x = sinh y, then y is the inverse hyperbolic sine of x, written as y = sinh-1 x or arcsinh x. sinh-1 x = ln e ( x + x 2 + 1)

cosh x =

e x + e−x e x − e−x sinh x e x − e − x = ; sinh x = ; tanh x = cosh x e x + e − x 2 2

1+ x 1 cosh −1 x = ln e ( x + x 2 − 1); tanh −1 x = ln e ; 2 1− x

coth x =

cosh x ex + ex 1 1 2 = = = ; sech x = ; cosh x e x + e − x e x − e − x tanh x sinh x

 1+ 1− x2  x +1 1 coth −1 x = ln e ; sech −1 x = ln e  ; x x −1 2  

csch x =

1 2 = sinh x e x − e − x

Fundamental Relationships sinh x + cosh x = ex; cosh x - sinh x = e-x; cosh2 x - sinh2 x = 1; sech2 x + tanh2 x = 1; coth2 x - csch2 x = 1; sinh 2x = 2 sinh x cosh x; cosh 2x = cosh2 x + sinh2 x = 1 + 2 sinh2 x = 2 cosh2 x - 1. tanh 2x = (2 tanh x)/(1 + tanh2 x); sinh (x ± y) = sinh x cosh y ± cosh x sinh y ; cosh (x ± y) = cosh x cosh y ± sinh x sinh y; 2 sinh2 x/2 = cosh x - 1; 2 cosh2 x/2 = cosh x + 1; sinh (-x) = -sinh x; cosh (-x) = cosh x; tanh (-x) = -tanh x. When u = a cosh x and u = a sinh x, then u2 - u2 = a2, which is the equation for a hyperbola. In other words, the hyperbolic functions in the parametric equations u = a cosh x and u = a sinh x have the same relation to the hyperbola u2 - u2 = a2 that the equations u = a cos q and u = a sin q have to the circle u2 + u2 = a2.

 1+ 1+ x2  csch −1 = ln e   x   Magnitude of the Hyperbolic Functions cosh x ≥ 1 with equality only for x = 0; -∞ < sinh x < ∞; -1 < tanh x < 1. cosh x ~ ex/2 as x → ∞; sinh x → ex/2 as x → ∞. APPROXIMATIOnS FOR TRIGOnOMETRIC FUnCTIOnS For small values of q (q measured in radians) sin q ≈ q, tan q ≈ q; cos q ≈ 1 - q2/2.

DIFFEREnTIAL AnD InTEGRAL CALCULUS References: Larson, R., and B. H. Edwards, Calculus, 10th ed., Brooks/Cole, Pacific Grove, Calif., 2013.

exists. This implies continuity at x = a. However, a function may be continuous but not have a derivative. The derivative function is

DIFFEREnTIAL CALCULUS

f ′( x ) =

Limits The limit of function f (x) as x approaches a (a is finite or else x is said to increase without bound) is the number N.

Differentiation Define Δy = f (x + Δx) - f (x). Then dividing by Δx gives ∆y f ( x + ∆x ) − f ( x ) = ∆x ∆x

lim f ( x ) = N x →a

This states that f (x) can be calculated as close to N as desirable by making x sufficiently close to a. This does not put any restriction on f (x) when x = a. Alternatively, for any given positive number e, a number d can be found such that 0 < |a - x| < d implies that |N - f (x)| < e. The following operations with limits (when they exist) are valid: lim bf ( x ) = b lim f ( x ) x →a

x →a

lim[ f ( x ) + g ( x )] = lim f ( x ) + lim g ( x ) x →a

x →a

x →a

lim[ f ( x ) g ( x )] = lim f ( x ) ⋅ lim g ( x ) x →a

x →a

x →a

f (x ) f ( x ) lim if lim g ( x ) ≠ 0 lim = x →a x →a x →a g ( x ) lim g ( x ) x →a

See “Indeterminant Forms” below when g(a) = 0. Continuity A function f (x) is continuous at the point x = a if lim [ f (a + h) − f (a )] = 0 h→0

Rigorously, it is stated that f (x) is continuous at x = a if for any positive e there exists a d > 0 such that | f (a + h) - f (a)| < e for all x with |x - a| < d. For example, the function (sin x)/x is not continuous at x = 0 and therefore is said to be discontinuous. Discontinuities are classified into three types: 1. Removable y = (sin x)/x at x = 0 2. Infinite y = 1/x at x = 0 1/x 3. Jump y = 10/(1 + e ) at x = 0+ y = 0+ x=0y=0 x = 0- y = 10 Derivative The function f (x) has a derivative at x = a, denoted as f ′(a), if lim h→0

f (a + h ) − f (a ) h

f ( x + h) − f ( x ) df = lim dx h → 0 h

Call Then

lim

∆x → 0

∆y dy = ∆ x dx f ( x + ∆x ) − f ( x ) dy = lim dx ∆x → 0 ∆x

Differential Operations The following differential operations are valid: f, g, … are differentiable functions of x; c and n are constants; e is the base of the natural logarithms. dc =0 dx

(3-1)

dx =1 dx

(3-2)

df dg d ( f + g) = + dx dx dx

(3-3)

df dg d ( f × g) = f +g dx dx dx

(3-4)

dy 1 = dx dx /dy

if

dx ≠0 dy

(3-5)

d n df f = nf n−1 dx dx

(3-6)

d  f  g (df /dx ) − f (dg /dx ) = dx  g  g2

(3-7)

df df d υ = × (chain rule) dx d υ dx

(3-8)

DIFFEREnTIAL AnD InTEGRAL CALCULUS df g =gf dx

g −1

df dg + f g ln f dx dx

(3-10)

d d d 2 d 3 d A xy + x+ y = x + dx dx dx dx dx dy dy 2x + 3 y 2 =1+ y + x +0 dx dx

u = sin x y = tan x Then, d tan x dy dy dx = = d sin x d υ dx d υ

by the rules in Eqs. (3-6), (3-6), (3-2), (3-4), and (3-1), respectively. Thus

dy 2 x − 1 − y = dx x − 3y2

d tan x 1 dx d sin x dx = sec2 x /cos x

dex = ex dx

(3-11)

d(a ) = a lna dx

(3-12)

d ln x = (1/x) dx

(3-13)

x

d log x = (log e/x) dx

(3-14)

d sin x = cos x dx

(3-15)

d cos x = -sin x dx

(3-16)

d tan x = sec x dx

(3-17)

d cot x = -csc2 x dx

(3-18)

d sec x = tan x sec x dx

(3-19)

d csc x = -cot x csc x dx

(3-20)

2

d sin x = (1 - x )

2 –1/2

-1

(3-21)

dx

d cos-1 x = -(1 - x2)–1/2 dx

(3-22)

d tan-1 x = (1 + x2)–1 dx

(3-23)

d cot-1 x = -(1 + x2)–1 dx

(3-24)

d sec-1 x = x–1(x2 - 1)–1/2 dx

(3-25)

d csc x = -x (x - 1)

(3-26)

–1

-1

2

–1/2

dx

d sinh x = cosh x dx

(3-27)

d cosh x = sinh x dx

(3-28)

d tanh x = sech x dx

(3-29)

d coth x = -csch2 x dx

(3-30)

d sech x = -sech x tanh x dx

(3-31)

d csch x = -csch x coth x dx

(3-32)

2

d sinh-1 x = (x2 + 1)–1/2 dx d cosh = (x - 1) -1

2

–1/2

(3-33)

d coth x = -(x - 1) dx 2

-1

d sech x = -(1/x)(1 - x )

2 –1/2

-1

d csch x = -x (x + 1) -1

–1

(3-8)

2

–1/2

dx

If f ′( x ) > 0 on (a, b), then f is increasing on (a, b). If f ′( x ) < 0 on (a, b), then f is decreasing on (a, b). The graph of a function y = f (x) is concave up if f ′ is increasing on (a, b); it is concave down if f ′ is decreasing on (a, b). If f ′′( x ) exists on (a, b) and if f ′′( x ) > 0, then f is concave up on (a, b). If f ′′( x ) < 0, then f is concave down on (a, b). An inflection point is a point at which a function changes the direction of its concavity. Indeterminate Forms: L’Hôpital’s Theorem Forms of the type 0/0, ∞/∞, 0 × ∞, etc., are called indeterminates. To find the limiting values that the corresponding functions approach, L’Hôpital’s theorem is useful: If two functions f (x) and g(x) both become zero at x = a, then the limit of their quotient is equal to the limit of the quotient of their separate derivatives, if the limit exists, or is +∞ or -∞. Example Find lim n→0

lim

Here

x →0

Example Find dy/dx for y = x cos (1 − x ) . dy d d cos (1 − x 2 ) + cos (1 − x 2 ) = x dx dx dx

d d cos (1 − x 2 ) = − sin (1 − x 2 ) (1 − x 2 ) dx dx

x →∞

Example Find lim (1 − x )1/ x . x →0

= − sin (1 − x 2 ) (0 − 2 x )

y = (1 − x )1/ x

(3-36)

Then

(3-37)

lim (ln y ) = lim

(3-16) (3-1), (3-6)

x3 6 = lim x = 0 x →∞ ex x →∞ e

lim x 3e − x = lim

Let

(3-4)

d sin x cos x sin x dx /lim = lim = lim =1 x →0 x → 0 dx x →0 x dx 1

x →∞

x →0

x →0

Using

x

sin x . x

Example Find lim x 3e − x .

=

2

(3-17), (3-15)

d 3 f (x ) d n f (x ) d 2 f (x ) df ( x ) = 0 for n ≥ 4 = 9 x 2 + 2, = 18 x , = 18, 2 3 dx dx n dx dx

(3-35)

(3-38)

dx

(3-5)

If the functions and derivatives are known only numerically at some point, the same formulas may be used. Higher Differentials The first derivative of f (x) with respect to x is denoted by f ′ or df/dx. The derivative of the first derivative is called the second derivative of f (x) with respect to x and is denoted by f ′′, f (2), or d 2f/dx2; and similarly for the higher-order derivatives. Example Given f (x) = 3x3 + 2x + 1, calculate all derivative values.

(3-34)

dx

d tanh-1 x = (1 - x2)–1 dx -1

Using

=

Differentials x

(3-6)

Example Find the derivative of tan x with respect to sin x. Let

Example Derive dy/dx for x2 + y3 = x + xy + A. Here

d x 1 −1/2 = x dx 2 dy 1 = 2 x 3/2 sin (1 − x 2 ) + x −1/2 cos (1 − x 2 ) dx 2

(3-9)

da x = (ln a ) a x dx

3-17

Therefore,

ln y = (1/x) ln (1 - x)

ln (1 − x ) lim x →0 ln (1 − x ) = lim x →0 x x

d [ln(1 − x )]/dx dx /dx x =0

x =0

=

1 (−1) 1− x

= −1 x =0

lim y = e −1 x →0

Partial Derivative The abbreviation z = f (x, y) means that z is a function of the two variables x and y. The derivative of z with respect to x, treating y as a constant, is called the partial derivative with respect to x and is usually denoted as ∂z/∂x or ∂f (x, y)/∂x or simply fx . Partial differentiation,

3-18

MATHEMATICS

like full differentiation, is quite simple to apply. Conversely, the solution of partial differential equations is appreciably more difficult than that of differential equations. 2

Example Find ∂z/∂x and ∂z/∂y for z = ye x + xe y . 2

2 ∂x ∂e x ∂z + ey =y = 2 xye x + e y ∂x ∂x ∂x

2 ∂y 2 ∂e y ∂z = e x + xe y +x = ex ∂y ∂y ∂y

Order of Differentiation It is generally true that the order of differentiation is immaterial for any number of differentiations or variables, provided the function and the appropriate derivatives are continuous . For z = f (x, y) it follows that ∂3 f ∂3 f ∂3 f = = 2 ∂ y ∂x ∂ y ∂x ∂ y ∂x ∂ y 2

MULTIVARIABLE CALCULUS APPLIED TO THERMODYnAMICS Many of the functional relationships needed in thermodynamics are direct applications of the rules of multivariable calculus . This section reviews those rules in the context of the needs of thermodynamics . These ideas were expounded in one of the classic books on chemical engineering thermodynamics (see Hougen, O . A ., et al ., Part II, “Thermodynamics,” in Chemical Process Principles, 2d ed ., Wiley, New York, 1959) . State Functions State functions depend only on the state of the system, not on history or how one got there . If z is a function of two variables x and y, then z(x, y) is a state function, since z is known once x and y are specified . The differential of z is dz = M dx + N dy The line integral

∫ ( M dx + N dy ) c

is independent of the path in xy space if and only if

General Form for Partial Differentiation 1 . Given f (x, y) = 0 and x = g(t), y = h(t) . Then

∂M ∂N = ∂ y ∂x

df ∂ f dx ∂ f dy = + dt ∂x dt ∂y dt

and dz is called an exact differential . The total differential can be written as

2

 ∂z   ∂z  dz =   dx +   dy  ∂x  y  ∂y  x

2

∂ 2 f dx dy ∂ 2 f  dy  ∂ f d 2 x ∂ f d 2 y d 2 f ∂2 f  dx  + + =   +   +2 ∂ x dt 2 ∂ y dt 2 ∂ x ∂ y dt dt ∂ y 2  dt  dt 2 ∂ x 2  dt  Example Find df/dt for f = xy, x = r sin t, and y = r cos t.

∂  ∂z  ∂  ∂z    = ∂ y  ∂ x  y ∂ x  ∂ y  x

= y (r cos t) + x(-r sin t) or

= r2 cos2 t - r2 sin2 t 2 . Given f (x, y) = 0 and x = g(t, s), y = h(t, s) .

Rearrangement gives the triple product rule (∂ y / ∂ x ) z  ∂ y   ∂z   ∂z   ∂z   ∂x   ∂ y  or       = − 1 (3-42)   = −     = −  ∂x  y  ∂ y  z  ∂z  x ∂x z  ∂ y  x (∂ y / ∂ z ) x ∂x y

Differentiation of Composite Function ∂ f /∂x dy =− dx ∂ f /∂y

Rule 2.

Given f (u) = 0 where u = g(x), then

 ∂ f  ≠ 0 . y ∂  

du df = f ′(u ) dx dx 2 d 2u du d2 f = f ′′ (u )   + f ′(u ) 2  dx  dx dx 2 Rule 3.

Given f (u) = 0 where u = g(x, y), then 2

∂2 f ∂2 u  ∂u  = f ′′   + f ′ 2 2  ∂x  ∂x ∂x 2

(3-41)

   ∂z   ∂z   0 =   dx +   dy   ∂ y  x  z   ∂ x  y

∂ f ∂ f ∂x ∂ f ∂y = + ∂s ∂x ∂s ∂y ∂s

Given f (x, y) = 0, then

∂2 z ∂2 z = ∂ y ∂x ∂x ∂ y Example Suppose z is constant and apply Eq . (3-40) .

∂ f ∂ f ∂x ∂ f ∂y = + ∂t ∂x ∂t ∂y ∂t

Rule 1.

(3-40)

and thus the following application of Eq . (3-39) guarantees path independence .

df ∂( xy )  d ρ sin t  ∂( xy )  d ρ cos t  =    + ∂ y  dt  ∂ x  dt  dt

Then

(3-39)

2

∂ f ∂ u ∂u ∂ u = f ′′ + f′ ∂x ∂ y ∂x ∂ y ∂x ∂ y

Alternatively, divide Eq . (3-40) by dy when holding some other variable w constant to obtain  ∂z   ∂z   ∂x   ∂z   ∂ y  =  ∂ x   ∂ y  +  ∂ y  y w w x

(3-43)

Also divide both numerator and denominator of a partial derivative by dw while holding a variable y constant to get the chain rule . (∂ z / ∂w ) y  ∂ z   ∂w   ∂z  = =  ∂ x  y (∂ x / ∂w ) y  ∂w  y  ∂ x  y

(3-44)

Thermodynamic State Functions In thermodynamics, the state functions include the internal energy U, enthalpy H, and Helmholtz and Gibbs free energies A and G, respectively, defined as follows: H = U + PV A = U - TS G = H - TS = U + PV - TS = A + PV

2

 ∂u  ∂2 f ∂2 u = f ′′   + f ′ 2 2 ∂y ∂y  ∂y 

where S is the entropy, T the absolute temperature, P the pressure, and V the volume . These are also state functions, in that the entropy is specified

DIFFEREnTIAL AnD InTEGRAL CALCULUS once two variables (such as T and P) are specified, for example. Likewise, V is specified once T and P are specified; it is therefore a state function. In an open system, extensive properties, such as the total internal energy, are functions of two thermodynamic variables plus the mass or moles of each component. The mathematical derivations below are for a single-component system of constant mass. They are applicable when the mass stays constant, i.e., in an intensive system (or else an additional variable for moles N must be added). However, the relations between the thermodynamic variables can be regarded as internal energy per moles in a closed system, or at a point in an open system. The formulas illustrate the use of calculus in thermodynamics. If a process is reversible and only P-V work is done, the first law and differentials can be expressed as follows: dU = T dS - P dV

(3-45)

dH = T dS + V dP

(3-46)

dA = -S dT - P dV

(3-47)

dG = -S dT + V dP

(3-48)

Alternatively, if the internal energy is considered a function of S and V, then the differential is  ∂U   ∂U  dV dS +  dU =   ∂V  S  ∂S  V This is the equivalent of Eq. (3-43) and gives the following definitions:  ∂U   ∂U  , P = − T =  ∂V  S  ∂S  V Since the internal energy is a state function, Eq. (3-44) must be satisfied. 2

2

∂U ∂U = ∂V ∂S ∂S ∂V  ∂P   ∂T     = −  ∂S  V ∂V  S

This is

This is one of the Maxwell relations, and the other Maxwell relations can be derived in a similar fashion by applying Eq. (3-41). See Sec. 4, Thermodynamics, “Constant-Composition Systems.” Partial Derivatives of Intensive Thermodynamic Functions The various partial derivatives of the thermodynamic functions can be classified into six groups. In the general formulas below, the variables U, H, A, G, and S are denoted by Greek letters (these can be extensive properties), while the variables V, T, and P are denoted by Latin letters (T and P can only be intensive properties). Type I (3 possibilities plus reciprocals)  ∂a  General:    ∂b  c

 ∂P  specific:    ∂T  V

Equation (3-42) gives

3-19

First evaluate the derivative, using Eq. (3-45). (∂S / ∂T )V  ∂S   ∂V   ∂V   =−   = −    ∂T V ∂S  T (∂S / ∂V )T ∂T  S Then evaluate the numerator and denominator as type II derivatives. Use Eq. (3-45) and Eq. (3-41) to get (∂S / ∂T )V = C v /T . Use Eqs. (3-47) and (3-41) to get the Maxwell relation (∂ P / ∂T )V = (∂S / ∂V )T . Finally use Eq. (3-42).  ∂V  Cv   Cv  ∂ P  T  ∂V  T =   = − ∂ ∂ ∂ V P V      ∂T S T  −    ∂T  P  ∂V  T ∂T  P These derivatives are of importance for reversible, adiabatic processes (such as in an ideal turbine or compressor), since then the entropy is constant. An example is the Joule-Thomson coefficient for constant H. 1   ∂V    ∂T  −V + T    =  ∂T  P  ∂ P  H C p  Type IV (30 possibilities plus reciprocals)  ∂α  General:    ∂β  c

 ∂G  specific:   ∂A  p

Use Eq. (3-47) to introduce a new variable T. (∂G / ∂T ) P  ∂G   ∂G   ∂T   =   =   ∂ A  P  ∂T  P  ∂ A  P (∂ A / ∂T ) P This operation has created two type II derivatives; using the differential Eqs. (3-47) and (3-48), we obtain S  ∂G  =  ∂ A  P S + P (∂V / ∂T ) P Type V (60 possibilities plus reciprocals)  ∂α  General:    ∂b  β

 ∂G  specific:    ∂P  A

Start from the differential for dG. Then we get  ∂T   ∂G   +V   = − S  ∂P  A ∂P  A The derivative is type III and can be evaluated by using Eq. (3-42). (∂ A / ∂ P )T  ∂G  +V =S  ∂ P  A (∂ A / ∂T ) P The two type II derivatives are then evaluated using the differential Eq. (3-47).

(∂V / ∂T ) P  ∂V   ∂ P   ∂P     =−   = −  ∂T  P  ∂V  T (∂V / ∂ P )T ∂T  V Type II (30 possibilities plus reciprocals)  ∂α  General:    ∂b  c

 ∂G  specific:    ∂T  V

The differential for G is from Eq. (3-48) or Eq. (3-43) with x → P :  ∂P   ∂G     = − S + V  ∂T  V ∂T V Using the other equations for U, H, A, or S gives the other possibilities. Type III (15 possibilities plus reciprocals)  ∂a  General:    ∂b  α

 ∂V  specific:    ∂T  S

SP (∂V / ∂ P )T  ∂G  +V =  ∂ P  A S + P (∂V / ∂T ) P These derivatives are also of interest for free expansions or isentropic changes. Type VI (30 possibilities plus reciprocals)  ∂α  General:    ∂β  γ

 ∂G  specific:   ∂A H

We use Eq. (3-44) to obtain two type V derivatives. (∂G / ∂T ) H  ∂G    = ∂ A  H (∂ A / ∂T ) H These can then be evaluated using the procedures for type V derivatives.

3-20

MATHEMATICS

InTEGRAL CALCULUS

2 2 2 ⌠ 4 − 9x dx . Let x = sin θ; then dx = cos θ d θ. Example Find  2 3 3 x ⌡

Indefinite Integral If f ′( x ) is the derivative of f (x), an antiderivative of f ′( x ) is f (x). Symbolically, the indefinite integral of f ′(x) is

2 2 ⌠ 2/3 1 − sin 2 θ  2 ⌠ (2/3) − x  dx = 3 3  cos θ d θ 2 2 2 x ⌡ ⌡ (2/3) sin θ  3

∫ f ′( x ) dx = f ( x ) + c where c is an arbitrary constant to be determined by the problem. By virtue of the known formulas for differentiation, the following relationships hold (a is a constant):

∫ (du + d υ + dw ) = ∫ du + ∫ d υ + ∫ dw

(3-49)

= −3 cot θ − 3θ + c by trigonometric transform

∫a dυ = a ∫dυ

(3-50)

=−

∫υ

n

d υ=

∫

υ n +1 +c n +1

(n ≠ − 1)

dυ = ln | υ | + c υ

∫a

υ

∫e

dυ = υ

aυ +c ln a υ

dυ = e + c

(3-51)

∫ cos υ d υ = sin υ + c

(3-56)

2

+ e x − 10) dx = 3 ∫ x 2 dx + ∫ e x dx − 10 ∫ dx = x 3 + e x − 10 x + c

Example: Constant of Integration By definition the derivative of x3 is 3x2, and x3 is therefore the integral of 3x2. However, if f = x3 + 10, it follows that f ′ = 3x2, and x3 + 10 is therefore also the integral of 3x2. For this reason the constant c in ∫3x2 dx = x3 + c must be determined by the problem conditions, i.e., the value of f for a specified x. Methods of Integration In practice it is rare when generally encountered functions can be directly integrated. For example, the integrand in ∫ sin x dx which appears quite simple has no elementary function whose derivative is sin x . In general, there is no explicit way of determining whether a particular function can be integrated into an elementary form. When they do not exist or cannot be found either from tabled integration formulas or directly, the only recourse is series expansion, as illustrated later. Indefinite integrals cannot be solved numerically unless they are redefined as definite integrals (see “Definite Integral”), that is, F (x) = ∫ f (x) dx is x indefinite, whereas F ( x ) = ∫ f (t ) dt is definite.

Partial Fractions Rational functions are of the type f (x)/g(x) where f (x) and g(x) are polynomial expressions of degrees m and n, respectively. If the degree of f is higher than the degree of g, perform the algebraic division— the remainder will then be at least one degree less than the denominator. Consider the following types: Example Reducible denominator to linear unequal factors. 1 1 = x 3 − x 2 − 4 x + 4 ( x + 2) ( x − 2) ( x − 1)

A = 1 12

3 x 3 +10 dx = ∫ (3 x 3 + 10)1/2 ( x 2 dx )

Trigonometric Substitution This technique is particularly well adapted to integrands in the form of radicals. For these the function is transformed to a trigonometric form. In the latter form they may be more easily recognizable relative to the identity formulas. These functions and their transformations are as follows: x 2 − a 2 Let x = a sec θ x 2 + a 2 Let x = a tan θ 2

a −x

2

Let x = a sin θ

=

A ( x − 2) ( x − 1) + B ( x + 2) ( x − 1) + C ( x + 2) ( x − 2) ( x + 2) ( x − 2) ( x − 1)

=

x 2 ( A + B + C ) + x (−3 A + B ) + (2 A − 2 B − 4C ) ( x + 2) ( x − 2) ( x − 1)

-3A + B = 0

2A - 2B - 4C = 1

C = −13 1 1 1 1 = + − x 2 − x 2 − 4 x + 4 12( x + 2) 4( x − 2) 3( x − 1)

Example Find ∫ x 2 3 x 3 +10 dx . Let υ = 3x3 + 10 for which dυ = 9x2 dx. Thus 1 1 = ∫ (3 x 3 + 10)1/2 (9 x 2 dx ) = ∫ υ1/2 d υ 9 9 1 υ3/2 [by Eq. (3 -51)] = + c 9 32 2 = (3 x 3 +10)3/2 + c 27

A B C + + x + 2 x − 2 x −1

A+B+C=0

a

2

=

Equate coefficients and solve for A, B, and C.

Direct Formula Many integrals can be solved by transformation in the integrand to one of the forms given previously.

∫x

3 − 3 sin −1 x + c in terms of x 2

y4 −3 3 ⌠ y dy 1 ⌠ x dx = 4 = ∫ y 2 ( y 4 − 3) dy  1/4 4 y  ⌡ (3 + 4 x ) ⌡ 7 3 1 1 y 3 y 1 = − + c = (3 + 4 x )7/4 − (3 + 4 x )3/4 + c 4 4 7 4 3 28

(3-54) (3-55)

x

x dx 4 3 Example Find ⌠ . Let 3 + 4x = y ; then 4 dx = 4y dy and  1/4 ⌡ (3 + 4 x )

(3-53)

∫ sin υ d υ = − cos υ + c

4 − 9x 2

Algebraic Substitution Functions containing elements of the type (a + bx)1/n are best handled by the algebraic transformation y n = a + bx.

(3-52)

Other integrals can be found at en.wikipedia.org/wiki/Lists_of_integrals. Example Find ∫ (3 x 2 + e x − 10) dx using Eq. (3-49).

∫ (3 x

cos 2 θ 2 = 3⌠  2 d θ = 3 ∫ cot θ d θ ⌡ sin θ

B = 14

Hence dx ⌠ dx + ⌠ dx - ⌠ dx ⌠ =  3   ⌡ x − x 2 − 4 x + 4 ⌡ 12( x + 2) ⌡ 4( x - 2) ⌡ 3( x - 1) Integration by Parts An extremely useful formula for integration is the relation d(uυ) = u dυ + υ du and

uυ = ∫u dυ + ∫υ du

or

∫u dυ = uυ - ∫u du

It is particularly useful for trigonometric and exponential functions. Example Find ∫xex dx. Let u = x    and    dv = ex dx du = dx υ = ex

DIFFEREnTIAL AnD InTEGRAL CALCULUS ∫xex dx = xex - ∫ex dx = xex - ex + c

Therefore

∂ ∂b ∂ ∂b

Example Find ∫e sin x dx. Let x

u = ex du = ex dx

du = sin x dx u = -cos x

u = ex du = ex dx

du = cos x dx u = sin x

∫

Series Expansion When an explicit function cannot be found, the integration can sometimes be carried out by a series expansion. 2 Example Find ∫e-x dx. Since

∫e

−x2

dx

d

∫

c

∫

When F ( x ) =

2

Example Find ∫

f ( x ) dx = − f (a )

b( x ) a(x )

if

∫

d

c

dα

a and b are constant

∫

b

a

f ( x , y ) dy

(3-57)

f ( x , α ) dx the Leibniz rule gives

∫

b( x ) a(x )

∂f dy ∂x

the incorrect value 2

x3 x5 x7 + − +  for all x 3 5(2!) 7(3!)

Definite Integral The value of a definite integral depends on the limits a and b and any selected variable coefficients in the function but not on the dummy variable of integration x. Symbolically indefinite integral where dF/dx = f (x)

2  1  ⌠ dx = −   = −2 ⌡0 ( x − 1)2  x − 1  0

Note that f (x) = 1/(x - 1)2 becomes unbounded as x → 1 and by rule 2 the integral diverges and hence is said not to exist. Methods of Integration All the methods of integration available for the indefinite integral can be used for definite integrals. In addition, several others are available for the latter integrals and are indicated below. Change of Variable This substitution is basically the same as previously indicated for indefinite integrals. However, for definite integrals, the limits of integration must also be changed: i.e., for x = f (t),

∫

b

F (a , b) = ∫ f ( x ) dx

b

dx . Direct application of the formula would yield ( x − 1)2

x4 x6 dx = ∫ dx − ∫ x dx + ∫ dx − ∫ dx +  2! 3!

F (x) = ∫ f (x) dx

a

f ( x ) dx = f (b)

dF db da f [ x , b( x )] − f [ x , a ( x )] + = dx dx dx

2

=x−

∫

b

f ( x , α) d α =

0

6

x x − + 2! 3!

2

e− x = 1 − x 2 +

b

a

∫ex sin x dx = -ex cos x + ex sin x - ∫ex sin x dx + c c = (e x /2) (sin x − cos x ) + 2

4

a

b ∂ f ( x , α) dF (α ) =∫ dx a ∂α dα

∫ex sin x dx = -ex cos x + ∫ex cos x dx Again

∫

3-21

definite integral

b

a

t1

f ( x ) dx = ∫ f [φ(t )] ϕ′ (t ) dt t0

a

t = t0 when x = a t = t1 when x = b

where

b

F (α ) = ∫ f ( x , α ) dxF a

There are certain restrictions of the integration definition: The function f (x) must be continuous in the finite interval (a, b) with at most a finite number of finite discontinuities. Relaxing two of these restrictions gives rise to so-called improper integrals and requires special handling. These occur when ∞ 1. The limits of integration are not both finite, i.e., ∫ e − x dx .

4

Example Find ∫

16 − x 2 dx . Let

0

x = 4 sin q

(x = 0, q = 0)

dx = 4 cos q dq

(x = 4, q = π/2)

0

2. The function becomes infinite within the interval of integration, i.e.,

∫

1 0

1 dx x

Techniques for determining when integration is valid under these conditions are available in the references. Properties The fundamental theorem of calculus states

∫

b

f ( x ) dx = F (b) − F (a )

a

dF ( x )/dx = f ( x )

where

Then

∫

4

0

16 − x 2 dx = 16 ∫

π/2

cos 2 θ d θ = 16[ 1 2 θ + 1 4 sin 2θ]0π/2 = 4 π

0

Integration It is sometimes useful to generate a double integral to solve a problem. By this approach, the fundamental theorem indicated in Eq. (3-57) can be used. 1

xb − xa dx . Example Find ⌠  ⌡0 ln x

∫

Consider

1

0

Other properties of the definite integral are as follows:

x α dx =

1 (α > − 1) α +1

Multiply both sides by dα and integrate between a and b.

∫

b

a

b

c[ f ( x ) dx ] = c ∫ f ( x ) dx a

b

∫ [ f ( x ) + f ( x )] dx = ∫ a

∫

b

∫

b

∫

b

a

a

a

1

2

b

a

f1 ( x ) dx +

∫

b

a

f 2 ( x ) dx

∫ ∫

f ( x ) dx = − ∫ f ( x ) dx b

f ( x ) dx =

∫

a

b

b a

d α ∫ x α dx = 1

0

∫

1 0

c

for some ξ in (a , b)

1

Therefore

1

⌠ xb − xa b dx ∫ x α d α =  dx a ⌡0 ln x

b

f ( x ) dx + ∫ f ( x ) dx

f ( x ) dx = (b − a ) f (ξ)

1 ⌠ dα b +1 d α ∫ x α dx =  = ln 0 ⌡a α + 1 a +1

But also

a

c

b a

b +1 ⌠ xb − xa  ln x dx = ln a + 1 ⌡0

3-22

MATHEMATICS

InFInITE SERIES References: de Brujin, N. G., Asymptotic Methods in Analysis, Dover, New York, 2010; Zwillinger, D., Table of Integrals, Series, and Products, 8th ed., Academic, New York, 2014.

where B1 = 1/b1 B2 = − b2 /b 31 B3 = (1/b 51 ) (2b 22 − b1b3 )

DEFInITIOnS

B4 = (1/b 71) (5b1b2b3 − b 21b4 − 5b 32)

A succession of numbers or terms formed according to some definite rule is called a sequence. The indicated sum of the terms of a sequence is called a series. A series of the form a0 + a1(x - c) + a2(x - c)2 + … + an(x - c)n + … is called a power series. Consider the sum of a finite number of terms in the geometric series (a special case of a power series). Sn = a + ar + ar2 + ar3 + … + ar n -1

(3-58)

For any number of terms n, the sum equals

∫

1− r 1− r

n

Sn = a

S = a + ar + ar2 + … + arn + …

(3-59)

However, the defined sum of the terms [Eq. (3-59)] 1 − rn 1− r

x2 x1

x2

f ( x ) dx = ∫ a0 dx + x1

∫

x2 x1

x2

a1 x dx + ∫ a2 x 2 dx +  x1

6. A power series may be differentiated term by term and represents the function df (x)/dx within the same region of convergence as f (x).

In this form, the geometric series is assumed finite. In the form of Eq. (3-58), it can further be defined that the terms in the series be nonending and therefore an infinite series.

Sn = a

Additional coefficients are available in the references. 3. Two series may be added or subtracted term by term provided each is a convergent series. The joint sum is equal to the sum (or difference) of the individuals. 4. The sum of two divergent series can be convergent. Similarly, the sum of a convergent series and a divergent series must be divergent. 5. A power series may be integrated term by term to represent the integral of the function within an interval of the region of convergence. If f (x) = a0 + a1x + a2x2 + …, then

r ≠1

while valid for any finite value of r and n, now takes on a different interpretation. In this sense it is necessary to consider the limit of Sn as n increases indefinitely: S = lim Sn n→∞

1 − rn n→∞ 1 − r

= a lim

The infinite series converges if the limit of Sn approaches a fixed finite value as n approaches infinity. Otherwise, the series is divergent. If r is less than 1 but greater than -1, the infinite series is convergent. For values outside of the range -1 < r < 1, the series is divergent because the sum is not defined. The range -1 < r < 1 is called the region of convergence. (We assume a ≠ 0.) There are also two types of convergent series. Consider the new series

TESTS FOR COnVERGEnCE AnD DIVERGEnCE In general, the problem of determining whether a given series will converge can require a great deal of ingenuity and resourcefulness. It is necessary to apply one or more of the developed theorems in an attempt to ascertain the convergence or divergence of the series under study. The following defined tests are given in relative order of effectiveness. For examples, see references on advanced calculus. 1. Comparison test. A series will converge if the absolute value of each term (with or without a finite number of terms) is less than the corresponding term of a known convergent series. Similarly, a positive series is divergent if it is termwise larger than a known divergent series of positive terms. 2. nth-Term test. A series is divergent if the nth term of the series does not approach zero as n becomes increasingly large. 3. Ratio test. If the absolute ratio of the n + 1 term divided by the nth term as n becomes unbounded approaches a. A number less than 1, the series is absolutely convergent. b. A number greater than 1, the series is divergent. c. A number equal to 1, the test is inconclusive. Example For the power series a0 + a1 ( x − x 0 ) + a2 ( x − x 0 )2 +  the absolute ratio gives ε = lim

n −>∞

1 1 1 1 S = 1 − + − +  + (−1)n + 1 +  2 3 4 n

1 an+1 x − x0 = x − x0 an R

In this case series (3-60) is defined as a conditionally convergent series. If the replacement series of absolute values also converges, the series is defined to converge absolutely. Series (3-60) is further defined as an alternating series, while series (3-61) is referred to as a positive series.

where R is the inverse of the limit. For convergence e < 1; therefore the series converges for x − x 0 < R . 4. Alternating-series Leibniz test. If the terms of a series are alternately positive and negative and never increase in value, the absolute series will converge, provided that the terms tend to zero as a limit. 5. Cauchy’s root test. If the nth root of the absolute value of the nth term, as n becomes unbounded, approaches a. A number less than 1, the series is absolutely convergent. b. A number greater than 1, the series is divergent. c. A number equal to 1, the test is inconclusive. 6. Maclaurin’s integral test. Suppose ∑an is a series of positive terms and f is a continuous decreasing function such that f (x) ≥ 0 for 1 ≤ x < ∞ and ∞ f (n) = an. Then the series and the improper integral ∫ f ( x ) dx either both 1 converge or both diverge.

OPERATIOnS WITH InFInITE SERIES

SERIES SUMMATIOn AnD IDEnTITIES

(3-60)

It can be shown that series (3-60) does converge to the value S = ln 2. However, if each term is replaced by its absolute value, the series becomes unbounded and therefore divergent (unbounded divergent): 1 1 1 1 S = 1 + + + + + 2 3 4 5

(3-61)

1. The convergence or divergence of an infinite series is unaffected by the removal of a finite number of finite terms. This is a trivial theorem but useful to remember, especially when using the comparison test to be described in the subsection “Tests for Convergence and Divergence.” 2. A power series can be inverted, provided the first-degree term is not zero. Given y = b1x + b2x + b3x + b4x + b5x + b6x + b7x + … 2

then

3

4

5

6

7

x = B1y + B2y2 + B3y3 + B4y4 + B5y5 + B6y6 + B7y7 + …

Sums for the First n Numbers to Integer Powers n

∑j= j =1 n

∑j

n (n + 1) = 1 + 2 + 3 + 4 ++ n 2

2

=

n (n + 1)(2n +1) 2 = 1 + 22 + 32 + 4 2 +  + n2 6

3

=

n 2 (n + 1)2 3 = 1 + 23 + 33 +  + n3 4

j =1 n

∑j j =1

COMPLEX VARIABLES This is simply a special case of Taylor’s series when h is set to zero. Exponential Series

Arithmetic Progression n

∑[a + (k − 1) d ] = a + (a + d ) + (a + 2d )

ex =1+ x +

k =1

+ (a + 3 d ) +  + [ a + (n − 1)]d

2

ln x =

Geometric Progression

∑ar

j -1

= a + ar + ar 2 + ar 3 +  + ar n - 1 = a

j =1

1- r 1- r

1

1

1

r ≠1

1

1

1

x3 x5 x7 + − +  −∞ < x < ∞ 3! 5! 7! 2 x x4 x6 cos x = 1 − + − +  −∞ < x < ∞ 2! 4! 6! x3 1 3 x5 1 3 5 x7 −1 sin x = x + + ⋅ ⋅ + ⋅ ⋅ ⋅ +  ( x 2 < 1) 6 2 4 5 2 4 6 7 1 1 1 tan −1 x = x − x 3 + x 5 − x 7 +  ( x 2 < 1) 3 5 7 sin x = x −

1

k=0

The reciprocals of the terms of the arithmetic progression series are called a harmonic progression. No general summation formulas are available for this series. Binomial Series (See Also Elementary Algebra) n (n − 1) 2 n (n − 1)(n − 2) 3 x ± x + 2! 3!

( x 2 < 1)

Taylor’s Series 2

or

x x f (h + x ) = f (h) + xf ′(h) + f ′′(h) + f ′′′(h) +  2! 3! f ′′′( x 0 ) f ′′′( x 0 ) ( x - x 0 )2 ( x − x 0 )3 +  f ( x ) = f ( x 0 ) + f ′( x 0 ) ( x − x 0 ) + 3! 2!

f ′( x ) = (1 + x )−1 , f ′′( x ) = − (1 + x )−2 , f ′′′( x ) = 2(1 + x )−3 , etc. f (0) = 0, f ′(0) = 1, f ′′(0) = −1, f ′′′(1) = 2, etc. ln ( x + 1) = x −

x2 x3 x4 xn + − +  + (−1)n + 1 +  2 3 4 n

which converges for -1 < x ≤ 1. Maclaurin’s Series f ( x ) = f (0) + xf ′(0) +

Taylor Series The Taylor series for a function of two variables, expanded about the point (x0, y0), is f (x , y ) = f (x0 , y 0 ) +

3

Example Find a series expansion for f (x) = ln (1 + x) about x0 = 0.

Thus

3

x − 1 1  x − 1 1  x − 1 +   +  ( x > 1 2)  +  x 2  x  3 x 

Trigonometric Series*

∑ a + kd = a + a + d + a + 2d + a + 3d + a + 4 d +  + a + nd

(1 ± x )n = 1 ± nx +

−∞ < x < ∞

 x − 1  1  x − 1  3  ln x = 2    +  ( x > 0) +   x + 1  3  x + 1  

n

Harmonic Progression n

x2 x3 xn + ++ + 2! 3! n!

Logarithmic Series

1 = na + n (n − 1)d 2

n

3-23

+

1  ∂2 f 2!  ∂ x 2

∂f ∂x

x0 , y0

( x − x 0 )2 + 2 x0 , y0

(x − x0 )+

∂2 f ∂x ∂ y

∂f ∂y

( y - y0 ) x0 , y0

( x - x 0 )( y - y 0 ) + x0 , y0

∂2 f ∂y 2

 ( y - y 0 )2  +  x0 , y0

Partial Sums of Infinite Series, and How They Grow Calculus textbooks devote much space to tests for convergence and divergence of series that are of little practical value, since a convergent series either converges rapidly, in which case almost any test (among those presented in the preceding subsections) will do, or it converges slowly, in which case it is not going to be of much use unless there is some way to get at its sum without adding an unreasonable number of terms. To find out, as accurately as possible, how fast a convergent series converges and how fast a divergent series diverges, see Boas, R. P., Jr., Am. Math. Mon. 84: 237–258 (1977). *The tan x series has awkward coefficients and should be computed as (sign) sin x   1 − sin 2 x  

x2 x3 f ′′(0) + f ′′′(0) +  2! 3!

COMPLEX VARIABLES References: Ablowitz, M. J., and A. S. Fokas, Complex Variables: Introduction and Applications, 2d ed., Cambridge University Press, New York, 2012; Asmar, N., and G. C. Jones, Applied Complex Analysis with Partial Differential Equations, Prentice-Hall, Upper Saddle River, N.J., 2002; Brown, J. W., and R. V. Churchill, Complex Variables and Applications, 9th ed., McGraw-Hill, New York, 2013; Kwok, Y. K., Applied Complex Variables for Scientists and Engineers, 2d ed., Cambridge University Press, New York, 2010. Numbers of the form z = x + iy, where x and y are real, i2 = -1, are called complex numbers. The numbers z = x + iy are representable in the plane, as shown in Fig. 3-42. The following definitions and terminology are used:

1. Distance OP = r = modulus of z written | z |. | z | = x 2 + y 2 2. x is the real part of z. 3. y is the imaginary part of z. 4. The angle θ, 0 ≤ θ < 2π, measured counterclockwise from the positive x axis to OP, is the argument of z. θ = arctan y/x = arcsin y/r = arccos x/r if x ≠ 0, θ = π/2 if x = 0 and y > 0. 5. The numbers r, θ are the polar coordinates of z. 6. z = x - iy is the complex conjugate of z. ALGEBRA Let z1 = x1 + iy1 and z2 = x2 + iy2. Equality z1 = z2 if and only if x1 = x2 and y1 = y2. Addition z1 + z2 = (x1 + x2) + i(y1 + y2). Subtraction z1 - z2 = (x1 - x2) + i(y1 - y2). Multiplication z1z2 = (x1x2 - y1y2) + i(x1y2 + x2y1). Division

FIG. 3-42

Complex plane.

z1 /z 2 =

x1 x 2 + y 1 y 2 x y − x1 y 2 , z 2 ≠ 0. + i 2 21 x 22 + y 22 x 2 + y 22

3-24

MATHEMATICS

SPECIAL OPERATIOnS 2

2

2

zz = x + y = | z | ; z1 ± z 2 = z1 ± z 2 ; z1 = z1 ; z1 z 2 = z1 z 2 ;| z1 ⋅ z 2 | = | z1 | ⋅ | z 2 |; arg (z1 ⋅ z2) = arg z1 + arg z2; arg (z1/z2) = arg z1 - arg z2; i4n = 1 for n any integer; i2n = -1 where n is any odd integer; z + z = 2x; z - z = 2iy. Every complex quantity can be expressed in the form x + iy.

General powers of z are defined by zα = eα log z. Since log z is infinitely many valued, so too is zα unless α is a rational number. DeMoivre’s formula can be derived from properties of ez. zn = rn (cos q + i sin q)n = rn (cos nq + i sin nq)

TRIGOnOMETRIC REPRESEnTATIOn

Thus

By referring to Fig. 3-42, there results x = r cos θ and y = r sin θ so that z = x + iy = r (cos q + i sin q), which is called the polar form of the complex number. cos q + i sin q = eiq. Hence z = x + iy = reiq. z = x - iy = re-iq. Two important results from this are cos q = (eiq + e-iq)/2 and sin q = (eiq - e-iq)/2i. Let z1 = r1eiq1 and z2 = r2eiq2. This form is convenient for multiplication for z1 z 2 = r1 r2e i ( θ1 +θ2 ) and for division for z1 /z 2 = (r1 /r2 )e i ( θ1 −θ2 ) , z 2 ≠ 0.

COMPLEX FUnCTIOnS (AnALYTIC)

POWERS AnD ROOTS If n is a positive integer, zn = (reiq)n = rneinq = rn(cos nq + i sin nq). If n is a positive integer,   θ + 2 kπ    θ + 2 kπ  + i sin  z 1/n = r 1/n e i [( θ+ 2 kπ )/n ] = r 1/n cos   n    n   and selecting values of k = 0, 1, 2, 3, …, n - 1 gives the n distinct values of z1/n. The n roots of a complex quantity are uniformly spaced around a circle with radius r1/n in the complex plane in a symmetric fashion. Example Find the three cube roots of -8. Here r = 8, q = π. The roots are z0 = 2(cos π/3 + i sin π/3) = 1 + i 3 , z1 = 2(cos π + i sin π) = -2, and z2 = 2(cos 5π/3 + i sin 5π/3) = 1 - i 3 .

(cos q + i sin q)n = cos nq + i sin nq

In the real-number system a greater than b (a > b) and b less than c (b < c) define an order relation. These relations have no meaning for complex numbers. The absolute value is used for ordering. Some important relations follow: |z| ≥ x; |z| ≥ y ; |z1 ± z2| ≤ |z1| + |z2|; |z1 - z2| ≥ ||z1| - |z2||; |z| ≥ (|x| + |y|)/ 2 . Parts of the complex plane, commonly called regions or domains, are described by using inequalities. Example  |z - 3| ≤ 5. This is equivalent to ( x − 3)2 + y 2 ≤ 5, which is the set of all points within and on the circle, centered at x = 3, y = 0 of radius 5. Example |z - 1| ≤ x represents the set of all points inside and on the parabola 2x = y2 + 1 or, equivalently, 2x ≥ y2 + 1. Functions of a Complex Variable If z = x + iy, w = u + iu and if for each value of z in some region of the complex plane one or more values of w are defined, then w is said to be a function of z, w = f (z). Some of these functions have already been discussed, such as sin z and log z. All functions are reducible to the form w = u(x, y) + iu(x, y), where u and u are real functions of the real variables x and y. Example z3 = (x + iy)3 = x3 + 3x2(iy) + 3x(iy)2 + (iy)3 = (x3 - 3xy2) + i(3x2y - y3). Differentiation The derivative of w = f (z) is

ELEMEnTARY COMPLEX FUnCTIOnS Polynomials A polynomial in z, anzn + an -1zn -1 + … + a0, where n is a positive integer, is simply a sum of complex numbers times integral powers of z which have already been defined. Every polynomial of degree n has precisely n complex roots provided each multiple root of multiplicity m is counted m times. Exponential Functions The exponential function ez is defined by the equation ez = ex + iy = ex ⋅ eiy = ex(cos y + i sin y). Properties: e0 = 1; e z1 e z2 = e z1 + z2 ; e z1 / z2 = e z1 − z2 ; e z +2 kπi = e z , k an integer. Trigonometric Functions sin z = (eiz - e-iz)/2i; cos z = (eiz + e-iz)/2; tan z = sin z/cos z; cot z = cos z/sin z; sec z = 1/cos z; csc z = 1/sin z. Fundamental identities for these functions are the same as their real counterparts. Thus cos2 z + sin2 z = 1, cos (z1 ± z2) = cos z1 cos z2  sin z1 sin z2, sin (z1 ± z2) = sin z1 cos z2 ± cos z1 sin z2. The sine and cosine of z are periodic functions of period 2π; thus sin (z + 2π) = sin z. For computation purposes sin z = sin (x + iy) = sin x cosh y + i cos x sinh y, where sin x, cosh y, etc., are the real trigonometric and hyperbolic functions. Similarly, cos z = cos x cosh y - i sin x sinh y. If x = 0 in the results given, cos iy = cosh y and sin iy = i sinh y. Example Find all solutions of sin z = 3. From previous data sin z = sin x cosh y + i cos x sinh y = 3. Equating real and imaginary parts gives sin x cosh y = 3 and cos x sinh y = 0. The second equation can hold for y = 0 or for x = π/2, 3π/2, … . If y = 0, cosh 0 = 1 and sin x = 3 is impossible for real x. Therefore, x = ±π/2, ±3π/2, …, ±(2n + 1)π/2, n = 0, ±1, ±2, … . However, sin 3π/2 = -1 and cosh y ≥ 1. Hence x = π/2, 5π/2, … . The solution is z = [(4n + 1)π]/2 + i cosh-13, n = 0, 1, 2, 3, … . Example Find all solutions of ez = -i. ez = ex(cos y + i sin y) = -i. Equating real and imaginary parts gives ex cos y = 0, ex sin y = -1 from the first y = ±π/2, ±3π/2, … . But ex > 0. Therefore, y = 3π/2, 7π/2, -π/2, … . Then x = 0. The solution is z = i[(4n + 3)π]/2. Two important facets of these functions should be recognized. First, sin z is unbounded; second, ez takes all complex values except 0. Hyperbolic Functions sinh z = (ez - e-z)/2; cosh z = (ez + e-z)/2; tanh z = sinh z/cosh z; coth z = cosh z/sinh z; csch z = 1/sinh z; sech z = 1/cosh z. Identities are cosh2 z - sinh2 z = 1; sinh (z1 + z2) = sinh z1 cosh z2 + cosh z1 sinh z2; cosh (z1 + z2) = cosh z1 cosh z2 + sinh z1 sinh z2; cosh z + sinh z = ez; cosh z - sinh z = e-z. The hyperbolic sine and hyperbolic cosine are periodic functions with the imaginary period 2πi. That is, sinh (z + 2πi) = sinh z. Logarithms The logarithm of z, log z = log |z| + i(q + 2nπ), where log |z| is taken to the base e and q is the principal argument of z, that is, the particular argument lying in the interval 0 ≤ q < 2π. The logarithm of z is infinitely many valued. If n = 0, the resulting logarithm is called the principal value. The familiar laws log z1z2 = log z1 + log z2, log z1/z2 = log z1 - log z2, and log zn = n log z hold for the principal value.

dw f ( z + ∆z ) − f ( z ) = lim dz ∆z → 0 ∆z and for the derivative to exist, the limit must be the same no matter how Δz approaches zero. If w1 and w2 are differentiable functions of z, the following rules apply: d (w1 ± w2 ) dw1 dw2 dw2 dw d (w1w2 ) = ± = w2 1 + w1 dz dz dz dz dz dz d (w1 /w2 ) w2 (dw1 /dz ) - w1 (dw2 /dz ) = dz w22 and

dw dw1n = nw1n - 1 1 dz dz

For w = f (z) to be differentiable, it is necessary that ∂u/∂x = ∂u/∂y and ∂u/∂x = -∂u/∂y. The last two equations are called the Cauchy-Riemann equations . The derivative ∂u ∂v ∂υ dw ∂u −i = +i = ∂y ∂x ∂ y dz ∂ x If f (z) possesses a derivative at z0 and at every point in some neighborhood of z0, then f (z) is said to be analytic or homomorphic at z0 . If the CauchyRiemann equations are satisfied and u , υ,

∂u ∂u ∂υ ∂υ , , , ∂x ∂ y ∂x ∂ y

are continuous in a region of the complex plane, then f (z) is analytic in that region . Example w = z z = x2 + y2 . Here u = x2 + y2, u = 0 . ∂u/∂x = 2x, ∂u/∂y = 2y, ∂u/∂x = ∂u/∂y = 0 . These are continuous everywhere, but the CauchyRiemann equations hold only at the origin . Therefore, w is nowhere analytic, but it is differentiable at z = 0 only . Example  w = ez = ex cos y + iex sin y. u = ex cos y and u = ex sin y. ∂u/∂x = ex cos y, ∂u/∂y = -ex sin y, ∂u/∂x = ex sin y, ∂u/∂y = ex cos y. The continuity and Cauchy-Riemann requirements are satisfied for all finite z. Hence ez is analytic (except at ∞) and dw/dz = ∂u/∂x + i(∂u/∂x) = ez. Example w =

y 1 x − iy x = −i = z x2 + y2 x2 + y2 x2 + y2

It is easy to see that dw/dz exists except at z = 0 . Thus 1/z is analytic except at z = 0 .

DIFFEREnTIAL EQUATIOnS Singular Points If f (z) is analytic in a region except at certain points, those points are called singular points. Example 1/z has a singular point at zero. Example tan z has singular points at z = ±(2n + 1)(π/2), n = 0, 1, 2, …. The derivatives of the common functions, given earlier, are the same as their real counterparts. Example (d/dz)(ln z) = 1/z, (d/dz)(sin z) = cos z. Harmonic Functions Both the real and the imaginary parts of any analytic function f = u + iu satisfy Laplace’s equation ∂2f/∂x2 + ∂2f/∂y2 = 0 . A function which possesses continuous second partial derivatives and satisfies Laplace’s equation is called a harmonic function. Example ez = ex cos y + iex sin y. u = ex cos y, ∂u/∂x = ex cos y, ∂2u/∂x2 = ex cos y, ∂u/∂y = -ex sin y, ∂2u/∂y2 = -ex cos y. Clearly ∂2u/∂x2 + ∂2u/∂y2 = 0 . Similarly, u = ex sin y is also harmonic . If w = u + iu is analytic, the curves u(x, y) = c and u(x, y) = k intersect at right angles, if w′(z) ≠ 0 . Integration In much of the work with complex variables a simple extension of integration called line or curvilinear integration is of fundamental importance . Since any complex line integral can be expressed in terms of real line integrals, we define only real line integrals . Let F (x, y) be a real, continuous function of x and y, and let c be any continuous curve of finite length joining points A and B (Fig . 3-43) . F(x, y) is not related to the curve c . Divide c into n segments, Δsi, whose projection on the x axis is Δxi and on the y axis is Δyi . Let (ei, hi) be the coordinates of an arbitrary point on Δsi . The limits of the sums

3-25

are known as line integrals . Much of the initial strangeness of these integrals b will vanish if it is observed that the ordinary definite integral ∫ f ( x ) dx is a just a line integral in which the curve c is a line segment on the x axis and F(x, y) is a function of x alone . The evaluation of line integrals can be reduced to evaluation of ordinary integrals . Example  ∫c y (1 + x) dy, where c: y = 1 - x2 from (-1, 0) to (1, 0) . Clearly y = 1 - x2, dy = -2x dx. Thus ∫c y (1 + x) dy = -2 ∫1-1 (1 - x2)(1 + x)x dx = -8⁄15 . Let f (z) be any function of z, analytic or not, and c any curve as above . The complex integral is calculated as ∫c f (z) dz = ∫c (u dx - u dy) + i ∫c (u dx + u dy), where f (z) = u(x, y) + i u(x, y) . Properties of line integrals are the same as for ordinary integrals . That is, ∫c [ f (z) ± g(z)] dz = ∫c f (z) dz ± ∫c g(z) dz; ∫c kf (z) dz = k ∫c f (z) dz for any constant k, etc . Example ∫ c (x2 + iy) dz along c: y = x, 0 to 1 + i. This becomes

∫ (x c

2

+ iy ) dz = ∫ ( x 2 dx - y dy ) c

1

1

1

0

0

0

+ i ∫ ( y dx + x dy ) = ∫ x 2 dx − ∫ x dx + i ∫ x dx + i 2

c

∫

1

0

x 2 dx = − 1 6 + 5i /6

lim ∑ F (ε i , ηi ) ∆y i = ∫ F ( x , y ) dy

Conformal Mapping Every function of a complex variable w = f (z) = u(x, y) + iu(x, y) transforms the x, y plane into the u, u plane in some manner . A conformal transformation is one in which angles between curves are preserved in magnitude and sense . Every analytic function, except at those points where f ′(z) = 0, is a conformal transformation . See Fig . 3-44 . Example w = z2 . u + iu = (x2 - y2) + 2ixy or u = x2 - y2, u = 2xy. These are the transformation equations between the (x, y) and (u, u) planes . Lines parallel to the x axis, y = c1 map into curves in the u, u plane with parametric equations u = x2 - c12, u = 2c1x. Eliminating x, u = (u2/4c12) - c12, which represents a family of parabolas with the origin of the w plane as focus, the line u = 0 as axis and opening to the right . Similar arguments apply to x = c2 . The principles of complex variables are useful in the solution of a variety of applied problems, including Laplace transforms (see Integral Transforms) and process control (Sec . 8) .

FIG. 3-43 Line integral .

FIG. 3-44 Conformal transformation .

n

lim ∑ F (εi , ηi ) ∆si = ∫ F ( x , y ) ds

∆si → 0

i =1

c

n

lim ∑ F (ε i , ηi ) ∆x i = ∫ F ( x , y ) dx

∆si → 0

i =1

c

n

∆si → 0

i =1

c

DIFFEREnTIAL EQUATIOnS References: Ames, W . F ., Nonlinear Partial Differential Equations in Engineering, Academic Press, New York, 1965; Aris, R ., and N . R . Amundson, Mathematical Methods in Chemical Engineering, vol . 2, First-Order Partial Differential Equations with Applications, Prentice-Hall, Englewood Cliffs, N .J ., 1973; Asmar, N . H ., Partial Differential Equations with Fourier Series and Boundary Value Problems, 3rd ed ., Pearson, New York, 2016 . Asmar, N ., Applied Complex Analysis with Partial Differential Equations, Prentice-Hall, Upper Saddle River, N .J ., 2002; Bronson, R ., and G . Costa, Schaum’s Outline of Differential Equations, 4th ed ., McGraw-Hill, New York, 2014; Brown, J . W ., and R . V . Churchill, Fourier Series and Boundary Value Problems, 8th ed ., McGraw-Hill Education, New York, 2011; Duffy, D ., Green’s Functions with Applications, 2d ed ., Chapman and Hall/CRC, New York, 2015; Kreyszig, E ., Advanced Engineering Mathematics, 10th ed ., Wiley, New York, 2011; Ramkrishna, D ., and N . R . Amundson, Linear Operator Methods in Chemical Engineering with Applications to Transport and Chemical Reaction Systems, Prentice-Hall, Englewood Cliffs, N .J ., 1985 . The natural laws in any scientific or technological field are not regarded as precise and definitive until they have been expressed in mathematical form . Such a form, often an equation, is a relation between the quantity of interest, say, product yield, and independent variables such as time and temperature upon which yield depends . When it happens that this equation involves, besides the function itself, one or more of its derivatives it is called a differential equation .

Example The rate of the homogeneous bimolecular reaction A + B k→ C is characterized by the differential equation dx/dt = k(a - x) (b - x), where a = initial concentration of A, b = initial concentration of B, and x = x(t) = concentration of C as a function of time t. Example The differential equation of heat conduction in a moving fluid with velocity components ux, uy is ∂T ∂T k  ∂2 T ∂2 T  ∂T = + +υy + υx ∂ y ρc p  ∂ x 2 ∂ y 2  ∂x ∂t where T = T(x, y, t) = temperature, k = thermal conductivity, r = density, and cp = specific heat at constant pressure . ORDInARY DIFFEREnTIAL EQUATIOnS When the function involved in the equation depends upon only one variable, its derivatives are ordinary derivatives and the differential equation is called an ordinary differential equation . When the function depends upon several independent variables, then the equation is called a partial differential equation . The theories of ordinary and partial differential equations are quite different . In almost every respect the latter is more difficult .

3-26

MATHEMATICS

Whichever the type, a differential equation is said to be of nth order if it involves derivatives of order n but no higher. The equation in the first example is of first order and that in the second example of second order. The degree of a differential equation is the power to which the derivative of the highest order is raised after the equation has been cleared of fractions and radicals in the dependent variable and its derivatives. A relation between the variables, involving no derivatives, is called a solution of the differential equation if this relation, when substituted in the equation, satisfies the equation. A solution of an ordinary differential equation which includes the maximum possible number of “arbitrary” constants is called the general solution. The maximum number of “arbitrary” constants is exactly equal to the order of the differential equation. If any set of specific values of the constants is chosen, the result is called a particular solution. Example The general solution of (d2x/dt2) + k2x = 0 is x = A cos kt + B sin kt, where A and B are arbitrary constants. A particular solution is x = ½ cos kt + 3 sin kt. In the case of some equations still other solutions exist called singular solutions. A singular solution is any solution of the differential equation which is not included in the general solution. Example y = x(dy/dx) - ¼(dy/dx)2 has the general solution y = cx - ¼c2, where c is an arbitrary constant; y = x2 is a singular solution, as is easily verified. ORDInARY DIFFEREnTIAL EQUATIOnS OF THE FIRST ORDER Equations with Separable Variables Every differential equation of the first order and of the first degree can be written in the form M(x, y) dx + N(x, y)dy = 0. If the equation can be transformed so that M does not involve y and N does not involve x, then the variables are said to be separated. The solution can then be obtained by quadrature, which means that y = ∫ f (x)dx + c, which may or may not be expressible in simpler form. Exact Equations The equation M(x, y) dx + N(x, y) dy = 0 is exact if and only if ∂M/∂y = ∂N/∂x. In this case there exists a function w = f (x, y) such that ∂f/∂x = M, ∂f/∂y = N, and f (x, y) = C is the required solution . f (x, y) is found as follows: treat y as though it were constant and evaluate ∫M(x, y) dx. Then treat x as though it were constant and evaluate ∫N(x, y) dy. The sum of all unlike terms in these two integrals (including no repetitions) is f (x, y) . Example (2xy - cos x) dx + (x2 - 1) dy = 0 is exact for ∂M/∂y = 2x, ∂N/∂x = 2x. ∫M dx = ∫(2xy - cos x) dx = x2y - sin x, ∫N dy = ∫(x2 - 1) dy = x2y - y. The solution is x2y - sin x - y = C, as may easily be verified . Linear Equations A differential equation is said to be linear when it is of first degree in the dependent variable and its derivatives . The general linear first-order differential equation has the form dy/dx + P(x)y = Q(x) . Its general solution is − P dx P dx y = e ∫  ∫ Qe ∫ dx + C   

Example A tank initially holds 200 gal of a salt solution in which 100 lb is dissolved . Six gallons of brine containing 4 lb of salt run into the tank per minute . If mixing is perfect and the output rate is 4 gal/min, what is the amount A of salt in the tank at time t ? The differential equation of A is dA/dt = 4 - 2A/[100 + t] . Its general solution is A = (4/3)(100 + t) + C/(100 + t)2 . At t = 0, A = 100; so the particular solution is A = (4/3)(100 + t) (1/3) ×106/(100 + t)2 . ORDInARY DIFFEREnTIAL EQUATIOnS OF HIGHER ORDER The higher-order differential equations, especially those of order 2, are of great importance because of physical situations describable by them . Equation y(n) = f (x). The superscript (n) means n derivatives . Such a differential equation can be solved by n integrations . The solution will contain n arbitrary constants . Linear Differential Equations with Constant Coefficients and Right-Hand Member of Zero (Homogeneous) The solution of y ′′ + ay ′ + by = 0 depends upon the nature of the roots of the characteristic equation m2 + am + b = 0 obtained by substituting the trial solution y = emx in the equation . Distinct Real Roots If the roots of the characteristic equation are distinct real roots, r1 and r2, say, the solution is y = Ae r1 x + Be r2 x , where A and B are arbitrary constants . Example y ′′ + 4 y ′ + 3 = 0 . The characteristic equation is m2 + 4m + 3 = 0 . The roots are -3 and -1, and the general solution is y = Ae–3x + Be–x. Multiple Real Roots If r1 = r2, the solution of the differential equation is y = e r1 x ( A + Bx ) . Example y ′′ + 4 y + 4 = 0 . The characteristic equation is m2 + 4m + 4 = 0 with roots -2 and -2 . The solution is y = e-2x(A + Bx) . Complex Roots If the characteristic roots are p ± iq, then the solution is y = e px × (A cos qx + B sin qx) .

Example The differential equation My ′′ + Ay ′ + ky = 0 represents the vibration of a linear system of mass M, spring constant k, and damping constant A. If A < 2 kM , the roots of the characteristic equation Mm 2 + Am + k = 0 are complex: −

A ±i 2M

k  A  −  M  2M 

2

and the solution is   k  A 2    k  A 2  t + ic2 sin  y = e − ( At /2 M ) c1 cos  − −   t    M  2 M     M  2M   This solution is oscillatory, representing undercritical damping . All these results generalize to homogeneous linear differential equations with constant coefficients of order higher than 2 . These equations (especially of order 2) have been much used because of the ease of solution . Oscillations, electric circuits, diffusion processes, and heat flow problems are a few examples for which such equations are useful . Second-Order Equations: Dependent Variable Missing Such an equation is of the form  dy d 2 y  F  x, , 2  = 0  dx dx  It can be reduced to a first-order equation by substituting p = dy/dx and dp/dx = d2y/dx2 . Second-Order Equations: Independent Variable Missing Such an equation is of the form  dy d 2 y  F  y, , 2  = 0  dx dx  dp d2y du = p, =p dy dx 2 dx

Set

The result is a first-order equation in p  dp  F  y , p, p  = 0 dy   Example The capillary curve for one vertical plate is given by d2y 4y = dx 2 c 2

  dy  2  1 +    dx  

3/2

Its solution by this technique is c c c x + c 2 − y 2 − c 2 − h02 =  cosh −1 − cosh −1  2 y h0  where c and h0 are physical constants . Example The equation governing chemical reaction in a porous catalyst in plane geometry of thickness L is D

dc d 2c (0) = 0, c ( L) = cυ = k f (c ), dx dx 2

where D is a diffusion coefficient, k is a reaction rate parameter, c is the concentration, kf (c) is the rate of reaction, and c0 is the concentration at the dc gives (Finlayson, 1980, p . 92) boundary . Making the substitution p = ds p

Integrating gives

dp k = f (c ) dc D

p2 k = 2 D

∫

c

c (0)

f (c ) dc

DIFFEREnTIAL EQUATIOnS If the reaction is very fast, c(0) ≈ 0 and the average reaction rate is related to p(L). This variable is given by 2k p ( L) =  D

∫

c (0)

0

1/2

f (c ) dc  

c0′ (0) + ac1′ (0) + a 2c2′ (0) +  = 0

Form of Particular Integral Then P(x) is

a (constant)

A (constant)

axn

Anxn + An-1 xn -1 + … + A1x + A0

aerx

Berx

c cos kx   d sin kx 

A cos kx + B sin kx

g x n e rx cos kx   h x n e rx sin kx 

(Anx + … + A0)e cos kx + (Bnx + … + B0)e sin kx n

rx

The goal is to find equations governing the functions {ci(x)} and solve them . Substitution into the equations gives the following equations: c0′′ ( x ) + ac1′′( x ) + a 2c2′′ ( x ) +  = a[c0 ( x ) + ac1 ( x ) + a 2c2 ( x ) + ]2

Thus, the average reaction rate can be calculated without solving the complete problem. Linear Nonhomogeneous Differential Equations Linear Differential Equations Right-Hand Member f (x) ≠ 0 Again the specific remarks for y ′′ + ay ′ + by = f ( x ) apply to differential equations of similar type but higher order. We shall discuss two general methods. Method of Undetermined Coefficients Use of this method is limited to equations exhibiting both constant coefficients and particular forms of the function f (x). In most cases f (x) will be a sum or product of functions of the type constant, xn (n a positive integer), emx, cos kx, sin kx. When this is the case, the solution of the equation is y = H(x) + P(x), where H(x) is a solution of the homogeneous equations found by the method of the preceding subsection and P(x) is a particular integral found by using the following table subject to these conditions: (1) When f (x) consists of the sum of several terms, the appropriate form of P(x) is the sum of the particular integrals corresponding to these terms individually. (2) When a term in any of the trial integrals listed is already a part of the homogeneous solution, the indicated form of the particular integral is multiplied by x.

If f (x) is

3-27

n

rx

c0 (1) + ac1 (1) + a 2c2 (1) +  = 1 Like terms in powers of a are collected to form the individual problems . c0′′= 0, c0′ (0) = 0, c0 (1) = 1 c1′′= c02 , c1′(0) = 0, c1 (1) = 0 c2′′= 2c0 c1 , c2′ (0) = 0, c 2 (1) = 0 The solution proceeds in turn . c0 ( x ) = 1, c1 ( x ) =

( x 2 − 1) 5 − 6x 2 + x 4 , c2 ( x ) = 2 12

SPECIAL DIFFEREnTIAL EQUATIOnS See Olver et al . (2010) in General References . Euler’s Equation The linear equation xny(n) + a1xn -1y n-1 + … + an-1xy′ + any = R(x) can be reduced to a linear equation with constant coefficients by the change of variable x = et . To solve the homogeneous equation substitute y = xr into it, cancel the powers of x, which are the same for all terms, and solve the resulting polynomial for r . In case of multiple or complex roots there results the form y = xr(log x)r and y = xα[cos (b log x) + i sin (b log x)] . Bessel’s Equation The linear equation x2(d2y/dx2) + x(dy/dx) + (x2 - p2) y = 0 is the Bessel equation of integer order . By series methods, not to be discussed here, this equation can be shown to have the solution x J p ( x ) =    2

p

∞

(−1) k ( x /2)2 k k = 0 k !( p + k )!

∑

(Bessel function of the first kind of order p) and Since the form of the particular integral is known, the constants may be evaluated by substitution in the differential equation. Example y ′′ + 2 y ′ + y = 3e2x - cos x + x3. The characteristic equation is (m + 1)2 = 0 so that the homogeneous solution is y = (c1 + c2x)e-x. To find a particular solution we use the trial solution from the table, y = a1e2x + a2 cos x + a3 sin x + a4x3 + a5x2 + a6x + a7. By substituting this in the differential equation and collecting and equating like terms, there results a1 = ⅓, a2 = 0, a3 = -½, a4 = 1, a5 = -6, a6 = 18, and a7 = -24 . The solution is y = (c1 + c2x)e-x + ⅓e2x - ½ sin x + x3 - 6x2 + 18x - 24 . Method of Variation of Parameters This method is applicable to any linear equation . The technique is developed for a second-order equation but immediately extends to higher order . Let the equation be y ′′ + a ( x ) y ′ + b( x ) y = R ( x ), and let the solution of the homogeneous equation, found by some method, be y = c1f1(x) + c2f2(x) . It is now assumed that a particular integral of the differential equation is of the form P(x) = uf1 + vf2, where u and v are functions of x to be determined by two equations . One equation results from the requirement that uf1 + vf2 satisfy the differential equation, and the other is a degree of freedom open to the analyst . The best choice proves to be u ′f1 + v ′f 2 = 0 and u ′f1′+ vf 2′ = 0 Then

u′ =

du f2 =− R(x ) dx f1 f 2′− f 2 f1′

v′ =

dv f1 R(x ) = dx f1 f 2′ − f 2 f1′

and since f1, f2, and R are known, u, v may be found by direct integration . Perturbation Methods If the ordinary differential equation has a parameter that is small and is not multiplying the highest derivative, perturbation methods can give solutions for small values of the parameter . Example Consider the differential equation for reaction and diffusion in a catalyst; the reaction is second-order: c″ = ac2, c′(0) = 0, c(1) = 1 . The solution is expanded in the following Taylor series in a. c(x, a) = c0(x) + ac1(x) + a c2(x) + … 2

Y p (x ) =

J p ( x ) cos ( pπ) − J − p ( x ) sin ( pπ)

(Bessel function of the second kind) (replace right-hand side by limiting value if p is an integer or zero) . The series converges for all x. Much of the importance of Bessel’s equation and Bessel functions lies in the fact that the solutions of numerous linear differential equations can be expressed in terms of them . Legendre’s Equation The Legendre equation (1 - x2)y″ - 2xy′ + n(n + 1) y = 0, n ≥ 0, has the solution Pn for n an integer . The polynomials Pn are the so-called Legendre polynomials, P0(x) = 1, P1(x) = x, P2(x) = ½(3x2 - 1), P3(x) = ½(5x3 - 3x), … For n positive and not an integer, see Olver et al . (2010) in General References . Laguerre’s Equation The Laguerre equation x(d2y/dx2) + (c - x) (dy/dx) - ay = 0 is satisfied by the confluent hypergeometric function . See Olver et al . (2010) in General References . Hermite’s Equation The Hermite equation y ′′ − 2 xy ′ + 2ny = 0 is satisfied by the Hermite polynomial of degree n, y = AHn(x), if n is a positive integer or zero . H0(x) = 1, H1(x) = 2x, H2(x) = 4x2 - 2, H3(x) = 8x3 - 12x, H4(x) = 16x4 - 48x2 + 12, Hr+1(x) = 2xHr(x) - 2rHr-1(x) . Chebyshev’s Equation The equation (1 − x 2 ) y ′′ − xy ′ + n 2 y = 0 for n a positive integer or zero is satisfied by the nth Chebyshev polynomial y = ATn(x) . T0(x) = 1, T1(x) = x, T2(x) = 2x2 - 1, T3(x) = 4x3 - 3x, T4(x) = 8x4 8x2 + 1; Tr+1(x) = 2xTr(x) - Tr -1(x) . PARTIAL DIFFEREnTIAL EQUATIOnS The analysis of situations involving two or more independent variables frequently results in a partial differential equation . Example The equation ∂T/∂t = k(∂2T/∂x2) represents the unsteady onedimensional conduction of heat . Example The equation for the unsteady transverse motion of a uniform beam clamped at the ends is ∂ 4 y ρ ∂2 y =0 + ∂ x 4 EI ∂t 2

3-28

MATHEMATICS

Example The expansion of a gas behind a piston is characterized by the simultaneous equations

The equations for flow and adsorption in a packed bed or chromatography column give a quasilinear equation .

∂u ∂u ∂ρ ∂u c 2 ∂ρ ∂u +ρ = 0 +u = 0 and +u + ∂x ∂x ∂t ∂x ρ ∂x ∂t The partial differential equation ∂2f/(∂x ∂y) = 0 can be solved by two integrations yielding the solution f = g(x) + h(y), where g(x) and h(y) are arbitrary differentiable functions . This result is an example of the fact that the general solution of partial differential equations involves arbitrary functions in contrast to the solution of ordinary differential equations, which involve only arbitrary constants . A number of methods are available for finding the general solution of a partial differential equation . In most applications of partial differential equations, the general solution is of limited use . In such applications the solution of a partial differential equation must satisfy both the equation and certain auxiliary conditions called initial and/or boundary conditions, which are dictated by the problem . Examples of these include those in which the wall temperature is a fixed constant T(x0) = T0, there is no diffusion across a nonpermeable wall, and the like . In ordinary differential equations, these auxiliary conditions allow definite numbers to be assigned to the constants of integration . Partial Differential Equations of Second and Higher Order Many of the applications to scientific problems fall naturally into partial differential equations of second order, although there are important exceptions in elasticity, vibration theory, and elsewhere . A second-order differential equation can be written as a

∂2 u ∂2 u ∂2 u +c 2 = f +b 2 ∂y ∂x ∂ y ∂x

where a, b, c, and f depend upon x, y, u, ∂u/∂x, and ∂u/∂y. This equation is hyperbolic, parabolic, or elliptic, depending on whether the discriminant b2 - 4ac > 0, = 0, or < 0, respectively . Since a, b, c, and f depend on the solution, the type of equation can be different at different x and y locations . If the equation is hyperbolic, discontinuities can be propagated . See Courant and Hilbert (1953, 1962) and LeVeque, R . J ., Numerical Methods for Conservation Laws, Birkhäuser, Basel, Switzerland, 1992 . Phenomena of propagation such as vibrations are characterized by equations of “hyperbolic” type which are essentially different in their properties from other classes such as those which describe equilibrium (elliptic) or unsteady diffusion and heat transfer (parabolic) . Prototypes are as follows: Elliptic Laplace’s equation ∂2u/∂x2 + ∂2u/∂y2 = 0 and Poisson’s equation ∂2u/∂x2 + ∂2u/∂y2 = g(x, y) do not contain the variable time explicitly and consequently represent equilibrium configurations . Laplace’s equation is satisfied by static electric or magnetic potential at points free from electric charges or magnetic poles . Other important functions satisfying Laplace’s equation are the velocity potential of the irrotational motion of an incompressible fluid, used in hydrodynamics; the steady temperature at points in a homogeneous solid; and the steady state of diffusion through a homogeneous body . Parabolic The heat equation ∂T/∂t = ∂2T/∂x2 + ∂2T/∂y2 represents nonequilibrium or unsteady states of heat conduction and diffusion . Hyperbolic The wave equation ∂2u/∂t2 = c2(∂2u/∂x2 + ∂2u/∂y2) represents wave propagation of many varied types . Quasilinear first-order differential equations are like a

∂u ∂u = f +b ∂y ∂x

φ

df ∂c ∂c ∂c =0 + (1 − φ) + φu dc ∂t ∂x ∂t

Here n = f (c) is the relation between concentration on the adsorbent and fluid concentration . The solution of problems involving partial differential equations often revolves about an attempt to reduce the partial differential equation to one or more ordinary differential equations . The solutions of the ordinary differential equations are then combined (if possible) so that the boundary conditions and the original partial differential equation are simultaneously satisfied . Three of these techniques are illustrated . Similarity Variables The physical meaning of the term “similarity” relates to internal similitude, or self-similitude . Thus, similar solutions in boundary-layer flow over a horizontal flat plate are those for which the horizontal component of velocity u has the property that two velocity profiles located at different coordinates x differ only by a scale factor . The mathematical interpretation of the term similarity is a transformation of variables carried out so that a reduction in the number of independent variables is achieved . There are essentially two methods for finding similarity variables, “separation of variables” (not the classical concept) and the use of “continuous transformation groups .” The basic theory is available in Ames (1965) . Example The equation ∂q/∂x = (A/y)(∂2q/∂y2) with the boundary conditions q = 0 at x = 0, y > 0; q = 0 at y = ∞, x > 0; q = 1 at y = 0, x > 0 represents the nondimensional temperature q of a fluid moving past an infinitely wide flat plate immersed in the fluid . Turbulent transfer is neglected, as is molecular transport except in the y direction . It is now assumed that the equation and the boundary conditions can be satisfied by a solution of the form q = f (y/xn) = f (u), where q = 0 at u = ∞ and q = 1 at u = 0 . The purpose here is to replace the independent variables x and y by the single variable u when it is hoped that a value of n exists which will allow x and y to be completely eliminated in the equation . In this case since u = y/xn, there results after some calculation ∂q/∂x = -(nu/x)(dq/du), ∂2q/∂y2 = (1/x2n)(d2q/du2), and when these are substituted in the equation, -(1/x)nu (dq/du) = (1/x3n)(A/u) (d2q/du2) . For this to be a function of u only, choose n = ⅓ . There results (d2q/du2) + (u2/3A)(dq/du) = 0 . Two integrations and use of the boundary conditions for this ordinary differential equation give the solution ∞

∞

u

0

θ = ∫ exp(-u 3 /9 A ) du / ∫

exp (-u 3 /9 A ) du

Group Method The type of transformation can be deduced using group theory . For a complete exposition, see Ames (1965) and Hill, J . M ., Differential Equations and Group Methods for Scientists and Engineers, CRC Press, New York, 1992; a shortened version can be found in Finlayson (1980) . Basically, a similarity transformation should be considered when one of the independent variables has no physical scale (perhaps it goes to infinity) . The boundary conditions must also simplify (and combine) since each transformation leads to a differential equation with one fewer independent variable . Example A similarity variable is found for the problem ∂c ∂  D (c ) ∂c  = , c (0, t ) = 1, c (∞ , t ) = 0, c ( x , 0) = 0 ∂t ∂ x  D0 ∂ x 

where a, b, and f depend on x, y, and u, with a2 + b2 ≠ 0 . This equation can be solved using the method of characteristics, which writes the solution in terms of a parameter s, which defines a path for the characteristic .

Note that the length dimension goes to infinity, so there is no length scale in the problem statement; this is a clue to try a similarity transformation . The transformation examined here is

du dy dx = a, = b, = f ds ds ds

t = a αt , x = a β x , c = a γ c

These equations are integrated from some initial conditions . For a specified value of s, the value of x and y shows the location where the solution is u. The equation is semilinear if a and b depend just on x and y (and not u), and the equation is linear if a, b, and f all depend on x and y, but not u. Such equations give rise to shock propagation, and conditions have been derived to deduce the presence of shocks . Courant and Hilbert (1953, 1962); Rhee, H . K ., R . Aris, and N . R . Amundson, First-Order Partial Differential Equations, vol . 1, Theory and Applications of Single Equations, Prentice-Hall, Englewood Cliffs, N .J ., 1986; and LeVeque (1992), ibid . An example of a linear hyperbolic equation is the advection equation for flow of contaminants when the x and y velocity components are u and v, respectively . ∂c ∂c ∂c =0 +v +u ∂y ∂x ∂t

With this substitution, the equation becomes a α−γ

∂  D ( a − γ c ) ∂c  ∂c = a 2β − γ   ∂ x  D0 ∂x  ∂t

Group theory says a system is conformally invariant if it has the same form in the new variables; here, that is γ=0

α - γ = 2b - γ

The invariants are η=

β x , δ= α tδ

or α = 2b

DIFFEREnTIAL EQUATIOnS and the solution is

Then u(x, t) satisfies c(x, t) = f (h)t

γ/α

We can take γ = 0 and d = b/α = ½. Note that the boundary conditions combine because the point x = ∞ and t = 0 gives the same value of h and the conditions on c at x = ∞ and t = 0 are the same. We thus make the transformation η=

x ∂2 u ∂u = D 2 , u ( x , 0) = − 1, u (0, t ) = 0, u ( L , t ) = 0 L ∂x ∂t Assume a solution of the form u(x, t) = X(x)T(t), which gives 1 dT 1 d 2 X = DT dt X dx 2

x , c ( x , t ) = f ( η) 4 D0t

The use of the 4 and D0 makes the analysis below simpler. The result is

Since both sides are constant, this gives the following ordinary differential equations to solve:

d  D (c ) df  df = 0, f (0) = 1, f (∞) = 0  + 2η  d η  D0 d η  dη Thus, we solve a two-point boundary-value problem instead of a partial differential equation. When the diffusivity is constant, the solution is the error function, a tabulated function. c ( x , t ) = 1 − erf η = erfc η η

2

∞

1 dT 1 d2X = −λ , = −λ DT dt X dx 2 The solution of these is T = Ae − λDt

0

The combined solution for u(x, t) is

0

Separation of Variables This powerful, well-utilized method is applicable in certain circumstances. It consists of assuming that the solution for a partial differential equation has the form U = f (x)g(y). If it is then possible to obtain an ordinary differential equation on one side of the equation depending on only x and on the other side on only y, the partial differential equation is said to be separable in the variables x and y. If this is the case, one side of the equation is a function of x alone and the other of y alone. The two can be equal only if each is a constant, say, l. Thus the problem has again been reduced to the solution of ordinary differential equations. Example Laplace’s equation ∂2V/∂x2 + ∂2V/∂y2 = 0 plus the boundary conditions V(0, y) = 0, V(l, y) = 0, V(x, ∞) = 0, V(x, 0) = f (x) represents the steady-state potential in a thin plate (in the z direction) of infinite extent in the y direction and of width l in the x direction . A potential f (x) is impressed (at y = 0) from x = 0 to x = 1, and the sides are grounded . To obtain a solution of this boundary-value problem, assume V(x, y) = f (x)g(y) . Substitution in the differential equation yields f ′′( x ) g ( y ) + f ( x ) g ′′( y ) = 0 or g ′′( y )/g ( y ) = − f ′′( x )/f ( x ) = λ 2 (say) . This system becomes g ′′( y ) − λ 2 g ( y ) = 0 and f ′′( y ) + λ 2 f ( y ) = 0 . The solutions of these ordinary differential equations are, respectively, g(y) = Aely + Be–ly and f (x) = C sin lx + D cos lx. Then f (x)g(y) = (Aely + Be–ly) (C sin lx + D cos lx) . Now V(0, y) = 0 so that f (0)g(y) = (Aely + Be-ly) D ≡ 0 for all y. Hence D = 0 . The solution then has the form sin lx (Aely + Be-ly) where the multiplicative constant C has been eliminated . Since V(l, y) = 0, sin ll(Aely + Be-ly) ≡ 0 . Clearly the bracketed function of y is not zero, for the solution would then be the identically zero solution . Hence sin ll = 0 or ln = nπ/l, n = 1, 2, …, where ln = nth eigenvalue . The solution now has the form sin (nπx/l)(Aenπy/l + Be-nπy/l) . Since V(x, ∞) = 0, A must be taken to be zero because ey becomes arbitrarily large as y → ∞ . The solution then reads Bn sin (nπx/l)e-nπy/l, where Bn is the multiplicative constant . The differential equation is linear and homogeneous ∞ so that ∑ n=1 Bn e − nπy /l sin (nπx/l) is also a solution . Satisfaction of the last boundary condition is ensured by taking 2 l f ( x ) sin (nπx/l) dx = Fourier sine coefficients of f (x) l ∫0

Further, convergence and differentiability of this series are established quite easily . Thus the solution is ∞

V ( x , y ) = ∑ Bn e − nπy /l sin n =1

nπx l

Example The diffusion problem in a slab of thickness L ∂2 c ∂c = D 2 , c (0, t ) = 1, c ( L , t ) = 0, c ( x , 0) = 0 ∂x ∂t can be solved by separation of variables . First transform the problem so that the boundary conditions are homogeneous (having zeros on the right-hand side) . Let c(x , t ) = 1 −

X = B cos λ x + E sin λ x

2

erf η = ∫ e − ξ d ξ / ∫ e − ξ d ξ

Bn =

3-29

x + u( x , t ) L

u = A ( B cos λ x + E sin λ x ) e − λDt Apply the boundary condition that u(0, t) = 0 to give B = 0 . Then the solution is u = A (sin λ x )e − λDt where the multiplicative constant E has been eliminated . Apply the boundary condition at x = L. 0 = A (sin λ L)e − λDt This can be satisfied by choosing A = 0, which gives no solution . However, it can also be satisfied by choosing l such that sin λ L = 0, λ L = n π Thus

λ=

n 2π2 L2

The combined solution can now be written as  sin nπx  − n 2 π 2 Dt / L2 e u= A  L  Since the initial condition must be satisfied, we use an infinite series of these functions . ∞

 sin nπx  − n 2 π 2 Dt / L2 e u = ∑ An   L  n =1 At t = 0, we satisfy the initial condition . ∞ x  sin nπ x  − 1 = ∑ An    L L  n =1

This is done by multiplying the equation by sin mπx L and integrating over x: 0 → L. (This is the same as minimizing the mean square error of the initial condition .) This gives L x Am L mπx = ∫  − 1 sin dx 0  L  2 L

which completes the solution . Integral-Transform Method A number of integral transforms are used in the solution of differential equations . Only one, the Laplace transform, is discussed here [ for others, see Integral Transforms (Operational Methods)] .

3-30

MATHEMATICS

The one-sided Laplace transform indicated by L[ f (t)] is defined by the equation ∞ L[ f (t)] ∫ f (t )e − st dt . It has numerous important properties. The ones of 0 interest here are L[ f ′(t )] = sL[ f (t )] − f (0) L[ f ′′(t )] = s 2 L[ f (t )] − sf (0) − f ′(0); L[ f (n)(t)] = snL[ f (t)] - sn -1f (0) - sn -2 f ′(0) - … - f (n -1)(0) for ordinary derivatives. For partial derivatives an indication of which variable is being transformed avoids confusion. Thus, if

∫

0

or

e − st

1 ∞ ∂c ∂2 c dt = ∫ e − st dt ∂t D 0 ∂x 2 sF d 2F = (1/D ) sF − c ( x ,0) = D dx 2

where F(x, s) = Lt[c(x, t)] . Hence

∂y  y = y ( x , t ), Lt   = sL[ y ( x , t )] − y ( x , 0)  ∂t 

d 2F  s  −   F =0 dx 2  D 

 ∂ y  dL [ y ( x , t )] Lt   = t dx  ∂x 

whereas

∞

since L[ y(x, t)] is “really” only a function of x. Otherwise the results are similar. These facts coupled with the linearity of the transform, i.e., L[af (t) + bg(t)] = aL[ f (t)] + bL[g(t)], make it a useful device in solving some linear differential equations. Its use reduces the solution of ordinary differential equations to the solution of algebraic equations for L[y]. the inverse transform must be obtained either from tables or by use of complex inversion methods. Example The equation ∂c/∂t = D(∂2c/∂x2) represents the diffusion in a semi-infinite medium, x ≥ 0 . Under the boundary conditions c(0, t) = c0 and c(x, 0) = 0, find a solution of the diffusion equation . By taking the Laplace transform of both sides with respect to t,

The other boundary condition transforms into F(0, s) = c0/s. Finally the solution of the ordinary differential equation for F subject to F(0, s) = c0/s and F remains finite as x → ∞ is F ( x , s ) = (c0 /s )e − s/ D x . Reference to a table shows that the function having this as its Laplace transform is 2  c ( x , t ) = c0 1 − π 

∫

π/2 Dt

0

2  x   e − u du  = C 0 erfc   4 Dt  

This is the same solution obtained above by the group method . Matched-Asymptotic Expansions Sometimes the coefficient in front of the highest derivative is a small number . Special perturbation techniques can then be used, provided the proper scaling laws are found . See Holmes, M . H ., Introduction to Perturbation Methods, 2d ed ., Springer, New York, 2013 .

DIFFEREnCE EQUATIOnS References: Elaydi, Saber, An Introduction to Difference Equations, 3d ed ., Springer-Verlag, New York, 2005; Kelley, W . G ., and A . C . Peterson, Difference Equations: An Introduction with Applications, 2d ed ., Harcourt/Academic, San Diego, Calif ., 2001 . Some models have independent variables that do not vary continuously, but have meaning only for discrete values . Stagewise processes such as distillation, staged extraction systems, absorption columns, and continuous stirred tank reactors (CSTRs) are such processes . The dependent variable varies between stages, and the independent variable is the integral number of the stage . Difference equations arise in discrete models of environmental problems (see Logan and Wolesensky) . Difference equations also arise in the solution of partial differential equations using the finite difference method, and those are treated below (Numerical Analysis and Approximate Methods) . Examined here are solution methods applicable to the chemical engineering problems; for more detailed information see the references . The methods for difference equations mirror those for differential equations . In particular, find complementary solution and then a particular solution . The order of the difference equation is the difference between the largest and smallest arguments . Consider the countercurrent cascade shown in Fig . 3-45 . We let yi be the ratio of the mass of solute to mass of solvent in the ith cell; xi is the ratio of mass of solute to mass of carrier solvent in the ith cell . For illustration we take the equilibrium relation as linear yi = Kxi

A material balance on the ith stage gives Lxi -1 + Vyi+1 - Lxi - Vyi = 0 Using the equilibrium relation transforms this equation to the form (L/K) yi-1 + Vyi+1 - (L/K)yi - Vyi = 0 or

yi+1 - [(L/VK) + 1] yi + (L/VK)yi-1 = 0

With α = L/VK the final form of the difference equation is yi+1 - (α + 1)yi + αyi-1 = 0 . The solution is obtained by trying the general form yi = r i . This gives the characteristic equation r2 - (α + 1)r + α = 0 . One root is r = 1, and call the other root b . The solution is then yi = A + B bi . This completes the complementary solution . The number of units is taken as N . The particular solution is found by choosing A and B to fit boundary conditions . Here they are taken as the inlet feed composition x0 and the inlet solvent composition yN+1 . Using y0 = Kx0, we obtain two equations for A and B . The solutions are A = Kx0 - B and B = (Kx0 - yN+1)/(1 - bN+1) . The exit concentration is y1 = A + B b . Nonlinear Difference Equations: Riccati Difference Equation The Riccati equation yi+1 yi + ayi+1 + byi + c = 0 is a nonlinear difference equation which can be solved by reduction to linear form . Set y = z + h. The equation becomes zi+1zi + (h + a)zi+1 + (h + b)zi + h2 + (a + b)h + c = 0 . If h is selected as a root of h2 + (a + b)h + c = 0 and the equation is divided by zi+1zi, there results (h + b)/zi+1 + (h + a)/zi + 1 = 0 . This is a linear equation with constant coefficients for wi = 1/zi. The solution is i

a+h 1 1 = K  − − yi − h  b + h  (a + h) + (b + h) y1

y2

L

x0

FIG. 3-45

cell 1

y3 y2 = K2x2

y1 = K1x1 x1

cell 2

y4

V

y3 = K3x3 x2

cell 3

x3

Countercurrent cascade .

where K is a constant chosen to fit conditions at one point . This equation is obtained in distillation problems, among others, in which the number of theoretical plates is required . If the relative volatility is assumed to be constant, the plates are theoretically perfect, and the molal liquid and vapor rates are constant, then a material balance around the nth plate of the enriching section yields a Riccati difference equation .

InTEGRAL EQUATIOnS References: Davis, H . T ., Introduction to Nonlinear Differential and Integral Equations, Dover, New York, 2010; Statgold, I ., and M . J . Holst, Green’s Functions and Boundary Value Problems, 3d ed ., Interscience, New York, 2011 .

An integral equation is any equation in which the unknown function appears under the sign of integration and possibly outside the sign of integration . If derivatives of the dependent variable appear elsewhere in the equation, the equation is said to be integrodifferential .

InTEGRAL TRAnSFORMS (OPERATIOnAL METHODS) CLASSIFICATIOn OF InTEGRAL EQUATIOnS Volterra’s integral equations have an integral with a variable limit, whereas Fredholm’s integral equations have a fixed limit. The Volterra equation of the second kind is

Integral equations can arise from the formulation of a problem by using Green’s function. The equation governing heat conduction with a variable heat generation rate is represented in differential form as d 2T Q ( x ) = dx 2 k

x

u ( x ) = f ( x ) + λ ∫ K ( x , t )u (t ) dt a

3-31

T (0) = T (1) = 0

In integral form the same problem is

whereas a Volterra equation of the first kind is 1

T (x ) =

x

u ( x ) = λ ∫ K ( x , t )u (t ) dt a

Equations of the first kind are very sensitive to solution errors so that they present severe numerical problems. Volterra equations are similar to initialvalue problems. A Fredholm equation of the second kind is b

u ( x ) = f ( x ) + λ ∫ K ( x , t )u (t ) dt

1 G ( x , y )Q ( y ) dy k ∫0

− x (1 − y ) G(x , y ) =  − y (1 − x )

x≤y y ≤x

The Poisson equation governs electric charges

a

∇ 2 Ψ = −4 πρ

whereas a Fredholm equation of the first kind is b

u ( x ) = ∫ K ( x , t )u (t ) dt

and the formulation as an integral equation is

a

The limits of integration are fixed, and these problems are analogous to boundary value problems. An eigenvalue problem is a homogeneous equation of the second kind, and solutions exist only for certain l.

Ψ (r) = ∫ ρ(r0 )G (r , r0 ) dV0 V

where Green’s function in three dimensions is 1 G (r , r0 ) = , r = ( x − x 0 )2 + ( y − y 0 )2 + ( z − z 0 )2 r

b

u ( x ) = λ ∫ K ( x , t )u (t ) dt a

An example of a Volterra equation is the heat conduction problem in a semi-infinite domain. ρC p

∂2 T ∂T =k 2 ∂x ∂t

T ( x , 0) = 0 limT ( x , t ) = 0 x →0

G (r , r0 ) = −2 ln r , r = ( x − x 0 )2 + ( y − y 0 )2 0 ≤ x < ∞, t > 0 ∂T (0, t ) = − g (t ) ∂x ∂T lim (x , t ) = 0 x →∞ ∂ x

If this is solved by using Fourier transforms [see Integral Transforms (Operational Methods)], the solution is 1

T (x ) =

1 G ( x , y )Q ( y ) dy k ∫0 1

T (x , t ) =

and in two dimensions is

2 1 1 e − x /4( t − s ) ds g (s ) π ∫0 t−s

See the references for other examples. Integral equations can be solved numerically, too. The methods are analogous to the usual methods for integrating differential equations (Runge-Kutta, predictor-corrector, Adams methods, etc.). Explicit methods are fast and efficient until the time step is very small, to meet the stability requirements. Then implicit methods are used, even though sets of simultaneous algebraic equations must be solved. The major part of the calculation is the evaluation of integrals, however, so that the added time to solve the algebraic equations is not excessive. Thus, implicit methods tend to be preferred. Volterra equations of the first kind are not well posed, and small errors in the solution can have disastrous consequences. The boundary element method uses Green’s functions and integral equations to solve differential equations. See Brebbia, C. A., and J. Dominguez, Boundary Elements—An Introductory Course, 2d ed., Computational Mechanics Publications, Southhampton, UK, 1992; and Mackerle, J., and C. A. Brebbia, eds., Boundary Element Reference Book, Springer Verlag, Berlin, 1988.

InTEGRAL TRAnSFORMS (OPERATIOnAL METHODS) References: Davies, B., Integral Transforms and Their Applications, 3d ed., Springer, New York, 2002; Debnath, L., and D. Bhatta, Integral Transforms and Their Applications, 3d ed., Chapman and Hall/CRC, New York, 2014; Duffy, D. G., Transform Methods for Solving Partial Differential Equations, Chapman & Hall/CRC, New York, 2nd ed., 2004; see also references for Differential Equations. The term operational method implies a procedure of solving differential and difference equations by which the boundary or initial conditions are automatically satisfied in the course of the solution. The technique offers a very powerful tool in the applications of mathematics, but it is limited to linear problems. Most integral transforms are special cases of the equation g (s) =

∫

b

a

f (t ) K ( s , t )dt in which g(s) is said to be the transform of f (t) and K(s, t)

is called the kernel of the transform. A tabulation of the more important kernels and the interval (a, b) of applicability follows. Name of transform

(a, b)

K(s, t) e-st

Laplace

(0, ∞)

Fourier

(–∞, ∞)

1 − ist e 2π

Fourier cosine

(0, ∞)

2 cos st π

Fourier sine

(0, ∞)

2 sin st π

3-32

MATHEMATICS

LAPLACE TRAnSFORM The Laplace transform of a function f (t) is defined by F(s) = ∞ L{ f (t )} = ∫ e − st f (t ) dt , where s is a complex variable. Note that the trans0 form is an improper integral and therefore may not exist for all continuous functions and all values of s. We restrict consideration to those values of s and those functions f for which this improper integral converges. The Laplace transform is used in process control (see Sec. 8). The function L[ f (t)] = g(s) is called the direct transform, and L-1[g(s)] = f (t) is called the inverse transform. Both the direct and the inverse transforms are tabulated for many often recurring functions. In general, L-1[ g ( s )] =

6. Transform of a derivative. Let f be a differentiable function such that both f and f ¢ belong to the class L. Then L{ f ¢ (t)} = sF(s) - f (0). 7. Transform of a higher-order derivative. Let f be a function which has continuous derivatives up to order n on (0, ∞), and suppose that f and its derivatives up to order n belong to the class L. Then L{ f (j)(t)} = s jF(s) - s j-1 f (0) - s j -2f ¢(0) - … - sf ( j -2)(0) - f (j -1)(0) for j = 1, 2, …, k. Example L{ f ″(t)} = s2L{ f (t)} - sf (0) - f¢ (0) Example Solve y ″ + y = 2et, y(0) = y¢(0) = 2. L[y ″] = -y¢(0) - sy(0) + s2L[y] = -2 - 2s + s2L[y]. Thus −2 − 2 s + s 2 L[ y ] + L[ y ] = 2 L[e t ] =

1 α+i∞ st e g ( s ) ds 2 πi ∫α−i∞

0

Laplace transform of f exists for all complex numbers s with a sufficiently large real part. Note that condition 3 is automatically satisfied if f is assumed to be piecewise continuous on every finite interval 0 ≤ t < T. The function f (t) = t-1/2 is not piecewise continuous on 0 ≤ t < T but satisfies conditions 1 to 3. Let L denote the class of all functions on 0 < t < ∞ which satisfy conditions 1 to 3. Example Let f (t) be the Heaviside step function at t = t0; that is, f (t) = 0 for t ≤ t0 and f (t) = 1 for t > t0. Then

Hence y = et + cos t + sin t. A short table (Table 3-2) of very common Laplace transforms and inverse transforms follows. The references and computer programs include more detailed tables. In Mathematica, the command∞ “Laplace Transform[cosh[a*t],t,s]” returns s/(s2−a2). note: Γ (n + 1) = x n e − x dx

∫

0

(gamma function); Jn(t) = Bessel function of the first kind of order n. t 1 1 0 8. L  ∫a f (t ) dt  = L[ f (t )] + ∫a f (t ) dt s s TABLE 3-2 Laplace Transforms f (t)

L{ f (t )} = ∫ e

− st

t0

∫

∞

0

dt = lim ∫ e T →∞

− st

t0

e − st0 1 dt = lim (e − st0 − e − sT ) = T →∞ s s

provided s > 0

Example Let f (t) = eαt, t ≥ 0, where a is a real number. Then L{eαt} = e − ( s −a ) t dt = 1/( s − a ) provided Re s > a.

Properties of the Laplace Transform 1. The Laplace transform is a linear operator: L{af (t) + bg(t)} = aL{ f (t)} + bL{g(t)} for any constants a and b and any two functions f and g whose Laplace transforms exist. 2. The Laplace transform of a real-valued function is real for real s. If f (t) is a complex-valued function f (t) = u(t) + iu(t), where u and u are real, then L{ f (t)} = L{u(t)} + iL{u(t)}. Thus L{u(t)} is the real part of L{ f (t)}, and L{u(t)} is the imaginary part of L{ f (t)}. 3. The Laplace transform of a function in the class L has derivatives of all orders, and L{t kf (t)} = (-1)k d kF(s)/dsk, k = 1, 2, 3, … , where F(s) is the Laplace transform of f (t). ∞ a st Example ∫0 e sin at dt = 2 2 , s > 0. s +a ∞ 2 as By property 3, L{t sin at } = ∫ e - st t sin at dt = 2 0 ( s + a 2 )2 Example By applying property 3 with f (t) = 1 and using the preceding results, we obtain dk 1 k! L{t k } = (−1) k k   = k+1 ds  s  s provided Re s > 0 for k = 1, 2, … . Similarly, we obtain L{t k e at } = (−1) k

dk  1  k! =  ds k  s − a  ( s − a ) k +1

4. Frequency-shift property (or, equivalently, the transform of an exponentially modulated function). If F (s) is the Laplace transform of a function f (t) in class L, then for any constant a, L{eatf (t)} = F(s - a). Example

L{te − at } =

1 ( s + a )2

( s > 0).

5. Time-shift property. Let u(t - a) be the unit step function at t = a. Then L{ f (t - a)u(t - a)} = e-asF(s).

f (t)

g(s)

1

1/s

e-at(1 - at)

tn, (n = + integer)

n! s n +1 Γ (n + 1) s n +1 s s2 + a2

t sin at 2a 1 sin at sinh at 2a 2 cos at cosh at

tn, (n ≠ + integer) cos at

T

∞

2s 2 1 1 s = + + ( s − 1)( s 2 + 1) s − 1 s 2 + 1 s 2 + 1

L[ y ] =

and to evaluate this integral requires a knowledge of complex variables, the theory of residues, and contour integration. A function is said to be piecewise continuous on an interval if it has only a finite number of finite (or jump) discontinuities. A function f on 0 < t < ∞ is said to be of exponential growth at infinity if there exist constants M and α such that | f (t)| ≤ Meat for sufficiently large t. Sufficient Conditions for the Existence of the Laplace Transform Suppose f is a function which is (1) piecewise continuous on every finite interval 0 < t < T, (2) of exponential growth at infinity, and δ (3) for which ∫ | f (t )| dt exists ( finite) for every finite d > 0. Then the

2 s −1

a s2 + a2 s s2 − a2

sin at cosh at

e-at e

sin at t J0(at)

e-bt sin at

1 −k e s

k 2 t

s3 s 2 + 4a 4 s2 s4 − a4 s3 s4 − a4 a tan −1 s 1 s2 + a2

s +b ( s + b)2 + a 2 a ( s + b)2 + a 2

cos at

erfc

½(cosh at + cos at)

a s2 − a2 1 s+a

sinh at

-bt

1 (sinh at + sin at ) 2a

g (s) s ( s + a )2 s ( s 2 + a 2 )2 s s 4 + 4a 4

na n

J n (at ) t

( s 2 + a 2 − s )n (n > 0) 1 − a/s e s Γ (n) (n > 0) ( s − a )n

J 0 (2 at ) t n −1e at

s

Example Find f (t) if L[ f (t )] =

1  1  1 1 . L sinh at  = 2 . s 2  s 2 − a 2   a  s − a2

t t1 1 sinh at  Therefore f (t ) = ∫  ∫ sinh at dt  dt = 2  − t .  0 a  a  0a 

∞  f (t )  = g ( s ) ds 9. L   t  ∫s

∞ ∞  f (t )  L  k  = ∫ ⋯∫ g ( s )(ds ) k s s  t      k integrals

Example

L  

∞ a ds sin at  ∞ s = L[sin at ] ds = ∫ 2 = cot −1 s s + a2 a t  ∫s

10. The unit step function 0 t < a u (t − a ) =  1 t > a

L[u (t − a )] =

e − as s

MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS 11. The unit impulse function is ∞ at t = a δ(a ) = u ′(t − a ) =  0 elsewhere

The Fourier transform is given by L[u ′(t − a )] = e − as

12. L-1[e-asg(s)] = f (t - a)u(t - a) (second shift theorem). 13. If f (t) is periodic of period b, that is, f (t + b) = f (t), then

F [ f (t )] =

F -1[ g ( s )] =

Example The partial differential equations relating gas composition to position and time in a gas chromatograph are ∂y/∂n + ∂x/∂q = 0 and ∂y/∂n = x - y, where x = mx′, n = (kGaP/Gm)h, θ = (mkGaP/ρB)t and GM = molar velocity, y = mole fraction of the component in the gas phase, ρB = bulk density, h = distance from entrance, P = pressure, kG = mass-transfer coefficient, and m = slope of the equilibrium line . These equations are equivalent to ∂2y/∂n ∂θ + ∂y/∂n + ∂y/∂q = 0, where the boundary conditions considered here are y(0, θ) = 0 and x(n, 0) = y(n, 0) + (∂y/∂n) (n, 0) = δ(0) (see property 11) . The problem is conveniently solved by using the Laplace transform of y with ∞ - ns respect to n; write g ( s , θ) = ∫0 e y (n , θ) dn . Operating on the partial differential equation gives s(dg/dθ) - (∂y/∂q) (0, q) + sg - y(0, q) + dg/dq = 0 or (s + 1) (dg/dq) + sg = (∂y/∂θ) (0, θ) + y(0, q) = 0 . The second boundary condition gives g(s, 0) + sg(s, 0) - y(0, 0) = 1 or g(s, 0) + sg(s, 0) = 1 (L[δ(0)] = 1) . A solution of the ordinary differential equation for g consistent with this second condition is 1 − sθ/( s +1) g ( s , θ) = e s +1 Inversion of this transform gives the solution y (n , θ) = e − ( n+θ) I 0 (2 nθ ) where I0 = zero-order Bessel function of an imaginary argument . For large u, In(u) ∼ e u / 2 πu . For large n, exp[ −( θ − n )2 ] 2 π1/2 (nθ)1/4

or for sufficiently large n, the peak concentration occurs near θ = n. Other applications of Laplace transforms are given under Differential Equations .

∞

In brief, the condition for the Fourier transform to exist is that ∫ | f (t )| dt < ∞, although certain functions may have a Fourier transform −∞ even if this is violated . 1− a ≤ t ≤ a a Example The function f (t ) =  has F [ f (t )] = ∫ e − ist dt −a 0 elsewhere a

a

a

0

0

0

= ∫ e ist dt + ∫ e - ist dt = 2 ∫ cos st dt =

2 sin sa s

Properties of the Fourier Transform Let F [ f (t)] = g(s); F -1[ g(s)] = f (t) . 1 . F [ f (n)(t)] = (is)nF [ f (t)] . 2 . F [a f (t) + bh(t)] = aF [ f (t)] + bF [h(t)] . 3 . F [ f (-t)] = g(-s) . 1  s 4 . F [ f (at )] = g   , a > 0 . a  a 5 . F [e-iwtf (t)] = g(s + w) . 6 . F [ f (t + t1)] = eist1g(s) . 7 . F [ f (t)] = G(is) + G(-is) if f (t) = f (-t) ( f even) F [ f (t)] = G(is) - G(-is) if f (t) = -f (-t) (f odd) where G(s) = L[ f (t)] . This result allows the use of the Laplace transform tables to obtain the Fourier transforms . Example Find F [e-a|t|] by property 7 . Now e-a|t| is even . So L[e-at] = 1/(s + a) . Therefore, F [e-a|t|] = 1/(is + a) + 1/(-is + a) = 2a/(s2 + a2) . FOURIER COSInE TRAnSFORM

The convolution integral of two functions f (t) and r(t) is x(t) = f (t)∗r(t) = t ∫ f (τ)r (t − τ)d τ . Example

1 ∞ g ( s )e ist dt = f (t ) 2 π ∫−∞

The Fourier cosine transform is given by

COnVOLUTIOn InTEGRAL

0

1 ∞ f (t )- ist dt = g ( s ) 2 π ∫−∞

and its inverse by

1  b − st L[ f (t )] =  e f (t )dt  1 − e − bs  ∫0

y (n , θ) 

3-33

t

t ∗ sin t = ∫ τ sin(t − τ) d τ = t − sin t . 0

Fc [ f (t )] = g ( s ) =

2 ∞ f (t )cos st dt π ∫0

Fc-1[ g ( s )] = f (t ) =

2 ∞ g ( s )cos st ds π ∫0

and its inverse by

L[ f (t)]L[h(t)] = L[ f (t)∗h(t)] FOURIER TRAnSFORM References: https://en .wikipedia .org/wiki/Fourier_transform#Tables_ of_important_Fourier_transforms; Varma and Morbidelli (1997), see General References .

The Fourier sine transform Fs is obtainable by replacing the cosine by the sine in these integrals . They can be used to solve linear differential equations; see the transform references .

MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS References: Anton, H ., and C . Rorres, Elementary Linear Algebra with Applications, 9th ed ., Wiley, New York, 2004; Bernstein, D . S ., Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory, 2d ed ., Princeton University Press, Princeton, N .J ., 2009 . MATRIX ALGEBRA Matrices n columns,

A rectangular array of mn quantities, arranged in m rows and  a11 ⋯ a1n  a ⋯ a  21 2n  A = (aij ) =  ⋮    amn   am1

is called a matrix . The elements aij may be real or complex . The notation aij means the element in the ith row and jth column; i is called the row index and j the column index. If m = n, the matrix is said to be square and of order n. A matrix, even if it is square, does not have a numerical value, as a determinant does . However, if the matrix A is square, a determinant can be formed

which has the same elements as matrix A. This is called the determinant of the matrix and is written det (A) or |A| . If A is square and det (A) ≠ 0, then A is said to be nonsingular; if det (A) = 0, then A is said to be singular . A matrix A has rank r if and only if it has a nonvanishing determinant of order r and no nonvanishing determinant of order > r. Equality of Matrices Let A = (aij), B = (bij) . Two matrices A and B are equal (=) if and only if they are identical; that is, they have the same number of rows and the same number of columns and equal corresponding elements (aij = bij for all i and j) . Addition and Subtraction The operations of addition (+) and subtraction (-) of two or more matrices are possible if and only if the matrices have the same number of rows and columns . Thus A ± B = (aij ± bij); i .e ., addition and subtraction are of corresponding elements . Transposition The matrix obtained from A by interchanging the rows and columns of A is called the transpose of A, written A¢ or AT . 1 2 1 3 4 AT =  3 1  Example A =     2 1 6   4 6  Note that (AT)T = A .

3-34

MATHEMATICS

Multiplication Let A = (aij), i = 1, …, m1; j = 1, …, m2, and B = (bij), i = 1, …, n1, j = 1, …, n2. The product AB is defined if and only if the number of columns of A (m2) equals the number of rows of B (n1), that is, n1 = m2. For two such matrices the product P = AB is defined by summing the elementby-element products of a row of A by a column of B. This is the row-by-column rule. Thus n1

Pij = ∑ aik bkj k =1

The resulting matrix has m1 rows and n2 columns.  −4 3 17 24  3 2   1 1   0 1 5 6  =  −2 1 6 9  Example     −2 0 1 3    −8 5 29 42  5 4  It is helpful to remember that the element Pij is formed from the ith row of the first matrix and the jth column of the second matrix. The matrix product is not commutative. That is, AB ≠ BA in general. Inverse of a Matrix A square matrix A is said to have an inverse if there exists a matrix B such that AB = BA = I, where I is the identity matrix of order n.      

The inverse B is a square matrix of the order of A, designated by A-1. Thus AA-1 = A-1A = I. A square matrix A has an inverse if and only if A is nonsingular. Certain relations are important: (1) (AB)-1 = B-1A-1 (2) (AB)T = BTAT (3) (A-1)T = (AT )-1 (4) (ABC)-1 = C-1B-1A-1 Scalar Multiplication Let c be any real or complex number. Then cA = (caij). Linear Equations in Matrix Form Every set of n nonhomogeneous linear equations in n unknowns a11 x 1 + a12 x 2 + ⋯ + a1n x n = b1 a21 x 1 + a22 x 2 + ⋯ + a2 n x n = b2 ⋮

an1 x1 + an 2 x 2 + ⋯ + ann x n = bn can be written in matrix form as AX = B, where A = (aij), XT = [x1 … xn], and BT = [b1 … bn]. The solution for the unknowns is X = A-1B. Special Square Matrices 1. A triangular matrix is a matrix all of whose elements above or below the main diagonal (set of elements a11, …, ann) are zero. If A is triangular, det (A) = a11a22 ann . 2. A diagonal matrix is one such that all elements both above and below the main diagonal are zero (that is, aij = 0 for all i ≠ j). If all diagonal elements are equal, the matrix is called scalar. If A is diagonal, A = (aij), A-1 = (1/aij). 3. If aij = aji for all i and j (that is, A = AT ), the matrix is symmetric. 4. If aij = -aji for i ≠ j but not all the aij are zero, the matrix is skew. 5. If aij = -aji for all i and j (that is, aii = 0), the matrix is skew symmetric. 6. If AT = A-1, the matrix A is orthogonal. 7. If the matrix A* = (aij )T and aij = complex conjugate of aij, then A* is the hermitian transpose of A. 8. If A = A-1, then A is involutory. 9. If A = A*, then A is hermitian. 10. If A = -A*, then A is skew hermitian. 11. If A-1 = A*, then A is unitary. If A is any matrix, then AAT and ATA are square symmetric matrices, usually of different order. By using a program such as MATLAB, these are easily calculated. Matrix Calculus Differentiation Let the elements of A = [aij(t)] be differentiable funcdA  daij (t )  tions of t. Then . = dt  dt  Example

 sin t cos t  A=   − cos t sin t 

t 2  A= 2 t t e 

Example

 t 2/2 2t  . 3 e t  

∫ Adt = t /3

The matrix B = A - lI is called the characteristic matrix or eigenmatrix of A. Here A is square of order n, l is a scalar parameter, and I is the n × n identity matrix. So det B = det (A - lI) = 0 is the characteristic equation (or eigenequation) for A. The characteristic equation is always of the same degree as the order of A. The roots of the characteristic equation are called the eigenvalues of A or characteristic values of A. 1 2  A=  3 8 

Example

1 2   λ 0  1 − λ 2 . B=  = −  3 8  0 λ   3 8 − λ 

Above is the characteristic matrix and f (l) = det (B) = det (A - lI) = (1 - l) (8 - l) - 6 = 2 − 9l + l2 = 0 is the characteristic equation. The eigenvalues of A are the roots of l2 - 9l + 2 = 0, which are (9 ± 73)/2 . A nonzero matrix Xi, which has one column and n rows, a column vector, satisfying the equation (A - lI)Xi = 0

1 0 ⋯⋅ 0   ⋅⋅ 0 1  ⋮ 1 0  0 ⋯⋅ 0 1 

⋮

Integration The integral ∫ A dt = [ ∫ aij (t ) dt ].

dA cos t − sin t  = dt sin t cos t 

and associated with the ith characteristic root li is called an eigenvector. Vector and Matrix Norms To carry out error analysis for approximate and iterative methods for the solutions of linear systems, one needs notions for vectors in Rn and for matrices that are analogous to the notion of length of a geometric vector. Let Rn denote the set of all vectors with n components, x = (x1, …, xn). In dealing with matrices it is convenient to treat vectors in Rn as columns, and so x = (x1, …, xn)T; however, here we shall write them simply as row vectors. A norm on Rn is a real-valued function f defined on Rn with the following properties: 1. f (x) ≥ 0 for all x ∈ Rn. 2. f (x) = 0 if and only if x = (0, 0, …, 0). 3. f (ax) = |a| f (x) for all real numbers a and x ∈ Rn. 4. f (x + y) ≤ f (x) + f (y) for all x, y ∈ Rn. The usual notation for a norm is f (x) = x . The norm of a matrix is κ ( A ) ≡ A A −1 where

A sup x ≠0 =

n Ax = max k ∑ a jk x j =1

The norm is useful when doing numerical calculations. If the computer’s floating-point precision is 10-6, then k = 106 indicates an ill-conditioned matrix. If the floating-point precision is 10-12 (double precision), then a matrix with k = 1012 may be ill-conditioned. Two other measures are useful and are more easily calculated: Ratio =

(k) max k a kk (k) min k a kk

V=

det A α 1α 2  α n

α1 = (α i21 + α i22 + + α in2 )1/2

where akk(k) are the diagonal elements of the LU decomposition. MATRIX COMPUTATIOnS The principal topics in linear algebra involve systems of linear equations, matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, and least-squares problems. The calculations are routinely done on a computer. LU Factorization of a Matrix Let L be an n × n lower triangular matrix with unit diagonal elements. Let U be an n × n upper triangular matrix. If all the principal submatrices of an n × n matrix A are nonsingular, then it is possible to represent A = LU. The Gauss elimination method is in essence an algorithm to determine L and U. Solution of Ax = b by Using LU Factorization Suppose that the indicated system is compatible and that A = LU. Let z = Ux. Then Ax = LUx = b implies that Lz = b. Thus to solve Ax = b we first solve Lz = b for z and then solve Ux = z for x. This procedure does not require that A be invertible and can be used to determine all solutions of a compatible system Ax = b. Note that the systems Lz = b and Ux = z are both in triangular form and thus can be easily solved. The LU decomposition is essentially a gaussian elimination, arranged for maximum efficiency. The chief reason for doing an LU decomposition is that it takes fewer multiplications than would be needed to find an inverse. Also, once the LU decomposition has been found, it is possible to solve for

MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS multiple right-hand sides with little increase in work. The multiplication count for an n × n matrix and m right-hand sides is 1 1 Operation count = n 3 − n + mn 2 3 3 If an inverse is desired, it can be calculated by solving for the LU decomposition and then solving n problems with right-hand sides consisting of all zeros except one entry. Thus 4n2/3 - n/3 multiplications are required for the inverse. The determinant is given by n

3-35

An m × m unitary matrix U is formed from the eigenvectors ui of the first matrix. U = [u1, u2, …, um] An n × n unitary matrix V is formed from the eigenvectors vi of the second matrix. V = [v1, v2, …, vn] Then matrix A can be decomposed into

Det A = ∏ aii( i ) i =1

where aii(i) are the diagonal elements obtained in the LU decomposition. A tridiagonal matrix is one in which the only nonzero entries lie on the main diagonal and on the diagonal just above and just below the main diagonal. The set of equations can be written as aixi-1 + bixi + cixi+1 = di The LU decomposition is b1 = b1 for k = 2, n do a a ak′ = k , bk′ = bk − k c k−1 bk′−1 bk′−1 enddo d1′ = d1 for k = 2, n do d k′ = d k − ak′ d k′−1

A = U∑V* where ∑ is a k × k diagonal matrix with diagonal elements dii = si > 0 for 1 ≤ i ≤ k. The eigenvalues of ∑*∑ are s2i. The vectors ui for k + 1 ≤ i ≤ m and vi for k + 1 ≤ i ≤ n are eigenvectors associated with the eigenvalue zero; the eigenvalues for 1 ≤ i ≤ k are s2i. The values of si are called the singular values of matrix A. If A is real, then U and V are real and hence orthogonal matrices. The value of the singular-value decomposition comes when a process is represented by a linear transformation and the elements of A and aij are the contribution to an output i for a particular variable as input variable j. The input may be the size of a disturbance, and the output is the gain (Seborg, D. E., T. F. Edgar, and D. A. Mellichamp, Process Dynamics and Control, 2d ed., Wiley, New York, 2004). If the rank is less than n, not all the variables are independent and they cannot all be controlled. Furthermore, if the singular values are widely separated, the process is sensitive to small changes in the elements of the matrix, and the process will be difficult to control. Example Consider the following example from Noble and Daniel (Applied Linear Algebra, Prentice-Hall, Upper Saddle River, N.J., 1987) with the MATLAB commands to do the analysis. Define the following real matrix with m = 3 and n = 2 (whose rank k = 1). >> a = [1 1 2 2

enddo x n = dn′/bn′

2 2]

for k = n - 1,1 do d′ − c x x k = k k k+1 d k′

The following MATLAB commands are used. a1 = a ∗ a

enddo

a 2 = a ∗ a′

The operation count for an n × n matrix with m right-hand sides is

[ v , d 1] = eig (a1) 2(n - 1) + m(3n - 2) If |bi| > |ai| + |ci|, no pivoting is necessary, and this is true for many boundaryvalue problems and partial differential equations. Sparse matrices are ones in which the majority of the elements are zero. If the structure of the matrix is exploited, the solution time on a computer is greatly reduced. See Duff, I. S., A. M. Erisman, and J. K. Reid, Direct Methods for Sparse Matrices, Clarendon Press, Oxford, UK, 1986; Davis, T. A., Direct Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics, Philadelphia, Penn., 2006. The conjugate gradient method is one method for solving sparse matrix problems, since it only involves multiplication of a matrix times a vector. Thus the sparseness of the matrix is easy to exploit. The conjugate gradient method is an iterative method that converges for sure in n iterations where the matrix is an n × n matrix. Matrix methods, in particular finding the rank of the matrix, can be used to find the number of independent reactions in a reaction set. If the stoichiometric numbers for the reactions and molecules are put in the form of a matrix, the rank of the matrix gives the number of independent reactions. See Amundson, N. R., Mathematical Methods in Chemical Engineering, Prentice-Hall, Englewood Cliffs, N.J., 1966, p. 50. See also Dimensional Analysis. QR Factorization of a Matrix If A is an m × n matrix with m ≥ n, there exists an m × m unitary matrix Q = [q1, q2, …, qm] and an m × n right triangular matrix R such that A = QR. The QR factorization is frequently used in the actual computations when the other transformations are unstable. Singular-Value Decomposition If A is an m × n matrix with m ≥ n and rank k ≤ n, consider the two following matrices. AA*

and

 A*A

[u , d 2] = eig (a 2) The results are v = [ −0.7071 0.7071 0.7071 0.7071] d 1 = [0 0 0 18] u = [ 0.8944 0.2981 0.3333 − 0.4472 0.5963 0.6667 0 − 0.7454 0.6667] d2 = 0 0 0 0 0 0 0 0 18 2

Thus, σ1 = 18 and the eigenfunctions are the rows of v and u. The second column of v is associated with the eigenvalue σ12 = 18, and the third column of u is associated with the eigenvalue σ12 = 18. If A is square and nonsingular, the vector x that minimizes ||Ax - b|| is obtained by solving the linear equation x = A-1b

(3-62)

3-36

MATHEMATICS

When A is not square, the solution to

mean by subtracting from each entry in the column the average of the column entries. Once this is done, the loadings are the vi and satisfy

Ax = b

cov(A) vi = σ i2 vi

is and the score vector ui is given by

x = Vy where yi = b′i/si for i = 1, …, k, b′ = UT b, and yk+1, yk+2, …, ym are arbitrary. The matrices U and V are those obtained in the singular-value decomposition. The solution which minimizes the norm, Eq. (3-62), is x with yk+1, yk+2, . . ., ym zero. These techniques can be used to monitor process variables. See Montgomery, D. C., Introduction to Statistical Quality Control, 6th ed., Wiley, New York, 2008; Piovos, M. J., and K. A. Hoo, “Multivariate Statistics for Process Control,” IEEE Control Systems 22(5):8 (2002). Principal Component Analysis (PCA) PCA is used to recognize patterns in data and reduce the dimensionality of the problem. Let the matrix A now represent data with the columns of A representing different samples and the rows representing different variables. The covariance matrix is defined as cov ( A ) =

AT A m −1

This is just the same matrix discussed with singular-value decomposition. For data analysis, however, it is necessary to adjust the columns to have zero

Avi = siui In process analysis, the columns of A represent different measurement techniques (temperatures, pressures, etc.), and the rows represent the measurement output at different times. In that case the columns of A are adjusted to have a zero mean and a variance of 1.0 (by dividing each entry in the column by the variance of the column). The goal is to represent the essential variation of the process with as few variables as possible. The ui, vi pairs are arranged in descending order according to the associated si. The si can be thought of as the variance, and the ui, vi pair captures the greatest amount of variation in the data. Instead of having to deal with n variables, one can capture most of the variation of the data by using only the first few pairs. An excellent example of this is given by Wise, B. M., and B. R. Kowalski, “Process Chemometrics,” Chap. 8 in Process Analytical Chemistry, eds. F. McLennan and B. Kowalski, Blackie Academic & Professional, London, 1995. When modeling a slurry-fed ceramic melter, they were able to capture 97 percent of the variation by using only four eigenvalues and eigenvectors, even though there were 16 variables (columns) measured.

nUMERICAL APPROXIMATIOnS TO SOME EXPRESSIOnS APPROXIMATIOn IDEnTITIES

Approximation

For the following relationships the sign @ means approximately equal to, when X is small. These equations are derived by using a Taylor’s series (see Series Summation and Identities). Approximation 1 ≅1 X 1± X

Approximation 1± X ≅1±

X 2

Approximation

(1 ± X)n @ 1 ± nX

(1 ± X)-n @ 1  nX

(a ± X)2 = a2 ± 2aX

ex @ 1 + X

sin X @ X(X rad)

tan X @ X

2Y + X Y (Y + X ) ≅ 2 Stirling’s approximation

X2  X   small  2Y  Y In N! @ N ln N - N Y 2 + X2 ≅Y +

nUMERICAL AnALYSIS AnD APPROXIMATE METHODS References: Ascher, U. M., and C. Greif, A First Course in Numerical Methods, SIAM-Soc. Ind. Appl. Math., 2011; Atkinson, K., W. Han, and D. E. Stewart, Numerical Solution of Ordinary Differential Equations, Wiley, New York, 2009; Burden, R. L., J. D. Faires, A. C. Reynolds, and A. M. Burden, Numerical Analysis, 10th ed., Brookes/Cole, Pacific Grove, Calif., 2015; Chapra, S. C., and R. P. Canal, Numerical Methods for Engineers, 5th ed., McGraw-Hill, New York, 2006; Heys, Jeffrey, J., Chemical and Biomedical Engineering Calculations Using Python, Wiley, New York (2017); Johnson, C., Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover, New York, 2009; Lau, H. T., A Numerical Library in C for Scientists and Engineers, CRC Press, Boca Raton, Fla., 3rd ed. 2007; LeVeque, R. J., Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge 2002; Morton, K. W., and D. F. Mayers, Numerical Solution of Partial Differential Equations: An Introduction, 2d ed., Cambridge University Press, Cambridge, 2005; Quarteroni, A., and A. Valli, Numerical Approximation of Partial Differential Equations, 2d ed., Springer, New York, 2008; Reddy, J. N., and D. K. Gartling, The Finite Element Method in Heat Transfer and Fluid Dynamics, 3d ed., CRC Press, Boca Raton, Fla., 2010; Zienkiewicz, O. C., R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 7th ed., Butterworth-Heinemann Elsevier, Oxford, UK, 2013. InTRODUCTIOn The goal of approximate and numerical methods is to provide convenient techniques for obtaining useful information from mathematical formulations of physical problems. Often this mathematical statement is not solvable by analytical means. Or perhaps analytic solutions are available but in a form that is inconvenient for direct interpretation. In the first case, it is necessary either to attempt to approximate the problem satisfactorily by one that will be amenable to analysis, to obtain an approximate solution

to the original problem by numerical means, or to use the two techniques in combination. Numerical methods have been used to model polymerization, yeast fermentation, chemical vapor deposition, catalytic converters, pressure swing adsorption, insulin purification, ion exchange, and affinity chromatography, plus many other chemical engineering applications. Numerical techniques therefore do not yield exact results in the sense of the mathematician. Since most numerical calculations are inexact, the concept of error is an important feature. The four sources of error are as follows: 1. Gross errors. These result from unpredictable human, mechanical, or electrical mistakes. 2. Rounding errors. These are the consequence of using a number specified by m correct digits to approximate a number which requires more than m digits for its exact specification. For example, approximate the irrational number 2 by 1.414. Such errors are often present in experimental data, in which case they may be called inherent errors, due either to empiricism or to the fact that the computer dictates the number of digits. Such errors may be especially damaging in areas such as matrix inversion or the numerical solution of partial differential equations when the number of algebraic operations is extremely large. 3. Truncation errors. These errors arise from the substitution of a finite number of steps for an infinite sequence of steps which would yield the exact result. To illustrate this error, consider the infinite series for e-x: e-x = 1 - x + x2/2 - x3/6 + ET(x), where ET is the truncation error, ET = (1/24)e-ex4, for 0 < e < x. If x is positive, e is also positive. Hence e-e < 1. The approximation e-x ≈ 1 - x + x2/2 - x3/6 is in error by a positive amount smaller than (1/24)x4. A variety of general-purpose computer programs are available commercially. Mathematica (http://www.wolfram.com/), Maple (http://www .maplesoft.com/), and Mathcad (https://www.ptc.com/en/engineeringmath-software/mathcad) and MATLAB (http://www.mathworks.com/

nUMERICAL AnALYSIS AnD APPROXIMATE METHODS product/symbolic) all have the capability of doing symbolic manipulation so that algebraic solutions can be obtained. Different packages can solve some ordinary and partial differential equations analytically, solve nonlinear algebraic equations, make simple graphs and do linear algebra, and combine the symbolic manipulation with numerical techniques. In this section, examples are given for the use of MATLAB (http://www.mathworks.com/), a package of numerical analysis tools, some of which are accessed by simple commands and others of which are accessed by writing programs in C. Spreadsheets can also be used to solve certain problems, and these are described below too. A popular program used in chemical engineering education is Polymath (http://www.polymath-software.com/), which can numerically solve sets of linear or nonlinear equations, ordinary differential equations as initial-value problems, and perform data analysis and regression.

The Wegstein method is a secant method applied to g(x) ≡ x - F(x). In Microsoft Excel, roots are found by using Goal Seek or Solver (an Add-In). Assign one cell to be x, put the equation for f (x) in another cell, and let Goal Seek or Solver find the value of x that makes the equation cell zero. In MATLAB, the process is similar except that a function (m-file) is defined and the command fzero (¢f ¢, x0) provides the solution x, starting from the initial guess x0. The Wegstein method is sometimes used to promote convergence when solving a mass and energy balance problem for a chemical process with recycle streams. METHODS FOR MULTIPLE nOnLInEAR EQUATIOnS Write a system of equations as

Method of Successive Substitutions nUMERICAL SOLUTIOn OF LInEAR EQUATIOnS See the section Matrix Algebra and Matrix Computation. nUMERICAL SOLUTIOn OF nOnLInEAR EQUATIOnS In OnE VARIABLE Methods for Nonlinear Equations in One Variable Successive Substitutions Let f (x) = 0 be the nonlinear equation to be solved. If this is rewritten as x = F(x), then an iterative scheme can be set up in the form xk+1 = F(xk). To start the iteration, an initial guess must be obtained graphically or otherwise. The convergence or divergence of the procedure depends upon the method of writing x = F(x), of which there will usually be several forms. However, if a is a root of f (x) = 0, and if |F ′(a)| < 1, then for any initial approximation sufficiently close to a, the method converges to a. This process is called first-order because the error in xk+1 is proportional to the first power of the error in xk for large k. One way of writing the equation is xk+1 = xk + b f (xk). The choice of b is made such that |1 + b df/dx(a)| < 1. Convergence is guaranteed by the theorem given for simultaneous equations. Methods of Perturbation Let f (x) = 0 be the equation. In general, the iterative relation is

αi = fi(`)

x 2 = x1 −

x1 − x 0 f ( x1 ) f ( x1 ) − f ( x 0 )

In each of the following steps αk is the slope of the line joining [xk, f (xk)] to the most recently determined point where f (xj) has the opposite sign from that of f (xk). This method is first-order. If one uses the most recently determined point (regardless of sign), the method is a secant method. Method of Wegstein This is a variant of the method of successive substitutions which forces and/or accelerates convergence. The iterative procedure xk+1 = F(xk) is revised by setting xˆk+1 = F ( x k ) and then taking x k+1 = qx k + (1 − q ) xˆk +1, where q is a suitably chosen number which may be taken as constant throughout or may be adjusted at each step. Wegstein found that suitable q’s are as follows: Behavior of successive substitution process

Oscillatory divergence

without Wegstein

½ 30 the intervals ± s and ± 2s will include roughly 68 and 95 percent of the sample values, respectively, when the distribution is normal. In applications, sample sizes are usually small and s is unknown. In these cases, the t distribution can be used where t = ( x − µ)( s / n )

x = µ + ts n

or

See Fig. 3-62. The t distribution is also symmetric and centered at zero. It is said to be robust in the sense that even when the individual observations x are not normally distributed, sample averages of x have distributions that tend toward normality as n gets large. Even for small n of 5 through 10, the approximation is usually relatively accurate. It is sometimes called the Student’s t distribution. Since the t distribution relies on the sample standard deviation s, the resultant distribution will differ according to the sample size n . To designate this difference, the respective distributions are classified according to what are called the degrees of freedom and abbreviated as df. In simple problems, the df are just the sample size minus 1. In general, degrees of freedom are the number of quantities minus the number of constraints. The mathematical definition of the t distribution is t

A (t , df ) =

Standard normal

 x2  1  1 +  ∫ df 1 df df 1/2 B  ,  − t 2 2 

df +1 2

dx

f(t)

z=

0.4

0.2 t for df = 1 0.1

0.0 –4

FIG. 3-62

–3

–2

–1

0 t

1

2

3

4

The t distribution function.

where B is the incomplete beta function. A(t, df) is the probability, for degrees of freedom df, that a certain statistic t (measuring the observed difference of means) would be smaller than the observed value if the means were in fact the same. Limiting values are A(0, df) = 0 and A(∞, df) = 1. The Microsoft Excel function TDIST(X, df,1) gives the right-tail probability, and TDIST(X, df, 2) gives twice that. The probability that t ≤ X is 1 - TDIST(X, df, 1) when X ≥ 0 and TDIST(abs(X), df, 1) when X < 0. The probability that -X ≤ t ≤ + X is 1 - TDIST(X, df, 2). To find the limits for a given confidence level, one uses the Microsoft Excel function TINV(α, df). For a two-tailed distribution, to achieve 95 percent confidence, the two tails represent 2.5 percent each, and one uses α = 0.05. Example For a sample size n = 5, what values of t define a midarea of 90 percent? For 4 df using Microsoft Excel, TINV(.1, 4) = 2.132. Thus, P[-2.132 ≤ t ≤ 2.132] = .90. Also, TDIST(2.132, 4, 2) = 0.10 and 1 - TDIST(2.132, 4, 2) = 0.90. t Distribution for the Difference in Two Sample Means with Equal Variances. The t distribution can be readily extended to the difference in two sample means when the respective populations have the same variance. Calculate the sample means x1 and x2 and sample variances s21 and s22, with sample sizes n1 and n2, respectively. The variance is estimated by pooling the sum of variances of both samples. s 2p =

(n1 − 1) s12 + (n2 − 1) s 22 (n1 − 1) + (n2 − 1)

(3-98)

The significance of the difference is measured by the ratio of the difference to its standard deviation, and it is denoted by t . t=

x1 − x 2 = s p 1/n1 + 1/n2

x1 − x 2 n +n sp 1 2 n1n2

(3-99)

Example Suppose we have two sets of data, each with 10 degrees of freedom. The means are 5.23 and 4.95, and the pooled sample variance is 0.3. Are these significantly different at the 10 percent level? Equation (3-99) gives t=

5.23 − 4.95 = 2.09 10 + 10 0.3 10 ∗10

There are 20 - 2 = 18 degrees of freedom, and TINV(0.1,18) = 1.07. Thus, the probability that t is between +1.07 and −1.07 is P[-1.07 ≤ t ≤ 1.07] = .90. These data are significantly different, and the hypothesis that they are from the same distribution is disproved. t Distribution for the Difference in Two Sample Means with Unequal Variances When population variances are unequal, an approximate t quantity can be used:

STATISTICS

We use the Microsoft Excel function CHIINV to answer this. CHIINV (0.025, 4) = 11.1 and CHIINV(0.975, 4) = 0.484. Then

x 1 − x 2 − (µ1 − µ 2 ) a+b a = s12 /n1 b = s 22 /n2 t=

with

and

df =

P[.484 ≤ (s2/s2)(4) ≤ 11.1] = .95 or

(a + b ) 2 = 2.09 a /(n1 − 1) + b 2 (n2 − 1)

P[.35 ≤ s/s ≤ 1.66] = .95

2

Chi-Square Distribution For some industrial applications, product uniformity is of primary importance. The sample standard deviation s is most often used to characterize uniformity. In dealing with this problem, the chi-square distribution can be used where c2 = (s2/s2) (df). The chi-square distribution is a family of distributions which are defined by the degrees of freedom associated with the sample variance. For most applications, df is equal to the sample size minus 1. See Fig. 3-63. The probability density function is

C (χ 2 , df ) =

(χ 2 )df/2-1 − χ2 /2 e 2 Γ (df/2) df/2

and the integral with respect to c2 from 0 to infinity is 1.0 and G is the gamma function. The cumulative probability function P(c2, df) is the integral of C from 0 to c2; different functions are obtained for different degrees of freedom. A plot of C is shown in Fig. 3-63 for 3 and 5 df. The shaded area gives the probability that the chi-squared for a correct model with df degrees of freedom is more than c2, here 0.0373. Thus the probability that the c2 is larger than 9.2 is .0373. Since the number is small, it means that the probability of getting a c2 that large or larger is 3.7 percent. The null hypothesis is that the two samples are from the same normal distribution. If the probability is very small, then there is evidence to reject the hypothesis. If the probability is larger, one can only say that the hypothesis is accepted. That is so because one example cannot prove a statement, but it can disprove a statement. Also P[ χ12 ≤ ( s 2 /σ 2 )(df ) ≤ χ 22 ] = 1 − α

This states that the sample standard deviation will be at least 35 percent and not more than 166 percent of the population variance 95 percent of the time. Conversely, 5 percent of the time the standard deviation will underestimate or overestimate the population standard deviation by the corresponding amount. The chi-squared distribution can be applied to other types of application which are of an entirely different nature. These include applications discussed under Goodness-of-Fit Test and Two-Way Test for Independence of Count Data. In these applications, the mathematical formulation and context are entirely different, but they do result in the same table of values. F Distribution To test if two samples are from the same population, it is necessary to test whether the means are the same and variances are the same, within some confidence level. The test for variances is done using the F test. The null hypothesis is that the two samples are from the same population. The F ratio is defined by the ratio of sample variances. F (df1 , df 2 ) = s12 /s 22 Here df 1 and df 2 correspond to the respective df ’s for the sample variances. The F distribution, similar to the chi-squared distribution, is sensitive to the basic assumption that sample values were selected randomly from a normal distribution. The Microsoft Excel function FINV(percent, df1, df2) gives the largest ratio (and the reciprocal gives the smallest ratio) that agrees with the null hypothesis at that level of significance. Example For two sample variances with 4 df each, what limits will bracket their ratio with a midarea probability of 90 percent? Use FINV with 4 df and Percent = 0.05 (to get both sides totaling 10 percent). FINV(.05, 4, 4) gives 6.39. Thus P[1/6.39 ≤ s12/s22 ≤ 6.39] = .90 or

where c12 corresponds to a lower-tail area of α/2 and c22 to an upper-tail area of α/2. The basic underlying assumption for the mathematical derivation of chi squared is that a random sample was selected from a normal distribution with variance s2. When the population is not normal but skewed, chi-squared probabilities could be substantially in error. Example On the basis of a sample size n = 5, what midrange of values will include the sample ratio s/s with a probability of 95 percent?

0.25

0.2

3-63

P[.40 ≤ s1/s2 ≤ 2.53] = .90

FDIST(X, df1, df2) gives the upper percentage points of the F distribution. FDIST(6.39, 4, 4) = 0.05. Confidence Interval for a Mean Suppose a change has been made in a process and one wishes to assess the confidence of the population mean (unknown). Thus, one wants s  s = 1− α ≤µ ≤ x +t P  x − t n  n  where t is defined for an upper-tail area of α/2 with n - 1 df. In this application, the interval x − ts / n limits are random variables which will cover the unknown parameter m with probability 1 - α. The converse—that we are 100(1 - α) percent sure that the parameter value is within the interval—is not correct. This statement defines a probability for the parameter rather than the probability for the interval. The probability density function is the t distribution and uses the Microsoft Excel commands TDIST and TINV. Example For the example in Normal Distribution, the sample variance of 25 measurements was 0.15. What is the 90 percent confidence interval for m? Using df = n - 1 = 24, x = 5.2, s2 = 0.15, and a 10 percent value in Microsoft Excel TINV(0.10, 24) gives t = 1.71. Thus

df = 3

f(x2)

0.15

0.1 df = 5 0.05

0

 0.15  0.15 < µ < 5.2 + 1.71 P 5.2 − 1.71  = .90 24  24  0

2

4

6

x2 FIG. 3-63

The c2 distribution function.

8

10

12

or

P(5.065 ≤ m ≤ 5.335) = 0.90

Confidence Interval for the Difference in Two Population Means The confidence interval for a mean can be extended to include

3-64

MATHEMATICS

the difference between two population means. This interval is based on the assumption that the respective populations have the same variance s2: x 1 − x 2 − ts p 1/n1 + 1/n2 ≤ µ1 − µ 2 ≤ x 1 − x 2 + ts p 1/n1 + 1/n2 The value of t is obtained from the t distribution, Microsoft Excel function TINV(α, df). To achieve 95 percent confidence, use α = 0.05. Confidence Interval for a Variance The chi-square distribution can be used to derive a confidence interval for a population variance s2 when the parent population is normally distributed. For a 100(1 - α) percent confidence interval (df ) s 2 (df ) s 2 ≤ σ2 ≤ 2 χ2 χ12 2 1

Test of Hypothesis for a Mean Procedure 2 2

where c corresponds to a lower-tail area of α/2 and c to an upper-tail area of α/2. Example For the example in Normal Distribution, the sample variance of 25 measurements was 0.15. What is range of the population variance s2 for a 90 percent confidence interval? Using df = n - 1 = 24, s2 = 0.15, and 5 percent and 95 percent values in Microsoft Excel function CHIINV gives CHIINV(0.05, 24) = 13.85 and CHIINV(0.95, 24) = 36.42. Thus

or

Nomenclature for All Examples m = mean of the population or differences from which the sample has been drawn s = standard deviation of the population or differences from which the sample has been drawn m0 = base or reference level H0 = null hypothesis H1 = alternative hypothesis α = significance level, usually set at .10, .05, or .01 n = number of observations t = t value corresponding to the significance level α. For a two-tailed test, each corresponding tail would have an area of α/2, and for a one-tailed test, one-tail area would be equal to α. If s2 is known, then z would be used rather than t .

24(0.15) 24(0.15) ≤ σ2 ≤ 36.4 13.8 0.0989 ≤ σ 2 ≤ 0.261 0.31 ≤ σ ≤ 0.51

Thus, the population variance will be between 0.0989 and 0.261 with 90 percent confidence. TESTS OF HYPOTHESIS General Nature of Tests The general nature of tests can be illustrated with a simple example. In a court of law, when a defendant is charged with a crime, the judge instructs the jury initially to presume that the defendant is innocent of the crime. The jurors are then presented with evidence and counterargument as to the defendant’s guilt or innocence. If the evidence suggests beyond a reasonable doubt that the defendant did, in fact, commit the crime, the jurors have been instructed to find the defendant guilty; otherwise, not guilty. The burden of proof is on the prosecution. Jury trials represent a form of decision making. In statistics, an analogous procedure for making decisions falls into an area of statistical inference called hypothesis testing . Suppose that a company has been using a certain supplier of raw materials in one of its chemical processes. A new supplier approaches the company and states that its material, at the same cost, will increase the process yield. If the new supplier has a good reputation, the company might be willing to run a limited test. On the basis of the test results it would then make a decision to change suppliers or not. Good management would dictate that an improvement must be demonstrated (beyond a reasonable doubt) for the new material. That is, the burden of proof is tied to the new material. In setting up a test of hypothesis for this application, the initial assumption would be defined as a null hypothesis and symbolized as H0. The null hypothesis would state that yield for the new material is no greater than for the conventional material. The symbol m0 would be used to designate the known current level of yield for the standard material and m for the unknown population yield for the new material. Thus, the null hypothesis can be symbolized as H0: m ≤ m0. The alternative to H0 is called the alternative hypothesis and is symbolized as H1: m > m0. To prove the alternative hypothesis, we must show that the null hypothesis is not valid within some probability. Given a series of tests with the new material, the average yield x would be compared with m0. If x < m0, the new supplier would be dismissed. If x > m0, the question would be: Is it sufficiently greater in the light of its corresponding reliability, i.e., beyond a reasonable doubt? If the confidence interval for m included m0, the answer would be no; but if it did not include m0, the answer would be yes. In this simple application, the formal test of hypothesis would result in the same conclusion as that derived from the confidence interval. However, the utility of tests of hypothesis lies in their generality, whereas confidence intervals are restricted to a few special cases.

t = ( x − µ 0 )/( s / n ) sample value of the test statistic Assumptions 1. The n observations x1, x2, …, xn have been selected randomly. 2. The population from which the observations were obtained is normally distributed with an unknown mean m and standard deviation s. In actual practice, this is a robust test, in the sense that in most types of problems it is not sensitive to the normality assumption when the sample size is 10 or greater. Test of Hypothesis 1. The null hypothesis is that the sample came from a population whose mean m is equivalent to some base or reference designated by m0. This can take one of the three forms shown in Table 3-4. 2. If the null hypothesis is assumed to be true, say, in form 1, then the distribution of the test statistic t is known. Given a random sample in a twosided test, one can predict how far its sample value of t might be expected to deviate from zero (the midvalue of t) by chance alone. If the sample value of t does, in fact, deviate too far from zero, then this is defined to be sufficient evidence to refute the assumption of the null hypothesis. It is consequently rejected, and the converse or alternative hypothesis is accepted. 3. The rule for accepting H0 is specified by selection of the α level, as indicated in Fig. 3-64. For forms 2 and 3 the α area is defined to be in the upper and the lower tail, respectively. The parameter α is the probability of rejecting the null hypothesis when it is actually true. 4. The decision rules for each of the three forms are defined as follows: If the sample t falls within the acceptance region, accept H0 for lack of contrary evidence. If the sample t falls in the critical region, reject H0 at a significance level of 100α percent.

TABLE 3-4 Options for null Hypothesis and Alternate Hypothesis Form 1

Form 2

Form 3

H0: m = m0

H0: m ≤ m0

H0: m ≥ m0

H1: m ≠ m0

H1: m > m0

H1: m < m0

Two-tailed test

Upper-tailed test

Lower-tailed test

FIG. 3-64 Acceptance region for two-tailed test. For a one-tailed test, area = α on one

side only.

STATISTICS Example Application . In the past, the yield for a chemical process has been established at 89.6 percent with a standard deviation of 3.4 percent. A new supplier of raw materials will be used and tested for 7 days. [Note: many problems with chemical processes arise because of bad raw materials.] Procedure 1. The standard of reference is m0 = 89.6 with a known s = 3.4. 2. It is of interest to demonstrate whether an increase in yield is achieved with the new material; H0 says it has not; therefore, H0: m ≤ 89.6

H1: m > 89.6

3. Select α = .05, and since s is known (assuming the new material would not affect the day-to-day variability in yield), we use z. The corresponding critical value is TINV(0.10, ∞) = 1.645. Remember TINV is the value for the two-tailed distribution, so the one-tailed distribution is TINV(2α, df). 4. The decision rule is Accept H0 if sample z < 1.645. Reject H0 if sample z > 1.645. 5. A 7-day test was carried out, and daily yields averaged 91.6 percent with a sample standard deviation s = 3.6 (this is not needed for the test of hypothesis). 6. For the data sample z = (91.6 - 89.6)/(3.4/√7) = 1.56. 7. Since this is less than 1.645, accept the null hypothesis for lack of contrary evidence; i.e., an improvement has not been demonstrated beyond a reasonable doubt. Example Application . In the past, the break strength of a synthetic yarn has averaged 34.6 lb. The first-stage draw ratio of the spinning machines has been increased. Production management wants to determine whether the break strength has changed under the new condition. Procedure 1. The standard of reference is m0 = 34.6. 2. It is of interest to demonstrate whether a change has occurred; therefore, H0: m = 34.6

H1: m ≠ 34.6

3. Select α = .05, and since with the change in draw ratio the uniformity might change, the sample standard deviation would be used, and therefore t would be the appropriate test statistic. 4. A sample of 21 ends was selected randomly and tested on an Instron with the results x = 35.55 and s = 2.041. 5. For 20 df and a two-tailed α level of 5 percent, TINV(0.05, 20) = ±2.086. Accept H0 if -2.086 < sample t < 2.086. Reject H0 if sample t < -2.086 or t > 2.086. 6. For the data sample t = (35.55 - 34.6)/(2.041/ 21) = 2.133. 7. Since 2.133 > 2.086, reject H0 and accept H1. It has been demonstrated that an improvement in break strength has been achieved. Two-Population Test of Hypothesis for Means Nature Two samples were selected from different locations in a plasticfilm sheet and measured for thickness. The thickness of the respective samples was measured at 10 close but equally spaced points in each of the samples. It was of interest to compare the average thickness of the respective samples to detect whether they were significantly different. That is, was there a significant variation in thickness between locations? From a modeling standpoint, statisticians would define this problem as a two-population test of hypothesis. They would define the respective sample sheets as two populations from which 10 sample thickness determinations were measured for each. To compare populations based on their respective samples, it is necessary to have some basis of comparison. This basis is predicated on the distribution of the t statistic. In effect, the t statistic characterizes the way in which two sample means from two separate populations will tend to vary by chance alone when the population means and variances are equal. Consider the following: Population 1

Population 2

Normal

Sample 1

Normal

Sample 2

m1

n1 x1 s12

m2

n2 x2 s22

s12

s22

3-65

Consider the hypothesis m1 = m2. If, in fact, the hypothesis is correct, that is, m1 = m2 (under the condition s12 = s22), then the sampling distribution of x1 - x2 is predictable through the t distribution. (We use t rather than z because the variance is unknown.) The observed sample values then can be compared with the corresponding t distribution. Example Application . Two samples were selected from different locations in a plastic-film sheet. The thickness of the respective samples was measured at 10 close but equally spaced points. Procedure 1. Demonstrate whether the thicknesses of the respective sample locations are significantly different from each other; therefore, H0: m1 = m2

H1: m1 ≠ m2

2. Select α = .05. 3. Summarize the statistics for the respective samples: Sample 1

Sample 2

1.473

1.367

1.474

1.417

1.484

1.276

1.501

1.448

1.484

1.485

1.485

1.469

1.425

1.462

1.435

1.474

1.448

1.439

1.348

1.452

x1 = 1.434

s1 = .0664

x2 = 1.450

s2 = .0435

4. The first step is to use the F test on the ratio of sample variances. The null hypothesis is H0: s12 = s22, and it would be tested against H1: s12 ≠ s22. Since this is a two-tailed test, the procedure is to use the largest ratio and the corresponding ordered degrees of freedom. However, since the largest ratio is arbitrary, it is necessary to define the true α level as twice the desired value. Therefore, using FINV(0.05, 9, 9) = 3.18 would be for a true α = .10. For the sample, Sample F = (.0664/.0435)2 = 2.33 Therefore, the ratio of sample variances is no larger than one might expect to observe when in fact s12 = s22. There is not sufficient evidence to reject the null hypothesis that s12 = s22. 5. Turn next to the t test. For 18 df and a two-tailed α level of 5 percent, the critical values of t are given by TINV(0.05, 18) = ±2.101. 6. The decision rule is Accept H0 if -2.101 ≤ sample t ≤ 2.101. Reject H0 otherwise. 7. For the sample the pooled variance estimate is given by Eq. (3-98). s 2p =

9(.0664)2 + 9(.0435)2 = .00315, s p = .056 9+9

8. The sample statistic value of t is given by Eq. (3-99). Sample t =

1.434 − 1.450 = −.64 .056 1/10 + 1/10

9. Since the sample value of t falls within the acceptance region, accept H0 for lack of contrary evidence; i.e., there is insufficient evidence to demonstrate that thickness differs between the two selected locations. Test of Hypothesis for Paired Observations Nature In some types of applications, associated pairs of observations are defined. For example, (1) pairs of samples from two populations are treated in the same way, or (2) two types of measurements are made on the same unit. For applications of this type, it is not only more effective but also necessary to define the random variable as the difference between the pairs of observations. The difference numbers can then be tested by the standard t distribution.

3-66

MATHEMATICS

Test of Hypothesis for Matched Pairs: Procedure Nomenclature di = sample difference between the ith pair of observations s = sample standard deviation of differences m = population mean of differences s = population standard deviation of differences t = value with (n - 1) df

6. The sample statistics, Eq. (3-97) d = −6.245 s 2 or

11 ∑ d 2 − (∑ d )2 = 52.59 11 × 10

s = 7.25 Sample t = (−6.245 − 0)/(7.25/ 11) = −2.86

t = (d − µ 0 )/( s / n ), the sample value of t Assumptions 1. The n pairs of samples have been selected and assigned for testing in a random way. 2. The population of differences is normally distributed with a mean m and variance s2. As in the previous application of the t distribution, this is a robust procedure, i.e., not sensitive to the normality assumption if the sample size is 10 or greater in most situations. Test of Hypothesis 1. Under the null hypothesis, it is assumed that the sample came from a population whose mean m is equivalent to some base or reference level, designated by m0. For most applications of this type, the value of m0 is defined to be zero; that is, it is of interest generally to demonstrate a difference not equal to zero. The hypothesis can take one of three forms shown in Table 3-4. 2. If the null hypothesis is assumed to be true, say, in the case of a lowertailed test, form 3, then the distribution of the test statistic t is known under the null hypothesis that limits m = m0. Given a random sample, one can predict how far its sample value of t might be expected to deviate from zero by chance alone when m = m0. If the sample value of t is too small, as in the case of a negative value, then this would be defined as sufficient evidence to reject the null hypothesis. 3. Select α. 4. The critical values or value of t would be defined by the value of t with n - 1 df corresponding to a tail area of α. For a two-tailed test use TINV(α, df), and for a one-tailed test use TINV(2α, df). 5. The decision rule for each of the three forms would be to reject the null hypothesis if the sample value of t fell in that area of the t distribution defined by α, which is called the critical region. Otherwise, the alternative hypothesis would be accepted for lack of contrary evidence. Example, Two-Sided Test Application . Pairs of pipes have been buried in 11 different locations to determine corrosion on nonbituminous pipe coatings for underground use. One type includes a lead-coated steel pipe and the other a bare steel pipe. Procedure 1. The standard of reference is taken as m0 = 0, corresponding to no difference in the two types. 2. It is of interest to demonstrate whether either type of pipe has a greater corrosion resistance than the other. Therefore, H 0: m = 0

H 1: m ≠ 0

3. Select α = .05. TINV(0.05, 10) = 2.228. 4. The decision rule is then

7. Since the sample t of -2.86 < tabled t of -2.228, reject H0 and accept H1; that is, it has been demonstrated that, on the basis of the evidence, leadcoated steel pipe has a greater corrosion resistance than bare steel pipe. Example, One-Sided Test Application . A stimulus was tested for its effect on blood pressure. Ten men were selected randomly, and their blood pressure was measured before and after the stimulus was administered. It was of interest to determine whether the stimulus had caused a significant increase in the blood pressure. Procedure 1. The standard of reference was taken as m0 ≤ 0, corresponding to no increase. 2. It was of interest to demonstrate an increase in blood pressure if in fact an increase did occur. Therefore, H0: m0 ≤ 0

H1: m0 > 0

3. Select α = .05. Since only increases are of interest, use a one-sided value TINV(0.05*2, 9) = 1.833. 4. The decision rule is Accept H0 if sample t < 1.833. Reject H0 if sample t > 1.833. 5. The sample of 10 pairs of blood pressure and their differences was as follows: Individual

Before

After

d = difference

1

138

146

8

2

116

118

2 -4

3

124

120

4

128

136

8

5

155

174

19

6

129

133

4

7

130

129

-1

Accept H0 if -2.228 ≤ sample t ≤ 2.228 Reject H0 otherwise

8

148

155

7

9

143

148

5

5. The sample of 11 pairs of corrosion determinations and their differences is as follows:

10

159

155

-4

Soil type

Lead-coated steel pipe

Bare steel pipe

d = difference

A

27.3

41.4

-14.1

B

18.4

18.9

-0.5

C

11.9

21.7

-9.8

D

11.3

16.8

-5.5

E

14.8

9.0

5.8

F

20.8

19.3

1.5

G

17.9

32.1

-14.2

H

7.8

7.4

0.4

I

14.7

20.7

-6.0

J

19.0

34.4

-15.4

K

65.3

76.2

-10.9

6. The sample statistics:

d = 4.4 s = 6.85 Sample t = (44 − 0)/(6.85/ 10) = 2.03

7. Since the sample t = 2.03 > critical t = 1.833, reject the null hypothesis. It has been demonstrated that the population of men from whom the sample was drawn tend, as a whole, to have an increase in blood pressure after the stimulus has been given. The distribution of differences d seems to indicate that the degree of response varies by individuals. Test of Hypothesis for a Proportion Nature Some types of statistical applications deal with counts and proportions rather than measurements. Examples are (1) the proportion

STATISTICS of workers in a plant who are out sick, (2) lost-time worker accidents per month, (3) defective items in a shipment lot, and (4) preference in consumer surveys. The procedure for testing the significance of a sample proportion follows that for a sample mean. In this case, however, owing to the nature of the problem the appropriate test statistic is Z . This follows from the fact that the null hypothesis requires the specification of the goal or reference quantity p0, and since the distribution is a binomial proportion, the associated variance under the null hypothesis is [p0(1 - p0)]n. The primary requirement is that the sample size n satisfy normal approximation criteria for a binomial proportion, roughly np > 5 and n(1 - p) > 5. Test of Hypothesis for a Proportion: Procedure Nomenclature p = mean proportion of the population from which the sample has been drawn p0 = base or reference proportion [p0(1 - p0)]/n = base or reference variance pˆ = x /n = sample proportion, where x refers to the number of observations out of n which have the specified attribute z = Z value corresponding to the significance level α z = ( pˆ − p0 )/ p0 (1 − p0 )/n , the sample value of the test statistic Assumptions 1. The n observations have been selected randomly. 2. The sample size n is sufficiently large to meet the requirement for the Z approximation. Test of Hypothesis 1. Under the null hypothesis, it is assumed that the sample came from a population with a proportion p0 of items having the specified attribute. For example, in tossing a coin the population could be thought of as having an unbounded number of potential tosses. If it is assumed that the coin is fair, this would dictate p0 = 1/2 for the proportional number of heads in the population. The null hypothesis can take one of three forms: Form 1

Form 2

Form 3

H0: p = p0

H0: p ≤ p0

H0: p ≥ p0

H1: p ≠ p0

H1: p > p0

H1: p < p0

Two-tailed test

Upper-tailed test

Lower-tailed test

3-67

outcome, this would lead one to question the assumption that p ≤ .02. That is, one would conclude that the null hypothesis is false. To test, set H0: p ≤ .02

H1: p > .02

3. Select α = .05. 4. With α = .05, the upper critical value of Z = TINV(0.05*2, ∞) = 1.645 for a one-sided test. 5. The decision rule: Accept H0 if sample z < 1.645. Reject H0 if sample z > 1.645. 6. The sample z is given by (16/600) − .02 (.02)(.98)/600 = 1.17

Sample z =

7. Since the sample z < 1.645, accept H0 for lack of contrary evidence; there is not sufficient evidence to demonstrate that the defect proportion in the shipment is greater than 2 percent. Test of Hypothesis for Two Proportions Nature In some types of engineering and management science problems, we may be concerned with a random variable that represents a proportion, for example, the proportional number of defective items per day. The method described previously relates to a single proportion. In this subsection two proportions will be considered. A certain change in a manufacturing procedure for producing component parts is being considered. Samples are taken by using both the existing and the new procedures to determine whether the new procedure results in an improvement. In this application, it is of interest to demonstrate statistically whether the population proportion p2 for the new procedure is less than the population proportion p1 for the old procedure on the basis of a sample of data. Test of Hypothesis for Two Proportions: Procedure Nomenclature pi = population i = 1 or 2 proportion ni = sample size from population 1 or 2

2. If the null hypothesis is assumed to be true, then the sampling distribution of the test statistic Z is known. Given a random sample, it is possible to predict how far the sample proportion x/n might deviate from its assumed population proportion p0 through the Z distribution. When the sample proportion deviates too far, as defined by the significance level α, this serves as the justification for rejecting the assumption, that is, rejecting the null hypothesis. 3. The decision rule is given by Form 1: Accept H0 if lower critical z < sample z < upper critical z . Reject H0 otherwise. Form 2: Accept H0 if sample z < upper critical z . Reject H0 otherwise. Form 3: Accept H0 if lower critical z < sample z . Reject H0 otherwise. Example Application . A company has received a very large shipment of rivets. One product specification required that no more than 2 percent of the rivets have diameters greater than 14.28 mm. Any rivet with a diameter greater than this would be classified as defective. A random sample of 600 was selected and tested with a go–no go gauge. Of these, 16 rivets were found to be defective. Is this sufficient evidence to conclude that the shipment contains more than 2 percent defective rivets? Procedure 1. The quality goal is p ≤ .02. It would be assumed initially that the shipment meets this standard; that is, H0: p ≤ .02. 2. The assumption in step 1 would first be tested by obtaining a random sample. Under the assumption that p ≤ .02, the distribution for a sample proportion would be defined by the z distribution. This distribution would define an upper bound corresponding to the upper critical value for the sample proportion. It would be unlikely that the sample proportion would rise above that value if, in fact, p ≤ .02. If the observed sample proportion exceeds that limit, corresponding to what would be a very unlikely chance

xi = number of observations out of that have the designated attribute pˆi = x i /ni , the sample proportion from population 1 or 2 z = Z value corresponding to the stated significance level α z=

pˆ1 − pˆ2 the sample value of Z ˆp1 (1 − pˆ1 )/n1 + pˆ2 (1 − pˆ2 )/n2

Assumptions 1. The respective two samples of n1 and n2 observations have been selected randomly. 2. The sample sizes n1 and n2 are sufficiently large to meet the requirement for the Z approximation; that is, x1 > 5 and x2 > 5. Test of Hypothesis 1. Under the null hypothesis, it is assumed that the respective two samples have come from populations with equal proportions p1 = p2. Under this hypothesis, the sampling distribution of the corresponding Z statistic is known. On the basis of the observed data, if the resultant sample value of Z represents an unusual outcome, that is, if it falls within the critical region, this would cast doubt on the assumption of equal proportions. Therefore, it will have been demonstrated statistically that the population proportions are in fact not equal. The various hypotheses can be stated: Form 1

Form 2

Form 3

H0: p1 = p2

H0: p1 ≤ p2

H0: p1 ≥ p2

H1: p1 ≠ p2

H1: p1 > p2

H1: p1 < p2

Two-tailed test

Upper-tailed test

Lower-tailed test

3-68

MATHEMATICS

2. The decision rule for form 1 is given by

Test Statistics: Chi Square

Accept H0 if lower critical z < sample z < upper critical z . Reject H0 otherwise. Example Application . A change was made in a manufacturing procedure for component parts. Samples were taken during the last week of operations with the old procedure and during the first week of operations with the new procedure. Determine whether the proportional numbers of defects for the respective populations differ on the basis of the sample information. Procedure 1. The hypotheses are H0: p1 = p2

H1: p1 ≠ p2

2. Select α = .05. Therefore, the critical values of z are ±1.96 since TINV(0.05, ∞) = 1.96. 3. For the samples, 75 out of 1720 parts from the previous procedure and 80 out of 2780 parts under the new procedure were found to be defective; therefore, pˆ1 = 75/1720 = .0436

pˆ2 = 80/2780 = .0288

4. The decision rule: Accept H0 if -1.96 ≤ sample z ≤ 1.96. Reject H0 otherwise.

(O j − E j )2

j =1

Ej

with df degrees of freedom

Test of Hypothesis 1. H0: The sample came from the specified theoretical distribution. H1: The sample did not come from the specified theoretical distribution. 2. For a stated level of α, Reject H0 if sample c2 > CHIINV c2. Accept H0 if sample c2 < CHIINV c2. Example Application . A production-line product is rejected if one of its characteristics does not fall within specified limits. The standard goal is that no more than 2 percent of the production should be rejected. Computation 1. Of 950 units produced during the day, 28 units were rejected; there are two cells, so r = 2. 2. The hypotheses: H0: process is in control H1: process is not in control 3. Assume that α = .05; therefore, the critical value of c2(1) is CHIINV (0.05, 1) = 3.84. 4. The decision rule: Reject H0 if sample c2 > 3.84. Accept H0 otherwise.

5. The sample statistic: Sample z =

r

χ2 = ∑

.0436 − .0288 = 2.53 (.0436)(.9564)/1720 + (.0288)(.9712)/2780

6. Since the sample z of 2.53 > z = 1.96, reject H0 and conclude that the new procedure has resulted in a reduced defect rate. Goodness-of-Fit Test Nature A standard die has six sides numbered from 1 to 6. If one were really interested in determining whether a particular die was well balanced, one would have to carry out an experiment. To do this, it might be decided to count the frequencies of outcomes, 1 through 6, in tossing the die N times. On the assumption that the die is perfectly balanced, one would expect to observe N/6 occurrences each for 1, 2, 3, 4, 5, and 6. However, chance dictates that exactly N/6 occurrences each will not be observed. For example, given a perfectly balanced die, the probability is only 1 chance in 65 that one will observe 1 outcome each, for 1 through 6, in tossing the die 6 times. Therefore, an outcome different from 1 occurrence each can be expected. Conversely, an outcome of six 3s would seem to be too unusual to have occurred by chance alone. Some industrial applications involve the concept outlined here. The basic idea is to test whether a group of observations follows a preconceived distribution. In the case cited, the distribution is uniform; i.e., each face value should tend to occur with the same frequency. Goodness-of-Fit Test: Procedure Nomenclature Each experimental observation can be classified into one of r possible categories or cells. r = total number of cells Oj = number of observations occurring in cell j Ej = expected number of observations for cell j based on the preconceived distribution r

N = total number of observations = ∑O j j =1

df = degrees of freedom for the test. In general, this will be equal to r - 1 minus the number of statistical quantities on which the Ej’s are based (see the examples that follow for details). Assumptions 1. The observations represent a sample selected randomly from a population that has been specified. 2. The number of expectation counts Ej within each category should be roughly 5 or more. If an Ej count is significantly less than 5, that cell should be pooled with an adjacent cell. Computation for Ej On the basis of the specified population, the probability of observing a count in cell j is defined by pj . For a sample of size N, corresponding to N total counts, the expected frequency is given by Ej = Npj .

5. Since it is assumed that p = .02, this would dictate that in a sample of 950 there would be on average (.02)(950) = 19 defective items and 931 acceptable items: Category

Observed Oj

Expectation Ej = 950pj

Acceptable Not acceptable Total

922  28 950

931   19 950

(922 − 931)2 (28 − 19)2 + 931 19 = 4.35 with critical χ 2 = 3.84

Sample χ 2 =

6. Conclusion. Since the sample value exceeds the critical value, the process is not in control. Example Application . A frequency count of 52 workers was tabulated according to the number of defective items that they produced. An unresolved question is whether the observed distribution is a Poisson distribution. That is, do observed and expected frequencies agree within chance variation? Computation 1. The hypotheses: H0: there are no significant differences, in number of defective units, between workers. H1: there are significant differences. 2. Assume that α = .05. 3. Test statistic: No. of defective units = nj

Oj

0 1 2 3 4 5

3 7 9 12 9 6

} 10

0 7 18 36 36 30

6 7 8 9 >10 Sum

3 2 0 1 0 52

 6 

18 14 0 9 0 168

O j nj

Ej

}

2.06 8.70 pool 6.64 10.73 11.55 9.33 6.03 3.24 1.50 0.60 0.22 0.10 52

  5.66 pool 

STATISTICS The expectation numbers Ej were computed as follows: For the Poisson distribution, l = E(x); therefore, an estimate of l is the average number of defective units per worker, that is, l = (1/52)(0 × 3 + 1 × 7 + … + 9 × 1) = 3.23. Given this approximation, the probability of no defective units for a worker would be (3.23)0/0!)e-3.23 = .0396. For the 52 workers, the number of workers producing no defective units would have an expectation E = 52(0.0396) = 2.06, and so forth. The sample chi-square value is computed from

Sample c2 Value χ2 = ∑ i, j

(10 − 8.70)2 (9 − 10.73)2 (6 − 5.66)2 + ++ 8.70 10.73 5.66 = .522

c ,r

8. Sample χ 2 =

∑(Oij − Eij )2 i, j

Eij

Assumptions 1. The observations represent a sample selected randomly from a large total population. 2. The number of expectation counts Eij within each cell should be approximately 2 or more for arrays 3 × 3 or larger. If any cell contains a number smaller than 2, appropriate rows or columns should be combined to increase the magnitude of the expectation count. For arrays 2 × 2, approximately 4 or more are required; if the number is less than 4, the exact Fisher test should be used. Test of Hypothesis Under the null hypothesis, the classification criteria are assumed to be independent, i.e., H0: criteria are independent H1: criteria are not independent For the stated level of α, Reject H0 if sample c2 > CHIINV c2. Accept H0 otherwise. Computation for Eij Compute Eij across rows or down columns by using either of the following identities: R Eij = C j  i  N

across rows

C Eij = R j  i  N

down columns

Eij

2

 O11O22 − O12O21 − 1 2 N  N χ = R1 R2C1C1 2

Example Application . A market research study was carried out to relate the subjective “feel” of a consumer product to consumer preference. In other words, is the consumer’s preference for the product associated with the feel of the product, or is the preference independent of the product feel? Procedure 1. It was of interest to demonstrate whether an association exists between feel and preference; therefore, assume H0: feel and preference are independent H1: they are not independent 2. A sample of 200 people was asked to classify the product according to two criteria: a . Liking for this product b . Liking for the feel of the product Like feel

Like product

i = 1, 2, …, r j = 1, 2, …, c 3. N = total number of observations 4. Eij = computed number for cell (i, j) which is an expectation based on the assumption that two characteristics are independent 5. Ri = subtotal of counts in row i 6. Cj = subtotal of counts in column j 7. c2 = critical value of c2 corresponding to the significance level α and (r - 1)(c - 1) df

(Oij − Eij )2

In the special case of r = 2 and c = 2, a more accurate and simplified formula that does not require the direct computation of Eij can be used:

χ2 =

4. The critical value of c2 would be based on 4 degrees of freedom. This corresponds to (r - 1) - 1 = 4, since one statistical quantity l was computed from the sample and used to derive the expectation numbers. 5. The critical value of c2 is CHIINV(0.05, 4) = 9.49; therefore, accept H0. Two-Way Test for Independence for Count Data Nature When individuals or items are observed and classified according to two different criteria, the resultant counts can be statistically analyzed. For example, a market survey may examine whether a new product is preferred and if it is preferred due to a particular characteristic. Count data, based on a random selection of individuals or items which are classified according to two different criteria, can be statistically analyzed through the c2 distribution. The purpose of this analysis is to determine whether the respective criteria are dependent. That is, is the product preferred because of a particular characteristic? Two-Way Test for Independence for Count Data: Procedure Nomenclature 1. Each observation is classified according to two categories: a . The first one into 2, 3, …, or r categories b . The second one into 2, 3, …, or c categories 2. Oij = number of observations (observed counts) in cell (i, j) with

3-69

Yes

No

Ri

114

13

127

No

55

18

73

Cj

169

31

200

Yes

3. Select α = .05; therefore, with (r - 1)(c - 1) = 1 df, the critical value of c2 is CHIINV(0.05, 1) =3.84. 4. The decision rule: Accept H0 if sample c2 < 3.84. Reject H0 otherwise. 5. The sample value of c2 by using the special formula is 2

 114 × 18 − 13 × 55 − 100  200 Sample χ 2 =  = 6.30 (169)(31)(127)(73) 6. Since the sample c2 of 6.30 > CHIINV c2 of 3.84, reject H0 and accept H1. The relative proportionality of E11 = 169(127/200) = 107.3 to the observed 114 compared with E22 = 31(73/200) = 11.3 to the observed 18 suggests that when the consumer likes the feel, the consumer tends to like the product, and conversely for not liking the feel. The proportions 169/200 = 84.5 percent and 127/200 = 63.5 percent suggest further that there are other attributes of the product which tend to nullify the beneficial feel of the product. LEAST SQUARES When experimental data are to be fit with a mathematical model, it is necessary to allow for the fact that the data have errors. The engineer is interested in finding the parameters in the model as well as the uncertainty in their determination. In the simplest case, the model is a linear equation with only two parameters, and they are found by a least-squares minimization of the errors in fitting the data. Multiple regression is just linear least squares applied with more terms. Nonlinear regression allows the parameters of the model to enter in a nonlinear fashion. See Press et al. (2007) in General References for a description of maximum likelihood as it applies to both linear and nonlinear least squares. Since many calculators include least-squares calculations, the emphasis here is on the estimates and their uncertainty. In a least-squares parameter estimation, it is desired to find parameters that minimize the sum of squares of the deviation between the experimental data and the theoretical equation. N  y − y ( x i ; a1 , a2 ,  , a M )  χ2 = ∑  i  σi i =1  

2

3-70

MATHEMATICS

where yi is the ith experimental data point for the value xi, si is the standard deviation for the ith point, yi, y (xi; a1, a2, …, aM) is the theoretical equation at xi, and the parameters {a1, a2, …, aM} are to be determined to minimize c2. If the uncertainties in yi are not known, then assume a constant s = si for all i. After calculation the variance will be minimized, giving s, and c2 can be calculated. [ y i − y ( x i ; a1 , a2 ,  , a M )]2 N i =1 N

σ2 = ∑

Linear Least Squares When the model is a straight line y i − a − bx i , one is minimizing N

χ 2 = ∑( y i − a − bx i )

with a two-sided test, the value would be rejected if outside the range given by t(α/2) = TINV(α, N - 2) in Microsoft Excel. When there are more terms, i.e ., multiple linear regression, similar formulas can be found, usually using the computer. Estimates for the variances and t tests are available, e.g., in Mendenhall and Sincich (2006). In Microsoft Excel, one simply adds columns to the spreadsheet for the additional independent variables. Polynomial Regression In polynomial regression, one expands the function in a polynomial in x and the same considerations apply. M

y ( x ) = ∑ a j x j −1 j =1

For N measurements write this as M

y i = ∑ a j x ij −1

2

j =1

i =1

In Microsoft Excel, the instructions above hold with the columns x i0 , x i1 , x i2 , x i3 , etc. Multiple Nonlinear Regression In multiple nonlinear regression, any set of functions can be used, not just polynomials, such as

The linear correlation coefficient r is defined by N

∑( x

i

− x ) ( yi − y )

i =1

r=

N

∑( x

i

− x)

M

2

i =1

N

∑( y

i

− y)

N

χ 2 = (1 − r 2 ) ∑ ( y i − y )2 i =1

where y is the average of the yi values. Values of r near 1 indicate a positive correlation; r near –1 means a negative correlation, and r near 0 means no correlation. These parameters are easily found by using standard programs. The solution for aˆ and bˆ is N N N  N  aˆ =  ∑ x i2 ∑ y i − ∑ x i ∑ x i y i  /dem  i =1 i =1  i =1 i =1 N N  N  bˆ =  N ∑ x i y i − ∑ x i ∑ y i  /dem  i =1  i =1 i =1 N  N  dem ≡ N ∑ x i2 −  ∑ x i   i =1  i =1

2

The variance of the estimate is the c2 given above with the N replaced by N - 2 since the line has two constraints. N

j =1

i =1

and

(

)

2

ˆ /( N − 2) s = ∑ y i − aˆ − bx i 2

y (x ) = ∑ = a j f j (x )

2

i =1

The variances of aˆ and bˆ are   2 1  s2 x  s 2 and sb2ˆ = N s a2ˆ =  + N N ∑( x i - x )2  ∑ ( x i - x )2  i =1 i =1 The solution is found in Microsoft Excel by putting the values for x and y in two columns ( for example, A1:A10, B1:B10). The commands = SLOPE(A1:A10,B1-B10), INTERCEPT(A1:A10,B1-B10), and RSQ(A1:A10,B1-B10) give the slope, intercept, and residual squared. You can also use the LINEST function. See Microsoft Excel Help menu for the function LINEST which can give the statistics for multiple linear regression. A t test can give the significance. For example, using t=

bˆ sbˆ

where the set of functions { fj(x)} is known and specified. Note that the unknown parameters {aj} enter the equation linearly. In this case, the spreadsheet can be expanded to have a column for x and then successive columns for fj (x). Then this works in the same way as for linear multiple regression. Nonlinear Least Squares There are no analytic methods for determining the most appropriate model for a particular set of data. In many cases, however, the engineer has some basis for a model. If the parameters occur in a nonlinear fashion, then the analysis becomes more difficult. For example, in relating the temperature to the elapsed time of a fluid cooling in the atmosphere, a model that has an asymptotic property would be the appropriate model (temp = a + b exp(-c time), where a represents the asymptotic temperature corresponding to t → ∞). In this case, the parameter c appears nonlinearly. The usual practice is to concentrate on model development and computation rather than on statistical aspects. In general, nonlinear regression should be applied only to problems in which there is a well-defined, clear association between the two variables; therefore, a test of hypothesis on the significance of the fit would be somewhat ludicrous. In addition, the generalization of the theory for the associate confidence intervals for nonlinear coefficients is not well developed. Example Application . Data were collected on the cooling of water in the atmosphere as a function of time. Sample data Time x 0 1 2 3 5 7 10 15 20

Temperature y 92.0 85.5 79.5 74.5 67.0 60.5 53.5 45.0 39.5

Model . The data are fit to the formula y = a + becx using optimization techniques in MATLAB, giving a = 33.54, b = 57.89, c = 0.11. The value of c2 is 1.83. Using an alternative form, y = a + b/(c + x), gives a = 9.872, b = 925.7, c = 11.27, and c = 0.19. Since this model had a smaller value of c2, it might be the chosen one, but it is only a fit of the specified data and may not be generalized beyond that. Both forms give equivalent plots. ERROR AnALYSIS OF EXPERIMEnTS Consider the problem of assessing the accuracy of a series of measurements. If measurements are for independent, identically distributed observations, then the errors are independent and uncorrelated. Then y, the experimentally determined mean, varies about E(y), the true mean, with variance s2/n, where n is the number of observations in y. Thus, if one measures something

STATISTICS several times today, and each day, and the measurements have the same distribution, then the variance of the means decreases with the number of samples in each day’s measurement n . Of course, other factors (weather, weekends) may make the observations on different days not distributed identically. Consider next the problem of estimating the error in a variable that cannot be measured directly but must be calculated based on results of other measurements. Suppose the computed value Y is a linear combination of the measured variables {yi}, Y = α1 y1 + α2 y2 + … . Let the random variables y1, y2, … have means E(y1), E(y2), … and variances s2(y1), s2(y2), … . The variable Y has mean E(Y) = α1E(y1) + α2 E(y2) + … and variance (Cropley, 1978) n

n

n

σ 2 (Y ) = ∑ α i2 σ i2 ( y i ) + 2∑ ∑ α i α j Cov (y i , y j ) i =1

i =1 j =i +1

If the variables are uncorrelated and have the same variance, then  n  σ 2 (Y ) =  ∑ α i2  σ 2  i =1  Next suppose the model relating Y to {yi} is nonlinear, but the errors are small and independent of one another. Then a change in Y is related to changes in yi by dY =

∂Y ∂Y dy 1 + dy 2 +  ∂ y1 ∂ y2

If the changes are indeed small, then the partial derivatives are constant among all the samples. Then the expected value of the change E(dY) is zero. The variances are related by the following equation (Box et al., 2005): 2

N  ∂Y  2 σ 2 (dY ) = ∑   σi i =1  ∂ y i 

can be quantitative or qualitative. The quantitative variables are ones you may fit to a model in order to determine the model parameters (see the section Least Squares). Qualitative variables are ones whose effect you wish to know, but you do not try to quantify that effect other than to assign possible errors or magnitudes. Qualitative variables can be further subdivided into Type I variables, whose effect you wish to determine directly, and Type II variables, which contribute to the performance variability and whose effect you wish to average out. For example, if you are studying the effect of several catalysts on yield in a chemical reactor, each different type of catalyst would be a Type I variable because you would like to know the effect of each. However, each time the catalyst is prepared, the results are slightly different due to random variations; thus, you may have several batches of what purports to be the same catalyst. The variability between batches is a Type II variable. Since the ultimate use will require using different batches, you would like to know the overall effect including that variation, since knowing precisely the results from one batch of one catalyst might not be representative of the results obtained from all batches of the same catalyst. A randomized block design, incomplete block design, or Latin square design (Box et al., 2005), for example, all keep the effect of experimental error in the blocked variables from influencing the effect of the primary variables. Other uncontrolled variables are accounted for by introducing randomization in parts of the experimental design. To study all variables and their interaction requires a factorial design, involving all possible combinations of each variable, or a fractional factorial design, involving only a selected set. Statistical techniques are then used to determine which are the important variables, what are the important interactions, and what the error is in estimating these effects. The discussion here is only a brief overview of the excellent book by Box et al. (2005). ANOVA Suppose we have two methods of preparing some product and we wish to see which treatment is better. When there are only two treatments, then the sampling analysis discussed in the section TwoPopulation Test of Hypothesis for Means can be used to deduce if the means of the two treatments differ significantly. When there are more treatments, the analysis is more detailed. The goal is to see if the treatments differ significantly from each other; that is, whether their means are different when the samples have the same variance. The hypothesis is that the treatments are all the same, and the null hypothesis is that they are different. The statistical validity of the hypothesis is determined by an analysis of variance. Example Suppose the experimental results of the four treatments are arranged as shown in the table: several measurements for each treatment. Are the treatments significantly different from each other? The data are a modified table from Box et al. (2005). Analysis of Variance: Estimating the Variance of Four Treatments

Thus, the variance of the desired quantity Y can be found. This gives an independent estimate of the errors in measuring the quantity Y from the errors in measuring each variable it depends upon. Example Suppose one wants to measure the thermal conductivity of a solid k. To do this, one needs to measure the heat flux q, the thickness of the sample d, and the temperature difference across the sample ΔT. Each measurement . has some error. The heat flux q may be the rate of electric heat input Q divided by the area A, and both quantities are measured to some tolerance. The thickness of the sample is measured with some accuracy, and the temperatures are probably measured with a thermocouple to some accuracy. These measurements are combined, however, to obtain the thermal conductivity, and it is desired to know the error in the thermal conductivity. The formula is k=

Treatment

Treatment average Grand average Sample variance

1

2

3

63 59 63

65 63 71 64 67

71 68 68 68

61.67

66.00 64.00 10.000

68.75

5.333

nt

2

2.250

4 62 61 63 56 64 56 60.33 12.267

The data for k = 4 treatments is arranged in the table. For each treatment, there are nt experiments, and the outcome of the ith experiment with treatment t is called yti. Compute the treatment average

d  Q A∆T

The variance in the thermal conductivity is then 2

3-71

2

2

 k k k k  2 σ 2k =   σ d2 +   σ Q2 +   σ 2A +  σ d  ∆T  ∆T  A  Q  AnALYSIS OF VARIAnCE (AnOVA) AnD FACTORIAL DESIGn OF EXPERIMEnTS Statistically designed experiments consider the effect of primary variables, but they also consider the effect of extraneous variables and the interactions between variables, and they include a measure of the random error. Primary variables are those whose effect you wish to determine. These variables

yt =

∑y

ti

i =1

nt

Also compute the grand average k

∑n y t

y=

t =1

N

t

k

, N = ∑ nt t =1

3-72

MATHEMATICS

Next compute the sum of squares of deviations from the average within the tth treatment nt

St = ∑ ( y ti − y t )2

Two-Level Factorial Design with Three Variables Variable Run

1

2

3

1 2 3 4 5 6 7 8

+ + + +

+ + + +

+ + + +

i =1

Since each treatment has nt experiments, the number of degrees of freedom is nt - 1. Then the sample variances are st2 =

St nt − 1

The within-treatment sum of squares is

The main effects are calculated by calculating the difference between results from all high values of a variable and all low values of a variable; the result is divided by the number of experiments at each level. For example, for the first variable

k

S R = ∑ St t =1

and the within-treatment sample variance is s R2 =

Effect of variable 1 =

SR = 8.482 N −k

Now, if there is no difference between treatments, a second estimate of s2 could be obtained by calculating the variation of the treatment averages about the grand average. Thus compute the between-treatment mean square k

ST = ∑ nt ( y t − y )2 , sT2 = t =1

ST = 69.08 k −1

Basically the test for whether the hypothesis is true hinges on a comparison of the within-treatment estimate sR2(with nR = N - k degrees of freedom) with the between-treatment estimate sT2 (with nT = k - 1 degrees of freedom). The ratio of variances sT2 /s R2 = 8.145. The test is made based on the F distribution for nT and nR degrees of freedom, FINV(α/2, nT, nR) = f (the order of the degrees of freedom is important) where Probability [1/f ≤ sT2 /s R2 ≤ f ] = α Here FINV(0.05, 3, 14) = 3.344; the rejection region is F > 3.344. Since the ratio of variances is 8.145 and larger than 3.344, the hypothesis is rejected; the four treatments are not statistically the same at the 10 percent level. Alternatively, F = 8.145 at a p value of about 0.002, and the null hypothesis is rejected. Randomized blocking can be used to eliminate the effect of some variable whose effect is of no interest, such as the batch-to-batch variation of the catalysts in the chemical reactor example. See Box et al., 2005 for details. Factorial Design To measure the effects of variables on a single outcome, a factorial design is appropriate. In a two-level factorial design, each variable is considered at two levels only, a high and low value, often designated as a + and -. The two-level factorial design is useful for indicating trends and showing interactions, and it is also the basis for a fractional factorial design. As an example, consider a 23 factorial design with 3 variables and 2 levels for each. The experiments are indicated in the factorial design table.

( y 2 + y 4 + y 6 + y 8 ) − ( y1 + y 3 + y 5 + y 7 ) 4

Note that all observations are being used to supply information on each of the main effects, and each effect is determined with the precision of a fourfold replicated difference. The advantage of a one-at-a-time experiment is the gain in precision if the variables are additive and the measure of nonadditivity if it occurs (Box et al., 2005). Interaction effects between variables 1 and 2 are obtained by calculating the difference between the results obtained with the high and low value of 1 at the low value of 2 compared with the results obtained with the high and low value of 1 at the high value of 2. The 12 interaction is

12 - interaction =

( y 4 − y 3 + y 8 − y 7 ) − ( y 2 − y1 + y 6 − y 5 ) 2

The key step is to determine the errors associated with the effect of each variable and each interaction so that the significance can be determined. Thus, standard errors need to be assigned. This can be done by repeating the experiments, but it can also be done by using higher-order interactions (such as 123 interactions in a 24 factorial design). These are assumed negligible in their effect on the mean but can be used to estimate the standard error. Then calculated effects that are large compared with the standard error are considered important, while those that are small compared with the standard error are considered to be due to random variations and are unimportant. In a fractional factorial design, one does only part of the possible experiments. When there are k variables, a factorial design requires 2k experiments. When k is large, the number of experiments can be large; for k = 5, 25 = 32. For a k this large, Box et al. (2005) do a fractional factorial design. In the fractional factorial design with k = 5, only 16 experiments are done. Cropley (1978) gives an example of how to combine heuristics and statistical arguments in application to kinetics mechanisms in chemical engineering.

DIMEnSIOnAL AnALYSIS Dimensional analysis allows the engineer to reduce the number of variables that must be considered to model experiments or correlate data. Consider a simple example in which two variables F1 and F2 have the units of force, and two additional variables L1 and L2 have the units of length. Rather than having to deduce the relation of one variable on the other three, F1 = fn(F2, L1, L2), dimensional analysis can be used to show that the relation must be of the form F1/F2 = fn(L1/L2). Thus considerable experimentation is saved. Historically, dimensional analysis can be done using the Rayleigh method or the Buckingham pi method. This brief discussion is equivalent to the Buckingham pi method but uses concepts from linear algebra; see Amundson, N. R., Mathematical Methods in Chemical Engineering, PrenticeHall, Englewood Cliffs, N.J., 1966, p. 54, for further information. The general problem is posed as finding the minimum number of variables necessary to define the relationship between n variables. Let {Qi} represent a set of fundamental units, such as length, time, force, and so on.

Let [Pi] represent the dimensions of a physical quantity Pi; there are n physical quantities. Then form the matrix αij

Q1 Q2 … Qm

[P1]

[P2]

…

[Pn]

α11 α21

α12 α22

… …

α1n α2n

αm1

αm2

…

αmn

in which the entries are the number of times each fundamental unit appears in the dimensions [Pi]. The dimensions can then be expressed as follows: [ Pi ] = Q1α1 i Q2α2 i  Qmαmi

PROCESS SIMULATIOn Let m be the rank of the α matrix. Then p = n - m is the number of dimensionless groups that can be formed. One can choose m variables {Pi} to be the basis and express the other p variables in terms of them, giving p dimensionless quantities. Example: Buckingham Pi Method—Heat-Transfer Film Coefficient It is desired to determine a complete set of dimensionless groups with which to correlate experimental data on the film coefficient of heat transfer between the walls of a straight conduit with circular cross section and a fluid flowing in that conduit. The variables and the dimensional constant believed to be involved and their dimensions in the engineering system are given below:

D

V

r

m

k

Cp

gc

1 0 -1 -1 -1

0 0 1 0 0

0 0 1 -1 0

0 1 -3 0 0

0 1 -1 -1 0

1 0 0 -1 -1

1 -1 1 0 -1

-1 1 1 -2 0

[C p ] = k 1µ −1 ; thus

NNu = f1(NPr, NRe)

in which K, a, and b are experimentally determined dimensionless constants. However, any other type of algebraic expression or perhaps simply a graphical relation among these three groups that accurately fits the experimental data would be an equally valid manner of expressing Eq. (3-100). Naturally, other dimensionless groups might have been obtained in the example by employing a different set of five repeating quantities that would not form a dimensionless group among themselves. Some of these groups may be found among those presented in Table 3-5. Such a complete set of three dimensionless groups might consist of Stanton, Reynolds, and Prandtl numbers or of Stanton, Peclet, and Prandtl numbers. Also such a complete set different from that obtained in the preceding example will result from a multiplication of appropriate powers of the Nusselt, Prandtl, and Reynolds numbers. For such a set to be complete, however, it must satisfy the condition that each of the three dimensionless groups is independent of the other two.

Here m ≤ 5, n = 8, and p ≥ 3. Choose D, V, m, k, and gc as the primary variables. By examining the 5 × 5 matrix associated with those variables, we can see that its determinant is not zero, so the rank of the matrix is m = 5; thus, p = 3. These variables are thus a possible basis set. The dimensions of the other three variables h, r, and Cp must be defined in terms of the primary variables. This can be done by inspection, although linear algebra can be used, too. hD h = is a dimensionless group k D −1 k

[ρ] = µ1V -1 D -1 ; thus

(3-100)

hD/k = K(cpm/k)a(DVr/m)b

h

[h ] = D −1 k +1 ; thus

The dimensionless group hD/k is called the Nusselt number, NNu, and the group Cpm/k is the Prandtl number, NPr. The group DVr/m is the familiar Reynolds number, NRe, encountered in fluid-friction problems. These three dimensionless groups are frequently used in heat-transfer-film-coefficient correlations. Functionally, their relation may be expressed as

It has been found that these dimensionless groups may be correlated well by an equation of the type

[Pi]

Qj

[ Pi ] hD ρVD C p µ : , , k µ Q1α1iQ1α 2 i Qmαmi k

or as

The matrix α in this case is as follows:

F M L q T

Thus, the dimensionless groups are

f(NNu, NPr, NRe) = 0

Film coefficient = h = F/LqT Conduit internal diameter = D = L Fluid linear velocity = V = L/q Fluid density = r = M/L3 Fluid absolute viscosity = m = M/Lq Fluid thermal conductivity = k = F/qT Fluid specific heat = cp = FL/MT Dimensional constant = gc = ML/Fq2

3-73

ρ ρVD = is a dimensionless group µ µ1V -1 D -1

p

Cp C pµ = is a dimensionless group k k +1µ −1

TABLE 3-5 Dimensionless Groups in the Engineering System of Dimensions Biot number Condensation number Number used in condensation of vapors Euler number Fourier number Froude number Graetz number Grashof number Mach number Nusselt number Peclet number Prandtl number Reynolds number Schmidt number Stanton number Weber number

NBi NCo NCv NEu NFo NFr NGz NGr NMa NNu NPe NPr NRe NSc NSt Nwe

hL/k (h/k)(m2/r2g)1/3 L3r2gl/(km Δt) gc(-dp)/rV 2 k q/rcL2 V2/Lg wc/kL L3r2bg ΔT/m2 V/Va hD/k DVrc/k cm/k DVr/m m/rDu h/cVr LV2r/sgc

PROCESS SIMULATIOn References:  Jana, A. K., Chemical Process Modelling and Computer Simulation, PHI Learning Pvt. Ltd., New Delhi, India, 2011; Jana, A. K., Process Simulation and Control Using Aspen, PHI Learning Pvt. Ltd., New Delhi, India, 2012; Mah, R. S. H., Chemical Process Structure and Information Flows, Butterworths-Heinemann, Oxford, 1990; Sandler, S. I., Using Aspen Plus in Thermodynamics Instruction, Wiley, New York, 2015; Schefflan, R., Teach Yourself the Basics of Aspen Plus, Wiley, New York, 2011; Seader, J. D., Computer Modeling of Chemical Processes, AIChE Monograph Series no. 15, American Institute of Chemical Engineers, New York, 1985; Seider, W. D., J. D. Seader, D. R. Lewin, and S. Widagdo, Product and Process Design Principles: Synthesis, Analysis, and Evaluation, 3d ed., Wiley, New York, 2009.

CLASSIFICATIOn Process simulation refers to the activity in which mathematical systems of chemical processes and refineries are modeled with equations, usually on the computer. The usual distinction must be made between steadystate models and transient models, following the ideas presented in the introduction to this section. In a chemical process, of course, the process is nearly always in a transient mode, at some level of precision, but when the time-dependent fluctuations are below some value, a steadystate model can be formulated. This subsection presents briefly the ideas behind steady-state process simulation (also called flowsheeting), which are embodied in commercial codes. The transient simulations are important

3-74

MATHEMATICS algebraic equations, and the latter model is an ordinary differential equation. Since streams enter at both ends, the differential equation is a two-point boundary-value problem, and numerical methods are used (see Numerical Solution of Ordinary Differential Equations as Initial-Value Problems). If one wants to model a process unit that has significant flow variation, and possibly some concentration distributions as well, one can consider using computational fluid dynamics (CFD) to do so. These calculations are very time-consuming, however, so that they are often left until the mechanical design of the unit. The exception would occur when the flow variation and concentration distribution had a significant effect on the output of the unit so that mass and energy balances couldn’t be made without it. The process units are described in greater detail in other sections of the Handbook. In each case, parameters of the unit are specified (size, temperature, pressure, area, and so forth). In addition, in a computer simulation, the computer program must be able to take any input to the unit and calculate the output for those parameters. Since the entire calculation is done iteratively, there is no assurance that the input stream is a “reasonable” one, so that the computer codes must be written to give some sort of output even when the input stream is unreasonable. This difficulty makes the iterative process even more complicated.

for designing the start-up of plants and are especially useful for the operation of chemical plants. THERMODYnAMICS The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Soave-Redlich-Kwong, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics, and Sandler (2015). It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. PROCESS MODULES OR BLOCKS At the first level of detail, it is not necessary to know the internal parameters for all the units, since what is desired is just the overall performance. For example, in a heat exchanger design, it suffices to know the heat duty, total area, and temperatures of the output streams; the details such as the percentage baffle cut, tube layout, or baffle spacing can be specified later when the details of the proposed plant are better defined. It is important to realize the level of detail modeled by a commercial computer program. For example, a chemical reactor could be modeled as an equilibrium reactor, in which the input stream is brought to a new temperature and pressure and the output stream is in chemical equilibrium at those new conditions. Or, it may suffice to simply specify the conversion, and the computer program will calculate the outlet compositions. In these cases, the model equations are algebraic ones, and you do not learn the volume of the reactor. A more complicated reactor might be a stirred tank reactor, and then you would have to specify kinetic information so that the simulation can be made, and one output would be either the volume of the reactor or the conversion possible in a volume you specify. Such models are also composed of sets of algebraic equations. A plug flow reactor is modeled as a set of ordinary differential equations as initialvalue problems, and the computer program must use numerical methods to integrate them. See Numerical Solution of Ordinary Differential Equations as Initial-Value Problems. Kinetic information must be specified, and one learns the conversion possible in a given reactor volume, or, in some cases, the volume reactor that will achieve a given conversion. The simulation engineer determines what a reactor of a given volume will do for the specified kinetics and reactor volume. The design engineer, however, wants to achieve a certain result and wants to know the volume necessary. Simulation packages are best suited for the simulation engineer, and the design engineer must vary specifications to achieve the desired output. Distillation simulations can be based on shortcut methods, using correlations based on experience, but more rigorous methods involve solving for the vapor-liquid equilibrium on each tray. The shortcut method uses relatively simple equations, and the rigorous method requires solution of huge sets of nonlinear equations. The computation time of the latter is significant, but the rigorous method may be necessary when the chemicals you wish to distill are not well represented in the correlations. Then the designer must specify the number of trays and determine the separation that is possible. This, of course, is not what she or he wants: the number of trays needed to achieve a specified objective. Thus, again, some adjustment of parameters is necessary in a design situation. Absorption columns can be modeled in a plate-to-plate fashion (even if it is a packed bed) or as a packed bed. The former model is a set of nonlinear

PROCESS TOPOLOGY A chemical process usually consists of a series of units, such as distillation towers, reactors, and so forth (see Fig. 3-65). If the feed to the process is known and the operating parameters of the units are specified by the user, then one can begin with the first unit, take the process input, calculate the unit output, carry that output to the input of the next unit, and continue the process. However, if the process involves a recycle stream, as nearly all chemical processes do, then when the calculation is begun, it is discovered that the recycle stream is unknown. This situation leads to an iterative process: the flow rates, temperature, and pressure of the unknown recycle stream are guessed, and the calculations proceed as before. When one reaches the end of the process, where the recycle stream is formed to return to the first unit, it is necessary to check to see if the recycle stream is the same as assumed. If not, an iterative procedure must be used to cause convergence. Possible techniques are described in Numerical Solutions of Nonlinear Equations in One Variable and Numerical Solution of Simultaneous Equations. The direct method (or successive substitution method) just involves calculating around the process over and over. The Wegstein method accelerates convergence for a single variable, and Broyden’s method does the same for multiple variables. The Newton method can be used provided there is some way to calculate the derivatives (possibly by using a numerical derivative). Optimization methods can also be used (see Optimization in this section). In the description given here, the recycle stream is called the tear stream: this is the stream that must be guessed to begin the calculation. When there are multiple recycle streams, convergence is even more difficult, since more guesses are necessary, and what happens in one recycle stream may cause difficulties for the guesses in other recycle streams. See Seader (1985) and Mah (1990). It is sometimes desired to control some stream by varying an operating parameter. For example, in a reaction/separation system, if there is an impurity that must be purged, a common objective is to set the purge fraction so that the impurity concentration into the reactor is kept at some moderate value. Commercial packages contain procedures for doing this, using what are often called control blocks. However, this can also make the solution more difficult to find. An alternative method of solving the equations is to solve them as simultaneous equations. In that case, one can specify the design variables and the desired specifications and let the computer figure out the process parameters that will achieve those objectives. It is possible to overspecify the system or to give impossible conditions. However, the biggest drawback to

6 6

6 2

1 Mixer

4 Reactor 3

FIG. 3-65

Prototype flowsheet.

5 Separator

PROCESS SIMULATIOn this method of simulation is that large sets (tens of thousands) of nonlinear algebraic equations must be solved simultaneously. As computers become faster, this is less of an impediment, provided efficient software is available. Dynamic simulations are also possible, and these require solving differential equations, sometimes with algebraic constraints. If some parts of the process change extremely quickly when there is a disturbance, that part of the process may be modeled in the steady state for the disturbance at any instant. Such situations are called stiff, and the methods for them are discussed in Numerical Solution of Ordinary Differential Equations as Initial-Value Problems. It must be realized, though, that a dynamic calculation can also be time-consuming, and sometimes the allowable units are lumped-parameter models that are simplifications of the equations used for the steady-state analysis. Thus, as always, the assumptions need to be examined critically before accepting the computer results. The dynamic simulators can also be used to simulate operations with the objective to maintain purity and standards of the product.

3-75

COMMERCIAL PACKAGES Computer programs are provided by many companies, and they range from empirical models to deterministic models. For example, if one wanted to know the pressure drop in a piping network, one would normally use a correlation for friction factor as a function of Reynolds number to calculate the pressure drop in each segment. A sophisticated turbulence model of fluid flow is not needed in that case. As computers become faster, however, more and more models are deterministic. Since the commercial codes have been used by many customers, the data in them have been verified, but possibly not for the case you want to solve. Thus, you must test the thermodynamics correlations carefully. In 2015, there were a number of computer codes, but the company names change constantly. Here are a few of them for process simulation: Aspen Tech (Aspen Plus), Chemstations (CHEMCAD), Honeywell (UniSim Design), ProSim (ProSimPlus), and Pro II. The CAPE-OPEN project is working to make details as transferable as possible.

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Section 4

Thermodynamics

J. Richard Elliott, Ph.D. Professor, Department of Chemical and Biomolecular Engineering, University of Akron; Member, American Institute of Chemical Engineers; Member, American Chemical Society; Member, American Society of Engineering Educators (Section Coeditor) Carl T. Lira, Ph.D. Associate Professor, Department of Chemical and Materials Engineering, Michigan State University; Member, American Institute of Chemical Engineers; Member, American Chemical Society; Member, American Society of Engineering Educators (Section Coeditor) Timothy C. Frank, Ph.D. Fellow, The Dow Chemical Company; Fellow, American Institute of Chemical Engineers (Section Coeditor) Paul M. Mathias, Ph.D. Senior Fellow and Technical Director, Fluor Corporation; Fellow, American Institute of Chemical Engineers (Section Coeditor)

InTRODUCTIOn Elementary Variables and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . System or Control Volume.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Density r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Internal Energy U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heat Capacity at Constant Volume CV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy H .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heat Capacity at Constant Pressure CP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Expansion/Contraction Work WEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass, Energy, and Entropy Balances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-4 4-4 4-4 4-4 4-4 4-4 4-4 4-4 4-4 4-5 4-5

GEnERAL BALAnCES The Mass Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass Balances for Chemical Manufacturing Processes. . . . . . . . . . . . . . . . . . . . . Example 4-1 Mass Balances for the DME Process . . . . . . . . . . . . . . . . . . . . . . . . . Introductory State Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phase Changes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The General Energy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Balances for Closed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 4-2 Adiabatic Reversible Compression of Air . . . . . . . . . . . . . . . . . . . . . Energy Balances for Steady-State Flow Processes . . . . . . . . . . . . . . . . . . . . . . . . . . Example 4-3 Continuous Adiabatic Reversible Compression of Air. . . . . . . . . Energy Balances for Chemical Manufacturing Processes . . . . . . . . . . . . . . . . . . . Example 4-4 Energy Balances for the DME Process. . . . . . . . . . . . . . . . . . . . . . . . The General Entropy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Entropy Balances for Composite Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 4-5 Carnot Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental Relations of Classical Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . The Fundamental Property Relation for Pure Fluids . . . . . . . . . . . . . . . . . . . . . . . Relations Using Desired Independent Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-5 4-5 4-5 4-6 4-6 4-6 4-6 4-7 4-7 4-7 4-7 4-7 4-8 4-8 4-8 4-8 4-8 4-9

Balance Applications to Flow Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Duct Flow of Compressible Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nozzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Throttling Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Turbines (Expanders) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 4-6 Turbine Process Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compressors.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-9 4-9 4-9 4-9 4-9 4-9 4-9 4-10

PROPERTY CALCULATIOnS FROM EQUATIOnS OF STATE Departure Functions from PVT Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chemical Potential, Fugacity, and Fugacity Coefficient . . . . . . . . . . . . . . . . . . . . . . . Applications of Departure Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Virial Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Extended Virial and Multiparameter Equations . . . . . . . . . . . . . . . . . . . . . . . . . Cubic Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 4-7 Estimating Enthalpy Using the PR EOS . . . . . . . . . . . . . . . . . . . . . . Pitzer (Lee-Kesler) Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wertheim’s Theory and SAFT Equations of State: . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid-Phase Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-10 4-10 4-11 4-11 4-11 4-11 4-12 4-12 4-13 4-13

SYSTEMS OF VARIABLE COMPOSITIOn Chemical Potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Molar Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Gibbs-Duhem Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of Ideal Gas Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Component Fugacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ideal Solution Model and Henry’s Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phase Equilibria Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phase Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 4-8 Application of the Phase Rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-13 4-14 4-14 4-14 4-14 4-14 4-15 4-15 4-15

The contributions of Profs. Hendrick C. van Ness and Michael A. Abbott, Section Editors, 8th ed., are acknowledged. 4-1

4-2

THERMODYnAMICS

Approaches for Phase and Reaction Equilibria Modeling . . . . . . . . . . . . . . . . . . . . . Component Fugacity and Activity Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . Excess Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Property Changes of Mixing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Excess and Departure Property Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Component Fugacity Coefficients from an EOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 4-9 Derivation of Fugacity Coefficient Expressions . . . . . . . . . . . . . . . Correlative Models for the Excess Gibbs Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Margules, Wilson, NRTL, UNIQUAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phase Equilibrium Data Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Data Reduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Predictive and Adaptive Models for the Excess Gibbs Energy . . . . . . . . . . . . . . . . . Predictive Models: UNIFAC, Solubility Parameter Models, COSMO . . . . . . . . . Adaptive Models LSER, NRTL-SAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Estimation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Model Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preliminary Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robbins’ Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 4-10 Entrainer Selection for Extractive Distillation . . . . . . . . . . . . . . . Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vapor/Liquid Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K Values, VLE, and Flash Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma/Phi Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Raoult’s Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modified Raoult’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 4-11 Bubble, Dew, Azeotrope, and Flash Calculations . . . . . . . . . . . . Equation-of-State Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-16 4-16 4-16 4-17 4-17 4-17 4-17 4-17 4-18 4-19 4-19 4-19 4-19 4-21 4-21 4-21 4-21 4-21 4-22 4-22 4-23 4-23 4-23 4-23 4-23 4-24 4-24

Solute/Solvent Systems—Henry’s Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 4-12 Solubility of Oxygen in Water by Henry’s Law . . . . . . . . . . . . . . . Example 4-13 Solubility of Hydrogen in Hydrocarbons . . . . . . . . . . . . . . . . . . . . Liquid/Liquid and Vapor/Liquid/Liquid Equilibria. . . . . . . . . . . . . . . . . . . . . . . . . . .

4-25 4-26 4-27 4-27

TREnDS In PHASE BEHAVIOR Pure Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-28 4-28

TEMPERATURE DEPEnDEnCE OF InFInITE-DILUTIOn ACTIVITY COEFFICIEnTS Fundamental Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-31 4-31

THERMODYnAMICS FOR COnCEPTUAL DESIGn Prediction of Species Partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-33

REACTInG SYSTEMS Chemical Reaction Stoichiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chemical Reaction Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Standard Property Changes of Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equilibrium Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 4-14 Single-Reaction Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Complex Chemical Reaction Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Henry’s Law for Reacting Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-33 4-33 4-33 4-34 4-35 4-35 4-35

THERMODYnAMICS nomenclature and Units

Symbol

Definition

A

Molar (or unit-mass) Helmholtz energy† or dimensionless equation of state parameter Cross-sectional area in flow Activity of species i in solution 2d virial coefficient or dimensionless equation of state parameter Interaction 2d virial coefficient Heat capacity at constant pressure Heat capacity at constant volume Fugacity of pure species i Fugacity of species i in solution Molar (or unit-mass) Gibbs energy† Acceleration of gravity Molar (or unit-mass) enthalpy† Henry’s volatility constant for solute species at T and P ° Equilibrium K value, yi/xi Equilibrium constant for chemical reaction j Henry’s solubility constant for solute species i in molal units Molar or unit-mass solution property† (A, G, H, S, U, V ) Molar or unit-mass pure-species property† (Ai, Gi, Hi, Si, Ui, Vi) Partial property of species i in solution

Ax ai B Bij CP CV fi ˆf i G g H hi Ki Ka,j kH,i M Mi

Mi

Correlation- and application-specific symbols are not shown . SI units J/mol [J/kg]

U .S . Customary System units Btu/lb ⋅ mol [Btu/lbm]

ME

M iE ∆M ∆ Mj° m m n n ni P Pi sat q Q Q R †

Symbol

Definition

S

Molar (or unit-mass) entropy† Rate of entropy generation per mole or unit mass† Temperature Critical temperature Molar (or unit-mass) internal energy† Fluid velocity Molar (or unit-mass) volume† Work per mole or unit mass† Shaft work for flow process† Shaft power for flow process† Mole fraction in general Mole fraction of species i in liquid phase Mole fraction of species i in vapor phase Compressibility factor Elevation above a datum level

Sgen

m2

ft2

Dimensionless

Dimensionless

cm3/mol

cm3/mol

cm3/mol

cm3/mol

v V

J/(mol ⋅ K)

Btu/(lb ⋅ mol ⋅ °R)

W

J/(mol ⋅ K)

Btu/(lb ⋅ mol ⋅ °R)

W s

kPa kPa

psi psi

J/mol [J/kg]

kPa

Btu/(lb ⋅ mol) [Btu/lbm] ft/s2 Btu/(lb ⋅ mol) [Btu/lbm] psi

Dimensionless Dimensionless

Dimensionless Dimensionless

mol/kg ⋅ kPa

mol/kg ⋅ psi

m/s2 J/mol [J/kg]

T Tc U

W S xi xi yi Z z

SI units

U.S. Customary System units

J/(mol ⋅ K) [J/(kg ⋅ K)] J/(K ⋅ mol ⋅ s) [J/(K ⋅ kg ⋅ s)]

Btu/(lb ⋅ mol ⋅ °R) [Btu/(lbm ⋅ °R)] Btu/(lb ⋅ mol ⋅ °R ⋅ s) [Btu/(lbm ⋅ °R ⋅ s)]

K K J/mol [J/kg]

J/(mol ⋅ s) [J/(kg ⋅ s]

°R °R Btu/(lb ⋅ mol) [Btu/lbm] ft/s ft3/(lb ⋅ mol) [ ft3/lbm] Btu/lb ⋅ mol [Btu/lbm] Btu/lb ⋅ mol [Btu/lbm] Btu/(lb ⋅ mol ⋅ s) [Btu/(lbm ⋅ s)]

Dimensionless m

Dimensionless ft

m/s m3/mol [m3/kg] J/mol [J/kg] J/mol [J/kg]

Superscripts cond dep E id ig L V vap ∞

Condensed phase, e.g. liquid or solid Departure thermodynamic property Excess thermodynamic property Value for an ideal solution Value for an ideal gas Liquid phase Vapor phase Phase transition, liquid to vapor Value at infinite dilution Subscripts

( Ai ,Gi , H i , Si ,U i ,Vi )

M dep

4-3

Departure thermodynamic property† (Adep, G dep, H dep, S dep, U dep, V dep) Excess thermodynamic property† (AE, G E, H E, S E, U E, V E ) Partial molar excess thermodynamic property Property change of mixing† (∆ A, ∆G, ∆H, ∆S, ∆U, ∆V ) Standard property change of reaction j (∆Gj°, ∆Hj°, ∆CPj°) Mass Mass flow rate Number of moles Molar flow rate Number of moles of species i Pressure Saturation or vapor pressure of species i Quality (vapor fraction) Heat per mole or mass†

kPa kPa

psi psi

Dimensionless J/mol [J/kg]

Rate of heat transfer per mole or mass† Universal gas constant

J/(mol ⋅ s) [J/kg ⋅ s] J/(mol ⋅ K)

Dimensionless Btu/lb ⋅ mol [Btu/lbm] Btu/(lb ⋅ mol ⋅ s) [Btu/(lbm ⋅ s)] Btu/(lb ⋅ mol ⋅ °R)

c cv fs n r R

Value for the critical state Control volume Flowing streams Normal boiling point Reduced value Reference state

α, b

As superscripts, identify phases Volume expansivity Reaction coordinate for reaction j Heat capacity ratio CP/CV Activity coefficient of species i in solution for the Lewis-Randall rule, a superscript * denotes Henry’s law activity coefficient Isothermal compressibility Chemical potential of species i Stoichiometric number of species i in reaction j Molar or mass density

Greek Letters

b εj g gi kg kg/s

lbm lbm/s κ μi νi,j r fi φˆ i ω

When underlined, denotes extensive thermodynamic property [e .g ., energy] or total work or heat [e .g ., energy] .

Fugacity coefficient of pure species i Fugacity coefficient of species i in solution Acentric factor

K-1 mol

°R-1 lb ⋅ mol

Dimensionless Dimensionless

Dimensionless Dimensionless

kPa-1

psi-1

J/mol

Btu/(lb ⋅ mol)

Dimensionless

Dimensionless

mol/m3 [kg/m3] Dimensionless

lb ⋅ mol/ft3 [lbm/ft3] Dimensionless

Dimensionless

Dimensionless

Dimensionless

Dimensionless

General References: 1. Abbott, M. M., and H. C. Van Ness, Schaum’s Outline of Theory and Problems of Thermodynamics, 2d ed., McGraw-Hill, New York, 1989. 2. Chen, C.-C., and P. M. Mathias, “Applied Thermodynamics for Process Modeling,” AIChE J . 48(2): 194–200 (2002). 3. Elliott, J. R., and C. T. Lira, Introductory Chemical Engineering Thermodynamics, 2d ed., Prentice Hall PTR, Upper Saddle River, N.J., 2012. 4. O’Connell, J. P., and J. M. Haile, Thermodynamics . Fundamentals for Applications, Cambridge University Press, London, 2005. 5. Poling, B. E., J. M. Prausnitz, and J. P. O’Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, 2001. 6. Prausnitz, J. M., R. N. Lichtenthaler, and E. G. de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 3d ed., Prentice-Hall PTR, Upper Saddle River, N.J., 1999.

7. Rafal, M., J. E. Berthold, N. C. Scrivner, and S. L. Grise, “Models for Electrolyte Solutions,” in Models for Thermodynamic and Phase Equilibria Calculations, ed. S. I. Sandler, Marcel Dekker, New York, 1994. 8. Sandler, S. I., Chemical, Biochemical, and Engineering Thermodynamics, 4th ed., Wiley, Hoboken, N.J., 2006. 9. Smith, J. M., H. C. Van Ness, and M. M. Abbott, Introduction to Chemical Engineering Thermodynamics, 7th ed., McGraw-Hill, New York, 2005. 10. Tester, J. W., and M. Modell, Thermodynamics and Its Applications, 3d ed., Prentice-Hall PTR, Upper Saddle River, N.J., 1997. 11. Walas, S. M., Phase Equilibria in Chemical Engineering, Butterworth-Heinemann, Boston, 1985. 12. Van Ness, H. C., and M. M. Abbott, Classical Thermodynamics of Nonelectrolyte Solutions: With Applications to Phase Equilibria, McGraw-Hill, New York, 1982.

InTRODUCTIOn Thermodynamics is the branch of science that deals with energy transformation and the state of equilibrium in macroscopic systems. The laws of thermodynamics are shown by experience to apply to all such transformations. The first law states that energy can take many forms, but it cannot be created or destroyed (except that nuclear reactions may contribute components outside the norm). The second law concerns the distribution of the energy and of the material components comprising a system, traditionally described in terms of the order or disorder of the system. It states that maintaining a nonequilibrium or unnaturally ordered state requires work. The systematic analysis of these two laws leads to profound insights pervading chemistry, physics, and biology, especially when combined with molecular insights through statistical thermodynamics. In the context of chemical engineering, it is important to include one additional conservation law, the material balance. Similar to energy, mass is neither created nor destroyed in (nonnuclear) systems. The material balance is not technically a law of thermodynamics, but it is necessary to fully characterize the equilibrium systems that are central to thermodynamics. While the first law of thermodynamics is the basis for the energy balance, the second law is the basis for the concept of entropy. The second law states that the entropy of the universe (defined in terms of reversible heat flow divided by absolute temperature) must increase through the conduct of any practical process, meaning that the entropy of individual subsystems may increase or decrease but the sum of entropy changes across all subsystems and surroundings must increase. As a consequence, thermal energy spontaneously flows from a hotter body to a cooler one, and statistical mechanics indicates a general tendency for a system to move toward spatial homogeneity. Energy, on the other hand, has a tendency to pull things together. Molecules are attracted to one another as evidenced by the energy of vaporization required to increase the intermolecular distances when converting liquid to vapor. Thus, nature exhibits a competition between energetic and entropic driving forces when temperature and pressure are fixed. When these competing driving forces are perfectly balanced, the situation is described as equilibrium. A simple form of equilibrium is evidenced by a vapor in equilibrium with a liquid at its boiling point. Entropy is driving the molecules toward the vapor while energy is pulling molecules into the liquid. At a given temperature for a pure fluid, the rate of evaporation equals the rate of condensation at one specific pressure, comprising equilibrium, and referred to as the saturation pressure or vapor pressure. Remarkably, the same equations and concepts of energy, entropy, and equilibrium describe all the phenomena of phase equilibria in mixtures. Tracing the energy transformations through a process is relatively straightforward. However, mixing and separation become quite complicated in the presence of aqueous streams mixed with organic compounds and possibly electrolytes, the mixing of which may form multiple solid, liquid, or vapor phases. The application of thermodynamic theory in chemical engineering practice yields models describing all these different phases at equilibrium. A deviation from the equilibrium composition is the driving force for many chemical separation processes, and many are modeled as equilibrium staged processes even when perfect equilibrium is not achieved at any particular point in the process. As a real process can only approach equilibrium (the thermodynamic limit), such an analysis allows the process designer to characterize separation difficulty and the magnitude of the opportunity for further improvement. Another form of equilibrium in mixtures occurs when one considers that individual atoms can be rearranged within and among molecules, also known as chemical reaction equilibrium. By controlling the components in a mixture and through the use of catalysts that favor selected pathways, 4-4

chemical engineers can synthesize desirable products from crude raw materials on a very large scale. Each step in the synthesis process is constrained by reaction thermodynamics. The desired products can be formed only if the equilibrium constant is favorable. The mass, energy, and entropy balances of multicomponent, multiphase, reacting systems at thermodynamic equilibrium comprise significant coverage of the chemical engineering discipline. The rates at which systems move toward equilibrium comprise another fundamental field of study, and often an analysis of process performance requires an assessment as to which phenomenon is the dominant factor controlling performance—the equilibrium state or the rate of mass transfer or chemical reaction exhibited by a system in moving toward that state ( for fundamentals, see Sections 5-7). Identifying and addressing key equilibrium limitations and/or rate-limiting resistances is a fundamental approach to improving process designs. For most chemical engineers, a process simulator is the primary interface for engaging thermodynamics. The intent of this section is to expose the thermodynamics while simplifying the computational rigor, with the emphasis placed on nonelectrolyte systems. ELEMEnTARY VARIABLES AnD DEFInITIOnS It is necessary to define several common quantities before developing the key equations to be applied in further analysis. Mass m Mass is the magnitude of the interaction of a physical body in response to an external force. (We ignore relativistic influences in this discussion.) Commonly, the external force is gravity, and the mass is given by the weight at sea level. The mass also describes the resistance of the body to acceleration in the presence of any force, as in F = ma. System or Control Volume A region in space that identifies the portion of the universe under consideration at a particular juncture. Density q The mass or moles per unit volume. We use the same symbol r for both mass and molar density where the units are inferred by the particular context. Pressure P The force per unit area of molecules on the surface of their container. Internal Energy U Energy can be transformed into many forms, such as work, heat, or kinetic energy. To be clear, it is necessary to define each form of energy distinctly. To begin, internal energy is energy inherent to a system as determined by the kinetic and intermolecular potential energy of its constituent molecules. The kinetic energy of the molecules is described below in terms of temperature. The intermolecular potential energy arises from the tendency of molecules to attract and repel one another. Attractions are responsible for the heat of vaporization. Repulsions explain why “you can’t put two things in the same place at the same time.” Depending on the reference state, U may also include the energy of forming the molecule from the elements. Heat Capacity at Constant Volume C V CV ≡ (∂U/∂T )V The translational and vibrational molecular energies are largely unaffected by changes in density and can be represented by the ideal gas heat capacity CVig . The departures of internal energy and heat capacity from ideal gas behavior are discussed in the subsection Departure Functions from PVT Correlations . Enthalpy H Enthalpy is a combination of internal energy, pressure, and molar volume (H ≡ U + PV) that is convenient for computations involving systems that are classified as “open,” as defined shortly after Eq . (4-3) . Note that molar volume V is the reciprocal of molar density . Heat Capacity at Constant Pressure CP CP ≡ (∂H/∂T)P Similar to the heat capacity at constant volume, the enthalpy of a fluid varies with

GEnERAL BALAnCES temperature. Empirical equations relating C Pig to T are available for many pure gases; a common form is either a polynomial like Eq. (4-1) or the form used by DIPPR, Eq. (4-2) (R. L. Rowley et al., DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, 2006) C Pig = A + BT + CT 2 + DT 3 + ET 4 2

 E /T   C /T  C Pig = A + B   + D  cosh( E /T )     sinh(C /T ) 

(4-1) 2

(4-2)

where A, B, C, D, and E are constants characteristic of the particular gas, and for Eq. (4-2) either C or D is zero. The DIPPR form derives from the plateaus inherent in heat capacity due to quantum energy levels [Aly, F. A., and L. L. Lee, Fluid Phase Equilibr. 6: 169 (1981)].

4-5

Expansion/Contraction Work WEC Work interaction of the system with the surroundings due to force at the surface of interaction through a distance is given by WEC = −∫ P dV

(4-3)

Mass, Energy, and Entropy Balances Mass, energy, and entropy balances for any system are written with respect to a region of space known as a system or control volume, bounded by an imaginary control surface that separates it from the surroundings, forming a system or subsystem . This surface may follow fixed walls or be arbitrarily placed; it may be rigid or flexible . A primary step in any chemical process analysis or design is the mass balance . A system is defined as open if any mass crosses the system boundary . If the mass flowing into the system equals the mass flowing out, and all intensive (state) variables are invariant with time at all positions within the system, then the system is said to be at steady state .

GEnERAL BALAnCES THE MASS BALAnCE Because mass is conserved, the time rate of change of mass within the control volume equals the net rate of flow of mass into the control volume (cv) . The flow is positive when directed into the control volume and negative when directed out . The mass balance is expressed mathematically by

∑

m i dt = d (mcv )

streams

1

2

3

4

(4-4) 7

6

5

The mass flow rate m can be expressed in terms of the stream velocity as m i = (ρvAx )i [=] kg/s

8

(4-5)

11

Substitution gives ∆(ρvAx )f s =

dmcv dt

10

(4-6)

The operator ∆ signifies the difference between exit and entrance flows, and the subscript fs indicates that the term encompasses all flowing streams . This form of the mass balance equation is often called the continuity equation, an important equation in the analysis of transport processes, such as fluid flow or absorption . For the special case of steady-state flow, the control volume contains a constant mass of fluid, and the right-hand side of Eq . (4-6) is zero . Additional constraints for steady-state systems are discussed in the subsection The General Energy Balance . Mass Balances for Chemical Manufacturing Processes Mass balances can be especially useful for multicomponent processes of multiple-unit operations . A spreadsheet calculation can suffice for many applications . A process flow diagram (PFD) is required, representing the unit operations and streams connecting them . Figure 4-1 shows a sample PFD for the dimethyl ether (DME) synthesis process (2CH3OH → CH3OCH3 + H2O) . Streams are numbered to provide unique identifiers . The masses in each stream are computed sequentially, depending on the unit operation . For example, the mass of each component in stream 2 is the sum of the component mass entering from stream 1 and stream 11 . Note that the flow of stream 11 may not be known at the outset, requiring an iterative process to determine its value . As another example, the mass of methanol in stream 5 is determined from the fractional conversion specification for methanol (X ), and the masses of the other components are determined by the reaction stoichiometry . The flow rates of components in streams 8 and 9 are determined from the split specifications on the distillation column . The split is defined as the fraction of the component that exits the column as distillate . The light key component is the least volatile component that has a split fraction greater than 0 .5 . In consequence, any components more volatile than the light key are often assumed to exit completely in the distillate with a split of 100 percent . Similarly, the heavy key is the most volatile component that has a split fraction less than 0 .5, and components less volatile than the heavy key are often assumed to exit the column with a split of 0 percent . The requisite computations to complete the mass balance are illustrated in Example 4-1 .

9 12 FIG. 4-1

PFD for DME synthesis .

Example 4-1 Mass Balances for the DME Process Dimethyl ether (DME) synthesis provides a simple prototype of many petrochemical processes . Ten tonnes (10,000 kg) per hour of methanol are fed at 25°C . The entire process operates at roughly 10 bar . The feed stream is mixed with the recycle stream (11), compressed and passed through a heat exchange to form stream 4 at 75°C . The methanol is 50 percent converted to DME and water at 250°C . The reactor effluent is cooled to 75°C and sent to a distillation column where 99 percent of the entering DME exits the top with 1 percent of the entering methanol and no water . This DME product stream (8) exits as liquid at 44°C while the bottom stream (9) exits at 152°C . The bottoms of the first column (9) are sent to a second column where 99 percent of the entering methanol exits the top as liquid at 136°C, along with all DME and 1 percent of the entering water, and is recycled . The bottoms of the second column exit at 179°C and are sent for wastewater treatment . Determine the masses of each component in each stream . Solution A preliminary step is to write the reaction stoichiometry: 2CH3OH → H2O + DME . Since the reaction requires mass balances in terms of molar stoichiometry, we convert 10,000 kg/h to 312 .11 kmol/h for stream 1 . The solution for stream 2 depends on the recycle stream, for which the flow is not known at the outset . Modern spreadsheets facilitate an iterative solution for the recycle stream . Making an initial guess that 50 percent of the feed methanol (156 .05 kmol/h) is being recycled in stream 11 with zero DME or H2O gives a flow of 468 .16 for stream 2, as tabulated below . With 50 percent conversion of the methanol in stream 2, the tabulated flows of methanol, DME, and H2O in stream 5 are obtained . The masses are unaffected by the heat exchanger, resulting in stream 7 . Applying the 99 and 1 percent splits gives the flow of streams 8 and 9 . Similar computations give the flow of streams 11 and 12, at which point we note that the initial guess for stream 11 was substantially in error . At this point, the correct component masses of stream 11 could be added to stream 1 and the next iteration could proceed . Alternatively, Microsoft Excel offers an “iteration” feature that can be enabled through the calculation options . Implementing this feature leads to the mass flows (kmol/h) in the second table .

4-6

THERMODYnAMICS

Initial guess assuming 156.05 kmol/h MeOH recycle. Stream

1

2

5

7

8

9

T (°C) Methanol DME H2O

25.0 312.11 0.00 0.00

73.3 468.16 0.00 0.00

250.0 234.08 117.04 117.04

75.0 234.08 117.04 117.04

44.0 2.34 115.87 0.00

152.0 231.74 1.17 117.04

11

12

136.0 179.0 229.42 2.32 1.17 0.00 1.17 115.87

Final result after iterating stream 11 to convergence. Stream

1

2

5

7

8

9

11

T (°C) Methanol DME H2O

25.0 312.11 0.00 0.00

80.9 612.04 1.55 1.55

250.0 306.02 154.56 154.56

75.0 306.02 154.56 154.56

45.0 3.06 153.01 0.00

152.0 302.96 1.55 154.56

For equation of state modeling of vapor phases, mixing process are usually included in the mixture departure function, resulting in H V = ( H V − H ig )T + T f ]. For equation of state modeling of liquid phases, ∑i x i [ ∫ 298.15C P dT + ∆ H 298.15 the mixing, pressure correction, and vaporization terms are included in the departure function, H L = ( H L − H ig )T + ∑ x i [ ∫ i

∆H vap = T ∆V vap

PV = RT or PV = nRT

dP sat dT

(4-13)

Known as the Clapeyron equation, this exact thermodynamic relation provides the connection between the properties of the liquid and vapor phases at saturation. An empirical parameter frequently used in characterization of fluid properties is the acentric factor, defined by

InTRODUCTORY STATE CALCULATIOnS Values of energy require calculation of fluid properties for each component relative to the reference state, plus the property state changes involved in mixing components. For changes in state properties in nonreactive systems, the reference state drops out. However, for reactive systems, the reference states must be included. The energy balances are generalized most easily by including a reference state of the elements that comprise each molecule in the stream. Most process simulators default to use a reference state of the elements in their naturally occurring state at 1 bar and 298.15 K. For expediency, we provide ideal gas properties here to introduce the energy balances and in subsection Departure Functions for PVT Relations we discuss the contributions due to nonideal gas behavior. For an ideal gas,

f C P dT + ∆H 298.15 ].

Phase Changes Vaporization of a pure fluid occurs at constant temperature at the species vapor pressure P sat(T). The heat of vaporization is directly related to the slope of the vapor-pressure curve.

12

139.0 179.0 299.93 3.03 1.55 0.00 1.55 153.01

T 298.15

ω ≡ −1 − log ( P sat /Pc ) T =0.7

(4-14)

r

where Tr ≡ T /Tc   is the reduced temperature. In application, an empirical vapor pressure versus temperature relation is commonly used such as the Antoine equation log ( P sat ) = A −

B T +C

(4-15)

Experimentally, log P sat is not quite linear with 1/T (in K −1); however, use of Eq. (4-15) with C = 0 and T in K is also sufficient for interpolation between reasonably spaced values of T. The acentric factor can be used for crude estimates of vapor pressure by neglecting the slight curvature

(4-7)

log ( P sat /Pc ) = (7/3)(1 + ω)(1 − Tc /T )

(4-16)

Using a reference state of the elements at 298.15 K and 1 bar, T

U ig =

∫C

f dT + ∆U 298.15

V

(4-8)

298.15

where ∆U is the energy of formation. More typically for flow problems, the enthalpy is used. Enthalpy is defined for convenience because the combination U + PV appears often: f 298.15

H ≡ U + PV

(4-9)

The enthalpy change of an ideal gas is

where T is in Kelvin. This approximation is sometimes referred to as Wilson’s vapor pressure equation, but the exact attribution has been lost. More accurate equations are listed in the correlations of Sec. 2. Accurate correlations for ∆H vap are available in Sec. 2, but in this section we apply a simple approximation ∆H vap = 7(1 − Tr )0.354 + 11ω (1 − Tr )0.456 RTc

when

P > P sat

(4-17)

Equations (4-16) and (4-17) are accurate to roughly 15 percent for hydrocarbons when Tr > 0.5.

T2

∆H ig = ∫ C P dT

(4-10)

T1

The enthalpy of an ideal gas is T

H ig =

∫C

P

f dT + ∆H 298.15

(4-11)

298.15

f is the enthalpy of formation. Enthalpies of formation are where ∆H 298.15 commonly available (c.f. Sec. 2, Tables 2-94 and 2-95). The energy of formation can be calculated from the enthalpy of formation by adapting Eq. (4-9), f f ∆U 298.15 = ∆H 298.15 − ∆( PV ) , where the PV term is on the basis of 1 mol of the substance being formed. The PV term is typically negligible for condensed phases (e.g., solid carbon), and the value is RT for each mole of ideal gas, so the correction term can typically be written ∆n ig RT when the formation reaction stoichiometry is balanced for 1 mol of the substance being formed. Gas-phase nonidealities are calculated with the departure function at the same temperature and pressure, denoted for enthalpy as ( H − H ig ) as discussed in the subsection Departure Functions from PVT Calculations T f V V ig resulting in H V = ∆H mix C P dT + ∆H 298.15 ]. For ,T + ∑i x i [( H − H )T + ∫ 298.15 condensed phases the enthalpy of phase transformations are added (subsection Phase Changes), and any state changes of mixing (subsection Property Changes of Mixing) and a pressure correction. Mixing changes are large for acids, bases, and salts with water, but are generally a small contribution for organic mixture streams. When mixing changes are included, the enthalpy of a liquid stream with conventional liquid components would be vap L V L sat ig H L = ∆H mix ,T + ∑ x i [Vi ( P − Pi ,T ) − ∆H T + ( H − H )T + i

T

∫

f C P dT + ∆H 298.15 ]

298.15

(4-12)

THE GEnERAL EnERGY BALAnCE Because energy, like mass, is conserved, the time rate of change of energy within the control volume equals the net rate of energy transfer into the control volume. Streams flowing into and out of the control volume have energy associated with them in the internal, potential, and kinetic forms, and all contribute to the energy change of the system. Energy may also flow across the control surface as heat and work. General References 1, 3 through 6, and 8 through 12 show that the general energy balance for flow processes is   v 2 zg  d  m U + +  2 g c g c  cv   dt

= Q + W +

 v 2 zg   +  m   H + 2 gc gc  i   streams

∑

(4-18)

The work rate W may be of several forms. Most commonly there is shaft work W s . Work may be associated with expansion or contraction of the control volume, and there may be stirring work. Note that when a gas expands from inlet to outlet across a pressure drop, flow work is inherently included in the definition of enthalpy and not the work term. The velocity v in the kinetic energy term is the bulk mean velocity as defined by the equation v = m / (ρAx ); z is elevation above a datum level, g is the local acceleration of gravity, and gc is the gravitational units conversion constant. Energy Balances for Closed Systems In closed systems, all mass flows across system boundaries are zero, so the last term of Eq. (4-18) is zero. The simplified energy balance then becomes   v 2 zg  d  m U + +  = Q dt + W dt 2 g c g c cv  

(4-19)

GEnERAL BALAnCES The most common form of energy balance is obtained by noting that changes in the velocity and altitude of most systems are usually negligible when temperature changes are present. Noting that Q ≡ ∫ Q dt and W ≡ ∫ W dt , we find that ∆U = Q + W

(4-20)

Example 4-2 Adiabatic Reversible Compression of Air One stroke of a positive displacement compressor is analogous to the piston-cylinder arrangement of a bicycle pump. If the stroke is fast enough, heat transfer can be neglected for the purpose of a single stroke. Suppose a pump is 35 cm long and has a 3-cm diameter with ambient air initial pressure P1 = 0.1 MPa. Estimate the pressure and temperature achieved at the end of the stroke using the ideal gas law and the work done (J/mol), assuming air enters at 25°C and a weight of 80 kg is applied. Solution dU = CV dT = dQ + dW = dWEC = −P dV = −RT dV/V; let L ≡ length (cm) of the cylinder after compression. Rearranging gives CV dT/T = R dV/V => T2/T1 = (V1 /V2 ) R /CV = ( P2 /P1 ) R /C P . For the given conditions, P2,weight = 80 kg/ (0.0152 π) = 113,177 kg/m2 ∙ 9 .8066 N/kg = 1 .1099 MPa = 161 psig, to which we add 0 .1 MPa for absolute pressure, P2 = 1 .21 MPa . By the ideal gas law, P2/P1 = (T2/T1)(35/L) = (P2/P1)R/CP(35/L) . Rearranging gives L = 35(P1/P2)CV /CP = 5 .89 cm; T2 = 608 K = 335°C . The work done is WEC = (5/2)(8 .314)(607 .9 − 273 .15) = 6960 J/mol . This example includes the ideal gas law approximation . Air near room temperature and pressure can be approximated as an ideal gas composed of nitrogen and oxygen, both of which have roughly constant CP values of 3 .5R, and CV = CP − R for ideal gases . Guidelines for ideal gas behavior are: T/Tc ≡ Tr > 0 .5 + 2(P/Pc) or V/Vc > 4 Conditions applicable to ideal gases

(4-21)

The definition of CV leads to the substitution for the dU term . The temperature rise during adiabatic compression can be quite large . We have implicitly assumed that the pressure inside the cylinder is uniformly equal to the pressure applied externally, signifying a reversible process . Hence the result for T2/T1 can be applied to any reversible, adiabatic, ideal gas process . Through the ideal gas law, this result becomes, T2/T1 = (V1/V2)

(R/Cv)

= (P2/P1)

(R/Cp)

γ

=> PV = constant, ad . rev . ideal gas, γ ≡ CP/CV

 1 v 2 zg     ∆  H + +  m = Q + Ws 2 gc gc   

well as individual subsystems . Thus it is valuable to extend PFD computations to include stream enthalpies as well as component mass flows . Highly accurate estimation of stream enthalpies is quite complicated because it involves accurate estimation of the enthalpy of compressed gases and nonideal liquids that may exhibit substantial heats of mixing . Such an approach would be very computationally intensive, hence the necessity of a process simulator . We convey the general concepts by presenting the general equations, and then we illustrate the connection between the general equations and the pathway to properties by using computationally expedient models . The general equations can be revisited at various stages to show improvements in accuracy with increasingly sophisticated computational models . The essential relation for estimating stream enthalpies is given by T   ig ig V H (T , P , z ) = ∑ zi  ∆H of ,ig ,i ,TR (TR ) + ∫ C P dT   + q ( H (T , y ) − H )   TR i

+ (1 − q )( H L (T , x ) − H ig )

(4-23)

Note that the sign appears to change relative to Eq . (4-18) because ∆ is defined as outlet – inlet and here the absolute values of the mass flows should be used, whereas outlet mass flows inherently have negative signs in Eq . (4-18) . Simplifying further, the most common energy balance for open steady-state systems neglects changes in kinetic energy and altitude .

(4-26)

where zi is the overall mole fraction, and q is the stream’s molar vapor fraction . Here we have assumed that the reference state is defined relative to the elements at 25°C and 1 bar as in Eq . (4-12) . To apply this rigorously, equations of state are used (see the subsection Departure Functions from PVT Correlations) . For shortcut calculations, the contributions can be written, L + ∑ x i (( H iV (T ,  Pi sat ) − H iig ) − ∆H Tvap + Vi L ( P − Pi sat ( H L (T , x ) − H ig ) = ∆H mix ,T )) i

(4-27)

V ( H V (T , y ) − H ig ) = ∑ x i ( H iV − H iig )  + ∆H mix  i 

(4-22)

Energy Balances for Steady-State Flow Processes Flow processes for which the left-hand side of Eq . (4-18) is zero are said to occur at steady state . As discussed with respect to the mass balance, this means that the mass of the system within the control volume is constant; it also means that no changes occur with time in the properties of the fluid within the control volume or at its entrances and exits . The only work of the process commonly present is shaft work, and the simplified form of the general energy balance for a single inlet and single outlet, becomes

4-7

(4-28)

where H ig is calculated using Eq . (4-11) . For the purpose of illustrating the pathway to computing stream enthalpies, we can make the following shortcut approximations: (1) CPig = CPig (25°C) = constant . This is reasonably accurate for T < 100°C . (2) (H V − H ig) = 0 . It neglects departures for compressed vapors and heats of mixing for vapors, but is reasonable when P < 5 bar . (3) (H L − H ig) = −∑ xi ∆Hivap . This neglects heats of mixing and enthalpy increases due to increased pressure . Example 4-4 Energy Balances for the DME Process The formulas above make it possible to compute an enthalpy flow (MJ/h) for each stream in Example 4-1 . Heats of formation for methanol, DME, and H2O are −200 .94, −184 .1, and −241 .835 kJ/mol . The ideal gas heat capacities at 25°C are 43 .9, 65 .7, and 33 .6 J/mol∙K . All the streams are liquid except stream 5 . Tabulate these enthalpies and compute (1) the net heat flow (kW) of the heat exchanger after the reactor and (2) the net power flow (kW) for the overall process . Solution Illustrating the procedure for one liquid stream and one vapor stream should suffice . Stream 5 is all vapor . From Example 4-1, the stream species flows are 306 .0, 154 .6, and 154 .6 kmol/h . Applying Eq . (4-28), H 5 = [306 .0(−200940 + 43 .9(250 − 25)) + 155 .6(−184100 + 65 .7(250 − 25))

∆H = Q + Ws

(4-24)

Example 4-3 Continuous Adiabatic Reversible Compression of Air The energy balance changes when the system is viewed from a steady-state perspective . The individual strokes of the compressor, or even whether it is a positive displacement or centrifugal compressor, are irrelevant . Only the continuous flows of energy into and out of the system matter . To illustrate, consider the following example where air enters a continuous reversible compressor at 25°C and 1 bar and is adiabatically compressed to 6 bar . Compute the outlet temperature and work requirement (J/mol) . Solution Due to the adiabatic assumption, the heat term drops out of Eq . (4-24) and we seek ∆H to find the work . The air is treated as an ideal gas . Noting the words adiabatic, reversible, and ideal gas, we can immediately apply Eq . (4-22) . The definition of C P leads to a subtle but significant distinction relative to the previous example . The energy balance simplifies as ∆H = ∫CP dT = Q + W = Ws  P  R /C P  − 1 Ws = C P (T2 − T1 ) = C P T1  2   P1  

(4-25)

Note that we retain a larger number of significant figures than would normally be warranted for such imprecise estimates . This is so because the heats of formation play a significant role in each stream enthalpy . When we take differences, the large heat of formation terms cancel for control volumes without reactions, but are necessary for control volumes that include reactions . Stream 7 is interesting as a sample stream that is liquid and relates to the heat exchanger . The ideal gas contribution can be computed as for stream 5 . H 7 (ig) = [306 .0(−200940 + 43 .9 (75 −25)) + 155 .6 (−184100 + 65 .7(75 − 25)) + 155 .6(−241835 + 33 .6(75 − 25))]/1000 = −125883 MJ/h Applying Eq . (4-17) at 75°C for stream 7 gives 35 .75, 14 .19, and 42 .99 kJ/mol for the heats of vaporization . Adding this to the ideal gas contribution gives H 7 = −125883 + [306 .0(−35750) + 155 .6(−14190) + 155 .6(−42990)]/1000 = −145661 MJ/h

Substituting numerical values gives T2 = T1(6/1)(1/3 .5) = 497 .5 K = 224 .3°C

+ 155 .6(−241835 + 33 .6(250 − 25))]/1000 = −120846 MJ/h

 , Repeating the procedure for the other streams gives the enthalpy flows H = nH Ws = 3 .5 × 8 .314(497 .5 − 298 .15) = 5801 J/mol Stream

Energy Balances for Chemical Manufacturing Processes Similar to mass balances, energy balances are applicable to composite systems as

H (GJ/h)

1

2

5

7

8

9

11

12

−75 .1

−143 .8

−120 .8

−145 .7

−31 .3

−110 .5

−68 .4

−42 .4

4-8

THERMODYnAMICS

 The energy balance for heat exchanger: No work is accomplished so ∆H = Q + W = Q. Q = (−145.7 + 120.8) (1,000,000)/(3600 s/h) = −6900 kW The net energy balance for process involves streams 1, 8, and 12: No pumps or turbines appear in this process, so ∆H = Q . Q = (−42.4 − 31.3 + 75.1)(1,000,000)/(3600 s/h) = 390 kW These results show that net heat addition is required even though the heat of reaction is negative. Note that the outlet streams are hotter than the inlet streams, and despite the exothermic heat of reaction, the heat exchangers, reboilers, and condensers must balance this heat duty.

THE GEnERAL EnTROPY BALAnCE The primary engineering purpose of entropy is to evaluate process thermodynamic reversibility. Entropy is defined in a closed system as T2

∆S = ∫

T1

Q rev Tcv

dT

CP P dT − R ln 2 T P1 T1

or

S ig =

By the first law:

| Wnet | = | QH | − | QC |

By the second law ( for a reversible process):

QH

CP P dT - R ln 2 + S ref T Pref Tref

∫

(4-30)

Commonly S ref = 0. If the reference state uses the elements in the naturally occurring state of aggregation, then ∆ STfref , Pref = (∆ H Tfref , Pref − ∆GTfref , Pref )/Tref is added to the last expression. The entropy balance differs from an energy balance in a very important way—entropy is not conserved and is generated by irreversibilities. Entropy generation is always S gen ≥ 0, where the equality applies for (hypothetical) reversible processes. The statement of balance for a control volume, expressed as rates, is therefore  Rate of entropy    net rate of      =  entropy transport   change of      control volume   into control volume    rate of entropy   rate of     entropy +  change due to heat  +        transfer at surfaces   generation 

QC TC

=0⇒

| QH | TH = | QC | TC

The initial implementation of the second law recognizes that heat flows are of opposite sign for heating and cooling . The second form helps to minimize sign confusion during application . In combination: T   T −T  | Wnet| = | QC |  H − 1 = | QH |  H C   TH   TC 

(4-31)

where S gen is the entropy generation term. This equation is the general rate form of the entropy balance, applicable at any instant. In general application, the contribution of flowing streams is most easily incorporated by adding the sum of entropy flow ∑ (mS  ) of the incoming streams and subtracting the sum of entropy flow of outgoing streams. The entropy calculations for streams extend the process set forth above for enthalpy. However, the entropy of mixing (see subsections Property Changes on Mixing and Ideal Solution Model and Henry’s Law) cannot and should not be neglected. For any process, the two kinds of irreversibility are (1) those internal to the control volume and (2) those resulting from heat transfer across finite temperature differences that may exist between the system and surroundings. When a temperature gradient exists at a boundary, the entropy balance for the boundary itself must be included when determining the entropy change of the universe. In the limiting case where for the universe (system + boundary + surroundings) S gen = 0, the process is completely reversible, implying that • The process is internally reversible within the control volume. • Heat transfer between the control volume and its surroundings is reversible. A sample application of the entropy balance is given below under the heading Turbines.

(4-32)

Here |Wnet| is the net work produced by the Carnot engine after accounting for both compression and expansion; | QH | is the heat transferred at the hot temperature, i .e ., to vaporize the propane; TH and TC are the hot and cold temperatures of the heat reservoirs between which the heat engine operates, or 340 and 260 K, respectively .

FUnDAMEnTAL RELATIOnS OF CLASSICAL THERMODYnAMICS Multivariable calculus provides a number of relations between thermodynamic variables that are quite useful for estimating stream properties . The key point is that specification of two independent variables suffices to define the state of a pure system . For example, if T and ρ are known, the other properties (such as P, U, H, S) and their changes from state are implied . Through the equations of classical thermodynamics, we find that all the properties can be derived from an equation of state P = P(ρ, T) by characterizing departures from ideal gas behavior . The Fundamental Property Relation for Pure Fluids Energy and entropy balances can be combined to eliminate references to heat and work in favor of state variables . For a single-component, reversible, closed system, Eq . (4-31) becomes d (S )cv =

The equivalent entropy balance is Q d (mS )cv = −∆(mS  )fs + ∑ + Sgen dt surfaces Tcv

+

(4-29)

T2

T2

Example 4-5 Carnot Efficiency A heat engine is to run between 340 and 260 K. As an approximation, we can assume that the engine follows the Carnot process of adiabatic reversible compression to 340 K, isothermal heat addition, adiabatic reversible expansion to 260 K, and isothermal heat removal. For the purposes of this illustration, assume the process is working on propane, where heat addition or removal could be accomplished isothermally by boiling and condensing. The entropies of the saturated vapor and saturated liquid at 340 K would define the entropy range of operation. The equations that apply to reversible Carnot engines are as follows:

TH

where Q rev is reversible heat transfer, and Tcv is the control volume temperature at the surface where heat is transferred. Entropy changes for an ideal gas using T and P as independent variables can be calculated using a formula derived from Eq. (4-29) by combining an isothermal step and an isobaric step: ∆S ig = ∫

Entropy Balances for Composite Systems As for the energy balance, entropy balances can be useful in analyzing processes from an overall perspective. The most common applications involve idealized 100 percent reversible processes such as the Carnot engine. However, it can be meaningful to consider irreversible processes using entropy as a measure of overall thermodynamic efficiency, as in the case of availability or exergy analysis.

Q dt Tcv

(4-33)

Similarly, Eqs . (4-33) and (4-19) combine to give for a simple system with uniform T, d (U )cv = Q dt + W dt = T dS + W dt

(4-34)

Noting that only WEC is relevant for a reversible, closed system, Eqs . (4-3) and (4-34) give dU = T dS − P dV

(4-35)

Equation (4-35) is the fundamental property relation . After substituting the definition of H ≡ U + PV, then dH = dU + d(PV ) = dU + P dV + V dP, and dH = T dS + V dP

(4-36)

The transformation from Eq . (4-35) to Eq . (4-36) suggests two additional relations, A ≡ U − TS and G ≡ U + PV − TS, resulting in dA = −S dT − P dV

(4-37)

dG = −S dT + V dP

(4-38)

GEnERAL BALAnCES Relations Using Desired Independent Variables For practical application, it is useful to select easily measured properties as desired independent variables for use in calculation of U, H, A, and G. Because the differentials of these state functions are exact differential expressions, application of the reciprocity relation for such expressions produces the common Maxwell relations as described in Sec. 3 in the subsection Multivariable Calculus Applied to Thermodynamics, and the four most frequently used Maxwell relations are developed in texts [see Elliott and Lira (2012)]. Combining Maxwell’s relations with Eqs. (4-35) through (4-38) and the chain rule provides a number of useful relations.    ∂P   ∂U   ∂U  dU (T ,V ) =   dT +   dV = CV dT + T   − P  dV  ∂T  V  ∂V  T   T ∂ V  

(4-39)

  ∂V   dH (T , P ) = C P dT + V − T    dP  ∂T P  

(4-40)

dS (T , P ) =

 ∂V  CP dT −   dP  ∂T  P T

(4-41)

dS (T ,V ) =

 ∂P  CV dT +   dV  ∂T  V T

(4-42)

As an example application of these differentials, consider the pressure correction for enthalpy due to pressure at constant temperature. If we neglect the usually small contribution of T (∂V / ∂T ) P in Eq. (4-40), then for a liquid where the fluid is approximately incompressible, the effect of pressure gives V L ( P2 − P1 ) as implemented in Eq. (4-27) relative to the species vapor pressure.

Duct Flow of Compressible Fluids Thermodynamics provides equations interrelating pressure changes, velocity, duct cross-sectional area, enthalpy, entropy, and specific volume within a flowing stream. Consider the adiabatic, steady-state, one-dimensional flow of a compressible fluid in the absence of shaft work and changes in potential energy. The appropriate energy balance Eq. (4-23) with Q, Ws , and ∆z all set equal to zero is ∆H + In differential form,

∆v 2 =0 2 gc

dH = −v dv/gc

(4-43)

(4-44)

Most common chemical engineering processes occur at fluid velocities substantially less than sonic. Therefore, we confine further discussion to subsonic flow. Discussion relating to near sonic or supersonic flow is available in Smith, Van Ness, and Abbott (2005). Flow rates should always be checked and recourse taken to account for supersonic effects if high flow rates are experienced. Nozzles Nozzle flow is quite specialized in that a properly designed nozzle varies its cross-sectional area with length in such a way as to make the flow nearly frictionless. The limit is adiabatic, reversible flow, for which the rate of entropy increase is zero. An analytical expression relating velocity to pressure in an isentropic nozzle is readily derived for an ideal gas with constant heat capacities. Combination of Eqs. (4-36) and (4-43) for isentropic flow gives v dv/gc = −V dP Integration, with nozzle entrance and exit conditions denoted by 1 and 2, yields for an ideal gas with constant γ ≡ C P /CV P2 ( γ−1)/ γ  v 22 − v12 2 γP1V1   P2  1 −    = − 2 ∫ V dP = gc γ− 1   P1   P1

Ws = ∆H = H2 − H1

(4-45)

(4-46)

The rate form of this equation is (4-47)

When inlet conditions T1 and P1 and discharge pressure P2 are known, the value of H1 is fixed. In Eq. (4-46) both H2 and Ws are unknown, and the energy balance alone does not allow their calculation. However, if the fluid expands reversibly and adiabatically in the turbine, then the process is isentropic (S2 = S1). This entropy balance establishes the final state of the fluid and allows calculation of H2. Equation (4-47) then gives the isentropic (reversible) work, and the prime denotes the reversible process: Ws′ = ∆ H ′

The mass balance (continuity) Eq. (4-6) here becomes d (ρvAx) = d (vAx/V ) = 0, which gives dV dv dAx − − =0 V vg c Ax

where the final term is obtained upon elimination of V by PV γ = constant, following Eq. (4-22). Throttling Processes Fluid flowing through a restriction, such as an orifice, without appreciable change in kinetic or potential energy undergoes a finite pressure drop. This throttling process produces no shaft work, and in the absence of heat transfer, Eq. (4-24) reduces to ∆H = 0 or H2 = H1. The process therefore occurs at constant enthalpy. The temperature of an ideal gas is not changed by a throttling process because dH ig = CP dT. For most real gases at moderate conditions of T and P, a reduction in pressure at constant enthalpy results in a decrease in temperature, although the effect is usually small. Throttling of a wet vapor causes the liquid to evaporate, resulting in a considerable temperature drop because of the evaporation of liquid, and depending on the pressure drop, the evaporation may be complete. If a saturated liquid is throttled to a lower pressure, some of the liquid vaporizes or flashes, producing a mixture of saturated liquid and vapor at the lower pressure. For a pure fluid, the outlet temperature is the saturation temperature at the outlet pressure, which may be very cold. Turbines (Expanders) High-velocity streams from nozzles impinging on blades attached to a rotating shaft from a turbine (or expander) through which vapor or gas flows in a steady-state expansion process that converts the internal energy of a high-pressure stream into shaft work. The motive force is usually provided by a (steam) turbine or a high-pressure (gas) expander. In any properly designed adiabatic turbine, heat transfer and changes in potential and kinetic energy are negligible. Equation (4-24) therefore reduces to

W s = m ∆H = m ( H 2 − H 1 )

BALAnCE APPLICATIOnS TO FLOW PROCESSES

4-9

(4-48)

The absolute value |Ws′| is the maximum work that can be produced by an adiabatic turbine with given inlet conditions and given discharge pressure. Because the actual expansion process is irreversible, expander efficiency is defined as ηE ≡

Ws Ws′

where Ws is the actual shaft work. By Eqs. (4-47) and (4-48), ηE =

ΔH ΔH ′

(4-49)

Values of ηE usually range from 0.7 to 0.8. Example 4-6 Turbine Process Design Steam is expanded in a turbine from 500°C and 1.4 MPa to an outlet of 0.6 MPa. If the turbine is 75 percent efficient, how much work can be obtained per kilogram of steam (kJ/kg)? Use the steam tables from Elliott and Lira (2012). Solution The inlet conditions are H1 = 3474.8 kJ/kg and S1 = 7.6047 kJ/kg ∙ K . To apply Eq . (4-49) the reversible calculation is performed first . Interpolating at the outlet state pressure using S2′ = 7 .6047 kJ/kg ∙ K gives H2′ = 3202 .8 kJ/kg . Then ∆H = WS = ∆H´ ηE = (3202 .8 − 3474 .8)(0 .75) = −204 kJ/kg . Compressors Compressors, pumps, fans, blowers, and vacuum pumps are all devices designed to produce pressure increases . The energy Eqs . (4-43) through (4-48) are the same for adiabatic compression, based on the same assumptions, as for turbines or expanders . A specialized equation of state (EOS) would be applied for steam or polar fluids, whereas a generalized EOS typically would be applied for the fluids involved in compressors .

4-10

THERMODYnAMICS

The isentropic work of compression, as given by Eq. (4-48), is the minimum shaft work required for compression of a gas from a given initial state to a given discharge pressure. Compressor efficiency is defined as (again using the prime to denote the reversible process) ηC ≡

dH = V dP (constant S)

Ws′ Ws

The relation between the reversible and actual process is inverted relative to a turbine. In view of Eqs. (4-46) and (4-48), this becomes ηC ≡

enthalpy of compressed (subcooled) liquids, and these are seldom available. The enthalpy relation, Eq. (4-36), provides an alternative. For an isentropic process,

ΔH ′ ΔH

Combining this with Eq. (4-48) yields P2

Ws′= ∆H ′ = ∫ V dP

(4-50)

Compressor efficiencies are usually in the range of 0.7 to 0.8. Pumps Liquids are moved by pumps, and the same equations apply to adiabatic pumps as to adiabatic compressors. Thus, Eqs. (4-46) to (4-48) and (4-50) are valid. However, application of Eq. (4-46) requires values of the

P1

The usual assumption for liquids (at conditions well removed from the critical point) is that V is independent of P. Integration then gives Ws´ = ∆H´ = V (P2 − P1) = ∆ P/ρ

(4-51)

PROPERTY CALCULATIOnS FROM EQUATIOnS OF STATE The most satisfactory calculation procedure for the thermodynamic properties of gases and vapors is based on ideal gas state heat capacities and quantification of the nonidealities using departure functions. Of primary interest are the enthalpy and entropy departures, defined as the difference between the state properties of the real fluid and an ideal gas at the same pressure and temperature: ( H − H ig ) ≡ H dep

(S − S ig ) ≡ S dep

and

A few EOSs may be reformulated to give P as a function of T and V or V as a function of T and P, in which case Eqs. (4-38) and (4-40) are more convenient. P

 ∂ Z  dP  ∂V   ∂H  H dep =− ∫ T    = V −T   ⇒   ∂T P P  ∂T P  ∂ P T RT 0

(4-52)

 ∂G  G dep = P   = PV ⇒  ∂P T RT

These departures are integrated into the process calculations, e.g., see Eq. (4-12). The reader is cautioned that departure functions are sometimes called residual properties, and sign conventions for the definitions differ in literature.

Z ≡ PV /( RT )

(4-53)

Analytical expressions for Z as functions of T and P or T and V are known as equations of state (EOSs). Since most EOSs are in terms of T and V, the most useful relations are Eqs. (4-37) and (4-39). Elliott and Lira (2012) show how these can be rearranged in the most convenient form:  ∂P   ∂U  U dep =   = T  −P ⇒  ∂T  V  ∂V  T RT ∂A  A dep   V = − PV ⇒ T ,V =  ∂V  T RT

ρ

∫ 0

ρ

 ∂ Z  dρ ρ ρ

∫ − T  ∂T  0

Z −1 dρ ρ

(4-54)

dep

dep T ,V

A A = − ln Z = RT RT

ρ

∫ 0

Z −1 dρ− ln Z ρ

(4-56)

Other departure functions can be derived from the definitions of U, H, A, G, and S. ρ

  ∂Z   dρ S dep U dep − A dep − ln Z = − ln Z = − ∫ T   + ( Z − 1)   ∂T ρ R RT  ρ 0 

(4-57)

G dep A dep = + Z −1 = RT RT

ρ

∫ 0

Z −1 dρ + Z - 1 - ln Z ρ

(4-58)

(4-59)

(4-62)

The chemical potential μ plays a vital role in both phase and chemical reaction equilibria. However, the chemical potential exhibits certain unfortunate characteristics that discourage its use in the solution of practical problems. For pure fluids, μ = G ≡ H − TS defines μ in terms of the internal energy and entropy, both primitive quantities for which absolute values are unknown. Moreover, μ approaches negative infinity when P approaches zero. While these characteristics do not preclude the use of chemical potentials, the application of equilibrium criteria is facilitated by introduction of the fugacity, a quantity that takes the place of μ and overcomes its less desirable characteristics. The Gibbs energy departure of a real fluid is related to the fugacity by G dep = G − G ig = RT ln

f P

(4-63)

The dimensionless ratio f/P is another new property called the fugacity coefficient f . Thus, G dep = RT ln φ

(4-64)

f P

(4-65)

where φ≡

or

f = φP

The definition of fugacity is completed by setting the ideal gas state fugacity of pure species i equal to its pressure, f i ig = P . Thus for the special case of an ideal gas, Gidep = 0, φ i = 1. From the phase equilibrium criterion, μα = μβ when phases α and β are in equilibrium. Substitution into Eq. (4-63) shows that f α = f β is equivalent. µα = μβ

ρ

 ∂ Z  dρ H dep U dep + PV − ( PV )ig + Z −1 = =− ∫ T    ∂T ρ ρ RT RT 0

(4-61)

CHEMICAL POTEnTIAL, FUGACITY, AnD FUGACITY COEFFICIEnT

(4-55)

The subscript T, V in Eq. (4-55) indicates that this departure is evaluated at ig the same T, V for the real fluid and ideal gas: ATdep ,V = A(T, V) − A (T,V). Most applications require residuals at given T, P. The properties of the real fluid imply unique values of T, P, and V, but the pressure obtained from the ideal gas equation given T, V is not equal to the real fluid’s P . A translation in the ideal gas state of ln Z is used to obtain Adep = A(T, P) − Aig(T, P).

0

Z −1 dP P

P  dP   ∂Z  S dep = − ∫ T   + Z − 1  ∂T ρ R  P 0 

DEPARTURE FUnCTIOnS FROM PVT CORRELATIOnS The departure functions of gases and vapors depend on their PVT behavior. This is often expressed through correlations for the compressibility factor Z, defined by

P

∫

(4-60)

fα=fβ

(4-66)

For condensed phases, Eq. (4-65) is used to calculate the saturation fugacity (at the vapor pressure or sublimation pressure), and then Eq. (4-38) is used to add a pressure correction, f cond = φ sat P sat exp[V cond ( P − P sat )/( RT )]

(4-67)

PROPERTY CALCULATIOnS FROM EQUATIOnS OF STATE where the exponential term is known as the Poynting correction, and V cond is the molar volume of the condensed phase. As written, the Poynting correction assumes the condensed phase is incompressible.

Values for the cross coefficients Bij, with i ≠ j, and their derivatives are provided by Eq . (4-72) written in extended form: Bij =

APPLICATIOnS OF DEPARTURE FUnCTIOnS Virial Equations of State The virial equation in density is an infinite series expansion of the compressibility factor Z in powers of molar density r (or reciprocal molar volume V -1) about the real gas state at zero density (zero pressure): Z = 1 + Bρ+ Cρ2 + Dρ3 + 

(4-68)

The density series virial coefficients B, C, D, … depend on temperature and composition only. In practice, truncation is to two terms. For engineering purposes, P is more convenient than density, and the pressure through mathematical reversion of the series is Z = 1 + BP/( RT ) + 

(4-69)

For a pure fluid, Eq. (4-61) gives φ = exp( BP /(RT ))

(4-70)

The composition dependency of B is given by the exact mixing rule B = ∑∑ y i y j Bij i

(4-71)

j

where yi and yj are mole fractions for a gas mixture and i and j identify species. The coefficient Bij characterizes a bimolecular interaction between molecules i and j, and therefore Bij = Bji. Two kinds of second virial coefficient arise: Bii and Bjj (the subscripts are the same), and Bij (they are different). The first is a virial coefficient for a pure species; the second is a mixture property, called a cross-coefficient. An extensive set of three-parameter corresponding-states correlations has been developed by Pitzer and coworkers [Pitzer, Thermodynamics, 3d ed., App. 3, McGraw-Hill, New York, 1995]: BPc (4-72) = B 0 +ωB 1 RTc with the acentric factor defined by Eq. (4-14). For pure chemical species B0 and B1 are functions of reduced temperature only. Substitution for B in Eq. (4-69) by this expression gives Z = 1 + ( B 0 +ωB 1 )

Pr Tr

(4-73)

where Tr = T /Tc and Pr = P /Pc are the reduced temperature and reduced pressure. Detailed discussion of B0 and B1 and their derivatives is given in Elliott and Lira (2012, p. 259): B 0 = 0.083 −

0.422 Tr1.6

(4-74)

B 1 = 0.139 −

0.172 Tr4.2

(4-75)

Substituting into Eqs. (4-60) and (4-62) and integrating give  1.0972 0.083  0.8944 0.139  H dep = − Pr  2.6 − + ω  5.2 −  RT Tr Tr   Tr  Tr

(4-76)

 0.675 S dep 0.722  = − Pr  2.6 + ω 5.2  R Tr   Tr

(4-77)

G dep H dep S dep = − RT RT R

(4-78)

Although limited to pressures where the two-term virial equation in pressure has approximate validity, these correlations are applicable for many chemical processing conditions. The second virial equation is reliable at higher pressures when the temperature is also higher in accordance with the following guideline: Tr > 0.686 + 0.439Pr

or

Vr > 2.0

(4-79)

4-11

RTcij 0 ( B +ωij B 1 ) Pcij

(4-80)

where B0 and B1 are the same functions of Tr as given by Eqs . (4-74) and (4-75), and Trij = T/Tcij . The combining rules for ωij, Tcij, and Pcij are given by Elliott and Lira (2012, p . 580) . A primary merit of Eqs . (4-74) and (4-75) for second virial coefficients is simplicity . Generalized correlations for B are given by Meng, Duan, and Li [Fluid Phase Equilibr . 226:109–120 (2004)] . More complex correlations of somewhat wider applicability include those by Tsonopoulos [AIChE J . 20: 263–272 (1974); 21: 827–829 (1975); 24: 1112–1115 (1978); Adv . in Chemistry Series 182, pp . 143–162 (1979)] . For polar and associating molecules, the correlation of Hayden and O’Connell [Ind . Eng . Chem . Proc . Des . Dev . 14: 209–216 (1975)] is generally preferred . For aqueous systems, see Bishop and O’Connell [Ind . Eng . Chem . Res . 44: 630–633 (2005)] . Extended Virial and Multiparameter Equations Another class of equations, known as an extended virial equation, was introduced by Benedict, Webb, and Rubin [ J . Chem . Phys . 8: 334–345 (1940); 10: 747–758 (1942)] . This equation contains eight parameters, all functions of composition . It and its modifications, despite their complexity, find application in the petroleum and natural gas industries for light hydrocarbons and a few other commonly encountered gases [Lee and Kesler, AIChE J . 21: 510–527 (1975)] . Similar in spirit to the Benedict, Webb, and Rubin (BWR) model, highly accurate equations can be developed when extensive experimental data are available . These equations are generally written as density expansions of the Helmholtz energy that may involve up to 54 parameters . For example, the IAPWS equation [Wagner, W ., and A . Pruss, J . Phys . Chem . Ref . Data 31: 387–535 (2002)] for the properties of steam applies this approach . Solution for the compressibility factor and internal energy can be obtained by differentiating the Helmholtz energy according to Z −1 =

ρ  ∂( A − A ig )T ,V    ∂ρ RT  T

1  ∂(( A − A ig )T ,V / T )  U − U ig =   RT RT  ∂(1/ T ) ρ

(4-81)

(4-82)

The NIST Chemistry Webbook [E . W . Lemmon, M . O . McLinden, and D . G . Friend, “Thermophysical Properties of Fluid Systems,” in NIST Standard Reference Database 69, eds . W . G . Mallard and P . J . Linstrom, http://webbook . nist .gov, Gaithersburg, MD, 2016 (retrieved Nov . 8, 2016)] implements the IAPWS equation and similar equations for roughly 100 compounds common in natural gas and refrigeration industries . The relatively small list of compounds for which multiparameter equations exist has been somewhat limiting for these types of models . Recent progress has expanded this list considerably, however, with the promise of greater expansions in the near future . Another traditional limitation has been the extension to mixtures, but similar recent progress has established the GERG-2008 model as a viable method for high-accuracy treatment of streams related to the natural gas industry [O . Kunz and W . Wagner, J . Chem . Eng . Data 57: 3032 (2012)] . It is likely that highly accurate equations will become available for 200 to 300 pure compounds and nonpolar mixtures within the next 5 to 10 years . Cubic Equations of State The modern development of cubic equations of state started in 1949 with publication of the Redlich-Kwong (RK) equation [Chem . Rev . 44: 233–244 (1949)], and many others have since been proposed . An extensive review is given by Valderrama [Ind . Eng . Chem . Res . 42: 1603–1618 (2003)] . Of the equations published more recently, the two most popular are the Soave-modified RK (SRK) equation [Chem . Eng . Sci . 27: 1197–1203 (1972)] and the Peng-Robinson (PR) equation [Ind . Eng . Chem . Fundam . 15: 59–64 (1976)] . Since these two are functionally equivalent, the present discussion focuses arbitrarily on the PR model P=

RT a (T ) a bρ 1 − − , Z= V − b (V 2 + 2Vb − b 2 ) 1 − bρ bRT [1 + 2bρ − (bρ)2 ]

(4-83)

where parameters a(T) and b are substance-dependent . a (T ) = 0.45723553 b = 0.0777960

α(Tr ) R 2Tc2 Pc

RTc Pc

(4-84) (4-85)

4-12

THERMODYnAMICS

Function α(Tr) is an empirical expression specific to a particular form of the equation of state. α ≡ 1 + κ (1 − Tr )

2

κ ≡ 0.37464 + 1.54226ω− 0.26992ω2

As an equation cubic in V or r, Eq. (4-83) has three roots, of which two may be complex numbers. Physically meaningful values of V are always real numbers, positive and greater than parameter b. The quantity br is effectively the packing fraction and must range between 0 and 1.0. When T > Tc, solution at any positive value of P yields only one real positive root. When T = Tc, this is also true, except at the critical pressure, where three roots exist, all equal. For T < Tc, only one real positive (liquid-like) root exists at high pressures, but for a range of lower pressures there are three. Here, the middle root is of no significance; the smallest root is a liquid or liquid-like volume, and the largest root is a vapor or vapor-like volume. In principle, cubic equations have the advantage that they can be solved analytically. This may be convenient for some calculations, but most process simulators apply iterative solution. Reasons are that the analytical solution may have round-off errors for the liquid root at low temperatures [R. MonroyLoperena, Ind . Eng . Chem . Res . 51: 6972 (2012)], and also because iterative Newton-like methods enable avoiding trivial solutions through the use of the pseudo-root technique, as described on page 4-25. Cubic equations of state may be applied to mixtures through expressions that give the parameters as functions of composition. No established theory strictly prescribes the form of this dependence, and empirical mixing rules are often used to relate mixture parameters to pure-species parameters. The simplest realistic expressions (known as van der Waal’s mixing rules) are a linear mixing rule for parameter b and a quadratic mixing rule for parameter a b = ∑ x i bi

(4-86)

i

a = ∑∑ x i x j aij i

(4-87)

j

with aij = aji . The aij are of two types: pure-species parameters (identical subscripts) and interaction parameters (unlike subscripts). Parameter bi is for pure species i. The interaction parameter aij is often evaluated from pure-species parameters by a geometric mean combining rule known as the Lorentz-Berthelot rule aij = (aiaj)½ (1 - kij)

(4-88)

where kij is an empirical binary parameter that should be fit to experimental data. These traditional equations yield mixture parameters solely from parameters for the pure constituent species. They are most likely to be satisfactory for mixtures composed of simple and chemically similar molecules. Because cubic equations provide reasonable results for nonpolar mixtures, and they have been available since the mid-1970s, they have become the workhorses for chemical process modeling. In cases where their deficiencies are unacceptable, customized empirical adaptations are generally developed. This leads to some fracturing of modeling efforts as specialists in different companies make the adaptations and they become private. Over the long term, however, there is a tendency for the more accurate adaptations to find their way into process simulators. In particular, the modified Huron-Vidal [cf. M. Michelsen, Fluid Phase Equilibr . 60: 213 (1990)] and Wong-Sandler [AIChE J. 38: 671 (1992)] mixing rules are similar in flexibility to the activity models discussed below, while maintaining the applicability of equations of state to dense, near-critical fluids. One desirable feature of the cubic EOSs is the simplicity of their working equations for departure functions. As an example, the departure functions for the Peng-Robinson EOS are H dep A  κ Tr   Z + (1 + 2) B  = Z −1 −  ln  1 +  RT B 8 α   Z + (1 − 2) B 

(4-89)

S dep A κ Tr  Z + (1 + 2) B  = ln ( Z − B ) − ln   R B 8 α  Z + (1 − 2) B 

(4-90)

 Z + (1 + 2) B  G dep A ln  ≡ ln φ = Z − 1 − ln( Z − B ) −  RT B 8  Z + (1 − 2) B 

B ≡ bP/(RT)

Z=

1 a bρ 1 A B /Z − = − 1 − bρ bRT [1 + 2bρ− (bρ)2 ] 1 − B / Z B [1 + 2 B / Z − ( B / Z )2 ]

(4-91)

(4-92)

and for a mixture, the parameters of Eqs. (4-86) to (4-88) are similarly made dimensionless. Do not confuse A with Helmholtz energy, nor confuse B with the virial coefficient.

(4-93)

Cross-multiplying and collecting terms give Z 3 - Z 2 (1 - B) + Z (A - 3B2 - 2B) - (AB - B2 - B3) = 0

(4-94)

In principle, solving for vapor pressure using an EOS involves trial and error. We can take Eq. (4-16) as an initial guess, giving P sat ≈ 0.130 MPa. This leads to A = 0.04178 and B = 0.003627. Solving the cubic equation with an initial guess of Z = 1 gives ZV = 0.9606 and f V = 0.1246 MPa. Solving with an initial guess of Z = 0 gives Z L = 0.004627 and f L = 0.1280 MPa. Iterating on P sat to obtain f V = f L gives P sat = 0.1332, with rV = 0.002329 g/cm3, (H dep)V = -93.63 J/mol; f V = 0.1280 MPa; rL = 0.4695 g/cm3, (H dep)L = -8200.51 J/mol; f L = 0.1280 MPa. A polynomial form for methane is CPig = 19.25 + 0.05213T + 1.197(10-5)T 2 - 1.132(10-8)T 3. Noting that ∆H °f = -74,893.6 J/mol and applying Eq. (4-26), we have H V = -5022.61 and H L = -5528.05 kJ/kg. Taking the difference gives ∆H vap = 505.4 kJ/kg. This compares to 506.4 from Eq. (4-17). The NIST Webbook gives P = 0.1322 MPa, H L = 11.687, and H V= 516.28, leading to ∆H vap = 504.6 kJ/kg. Using the Webbook as a basis for comparison, the PR EOS gives a 0.76 percent deviation in P sat and 0.17 percent in H vap. Equations (4-16) and (4-17) give 2.0 percent and 0.34 percent deviations. Example 4-7 gives a 0.040 percent deviation in ∆H vap. Several notes can be made about these results: 1. These deviations pertain to comparisons at only a single point. Similar comparisons at 100 K give 1.2 percent and 0.087 percent deviations in P sat and ∆H vap for the PR EOS relative to 2.4 percent and 1.8 percent for Eqs. (4-16) and (4-17), respectively. More comparisons at 175 K give 0.81 percent and 3.6 percent deviations in P sat and ∆H vap for the PR EOS relative to 2.2 percent and 0.53 percent for Eqs. (4-16) and (4-17). 2. For whatever model an engineer may be using, the model estimates should be validated against the experiment. When a multiparameter EOS is available, the NIST results can be relied upon as accurate characterizations of experimental data. In general, NIST’s ThermoLit resource [http://trc.nist.gov/thermolit/main/home.html#home] provides a reliable summary of the available experimental literature. The above example illustrates the procedure for validating models for P sat and ∆H vap. It is simply a summary of deviations over the conditions’ range of interest. 3. The PR EOS generally provides superior accuracy relative to Eqs. (4-16) and (4-17). This might be more apparent if our comparison were based on a component other than methane, which played a substantial role in the development of Eqs. (4-16) and (4-17). 4. Equations (4-16) and (4-17) provide reasonable estimates, especially for methane. Equation (4-16) is exact at Tr = 0.7 and 1.0 because it is a linear interpolation between these two points, so comparisons at these conditions (133 K and 191 K for methane) would make the model look uncharacteristically accurate. 5. When using Eq. (4-17) with (4-27), the accuracy of H L depends on inclusion of the (H dep)V even when Eq. (4-17) is accurate. While it might be possible to provide a shortcut estimate of (H dep)V, the PR EOS is reliable and readily available in process simulators. Shortcut estimates should only be used as checks that can be performed with hand calculations. 6. The values of enthalpy from the various sources cannot be compared directly. For example, the values of H V at 115 K are -5022.61 kJ/kg by the PR EOS, and 516.28 on the Webbook. These large discrepancies are due to different reference states. If interest is limited to a single component, then the reference state can be chosen arbitrarily, but that would be a poor practice in the general case of multicomponent process simulations. 7. Solving for vapor pressure of an EOS requires iteration until the fugacities of vapor and liquid are equal. 8. Incorporation of the PR EOS into manual calculations is facilitated by software available at websites such as CheThermo.net. The PREOS.xls workbook was used for the computations illustrated here.

Pitzer (Lee-Kesler) Correlations In addition to the correspondingstates correlation for the second virial coefficient, Pitzer and coworkers [Thermodynamics, 3d ed., App. 3, McGraw-Hill, New York, 1995] developed a full set of generalized correlations. They have as their basis an equation for the compressibility factor, given by Z = Z 0 + ωZ1 0

where the parameters are made dimensionless A ≡ aP/(RT)2

Example 4-7 Estimating Enthalpy Using the PR EOS Compute the enthalpies (kJ/kg) of saturated vapor and liquid methane and the enthalpy of vaporization, using the PR EOS at 115 K, and compare to the values given in the NIST Webbook. Also compare the heat of vaporization computed by the shortcut equation. Use the ideal gas elements at 25°C and 1 bar as the reference state for the PR EOS. Solution The density is most easily solved by rearranging the PR EOS in terms of Z:

1

(4-95)

where Z and Z are each functions of reduced temperature Tr and reduced pressure Pr. The acentric factor ω is defined by Eq. (4-14). Pitzer’s original correlations for Z and the derived quantities were determined graphically and presented in tabular form. Since then, analytical refinements to the tables have been developed, with extended range and accuracy. The most popular Pitzer-type correlation is that of Lee and Kesler [AIChE J . 21: 510–527 (1975)]; the advent of computers has made the original tabular and graphical implementations obsolete. Although the Pitzer correlations are based on data for pure materials, they may also be used for the calculation of mixture properties. A set of recipes is

SYSTEMS OF VARIABLE COMPOSITIOn required relating the parameters Tc, Pc, and ω for a mixture to the pure-species values and to composition. One such set is given by Eqs. (2-80) through (2-82) in the Seventh Edition of Perry’s Chemical Engineers’ Handbook (1997). These equations define pseudoparameters, so called because the defined values of Tpc, Ppc, and ωpc have no physical significance for the mixture. The Lee-Kesler correlations provide reliable data for nonpolar and slightly polar fluids; errors of less than 3 percent are likely. Larger errors can be expected in applications to highly polar and associating fluids. Wertheim’s Theory and SAFT Equations of State The reader may have noticed caveats pertaining to polar molecules for all the models mentioned so far. To clarify, the term polar is generally applied to molecules that may be either mildly polar, such as CO2, or associating, such as H2O. A particularly common form of association is hydrogen bonding, which occurs in H2O, alcohols, aldehydes, some amides, and some amines. The primary distinction between association and mild polarity is that association leads to specific orientations between molecules where interactions are quite strong, while polarity leads to a broader distribution of orientations that are generally favored. For example, inaccuracies in the PR EOS may be small for mildly polar pure fluids, but larger for associating fluids. The inaccuracies might be much larger when mixing mildly polar fluids with associating fluids because polarity without association is generally correlated with strong asymmetry in either acid or base character. The statistical associating fluid theory (SAFT) family of equations was developed to address limitations related to molecular polarity [W. G. Chapman, K. E. Gubbins, G. Jackson, and M. Radosz, Fluid Phase Equilibr . 52: 31 (1989)]. Many implementations of this theory have been developed since the 1990s. A recent review [S. P. Tan, H. Adidharma, and M. Radosz, Ind . Eng . Chem . Res. 47: 8063 (2008)] concluded that PC-SAFT [J. Gross and G. Sadowski, Ind . Eng . Chem . Res. 40: 1244 (2001)] provided a reasonable representation of what can generally be achieved. The SAFT EOSs are best expressed in terms of the Helmholtz energy: ( A − A ig ) T , V ( A0 − A ig ) T , V A1 A2 = + + 2 + A assoc RT RT T T

(4-96)

The equations for A0, A1, A2, and Aassoc are semiempirical in the sense that their qualitative behavior has been validated with comparison to molecular simulation data. The association term was specifically developed based on Wertheim’s theory, a rigorous theory for associating molecules [M. S. Wertheim, J . Stat . Phys . 35: 19 (1984)]. Wertheim’s theory is equivalent to modeling association as weak chemical reactions under certain conditions [J. R. Elliott, S. J. Suresh, M. D. Donohue, Ind . Eng . Chem . Res . 29: 1476, (1990), A. M. Bala, C. T.

4-13

Lira, Fluid Phase Equilibr, 430: 47 (2016)], but Wertheim’s use of site balances rather than species balances facilitates more general application. Molecules that are polar but not strictly associating can also be approximated with this theory. The significance of having a close relationship between the equation of state and the rigors of molecular simulation is that the firm theoretical basis provides insights into the proper mixing rules. Another advantage of Wertheim’s theory is realized when taking the limit of the association energy to infinity. A reasonable model of a covalently bonded chain is obtained, mimicking polymeric species, again with validated behavior relative to molecular simulation. Wertheim’s theory has also been implemented to achieve a smooth transition between cubic equations and an association model. The Cubic Plus Association (CPA) model applies the SRK model for nonassociating species and an adaptation of Wertheim’s theory for associating species [G. M. Kontogeorgis, M. L. Michelsen, G. K. Folas, S. Derawi, N. von Solms, and E. H. Stenby, Ind . Eng . Chem . Res. 45: 4869 (2006)]. This has the advantage of carrying over accumulated expertise based on the SRK model while gaining the benefits of Wertheim’s theory when necessary. A related alternative is the ESD model [S. J. Suresh, J. R. Elliott, Ind . Eng . Chem . Res . 31: 2783 (1992)], which naturally reduces to a cubic equation in the absence of association. When molecules in a mixture have similar site types such that the geometric mean of the association constants can be used for cross-interactions, computational efficiency can be improved [J. R. Elliott, Ind . Eng . Chem . Res. 35: p. 1624, (1996)], which sacrifices slightly on generality but is roughly 3 times faster for binary mixtures, and much faster for multicomponent mixtures. At present, SAFT models are superior to cubic equations for mixtures involving molecules with high molecular weights, above about 1200 g/mol. Readers should be careful to validate the model as implemented in their software of choice. Check that parameters are available for the components of interest, especially the association parameters. As always, include comparison of the model to experimental data for as many systems as are available. LIQUID-PHASE PROPERTIES The simplicity and generality of Eq. (4-26) recommend it when properties need to be computed consistently for streams that may contain mixed phases and reactive compositions, and modern equations of state can provide accurate characterizations of vapor-liquid transitions. However, calculation of property changes from one liquid state to another can be based on Eqs. (4-40) and (4-41) where the pressure-dependent contributions are either ignored or treated as small corrections. The main challenge for mixtures is to estimate the properties with greater accuracy than can be obtained from the pathway of Eq. (4-26).

SYSTEMS OF VARIABLE COMPOSITIOn The composition of a system may vary because the system is open or because of chemical reactions even in a closed system. The equations developed here apply regardless of the cause of composition changes. The objectives of this analysis are twofold: (1) to enable more accurate estimation of mixed stream properties with Eq. (4-26) through a more detailed treatment of departure functions and heats of mixing and (2) to articulate the necessary relations for evaluating the activities of components in mixtures. While computations of thermodynamic properties such as U, H, and S dominate in the analysis of processes involving pure compounds, processes involving mixtures tend to focus foremost on computing the equilibrium phase behavior. State conditions such as T, P that lead to a vapor phase at one composition may yield a liquid at another composition, so determining the state(s) of the phase(s) in question is not as straightforward as for singlecomponent systems. Occasionally, paradoxical quantities are encountered, such as the liquid solubility of a “noncondensable” gas. Computation of bulk phase thermodynamic properties is straightforward once the phase behavior has been resolved. Coverage of mixtures begins with a review of fundamentals. Briefly, the Gibbs energy is minimized at equilibrium, suggesting the importance of derivative properties. This leads to the formulation of phase and reaction equilibrium criteria. These criteria are general, but they require models of the Gibbs energy for implementation. The two classes of models most commonly used are equations of state and activity models. Activity models are quite successful for modeling in most common industrial situations. Therefore, we cover first activity models and then EOSs. We return to Henry’s law after EOSs to facilitate discussion of how gaseous species are treated in the two approaches.

CHEMICAL POTEnTIAL For an open single-phase system, we add the dependence of energy on composition, nU = U(nS, nV, n1, n2, n3, …). In consequence,  ∂(nU )  d (nU ) = T d (nS ) − P d (nV ) + ∑  dni  i  ∂ni  nS , nV , n j ≠i

(4-97)

where the summation is over all species present in the system and subscript nj≠i indicates that all mole numbers are held constant except the i th. Equation (4-97) is the fundamental property relation for mixed single-phase PVT systems, from which all other equations connecting properties of such systems are derived. The partial derivative in Eq. (4-97) has special significance for phase equilibria in mixtures, and it is called the chemical potential . Treatment of the other basic properties H, A, and G results in similar relations, the most important of which is  ∂(nG )  d (nG ) = −nS dT + nV dP + ∑  dni  i  ∂ni  T , P , n j ≠i

(4-98)

where chemical potential is given equivalently by  ∂(nU )   ∂(nG )  µi ≡  =    ∂ni  nS , nV , n j ≠i  ∂ni  T , P , n j ≠i

(4-99)

4-14

THERMODYnAMICS

PARTIAL MOLAR PROPERTIES

Integration at constant temperature and standard state pressure P ° gives

For a homogeneous PVT system composed of any number of chemical species, let symbol M represent the molar value of an extensive thermodynamic property, say, U, H, S, A, or G. The extensive quantity can be expressed as nM = M(T, P, n1, n2, n3, …) Their derivatives at constant T, P and all n except i are given the generic symbol M i and are defined as a partial molar property by  ∂(nM )  Mi ≡    ∂ni T ,P ,n j ≠i

(4-100)

nM = ∑ni M i

and

(4-101)

i

i

The definition of a partial molar quantity can be applied to all intensive properties yielding the partial-property relations H i = U i + PVi

Ai = U i − TSi

These equations illustrate the parallelism that exists between the equations for a constant-composition solution and those for the corresponding partial properties. This parallelism exists whenever the solution properties in the parent equation are related linearly (in the algebraic sense). The partial molar Gibbs energy should be recognized as the chemical potential, μ. The Gibbs-Duhem Equation Partial molar quantities must satisfy the Gibbs-Duhem relation [cf. Tester and Modell (1997)]

i

i

=0

(4-109)

G ig = ∑ y i Γ i (T ) + RT ∑ ln ( y i P )

(4-110)

(constant T , P )

i

A dimensional ambiguity is implied with Eqs. (4-108) through (4-110) in that P has units, whereas ln P must be dimensionless. Although the units cancel with the standard state pressure, in practice this is of no consequence, because only differences in Gibbs energy appear, along with ratios of the quantities with units of pressure in the arguments of the logarithm. Consistency in the units of pressure is, of course, required; if the standard state is 1 bar, use bars for all computations involving reactions. COMPOnEnT FUGACITY

µ i ≡ Γ i (T ) + RT ln ˆf i

(4-103)

i

(4-111)

where the partial pressure yiP is replaced by ˆf i , the fugacity of species i in solution. Because it is not a partial property, it is identified by a circumflex rather than an overbar. The fugacity of an ideal gas component is apparent by comparing Eqs. (4-111) and (4-109): ˆf i ig = y i P

(4-102)

Frequently, the first two terms are small, resulting in the approximate relation

∑ x dM

leading to

µ iig = Giig = Γ i (T ) + RT ln ( y i P )

The definition of the fugacity of a species in solution is parallel to the definition of the pure-species fugacity. An equation analogous to the ideal gas expression, Eq. (4-109), is written for species i in a fluid mixture

Gi = H i − TSi

 ∂M   ∂M   dP − ∑ x i dM i = 0  dT +    ∂ P T ,x  ∂T P ,x i

(4-108)

where the integration constant Γi(T) includes RT ln P ° and is a function of temperature and standard state pressure only. Equation (4-107) now becomes

i

where the derivative constraints are part of the definition. A result of this definition is that the molar property can be obtained by M = ∑ xi Mi

Giig = Γ i (T ) + RT ln P

(4-112)

Ideal Solution Model and Henry’s Law The ideal gas model is useful as a standard of comparison for real gas behavior. This is formalized through departure functions. The ideal solution is similarly useful as a standard to which real solution behavior may be compared and is common for liquid solutions. The partial molar Gibbs energy or chemical potential of species i in an ideal gas mixture is given by Eq. (4-107), written as

PROPERTIES OF IDEAL GAS MIXTURES

µ iig = Giig = Giig (T , P ) + RT ln y i

The ideal gas mixture model is useful because it is molecularly based, is analytically simple, is realistic in the limit of zero pressure, and provides a conceptual basis for solution thermodynamics. A simple molar average applies for internal energy, U, and volume, V, and thus enthalpy, H = U + PV,

This equation takes on new meaning when Giig(T, P) is replaced by Gi (T, P), the Gibbs energy of pure species i in its real physical state of gas, liquid, or solid at the mixture T and P. The ideal solution is therefore defined as one for which

M ig = ∑ y i M iig

µ iid = Giid ≡ Gi (T , P ) + RT ln x i

(4-104)

i

where M ig can represent U, V, or H. For the entropy an additional term is required to account for the distinguishability of species in a mixture: S ig = ∑ y i Siig − R ∑ y i ln y i i

Vi id = Vi ; and

For the Gibbs energy, G ig = H ig −TS ig whence by Eqs. (4-104) and (4-105) G ig = ∑ y i Giig + RT ∑ y i ln y i i

where superscript id denotes an ideal solution property and xi represents the mole fraction because application is usually to liquids. This relation requires

(4-105)

i

The ideal gas model may serve as a reasonable approximation to reality under conditions indicated by Eq. (4-21), where molar averages are applied to the critical properties. Chemical potential for an ideal gas is obtained by applying Eq. (4-100)

U iid = U i

id

Si = Si − R ln x i

H iid = H i

(4-107)

(4-115)

(4-116)

The mixture property can be calculated by the mole-fraction-weighted sum of partial molar properties, Eq. (4-101). For the special case of an ideal solution, incorporating Eqs. (4-113) through (4-116) gives: G id = ∑ x iGi + RT ∑ x i ln x i i

µ iig ≡ Giig = Giig + RT ln y i

(4-114)

Because H iid = Giid + TSiid , substitutions by Eqs. (4-113) and (4-115) yield

(4-106)

i

(4-113)

(4-117)

i

V id = ∑ x iVi

(4-118)

i

Elimination of Giig from this equation is accomplished through Eq. (4-38), written for pure species i as an ideal gas at the temperature of the system: dGiig = Vi ig dP =

RT dP = RT d ln P P

(constant T )

S id = ∑ x i Si − R ∑ x i ln x i i

(4-119)

i

H id = ∑ x i H i i

(4-120)

SYSTEMS OF VARIABLE COMPOSITIOn A simple equation for the fugacity of a species in an ideal solution follows. For the special case of species i in an ideal solution, Eq. (4-113) becomes µ iid = Giid = Γ i (T ) + RT ln ˆf i id

ˆf i id = x i f i

(4-122)

This equation, known as the Lewis-Randall rule, shows that the fugacity of each species in an ideal solution is proportional to its mole fraction; the proportionality constant is the fugacity of pure species i in the same physical state as the solution and at the same T and P. Division of both sides of ˆ iid for ˆf i id/x i P [Eq. (4-130)] and of φ i Eq. (4-122) by xi P and substitution of φ for fi/P [Eq. (4-64)] give the alternative form for equations of state φˆ iid = φ i

(4-123)

Thus the fugacity coefficient of species i in an ideal solution equals the fugacity coefficient of pure species i in the same physical state as the solution and at the same T and P. Ideal solution behavior is often approximated by solutions composed of molecules not too different in size and of the same chemical nature. Thus, a mixture of isomers conforms very closely to ideal solution behavior. So do mixtures of adjacent members of a homologous series. An alternative ideal solution results when the standard state is at infinite dilution rather than at purity, which results in the Henry law ideal solution, here written using the Henry volatility constant common in chemical engineering literature: ˆf i id = x i hi

(4-124)

While Eqs. (4-122) and (4-124) hint that hi and fi might be the same, they are equal only when a solution follows ideal solution behavior at all compositions, which is rare. Henry’s law is named after the English chemist who examined the solubilities of gases in water in the early 19th century [Phil . Trans . R . Soc . Lond. 93: pp. 29 and 274 (1803)]. In casual terms we would state that the concentration of a dissolved solute in a liquid is proportional to its partial pressure in the vapor phase, and the proportionality constant, at a given temperature, is referred to as Henry’s “constant” (although it varies with temperature). Formally, Henry’s law can be expressed as a limiting fugacity ˆf i x i →0 x i

hi = lim

(4-125)

where ˆf i is the fugacity of component i and xi is its liquid mole fraction. Application of the rigorous limit is often a problem in practice, and hence other considerations need to be adopted. For example, a reference fluid of pure sodium ions would be impractical when concerned with salt solutions. Over the past two centuries, scientists and engineers have built upon Henry’s seminal discovery to develop a comprehensive theoretical framework and extensive databases for the correlation of solute solubilities over a wide range of temperature, pressure, and liquid- and vapor-phase concentrations. This background is presented in the section following discussion of activity models.

The criteria for internal thermal and mechanical equilibrium simply require uniformity of temperature and pressure throughout the system. The criteria for phase equilibria at constant T and P require that the Gibbs energy for the overall system be minimized. For a two-phase system, each phase taken separately is an open system, capable of exchanging mass with the other. The criteria for phase equilibria are derived in textbooks. The general result is (4-126)

Substitution for each µi by Eq. (4-111) produces the equivalent result: ˆf i ′= ˆf i ′′= ˆf i ′′′=

∑µ

i

dni = 0

(4-128)

i

For a system in which both phase and chemical reaction equilibrium prevail, the criteria of Eqs. (4-127) and (4-128) are superimposed. PHASE RULE The intensive state of a PVT system is established when its temperature and pressure and the compositions of all phases are fixed. However, for equilibrium states not all these variables are independent, and fixing a limited number of them automatically establishes the others. This number of independent intensive variables is given by the phase rule, and it is called the number of degrees of freedom of the system. It is the number of variables that may be arbitrarily specified and that must be so specified in order to fix the intensive state of a system at equilibrium. This number is the difference between the number of variables needed to characterize the system and the number of equations that may be written connecting these variables. For a system containing N chemical species distributed at equilibrium among π phases, the phase rule variables are T and P, presumed uniform throughout the system, and N − 1 mole fractions in each phase. The number of these variables is 2 + (N − 1)π. The masses of the phases are not phase rule variables, because they have nothing to do with the intensive state of the system. The equilibrium equations that may be written to express chemical potentials or fugacities as functions of T, P, the phase compositions, and the phase rule variables: 1. Equation (4-127) for each species, giving (π − 1)N phase equilibrium equations 2. Equation (4-128) for each independent chemical reaction, giving r equations The total number of independent equations is therefore (π − 1)N + r. Because the degrees of freedom F is the difference between the number of variables and the number of equations, F = 2 + (N − 1)π − (π − 1)N − r or

F=2−π+N−r

(4-129)

The number of independent chemical reactions r can be determined as follows: 1. Write formation reactions from the elements for each chemical compound present. 2. Combine these reaction equations so as to eliminate from the set all elements not present as elements in the system. A systematic procedure is to select one equation and combine it with each of the other equations of the set so as to eliminate a particular element. This usually reduces the set by one equation for each element eliminated, although two or more elements may be simultaneously eliminated. The resulting set of r equations is a complete set of independent reactions. More than one such set is often possible, but all sets number r and are equivalent. Example 4-8 Application of the Phase Rule Consider the following cases. a . For a system of two miscible nonreacting species in vapor/liquid equilibrium, F=2−π+N−r=2−2+2−0=2

PHASE EQUILIBRIA CRITERIA

µ i′ = µ i′′ = µ ′′′ =

For the case of equilibrium with respect to chemical reaction within a single-phase closed system, at constant T and P, Eq. (4-98) simplifies to

(4-121)

When this equation and Eq. (4-111) are combined with Eq. (4-117), Γi (T ) is eliminated, and the resulting expression reduces to

4-15

(4-127)

These are the criteria of phase equilibrium applied in the solution of practical problems.

The 2 degrees of freedom for this system may be satisfied by setting T and P, or T and y1, or P and x1, or x1 and y1, etc., at fixed values. Thus for equilibrium at a particular T and P, this state (if possible at all) exists only at one liquid and one vapor composition. Once the 2 degrees of freedom are used up, no further specification is possible that would restrict the phase rule variables. For example, one cannot in addition require that the system form an azeotrope (assuming this is possible), for this requires x1 = y1, an equation not taken into account in the derivation of the phase rule. Thus the requirement that the system form an azeotrope imposes a special constraint, making F = 1. b . For a gaseous system consisting of CO, CO2, H2, H2O, and CH4 in chemical reaction equilibrium, F=2−π+N−r=2−1+5−2=4 The value of r = 2 is found from the formation reactions: C + 12 O 2 → CO

C + O 2 → CO 2

H 2 + O2 → H 2O

C + 2H 2 → CH 4

1 2

4-16

THERMODYnAMICS

Systematic elimination of C and O2 from this set of chemical equations reduces the set to 2. Three possible pairs of equations may result, depending on how the combination of equations is effected. Any pair of the following three equations represents a complete set of independent reactions, and all pairs are equivalent.

Applications of Eq. (4-135) represent the gamma/phi approach to VLE calculations, generally applicable below 10 bar. For Henry’s law, we use Eq. (4-131) for the vapor phase and Eq. (4-133) for the liquid phase,

CH4 + H2O → CO + 3H2

 P v∞  φˆ i y i P = hi (T , Pi o ) x i γ∗i exp ∫ i dP   Pio RT 

CO + H2O → CO2 + H2 CH4 + 2H2O → CO2 + 4H2 The result, F = 4, means that one is free to specify, for example, T, P, and two mole fractions in an equilibrium mixture of these five chemical species, provided nothing else is arbitrarily set. Thus it cannot simultaneously be required that the system be prepared from specified amounts of particular constituent species.

Component Fugacity and Activity Coefficients While Eqs. (4-126) to (4-128) form the basis of phase and chemical equilibria, they do not dictate the methods to be used to calculate the properties of the phases. Acknowledging that equilibria can be expressed in terms of chemical potential or fugacity, chemical engineering practice has evolved to use fugacity. We express the fugacity of the real gas or liquid relative to one of the idealized states (ideal gas, Lewis-Randall ideal solution, or Henry’s law ideal solution). When the fugacity is calculated relative to the ideal gas, the departure function is used, resulting in the component fugacity coefficient . Subtracting Eq. (4-107) from Eq. (4-111), both written for the same temperature, pressure, and composition, yields after including (4-108) µ i −µ iig = RT ln

ˆf i ≡ RT ln φˆ i yi P

When Henry’s law is applied, it is common to use it for some of the components (normally noncondensable components) while using the LewisRandall approach, Eq. (4-135), for the remainder of components. Excess Properties An excess property M E is defined as the difference between the actual property value of a solution and the value it would have as an ideal solution at the same T, P, and composition. Thus, M E ≡ M − M id

APPROACHES FOR PHASE AnD REACTIOn EQUILIBRIA MODELInG

(4-137)

where M represents the molar (or unit-mass) value of any extensive thermodynamic property (say, V, U, H, S, G). This definition is similar to the definition of a departure function as given by Eq. (4-52). However, excess properties have no meaning for pure species, whereas departure functions exist for pure species as well as for mixtures. Partial molar excess properties M iE are defined analogously: M iE = M i − M iid

(4-138)

Of particular interest is the partial molar excess Gibbs energy. Rewriting Eq. (4-111) as Gi = Γ i (T ) + RT ln ˆf i

(4-130) in accord with Eq. (4-122) for an ideal solution, this becomes

where by definition φˆ i  ≡ ˆf i / ( y i P ), or

Giid = Γ i (T ) + RT ln x i f i

ˆf i = y i φˆ i P

(4-131)

The dimensionless ratio φˆ i is called the fugacity coefficient of species i in solution. Using the Lewis-Randall rule, typically for condensed phases and thus the use of x gives  V cond ( P - Pi sat )  sat ˆf i cond = x i γi f i cond = x i γi φ sat exp i  i Pi RT  

  P vi∞ ˆf i L = hi (T , Pi o ) x i γ i∗ exp dP  ∫ RT o   Pi

(4-133)

The activity coefficient γi∗ of Eq. (4-133) is related, but not equal to the activity coefficient γi in Eq. (4-132) as discussed later in Eq. (4-199). For the EOS approach, we use Eq. (4-131) for both vapor and liquid phases, resulting in φˆ Vi y i = φˆ iL x i

(4-134)

This introduces compositions xi and yi into the equilibrium equations, but neither is explicit, because the φˆ i are functions of composition as well as T and P. Thus, Eq. (4-134) represents N complex relationships connecting T, P, {xi}, and {yi}. The EOS approach is typically successful for nonpolar substances and must be used when fluids are near critical points. Polar substances can be modeled by including association effects or by use of sophisticated mixing rules. For polar substances the gas phase may be modeled with the EOS approach, while the liquid phase is modeled with deviations from the Lewis-Randall rule. The fugacity of species i in the liquid phase is given by Eq. (4-132), and the vapor-phase fugacity is given by Eq. (4-131). By Eqs. (4-127) and (4-132) the relation becomes i = 1,2,…, N

By differences

(4-135)

Identifying superscripts L and V are omitted here with the understanding that γi is a liquid-phase property, whereas φˆ i is a vapor-phase property.

Gi − Giid = RT ln

ˆf i x i fi

The left side is the partial excess Gibbs energy GiE ; the dimensionless ratio ˆf i /x i f i on the right is the activity coefficient of species i in solution, given the symbol γi , and by definition,

(4-132)

where the activity coefficient γi characterizes the deviations from an ideal solution and f i cond is given by Eq. (4-67). For Henry’s law volatility constant, typically used for liquid phases,

sat γi x i φ sat exp(V L ( P − Pi sat )/( RT )) = φˆ i y i P i Pi

(4-136)

ˆf i x i fi

(4-139)

GiE = RT ln γi

(4-140)

γi ≡ Thus,

Comparison with Eq. (4-130) shows that Eq. (4-140) relates γi to GiE exactly as Eq. (4-130) relates φˆ i to Gidep. For an ideal solution, GiE = 0, and therefore γiid = 1. Activity coefficients are key descriptors in the design of chemical separation and reaction operations, liquid product formulations, and other technologies where liquid composition is a key factor affecting performance. In practice, the value of γi serves as a correction factor for the solute mole fraction concentration xi to better account for the solute’s true chemical potential–driven activity which determines phase equilibrium behavior and reactivity, µ i − Gi ° = RT ln ai

(4-141)

where activity is given by ai ≡ ˆf i /( f i °) and for the Lewis-Randall rule, ai = γi xi. For a Lewis-Randall ideal solution, γi is unity; each component acts as if surrounded by its own kind, so phase equilibrium properties are determined according to molar concentration or mole fraction (ai = xi). For other mixtures, the solute’s activity coefficient is usually greater than unity, and the solute behaves as if there is more of it present in the mixture than its mole fraction would indicate (ai > xi, a positive deviation from ideality). This may indicate that solute-solvent interactions are repulsive relative to solventsolvent interactions or may lead to segregation of the mixture (negative entropic effects). For a vapor-liquid system, such a component has an enhanced tendency to escape from the liquid into the vapor. The solute activity coefficient can also be less than unity such that its effective mole fraction in the mixture is reduced (ai < xi, a negative deviation). This behavior may result from mixing molecules that differ greatly in molecular size (an entropic effect) or by exothermic formation of multicomponent molecular structures

SYSTEMS OF VARIABLE COMPOSITIOn or complexes in solution. The activity coefficient is used to quantify a deviation from ideal mixture behavior, although often the molecular mechanisms responsible for the observed deviation are not fully understood. The infinite-dilution (or limiting) activity coefficient γij∞ = lim γi is a particux i →0 larly useful quantity because it represents nonideal interactions for a solute i completely surrounded by solvent j. Its value normally is the most extreme γi value for a given binary, and so it serves to characterize the nonideality of the mixture. The limiting activity coefficient is related to the partial molar excess Gibbs energy involved in moving a molecule of solute i from its pure liquid reference state into a pool of solvent j molecules: E ,∞

E ,∞

E ,∞

RT ln γij∞ = G ij = H ij − T S ij

(4-142)

Once a value for γij has been determined, by either experiment or prediction, values at other compositions can be estimated by extrapolation using a suitable correlation equation such as those discussed below. In many cases, ∞ knowledge of γij for all binary pairs allows reliable extrapolation to higher concentrations in multicomponent mixed solution—with results suitable for many applications or at least for initial screening studies. In special cases, data for ternary or higher numbers of components in solution may be needed to improve the correlation for final design purposes, especially for systems with unusually strong multicomponent intermolecular interactions or strong association of molecules of the same kind. A database of over ∞ 4000 values of γij has been published by Lazzaroni et al. [Ind . Chem . Eng . Res . 44: 4075–4083 (2005)]. Property Changes of Mixing A property change of mixing is defined by ∞

∆M ≡ M − ∑ x i M i

(4-143)

i

where M represents a molar thermodynamic property of a homogeneous solution and Mi is the molar property of pure species i at the T and P of the solution and in the same physical state. In addition, ∆G, ∆V, ∆S, and ∆H are the Gibbs energy change of mixing, the volume change of mixing, the entropy change of mixing, and the enthalpy change of mixing, respectively. Applications are usually to liquids. Each of Eqs. (4-117) through (4-120) is an expression for an ideal solution property, and each may be combined with the defining equation for an excess property. For an ideal solution, each excess property is zero. Property changes of mixing and excess properties are easily calculated one from the other. The most common property changes of mixing are the volume change of mixing ∆V and the enthalpy change of mixing ∆H, commonly called the heat of mixing. These properties are identical to the corresponding excess properties. Moreover, they are directly measurable, providing an experimental entry into the network of equations of solution thermodynamics. Excess and Departure Property Relations Equations for excess properties are developed in much the same way as those for departure properties. The following equations are in complete analogy to those for departure properties: V E  ∂(G E /RT )  =  RT  ∂ P  T ,x

(4-144)

 ∂(G E /RT )  HE = −T   RT  P ,x  ∂T

(4-145)

 ∂n (G E /RT )  ln γi =   ∂ni  T ,P ,n j ≠1 

(4-146)

This last equation demonstrates that ln γi is a partial property with respect to G E/RT, implying also the sum of mole-fraction-weighted partial molar properties to give the excess Gibbs energy can be written using activity coefficients E

G = ∑ x i ln γi RT i

(4-147)

 ∂ ln γi  Vi E  =   ∂ P T ,x RT

(4-148)

 ∂ ln γi  H iE   =− 2  ∂T P ,x RT

(4-149)

4-17

Equation (4-149) is a version of the Gibbs-Helmholtz equation. For a detailed discussion of the origins of this equation, see Mathias [Ind . Eng . Chem . Res . 55: 1076–1087 (2016)]. Analogous to Eqs. (4-144) and (4-145), we can write  ∂(G dep/RT )  =  ∂P  T ,x

(4-150)

 ∂(G dep/RT )  H dep = −T   RT ∂T  P ,x

(4-151)

V dep RT

Also implicit in Eq. (4-130) is the relation  ∂n (G dep/RT )  ln φˆ i =   ∂ni  T ,P ,n j ≠i

(4-152)

This equation demonstrates that ln φˆ i is a partial property with respect to G dep/RT. The sum of the mole-fraction-weighted partial molar properties to give the mixture property, relation (4-101), therefore applies, and G dep = ∑ x i ln φˆ i RT i

(4-153)

Recognizing ln φˆ i as a partial property leads to  ∂ ln φˆ i  V dep  = i  P ∂ T ,x RT 

(4-154)

 ∂ ln φˆ i  H dep  = − i 2  RT  ∂T P ,x

(4-155)

Component Fugacity Coefficients from an EOS Equation (4-152) can be applied readily only to departure functions explicit in T and P. For departure functions explicit in T and V, such as a cubic equation of state, an alternative method is used:  ∂n ( A dep/RT )  ln φˆ i =  − ln Z  ∂ni  T ,V ,n j ≠i

(4-156)

Example 4-9 Derivation of Fugacity Coefficient Expressions Application of Eq. (4-152) to an expression giving G dep as a function of composition yields an equation for ln φˆ i . In the simplest case of a gas mixture for which the virial equation [Eqs. (4-69) and (4-71)] is appropriate, Eq. (4-61) provides the relation nG dep P (nB ) = RT RT Differentiation in accord with Eqs. (4-152) yields

(

)

 ∂ 1 ∑ ∑ nk n j Bkj  n ˆ i  ∂(nB )  RT ln φ n  = = 2∑ y j Bij − B =   T ,n j ≠i P ∂ni  ∂ni  T ,n j ≠i  1

(4-157)

For EOSs involving Z(T, V ) such as cubic EOSs, the differentiation follows Eq. (4-156). For example, when the mixing and combining rules follow Eqs. (4-86) to (4-88) as nondimensionalized by Eq. (4-92), the component fugacity coefficient for the PR EOS is given by  fα  B ln φˆ iα = ln  i  = αi ( Z α − 1) − ln( Z α − B α )  yi P  B A α  2 Σz j Aij Bi   Z α + (1 + 2) B α  − α  − α  ln  α  B 8  Aα B   Z + (1 − 2) B α 

(4-158)

where α indicates the phase (that is, V or L) and zj indicates the mole fraction in that phase (typically yj for vapor and xj for liquid). The A here is not Helmholtz energy and B here is not the virial coefficient. Although the formula is the same for all phases, the values of ZV and ZL are naturally quite distinct. Similarly, AV, AL and BV, and BL differ owing to compositions. Standard texts describe this derivation in detail.

CORRELATIVE MODELS FOR THE EXCESS GIBBS EnERGY Excess properties find application in the treatment of liquid solutions. The excess volume for liquid mixtures is usually small, and in accord with Eq. (4-144) the pressure dependence of G E is usually ignored. Thus, engineering efforts to model G E center on representing its composition and

4-18

THERMODYnAMICS

temperature dependence. For educational purposes, G E models such as the Redlich-Kister expansion, Margules models, and the van Laar model are typically covered, but these are simple empirical or semiempirical relations that are best applied to binary systems. Since most realistic applications focus on multicomponent systems, we focus our discussion here on multicomponent G E models. All of these are typically available in chemical process simulators. Margules, Wilson, NRTL, UNIQUAC When experimental data are available for a system of interest, correlative models are preferred over predictive models if the quality of the data is high. We provide in later sections some recommendations for assessing data by evaluating trends in homologous series of compounds. Methods used to assess thermodynamic consistency are discussed by Kang et al. [ J . Chem . Eng . Data 55: 3631 (2010)]. If pure component vapor pressure data are in error, the thermodynamic consistency tests and reliability of the resulting model for multicomponent mixtures likely will be poor. Two subsections immediately following this one address sources of data and methods of reducing the data to relevant model parameters. Four G E models are applied to correlation most often, most based on the concepts of local compositions and Lewis-Randall activity coefficients: the Margules model, the Wilson model, the NRTL model, and the UNIQUAC model. To illustrate the general form of each model, in the discussion that follows formulas are listed for the activity coefficients of a binary mixture and evaluated for 1-propanol and water at 120°C as an example. Margules Equation The Margules equation is empirical. It is typically equivalent to the Redlich-Kister expansion in its one- to three-parameter form. The two-parameter Gibbs excess energy and activity coefficients can be written as GE = x 1 x 2 ( A21 x 1 + x 2 A12 ) RT

(4-159) (4-160)

ln γ 2 = x 12 ( A21 + 2( A12 − A21 ) x 2 )

(4-161)

For a mixture of 20 mol% propanol in water: A12 = 1.164; A21 = 2.244; γ1 = 2.777; and γ2 = 1.021. The Margules two-parameter model reduces to the one-parameter model when A12 = A21. The most common extension of the Margules model to multicomponent mixtures is Wohl’s expansion [cf. Prausnitz, Lichtenthaler, and de Azevedo (1999, Sec. 6.14)]. Extension of polynomial models for GE to multicomponent mixtures must be done carefully because the expression for GE must be invariant to division into identical subcomponents [Michelsen and Kistenmacher, Fluid Phase Equilib. 58: 229 (1990); Mathias, Klotz, and Prausnitz, Fluid Phase Equilib . 67: 31 (1991)]—the so-called invariance criterion. The Wohl expansion shown in the reference does not violate the invariance criterion. However, when models with higher-order binary summations are used, they should be evaluated to ensure that they do not violate this criterion. Theoretical developments in the molecular thermodynamics of liquid solution behavior are often based on the concept of local composition, presumed to account for the short-range order and nonrandom molecular orientations resulting from differences in molecular size and intermolecular forces. Introduced by G. M. Wilson [ J . Am . Chem . Soc . 86: 127–130 (1964)] with the publication of a model for G E, this concept prompted the development of alternative local composition models, most notably the NRTL (non-random two-liquid) equation of Renon and Prausnitz [ AIChE J. 14: 135–144 (1968)] and the UNIQUAC (UNIversal QUAsi-Chemical) equation of Abrams and Prausnitz [ AIChE J. 21: 116–128 (1975)]. Wilson Equation The Wilson equation contains just two parameters per binary system (aij and aji),

x Λ ln γi = 1 − ln ∑ x j Λ ij  − ∑ k ki  j  k ∑ j x j Λ kj

∞ ∞ ln γ 1,2 = − ln Λ12 + 1 − Λ 21 ; ln γ 2,1 = − ln Λ 21 + 1 − Λ12

By Eq . 4-164, both Λ12 and Λ21 must be positive numbers . These binary relations may be helpful when inferring values of the parameters from experimental data . For a mixture of 20 percent propanol in water, a12 = 3793 J/mol; a21 = 5844; V1 = 18 .76; V2 = 85 .71; γ1 = 2 .561; and γ2 = 1 .168 . The Wilson equation has a well-known limitation owing to the positive nature of Eq . (4-164); it cannot correlate liquid-liquid equilibria (LLE) . This can be an advantage for systems that exhibit large positive deviations from ideality, but do not exhibit LLE . More often it is a disadvantage because most systems with such nonideality do phase-separate at some set conditions . NRTL Equation The NRTL equation contains three parameters for a binary system and is written in multicomponent form as [C . Cohen and H . Renon, Canadian J . Chem . Eng . 48: 291–296 (1970)] ∑ j x j τ jiG ji GE = ∑x i RT ∑ k x kGki i ln γ i =

∑ j x j τ jiG ji ∑ k x kGki

+∑ j

∑ m x m τ mjGmj  x iGij  τij − ∑ k x kGkj  ∑ k x kGkj 

(4-162)

and

Vi

exp

−aij RT

i≠ j

(4-167)

α12 = α21 ≡ α for a single binary; τ12 =

b12 b ; τ 21 = 21 RT RT

where α, b12, and b21, parameters specific to a particular pair of species, are independent of composition and temperature . The infinite-dilution values of binary activity coefficients are ∞ = τ 21 + τ 12 exp(−ατ12 ) ln γ1,2

∞ = τ 12 + τ 21 exp(−ατ 21 ) ln γ 2,1

For 20 percent propanol in water with α = 0 .3: b12 = 75 .3 J/mol; b21 = 7259; γ1 = 2 .772; and γ2 = 1 .131 . UNIQUAC Equation The UNIQUAC equation treats G E/RT as made up of two additive parts, a combinatorial term G comb, accounting for molecular size and shape differences, and a residual term G res (which is not the same as “residual property,” i .e ., departure function), accounting for molecular interactions: G E = G comb + G res

(4-168)

Function G comb contains pure-species parameters only, whereas function G res incorporates two binary parameters for each pair of molecules . For a multicomponent system, G comb Φ θ = ∑ x i ln i + 5∑qi x i ln i RT xi Φi i i G res = − ∑qi x i ln ∑θ j τ ji  RT i  j 

(4-169)

(4-170)

where q is a relative surface area of the molecule and r is the relative molecular volume . (4-163)

Φi ≡

x i ri

∑x r

; θi ≡

(4-164)

where Vj and Vi are the molar volumes of pure liquids j and i, respectively, and aij is a constant independent of composition and temperature. Molar volumes Vj and Vi, themselves weak functions of temperature, form ratios that in practice may be taken as independent of T and are usually evaluated at or near 25°C, Λij = 1 for i = j, etc. All indices in these equations refer to the same species, and all summations are over all species. For each i, j pair there are two parameters, because Λij ≠ Λji . For example, in a ternary system

x i qi

∑x q j

j

The temperature dependence of the parameters is estimated by Vj

(4-166)

where G and τ are intermediate variables . Here i identifies the species, and j, k, m are dummy variables .

j j

Λ ij =

(4-165)

Gij = exp(−α ij τij )

ln γ1 = x 22 ( A12 + 2( A21 − A12 ) x 1 )

GE = − ∑ x i ln ∑ x j Λ ij  RT i   j

the three possible i, j pairs are associated with the parameters Λ12, Λ21; Λ13, Λ31; and Λ23, Λ32 . At infinite dilution for a binary mixture,

(4-171) j

j

Subscript i identifies species, and j is a dummy index; all summations are over all species . Note that τji ≠ τij; nevertheless, when i = j, then τii = τjj = 1 . In these equations ri (a relative molecular volume) and qi (a relative molecular surface area) are pure-species constants . The influence of temperature on G E/RT enters through the interaction parameters τji of Eq . (4-170), which are temperature-dependent: τ ji = exp

−a ji RT

Parameters for the UNIQUAC equation are therefore values of aji .

(4-172)

SYSTEMS OF VARIABLE COMPOSITIOn An expression for ln γi is found by application of Eq. (4-146) to the UNIQUAC model for G E/RT [Eq. (4-168)]. The result is given by the following equations: ln γi = ln γicomb + ln γires

4-19

methods discussed next may be used to generate excess Gibbs energy or activity coefficient information, and then the model parameters can be regressed against the predictions to provide a tractable multicomponent engineering process model.

(4-173)

 Φ Φ Φ Φ  ln γicomb = 1 − i + ln i − 5 qi 1 − i + ln i  xi xi θi θi  

(4-174)

 τ ij  ln γires = qi 1 − ln ∑θ k τ ki − ∑θ j  ∑ k θ k τ kj  k j 

(4-175)

Again subscript i identifies species, and j and k are dummy indices. For a mixture of 20 percent propanol in water: a21 = 20.4 J/mol; a12 = 2551; r1 = 3.25; q1 = 3.13; r2 = 0.94; q2 = 1.40; γ1 = 2.721; and γ2 = 1.140. The NRTL equation is the most flexible for fitting experimental data because it has three parameters per binary system, compared to two parameters for the Wilson or UNIQUAC models. For most applications, the default value of α = 0.3 suffices for the NRTL model, making it similar to the others when limited data are available. For multicomponent systems, the subscripted form of α should be used to distinguish, say, α12 (= α21) from α13 (= α31). The Wilson parameters Λij , NRTL parameters Gij , and UNIQUAC parameters τij inherit a Boltzmann-type T dependence from the origins of the expressions for G E, but it is only approximate. Computations of properties sensitive to this dependence (e.g., heats of mixing and liquid/liquid solubility) are in general only qualitatively correct. All parameters can be characterized from data for binary systems (in contrast to multicomponent), and this makes parameter determination for the local composition models a manageable task. PHASE EQUILIBRIUM DATA SOURCES The literature on phase equilibrium measurements is vast and continually increasing. Keeping track of all the data generated throughout time and across the globe is part of the mission of the Thermodynamics Research Center (TRC) in Boulder, Colorado, a part of the Physical and Chemical Properties Division of the National Institute of Standards and Technology (NIST). The NIST TRC group has developed a website (ThermoLit [ibid]) that compiles literature sources ostensibly covering all known physical property data pertaining to one-, two-, or three-component systems. The resource compiles citations of data for vapor-liquid, liquid-liquid, and solid-fluid equilibria. The Korean Database (KDB) (http://www.cheric.org/ research/kdb/hcvle/hcvle.php) provides online tabulation of some experimental data. Another database available in many university libraries is the DECHEMA database of Gmehling, Onken, and Arlt [Vapor-Liquid Equilibrium Data Collection, Chemistry Data Series, vol. 1, parts 1–8, DECHEMA, Frankfurt/Main, 1974–1990]. An older but still useful data collection is that of Stephens and Stephens [Solubilities of Inorganic and Organic Compounds, vol. 1, pts. 1 and 2, Pergamon, Oxford, England, 1960]. A database of infinite-dilution activity coefficients is included in the supporting information submitted with the article by Lazzaroni et al. [Ind . Eng . Chem . Res. 44(11): 4075–4083 (2005)]. A number of other sources have compiled data from the literature into a single volume or series that may be more convenient than referring to the original literature. Comprehensive collections of phase equilibrium data (including vapor-liquid, liquid-liquid, and solid-liquid data) and infinitedilution activity coefficients are maintained by the TRC and by DDBST, GmbH. Another database called Infotherm is available from Wiley. Other sources of thermodynamic data include the IUPAC Solubility Data Series published by Oxford University Press. Additional sources of data are discussed by Skrzecz [Pure Appl . Chem . (IUPAC), 69(5): 943–950 (1997)]. Data Reduction Correlations for G E and the activity coefficients are based on VLE data taken at low to moderate pressures. The process of finding a suitable analytic relation for G E/RT as a function of its independent variables T and x1, thus producing a correlation of VLE data, is known as data reduction. Although in principle G E/RT is also a function of P, the dependence is so weak as to be usually neglected. The adjustable parameters of the models are regressed by minimizing the residuals. The maximum-likelihood method [T. F. Anderson and J. M. Prausnitz, Ind . Eng . Chem . Proc . Res . Dev . 17: 552 (1978)] provides consideration that every measurement may include experimental error, but sometimes the method is difficult to reliably converge and thus a least-squares approach on bubble pressure, bubble temperature, or liquid-liquid phase behavior is typical. See also Van Ness [ J . Chem . Thermodyn. 27: 113–134 (1995); Pure & Appl . Chem . 67: 859–872 (1995)]. Although the discussion focuses on fitting experimental data, recognize that the predictive

PREDICTIVE AnD ADAPTIVE MODELS FOR THE EXCESS GIBBS EnERGY Predictive Models: UNIFAC, Solubility Parameter Models, COSMO For the design of processes that often involve synthesis of new compounds in new combinations or at new conditions, the need to predict mixture behavior is inevitable. Some models, such as UNIFAC, represent extensive correlations with large databases and scores of parameters based on regression of group contributions. Because UNIFAC is correlated by fitting group parameters to experimental data, it might be viewed as interpolations with molecular structure as the independent variable. The group contribution approach makes UNIFAC work well computationally, but provides little intuitive insight. Other models rely on leveraging insights from the analysis of the chemical nature of the molecular structure, such as hydrogen bonding tendencies or localized electron density. These models may be less accurate when compared to a large database, but can be helpful during the conceptual stages of process or product design. The UNIFAC Model Perhaps the most widely used activity model is the UNIFAC family of group contribution methods. These methods are based on the UNIQUAC equation, such that UNIFAC stands for UNIQUAC functional-group activity coefficients, proposed by Fredenslund, Jones, and Prausnitz [AIChE J. 21: 1086–1099 (1975)] and given detailed treatment by Fredenslund, Gmehling, and Rasmussen [Vapor-Liquid Equilibrium Using UNIFAC, Elsevier, Amsterdam, 1977], Fredenslund et al. [Ind . Eng . Chem . Proc . Des . Dev . 16(4): 450–462 (1977)]; and Wittig et al. [Ind . Eng . Chem . Res . 42(1): 183–188 (2003)]. Also see Jakob et al. [Ind . Eng . Chem . Res. 45: 7924–7933 (2006)]. Subsequent development has led to a variety of separate correlations, each focused on specific applications, including liquid/liquid equilibria [Magnussen, Rasmussen, and Fredenslund, Ind . Eng . Chem . Process Des . Dev . 20: 331–339 (1981)], solid/liquid equilibria [Anderson and Prausnitz, Ind . Eng . Chem . Fundam . 17: 269–273 (1978)], solvent activities in polymer solutions [Oishi and Prausnitz, Ind . Eng . Chem . Process Des . Dev . 17: 333–339 (1978)], vapor pressures of pure species [Jensen, Fredenslund, and Rasmussen, Ind . Eng . Chem . Fundam . 20: 239–246 (1981)], gas solubilities [Sander, Skjold-Jørgensen, and Rasmussen, Fluid Phase Equilibr . 11: 105–126 (1983)], and excess enthalpies [Dang and Tassios, Ind . Eng . Chem . Process Des . Dev . 25: 22–31 (1986)]. The range of applicability of the original UNIFAC model has been greatly extended and its reliability enhanced. Its most recent revision and extension is treated by Wittig et al. (2003), wherein are cited earlier pertinent papers. Because it is based on temperature-independent parameters, its application is largely restricted to 0 to 150°C. Two modified versions of the UNIFAC model, based on temperaturedependent parameters, have come into use. Not only do they provide a wide temperature range of applicability, but also they allow correlation of various kinds of property data, including phase equilibria, infinite-dilution activity coefficients, and excess properties. The most recent revision and extension of the modified UNIFAC (Dortmund) model is provided by Gmehling et al. [Ind . Eng . Chem . Res . 41: 1678–1688 (2002)]. An extended UNIFAC model called KT-UNIFAC is described in detail by Kang et al. [Ind . Eng . Chem . Res . 41: 3260–3273 (2003)], and updated [Fluid Ph . Equilibr. 309: 68–75 (2011)]. The use of UNIFAC for estimating LLE is discussed by Gupte and Danner [Ind . Eng . Chem . Res . 26(10): 2036–2042 (1987)] and by Hooper, Michel, and Prausnitz [Ind . Eng . Chem . Res . 27(11): 2182–2187 (1988)]. Vakili-Nezhand, Modarress, and Mansoori [Chem . Eng . Technol . 22(10): 847–852 (1999)] discuss its use for representing a complex stream containing a large number of components for which available LLE data are incomplete. Similar to UNIQUAC, UNIFAC calculates activity coefficients in two parts: ln γi = ln γicomb + ln γires

(4-176)

is calculated from pure-component propThe combinatorial part ln γ comb i erties. The residual part ln γ ires is calculated by using binary interaction parameters for solute-solvent group pairs determined by regressing the group parameters against a large set of phase equilibrium data. Thus, the predictions are most reliable when the method is applied to monofunctional molecules similar to those used in the regression. With this approach, a molecule is treated as a mixture of various functional groups. The proximity of the groups to one another in the molecule is not taken into account. Solubility Parameter Models A number of methods based on regular solution theory are also available. Only pure-component parameters are needed to make estimates, so they may be applied when UNIFAC group-interaction parameters are not available. These methods are also sufficiently simple that

4-20

THERMODYnAMICS

they provide intuitive guides as to what compounds might blend well or contribute to desirable solution behavior, such as increasing solution ideality. Scatchard-Hildebrand Theory Scatchard-Hildebrand solution theory defines G E in terms of GE U E = = ∑ x iVi (δ i − < δ >)2 + V > RT RT

(4-177)

RT ln γi = Vi [(δi − < δ >)2 + 2 < kim > − >]

(4-178)

where < δ > = ∑Φj δj, > = ∑Φi δi < kim >, < kim > = ∑Φj δj kij, Φi = xi Vi/(∑ xj Vj), and kij = kji = a single binary parameter per binary system. The parameter δ is known as the Hildebrand solubility parameter and defined in terms of pure-component properties at 25°C. δ≡

ΔU vap ∆H vap − 298.15 R ≈ L V VL

(4-179)

Assuming kij = 0 for all i, j, the theory is predictive, but always predicts positive deviations from ideal solution behavior. This theory is generally reasonable for hydrocarbons and slightly polar substances, but not for complexing or hydrogen bonding systems. The theory can be derived from the van der Waals EOS based on the assumption of a constant packing fraction for all liquids, so its pedigree is similar in quality to that of most EOS methods. There are two guidelines that are apparent from the defining equations: (1) Systems are more nearly ideal (G E ≈ 0) when all the solubility parameters are equal. (2) Larger molecules tend to amplify the nonideality. The first guideline may be more familiar in the form “like dissolves like,” although the mathematical model provides a more quantitative suggestion. The second guideline may sound reasonable if you are familiar with the poor mutual solubility of polymers in one another; even polyethylene and polypropylene blend poorly. Flory-Huggins Model For polymer solutions and blends, the primary workhorse continues to be the Flory-Huggins model. This model is very similar to regular solution theory, but adds a term to recognize that excess entropy (S E ) is significant for polymers as well as excess energy (U E ).

(

ln γ i = Vi [(δ i − < δ >)2 + 2 < kim > − > ]/(RT ) + 1 −

Φi

) (Φ x )

x i + ln

i

Hansen Solubility Parameters The Hansen solubility parameter model divides the Hildebrand solubility parameter into three parts to obtain parameters δd, δ p, and δ h accounting for nonpolar (dispersion), polar, and hydrogen-bonding effects [Hansen, J . Paint Technol . 39: 104–117 (1967)]. An activity coefficient may be estimated by using an equation of the form (4-181)

where δ2 = (δd )2 + 0.25[(δ p )2 + (δ h)2] [Frank, Downey, and Gupta, Chem . Eng . Prog . 95(12): 41–61 (1999)]. Equation (4-181) is equivalent to Eq. (4-178) for nonpolar mixtures with zero binary interaction parameters. The Hansen model has been used for many years to screen solvents and facilitate development of product formulations. Hansen parameters have been determined for more than 500 solvents [Hansen, Hansen Solubility Parameters: A User’s Handbook, CRC, Boca Raton, Fla., 2000); and CRC Handbook of Solubility Parameters and Other Cohesion Parameters, 2d ed., ed. Barton (CRC, Boca Raton, Fla., 1991)]. MOSCED and SPACE Models MOSCED (Modified Separation of Cohesive Energy Density) is another modified Scatchard-Hildebrand solution model. MOSCED utilizes two parameters to represent hydrogen bonding: one for proton donor capability (acidity) and one for proton acceptor capability (basicity) [Thomas and Eckert, Ind . Eng . Chem . Proc . Des . Dev. 23(2): 194–209 (1984)]. This provides a more realistic representation of hydrogen bonding that allows more accurate modeling of a wider range of solvents, and unlike the Hansen model, MOSCED can predict negative deviations from ideal solution (activity coefficients less than 1.0). MOSCED calculates infinite-dilution activity coefficients by using 2  2 q 2 q 2 ( τT − τT ) (αT −α1T )(βT2 −β1T )   RT ln γ∞2,1 = V2 (δ2d −δ1d ) + 1 2 2 1 + 2 ψ1 ξ1  

(

+ 1 − V2 V

1

)

aa

( )

+ aa ln V2 V 1

0.8

0.4

There are five adjustable parameters per molecule: the dispersion parameter δd originally represented as λ by Thomas and Eckert; the induction parameter q; the polarity parameter τ; the hydrogen-bond acidity parameter α; and the hydrogen-bond basicity parameter β. The induction parameter q often is set to a value of 0.9 or 1.0, yielding a four-parameter model. The terms aa, ψ, and ξ are asymmetry factors calculated from α, β, and τ as a function of temperature. The complete model equations and a database of parameter values for approximately 150 compounds are given by Lazzaroni et al. [Ind . Eng . Chem . Res. 44(11): 4075–4083 (2005)]. An application of MOSCED in the study of liquid-liquid extraction is described by Escudero, Cabezas, and Coca [Chem . Eng . Comm. 173: 135–146 (1999)]. Also see Frank et al. [Ind . Eng . Chem . Res . 46: 4621–4625 (2007)]. Methods for predicting unavailable MOSCED parameters have been discussed by Gnap and Elliott, [Fluid Phase Eq ., in press (2018)]. Another method closely related to the MOSCED model is the SPACE model for estimating infinite-dilution activity coefficients [Hait et al., Ind . Eng . Chem . Res. 32(11): 2905–2914 (1993)]. The SPACE model utilizes refractive indices and solvatochromic parameters. The solvatochromic parameters are α (acidity), β (basicity), π (polarity), and δ (polarizability). These have been measured independently of phase equilibria data using spectroscopic techniques such as NMR and UV. The number of parameters is fewer in the SPACE model, in principle, but there are several generalized correlations required to implement the method. The more recent paper by Lazzaroni et al. offers the simplest and most reliable method between SPACE and MOSCED. Table 4-1 shows typical values for MOSCED parameters over a range of compounds. In the absence of hydrogen bonding, as in the case of acetone + n-octane, mixing follows the formula based on differences in δd and τ; positive deviations are predicted. The acidity and basicity provide the strongest indication of solution nonideality. When both α and β are significant for a given compound, mixing with a compound that has small α and β leads to large positive deviations from ideality, as in the case of phenol + n-decane. An azeotrope or liquid-liquid equilibrium should be suspected for such a system. When one compound is relatively acidic and the other relatively basic, as for phenol + pyridine, negative (exothermic) deviations from ideality should be expected. Finally, when both compounds have similar acidity and basicity, the influences of hydrogen bonding may cancel and the mixture behavior returns to being ideal, as in the case of phenol + benzyl alcohol.

i

(4-180)

RT ln γi = Vi {(δid − < δd >)2 + 0.25[(δip − < δ p >)2 + (δih − < δh >)2 ]}

0.8

 293   293   293  where αTi = αi    , τTi = τ i   , βTi = βi   T   T   T 

(4-182)

TABLE 4-1 Sampling of MOSCED Parameters

Acetic Acid Acetone Aniline Benzene Benzyl Alcohol Chloroform n-Decane Ethanol Iso-octane Methanol MTBE n-Octane Phenol Pyridine Water p-xylene

ρ298

δ( J/cm3)1/2

α

β

δd

τ

1.04 0.79 1.02 0.87 1.04 1.48 0.73 0.79 0.7 0.79 0.74 0.7 1.06 0.98 1 0.86

19 19.64 24.12 18.73 24.7 18.92 15.7 26.13 14.11 29.59 15.17 15.5 24.63 21.56 47.86 17.9

24.03 0 6.51 0.63 15.01 5.8 0 12.58 0 17.43 0 0 25.14 1.61 52.78 0.27

7.5 11.14 6.34 2.24 6.69 0.12 0 13.29 0 14.49 7.4 0 5.35 14.93 15.86 1.87

14.96 13.71 16.51 16.71 16.56 15.61 15.7 14.37 14.11 14.43 15.17 15.5 16.66 16.39 10.58 16.06

3.23 8.3 9.41 3.95 5.03 4.5 0 2.53 0 3.77 2.48 0 4.5 6.13 10.48 2.7

In general, perusing Table 4-1 shows that most alcohols exhibit balanced acidity and basicity, although the magnitudes of α and β decrease as the molecular volume increases. Ketones, ethers, aldehydes, amines, and esters tend to be relatively basic. Distinctly acidic behavior is less common, except for aromatic alcohols and, of course, carboxylic acids. These elementary insights can go a long way toward making solution behavior seem less mysterious. We revisit these insights when we consider the guidelines of phase diagrams and Robbins’ table. COSMO Models: COSMO-RS and COSMO-SAC The thermodynamic methods described above glean information from available data to make estimates for other systems. As an alternative approach, quantum chemistry calculations and molecular simulation methods are finding greater use in engineering applications [Gupta and Olson, Ind . Eng . Chem . Res. 42(25): 6359–6374 (2003); and Chen and Mathias, AIChE J. 48(2): 194–200 (2002)]. These methods minimize the need for data; however, the computational effort and specialized expertise required to use them are generally higher, and the accuracy of the

SYSTEMS OF VARIABLE COMPOSITIOn results may not be known. An important method gaining increasing application in the chemical industry is the conductor-like screening model (COSMO) introduced by Klamt and colleagues [Klamt, J . Phys . Chem. 99: 2224 (1995); Klamt and Eckert, Fluid Phase Equilibr. 172: 43–72 (2000); Eckert and Klamt, AIChE J. 48(2): 369–385 (2002); and Klamt, From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design, Elsevier, Amsterdam, 2005]. Also see Grensemann and Gmehling, Ind . Eng . Chem . Res . 44(5): 1610–1624 (2005). This method utilizes computational quantum mechanics to calculate a twodimensional electron density profile to characterize a given molecule. This profile is then used to estimate phase equilibrium through application of statistical mechanics and solvation theory. The Klamt model is called COSMO-RS ( for realistic solvation). A similar model is COSMO-SAC ( for segment activity coefficient) published by Lin and Sandler [Ind . Eng . Chem . Res . 41(5): 899–913, 2332 (2002)]. Databases of electron density profiles (sigma profiles) are available from a number of vendors and universities. A sigma-profile database of more than 1000 molecules is available from the Virginia Polytechnic Institute and State University [Mullins et al., Ind . Eng . Chem . Res . 45(12): 4389–4415 (2006)]. An application of COSMOS-RS to predict liquid-liquid equilibria is discussed by Banerjee et al. [Ind . Eng . Chem . Res. 46(4): 1292–1304 (2007)]. Adaptive Models LSER, NRTL-SAC When data are available for a homologous series of compounds, but not the specific compound of interest, linear solvation energy relationships (LSERs) may be useful. A method developed by Meyer and Maurer [Ind . Eng . Chem . Res. 34(1): 373–381 (1995)] uses the LSER model [Taft et al., Nature 313: 384 (1985); and Taft et al., J . Pharma Sci. 74: 807–814 (1985)] to estimate infinite-dilution partition ratios for solutes distributed between water and an organic solvent. The model uses 36 generalized parameters and 4 solvatochromic parameters to characterize a given solute. Also see Abraham, Ibrahim, and Zissimos, J . Chromatography 1037: 29–47 (2004). Other Estimation Methods Another method for estimating activity coefficients is described by Chen and Song [Ind . Eng . Chem . Res. 43(26): 8354– 8362 (2004); 44(23): 8909–8921 (2005)]. This method involves regression of a small data set in a manner similar to the way the Hansen and MOSCED models typically are used. The model is based on a modified NRTL framework called NRTL-SAC ( for segment activity coefficient) that utilizes only pure-component parameters to represent polar, hydrophobic, and hydrophilic segments of a molecule. An electrolyte parameter may be added to characterize ion-ion and ion-molecule interactions attributed to ionized segments of species in solution. The resulting model may be used to estimate activity coefficients and related properties for nonionic organics plus electrolytes in aqueous and nonaqueous solvents. Another approach involves use of molecular simulation or electron density calculations to predict values of parameters for phase equilibrium models. An example involves prediction of MOSCED parameters [R. Ley, G. Fuerst, B. Redeker, and A. Paluch, Ind . Eng . Chem . Res. 55(18): 5415–5430 (2016); J. Phifer, K. Soloman, K. Young, and A. Paluch, AIChE J . 63: 781–791 (2017)]. This approach combines molecular modeling and phase equilibrium theory to obtain a predictive tool well suited to early-stage process development. MODEL SELECTIOn Model selection can seem overwhelming due to the large number of possible models. Use of correlative methods fitted to experimental data is preferred over predictive methods, and sometimes a local fit of parameters is necessary [P. M. Mathias, J . Chem . Eng . Data . 61: 4077–4084 (2016)]. Predictive methods should be used cautiously when the compounds of interest differ from those used in the model development or when multifunctional molecules are present. For subcritical systems (say, P < 15 bar), an activity model is likely to suffice. The NRTL model has the advantage of a third parameter when needed, so try it first with α = 0.3, then adjust α if necessary. If the comparison indicates liquidliquid equilibrium where there is none, try the Wilson model. LLE is indicated by a minimax in the predicted y-x curve. If a substantial gap exists in the experimental data along the x axis, it may be that the system exhibits LLE. Careful model validation against experiment is especially critical for the heavy and light key components in distillation. Multiple columns would have multiple keys so each pair would need to be checked. For the components of secondary importance, experimental data should be sought but predictive methods (such as UNIFAC) can be applied if necessary. Generally, different model parameters are needed for VLE and LLE, even with the same model. If a different model or parameter set is best for different unit operations, customize each operation. If multicomponent data are available, a y-x comparison to experiment is possible by applying a pseudocomponent basis, y ′ = yL/(yL + yH), for example. Of course, the experimental data should be as close to process conditions as possible, but data within 50°C of process conditions should suffice. Processes involving components with significant association in the vapor phase (e.g., carboxylic acids) should include an association model such as that of Hayden-O’Connell. For processes with fluids near a critical point or with retrograde condensation, it is advisable to try an EOS method. The General References include

4-21

discussions of phase diagrams in the critical region [e.g., Elliott and Lira, chapter 16 (2012)]. It may be necessary to compare several models in these cases. For predictions, the predictive SRK method provides a reasonable start [Horstmann et al., Fluid Phase Equilibr . 167: 173–186 (2000)]. For correlation, the modified Huron-Vidal method prevails in most comparisons. If systems involve heavy components or polymers in important roles, the PC-SAFT model should be considered. The PC-SAFT model shows promise as a basis for both prediction and correlation, but it has not been fully implemented in all process simulators. After EOS methods are tried, activity models should be considered also as long as one of the key components is not supercritical. The model that agrees best with experiment is preferred. PRELIMInARY ESTIMATES It may be advisable to consider some relatively quick guidelines before delving deeply into computer calculations. Often, considering the kinds of phase behavior to be encountered before seeing the computational output may facilitate a critical evaluation of the output. In other cases, applications of interest may require formulations that involve multiple components designed to achieve a certain process objective such as moderating the solution nonideality for an extractive distillation or finding a liquid solvent that extracts the solute of interest from a diluent while maintaining minimal mutual solubility between solvent and diluent. A purely computational approach might involve many random trials and errors, while phenomenological consideration of a model such as MOSCED could help to guide the search. Two useful approaches are outlined briefly below. Robbins’ Table The interactions of polar and hydrogen bonding forces evident in the MOSCED, Hansen, and COSMO models lead to intuitive insights about how combinations of chemicals may behave in solution. This insight can be helpful when choosing an entrainer for an azeotropic system or a solvent for liquid-liquid extraction, for example. A well-known guide is Robbins’ table (Table 4-2) of solute-solvent interactions [Chem . Eng . Prog. 76(10): 58–61 (1980).] This table indicates whether interactions between compounds are likely to yield positive, negative, or near-zero deviations from ideal solution behavior. Similar tables for anticipating solvent-solute interactions are often cited in discussions of distillation and liquid extraction. These rely largely on classifications of hydrogen bonding and polarity that are similar to the intent to those of Robbins’ table, with similar results. TABLE 4-2 Robbins’ Table (Modified by Gnap and Elliott) of Solute–Solvent Interactions* α′(J)½ β′(J)½ Acids, etc. Thiol Alcohol, water Ketones, etc. 3′amine 2′amine 1′amines, etc. Ethers, etc. Esters, etc. Aromatics, etc. Nonpolar

157 11 200 0.1 0.1 13 65 0.1 0.1 0.1 0.1

Class

1

2

3

4

5

6

7

8

9 10 11

1 2 3 4 5 6 7 8 9 10 11

0 0 0 – – – 0 – – + +

0 0 + – – 0 0 0 0 + +

0 + 0 + 0 – – + + + +

– – + 0 0 + + 0 0 0 +

– – 0 0 0 + + 0 + 0 0

– 0 – + + 0 0 0 0 0 +

0 0 – + + 0 0 + + + +

– 0 + 0 0 0 + 0 0 0 +

– 0 + 0 + 0 + 0 0 0 +

11 55 70 26 33 211 755 33 99 4 0

+ + + 0 0 0 + 0 0 0 0

+ + + + 0 + + + + 0 0

∗Detailed class descriptions are given in the text.

The listings of acidity and basicity may be viewed in terms of average acidity or basicity as characterized by the MOSCED model. The entries in the classic Robbins’ table can be predicted about 70 percent of the time with the formula ∆is =

(α′2 − α′1 )(β′2 − β′1 ) (α′2 + α′1 )(β′2 + β′1 )

(4-183)

where αi′ and βi′ are the generalized values. When ∆is < −0.2, a negative deviation is indicated. When ∆is > 0.4, a positive deviation is indicated. For −0.2 < ∆is < 0.4, relatively ideal solution behavior can be expected. The primary source of discrepancies between Eq. (4-183) and Robbins’ table involves differences in the assessment of polarity. For example, mixtures of esters with paraffins normally give positive deviations from ideality, but calculated ∆is values can be close to zero. This discrepancy might be anticipated by including the MOSCED term for polarity in the assessment, but this level of detail would undermine the simplicity of Robbins’ table. In this modified version, the classifications of phenols, acids, and halogenated acids have been adjusted somewhat to take polarity effects into account. The detailed groupings for each classification are as follows: (1) Acids, phenols, active H on multihalogen paraffin; (2) thiols; (3) alcohol,

4-22

THERMODYnAMICS Phase Diagrams Either solutions can be ideal, or they can exhibit positive (γ > unity) or negative (γ < unity) deviations from ideality. Ideal solutions cannot exhibit liquid-liquid equilibrium (LLE) or azeotropes. Negative deviations from ideality cannot result in LLE, but they can result in azeotrope formation. Positive deviations from ideality can result in azeotropes and LLE if the activity coefficients are large enough. For a binary solution, if the geometric mean of the infinite-dilution activity coefficients exceeds 10, the prospect of LLE should be checked. In the case of vapor-liquid equilibria (VLE), the relative volatility is important to consider.

water; (4) ketones, tertiary amide, sulfone, phosphine; (5) tertiary amine; (6) secondary amine; (7) primary amine, primary amide, NH3; (8) ether, oxide, sulfoxide; (9) ester, aldehyde, carbonate, phosphate, nitrate, nitrite, nitrile, intramolecular H bonding (e.g., o-nitrophenol); (10) aromatic, olefin, halogenated aromatic, multihalogen paraffin without active H, and monohalogen paraffin; (11) paraffin and carbon disulfide. Example 4-10 Entrainer Selection for Extractive Distillation A common problem in gasohol production is overcoming the ethanol + water azeotrope. Extractive distillation involves the addition of a relatively nonvolatile entrainer that is miscible in both components. interacts favorably with the less volatile component (water in this case), and moderates the solution nonideality. Candidates for the entrainer are glycerol triacetate, monoethanolamine, and ethylene glycol. Which candidate is most promising from the perspective of Robbins’ table? Solution Glycerol triacetate is an ester with a boiling point near 258°C, monoethanolamine is an alcohol/primary amine with boiling point near 170°C, and ethylene glycol is a diol with a boiling point of 198°C (chemspider.com is convenient for this kind of search). Although the acid/base combination seems favorable for the triacetate, Robbins’ table indicates a positive deviation from ideality. The glycol is simply another alcohol, so it indicates zero deviation. The ethanolamine is similar to glycol except that one hydroxyl has been replaced by a primary amine. The primary amine indicates a negative deviation from ideality, suggesting that it should provide more powerful suppression of the water activity, requiring less entrainer. Therefore, monoethanolamine would be recommended by Robbins’ perspective. Other considerations such as cost, toxicity, reactivity (the acetate would likely hydrolyze and monoethanolamine may react with trace impurities), or ease of entrainer regeneration must also be considered.

αij ≡

K i γi Pi sat = K j γ j Pjsat

(4-184)

where Ki = yi /xi is the ratio of vapor mole fraction to liquid mole fraction and the order of i and j is chosen such that Pisat > P jsat, indicating that αij > 1 for an ideal solution. If αij < 1 for some range of compositions, an azeotrope occurs. Azeotropes are important because distillation fails when the vapor and liquid phases have the same composition. Checking the relative volatility of key components at both top and bottom of the column is recommended, deliberately verifying whether it crosses unity. These cases can be illustrated by Fig. 4-2. T-xy diagrams have two advantages: (1) the onset of LLE is easier to show than in a P-xy diagram and (2) most

475

470 460 450 Temperature (K)

Temperature (K)

470

465

460

440 430 420 410 400

455

390 450

380 0

0.2

(a)

0.4 0.6 0.8 Mole fraction of phenol

1

0

(b)

0.2

0.4

0.6

0.8

1

Mole fraction of pyridine 380

30

370 360 Temperature (K)

Pressure (kPa)

25

20

350 340 330 320

15

310 10 (c)

300 0

0.2

0.4 0.6 0.8 Mole fraction of decane

1 (d)

0

0.2

0.4

0.6

0.8

1

Mole fraction of decane

FIG. 4-2 Phase diagrams fit using the NRTL model. (a) T-xy for phenol(1) + p-cresol(2) at 96.4 kPa. b12 = 1567.2 J/mol, b21 = −2010.3, α = 0.3. Data of Selvam et al. [Fluid Phase Equilibr . 78: 261–267 (1992). γ1∞(NRTL) = 0 .85, γ2∞ = 0 .81 . Dotted lines show the ideal solution model . (b) T-xy for pyridine(1) + phenol(2) at 101 .32 kPa . b12 = −7235 .8 J/mol, b21 = 1886 .5, α = 0 .3 . Data of F . A . Assal [Bull . Acad . Pol . Sci . Ser . Sci . Chim . 14: 603 (1966)] . γ1∞(NRTL) = 0 .055, γ2∞ = 0 .17 . (c) P-xy for n-decane(1) + phenol(2) at 119 .8°C . Solid lines use b12 = 4259 .6 J/mol, b21 = 5729 .5, α = 0 .43, γ1∞(NRTL) = 12 .2, γ2∞ = 8 .4 . Dotted lines use parameters from figure (d ), γ1∞(NRTL) = 2 .5, γ2∞ = 1 .5 . (d ) T-xy for n-decane(1) + phenol(2) at 5 kPa . Solid lines use b12 = −71 .382T (K) + 26038 J/mol, b21 = 1 .9217T(K) + 4704 .8, α = 0 .3 . Dotted lines using parameters from (c) . Figures (c) and (d) use data of Gmehling [ J . Chem . Eng . Data 27: 371 (1982)] .

SYSTEMS OF VARIABLE COMPOSITIOn phase separation processes are conducted at nearly constant pressure. Figure 4-2a shows the case of a nearly ideal solution. Figure 4-2b shows a maximum boiling azeotrope. When phenol mixes with p-cresol, the solution is nearly ideal, but when it mixes with pyridine, an exothermic acidbase interaction ensues. Since the vapor pressures of phenol and pyridine are similar, the ratio of activity coefficients overwhelms the ratio of vapor pressures in the relative volatility, and a maximum boiling azeotrope results. A similar phenomenon occurs for n-decane + phenol, but with large positive deviations from ideality overwhelming the vapor pressure ratio and causing a minimum boiling azeotrope, as shown in Fig. 4-2c and d. The rationale for associating the system with a minimum boiling azeotrope is most evident in Fig. 4-2d, where it is evident that boiling refers to the bubble temperature, not bubble pressure. Figure 4-2c shows that the P-xy diagram is the flipped top-to-bottom image of the T-xy diagram for the same system. Also evident in Fig. 4-2d is the onset of LLE at temperatures below the bubble point. At higher pressures, the bubble curve would increase to higher temperatures and the LLE would be relatively unaffected. In some mixtures, where the nonideality is larger than for the system illustrated, the VLE curve may intersect with the LLE curve, resulting in VLLE. Finally, Fig. 4-2c and d illustrates a challenge in representing VLE and LLE simultaneously with universal parameters. The parameters fitted to VLE in Fig. 4-2c give a poor representation of LLE in Fig. 4-2d. Similarly, the parameters fitted to LLE in Fig. 4-2d give a poor representation of VLE in Fig. 4-2c. Therefore, the “optimal” assessment depends on the job at hand. VAPOR/LIQUID EQUILIBRIUM Vapor/liquid equilibrium (VLE) relationships (as well as other interphase equilibrium relationships) are needed in the solution of many engineering problems. The general VLE problem treats a multicomponent system of N constituent species for which the independent variables are T, P, N − 1 liquid-phase mole fractions and N − 1 vapor-phase mole fractions. (Note that ∑i xi = 1 and ∑i yi = 1, where xi and yi represent liquid and vapor mole fractions, respectively.) Thus there are 2N independent variables, and application of the phase rule shows that exactly N of these variables must be fixed to establish the intensive state of the system. This means that once N variables have been specified, the remaining N variables can be determined by simultaneous solution of the N equilibrium relations [Eq. (4-127)]. In practice, either T or P and either the liquid-phase or vaporphase composition are specified, thus fixing 1 + N − 1 = N independent variables. K Values, VLE, and Flash Calculations A measure of the distribution of a chemical species between liquid and vapor phases is the K value, defined as the equilibrium ratio: yi xi

Ki ≡

(4-185)

It has no thermodynamic content, but may make for computational convenience through elimination of one set of mole fractions in favor of the other. It does characterize “lightness” of a constituent species. A “light” species, with K > 1, tends to concentrate in the vapor phase, whereas a “heavy” species, with K < 1, tends to concentrate in the liquid phase. In practice, at least one K i ≥ 1, and at least one K i ≤ 1. The defining equation for K can be rearranged as yi = Ki xi . The sum ∑i yi = 1 then yields

∑K x i

i

=1

(4-186)

i

With the alternative rearrangement xi = yi/Ki, the sum ∑i xi = 1 yields yi

∑K i

=1

(4-187)

4-23

are here T and P, and systems are formed from given masses of nonreacting chemical species. For F moles fed of a system with overall composition represented by the set of mole fractions {zi}, let L represent the moles of the system that are liquid (mole fractions {xi}) and let V represent the moles that are vapor (mole fractions {yi}). The material balance equations are L+V=F

ziF = xiL + yiV

i = 1, 2, . . . , N

(4-188)

x i = zi /(1 + (V /F )( K i − 1)), y i = zi K i /(1 + (V /F )( K i − 1))

(4-189)

and

Rearranging for xi and yi yields

Taking the difference in the sums results in the Rachford-Rice flash method [Elliott and Lira (2012, Sec. 10.3)] zi (1 − K i ) =0 i − 1)

∑1 + (V /F )( K i

(4-190)

The initial step in solving a P, T flash problem is to find the value of V/F which satisfies Eq. (4-190), and then mole fractions are determined by Eq. (4-189). Gamma/Phi Approach For many VLE systems of interest, the presˆ is usually by Eq. (4-157), based on sure is low enough that evaluation of φ i the two-term virial equation of state. Liquid-phase behavior, on the other hand, uses activity coefficients γi , based on Eq. (4-146) applied to an expression for G E/RT, as described in the section Models for the Excess Gibbs Energy. Equation (4-135) may now be written as y i PΦi = x i γi Pi sat

where

Φi =

i = 1,2,…, N

φˆ i

 -V L ( P - Pi sat )  exp  i   φ RT sat i

(4-191)

(4-192)

sat ˆ If evaluation of φ sat i is based on Eq. (4-70) evaluated at P , and φi by Eq. (4-157), this reduces to

  sat sat l  P (2∑ y k Bki − B ) − Pi Bii − Vi ( P − Pi )  k  Φi = exp    RT

(4-193)

The N equations represented by Eq. (4-191) in conjunction with Eq. (4-193) may be solved for N unknown phase equilibrium variables. For a multicomponent system the calculation is best done by computer. Raoult’s Law When Eq. (4-191) is applied to VLE for which the vapor phase is an ideal gas and the liquid phase is an ideal solution, it reduces to ˆ and φsat are a very simple expression. For ideal gases, fugacity coefficients φ i i unity, and the right side of Eq. (4-192) reduces to the Poynting factor. For the systems of interest here, this factor is always very close to unity, and for practical purposes Φi = 1. For ideal solutions, the activity coefficients γi are also unity, and Eq. (4-191) reduces to y i P = x i Pi sat ,

K i = Pi sat /P

i = 1, 2,…, N

(4-194)

i

Thus for bubble point calculations, where the xi are known, the problem is to find the set of K values that satisfies Eq. (4-186), whereas for dew point calculations, where the yi are known, the problem is to find the set of K values that satisfies Eq. (4-187). The flash calculation is a very common application of VLE. Considered here is the P, T flash, in which are calculated the quantities and compositions of the vapor and liquid phases in equilibrium at known T, P, and overall composition. This problem is determinate on the basis of Duhem’s theorem: For any closed system formed initially from given masses of prescribed chemical species, the equilibrium state is completely determined when any two independent variables are fixed . The independent variables

an equation which expresses Raoult’s law. It is the simplest possible equation for VLE and as such fails to provide a realistic representation of real behavior for most systems. Nevertheless, it is useful as a standard of comparison. Modified Raoult’s Law Of the qualifications that lead to Raoult’s law, the one least often reasonable is the supposition of solution ideality for the liquid phase. Real solution behavior is reflected by values of activity coefficients that differ from unity. When γi of Eq. (4-191) is retained in the equilibrium equation, the result is the modified Raoult’s law: y i P = x i γi Pi sat , K i = γi Pi sat /P i = 1, 2, …, N

(4-195)

4-24

THERMODYnAMICS

This equation is often adequate when applied to systems at low to moderate pressures and is therefore widely used. Bubble point and dew point calculations are only a bit more complex than the same calculations with Raoult’s law. For a bubble calculation, because ∑i yi = 1, Eq. (4-195) may be summed over all species to yield P = ∑ x i γ i Pi sat

(4-196)

i

As discussed in relation to Eq. (4-139), the value of γi serves as a correction factor for the solute mole fraction concentration xi to better account for the solute’s true chemical potential–driven activity which determines phase equilibrium behavior and reactivity, where activity is given by ai = γi xi . For dew calculation, Eq. (4-195) may be solved for xi, in which case summing over all species yields P=

1

∑ y /γ P i

(4-197)

sat

i i

i

The application of this equation requires iteration because the values of γi cannot be determined without an estimate of {xi}. Example 4-11 Bubble, Dew, Azeotrope, and Flash Calculations As indicated by Example 4-8, a binary mixture in vapor/liquid equilibrium has 2 degrees of freedom. Thus of the four phase rule variables T, P, x1, and y1, two must be fixed to allow calculation of the other two, regardless of the formulation of the equilibrium equations. Modified Raoult’s law [Eq. (4-195)] may therefore be applied to the calculation of any pair of phase rule variables, given the other two. The necessary vapor pressures and activity coefficients are supplied by data correlations. For the system acetone(1)/n-hexane(2), vapor pressures are given by Eq. (4-15), with parameters for Pisat (kPa) and T (K), i Ai Bi Ci 1 14.3145 2756.22 −45.090 2 13.8193 2696.04 −48.833 Activity coefficients are calculated by Eq. (4-163), the Wilson equation, here adapted for a binary system in Eqs. (A) and (B) which will be referenced below: ln γ1 = − ln(x1 + x2Λ12) + x2λ

(A)

ln γ2 = − ln(x2 + x1Λ21) − x1λ

(B)

Λ12 Λ 21 − x1 + x 2 Λ 12 x 2 + x1Λ 21

where

λ≡

By Eq. (4-164)

V −a Λ ij = j exp ij Vi RT

a. b. c . d. e. f. g .

T (K)

P1sat (kPa)

P2sat (kPa)

γ1

γ2

325 .15 325 .15 317.24 322.98 319 .15 322.58 325 .15

87.616 87.616 65.830 81.125 70.634 79.986 87.616

58.105 58.105 43.591 53.779 46.790 53.021 58.105

1.8053 3.5535 2.1286 1.6473 1.2700 1.2669 2.5297

1.2869 1.0237 1.1861 1.3828 1.9172 1.9111 1.0997

x1

y1

0 .4000 0.5851 0.1130 0 .4000 0 .3200 0.5605 0.4550 0 .6000 0.6445 = 0.6445 0.6454 = 0.6454 0.2373 0.5190

P (kPa) 108.134 87.939 80 .000 101 .330 89.707 101 .330 101 .330

Equation-of-State Approach The gamma/phi method is generally applicable to systems away from critical points. Equations of state can treat near-critical conditions and the transition to supercritical conditions seamlessly. Of course, there is a cost in terms of robustness of convergence and computational complexity. By Eq. (4-134), x i φˆ il = y i φˆ iυ ⇒ K i = φˆ il /φˆ iυ , i = 1, 2, …, N

(4-198)

i≠ j

with parameters [Gmehling et al., Vapor-Liquid Data Collection, Chemistry Data Series, vol. 1, part 3, DECHEMA, Frankfurt/Main, 1983] a12

a21

V1

V2

cal mol −1

cal mol −1

cm3 mol −1

cm 3 mol −1

985.05

453.57

74.05

131.61

When T and x1 are given, the calculation is direct, with final values for vapor pressures by Eq. (4-15) and activity coefficients from Eqs. (A) and (B) above. In all other cases either T or x1 or both are initially unknown, and calculations require iteration. For each part of this example, results are tabulated in the table at the end where given values are in italic; calculated values are in boldface. a . BUBL P calculation: Find y1 and P, given x1 = 0 .40 and T = 325 .15 K (52°C). Noting that T and x1 are given and following the procedure above yields the values listed in the summary table in the following column. Equations (4-196) and (4-195) then become P = x i γi P1sat + x 2 γ 2 P2sat = (0.40)(1.8053)(87.616) + (0.60)(1.2869)(58.105) = 108.134 kPa yi =

iteration scheme based on Eq. (4-197) is easily developed. Starting values result from setting each γi = 1 and refining by using Eqs. (A) and (B) after finding {x}; results of successive substitution of {x} to refine γi values are listed in the accompanying table. c . BUBL T calculation: Find y1 and T, given x1 = 0.32 and P = 80 kPa. With T unknown, neither the vapor pressures nor the activity coefficients can be initially calculated. An iteration scheme based on Eq. (4-196) matches P and results in values listed in the accompanying table. d . DEW T calculation: Find x1 and T for y1 = 0 .60 and P = 101 .33 kPa. Start with γ i = 1. sat sat Iterate on ∑ y i P /( γ i Pi ) = 1. Find x i = y i P /( γ i Pi ) and new values of γ i using Eqs. (A) and (B). Iterate. Results are listed in the accompanying table. e., f . Azeotrope calculations: Find the azeotrope composition and (e) P at 46°C and ( f ) T at 101.33 kPa. As noted in Example 4-8, only a single degree of freedom exists for this special case. The most sensitive quantity for identifying the azeotropic state is the relative volatility defined in Eq. (4-184). Because y i = xi for the azeotropic state, α12 = 1. Substitution for the K ratios by Eq. (4-195) provides an equation for calculation of α12 = γ1 P1sat / ( γ 2 P2sat ). Because α12 is a monotonic function of x1, the test of whether an azeotrope exists at a given T or P is provided by values of α 12 in the limits of x 1 = 0 and x1 = 1. If both values are either >1 or ~2 (see Fig . 4-8) . This behavior is counterintuitive, but it is also borne out in EOS models of gas solubility . For a component such as hydrogen, the gas solubility increases with increasing temperature at all common conditions, although it is generally quite a small solubility nevertheless . To obtain a general estimate of Henry’s constant, it is necessary to include an estimate for the activity coefficient at infinite dilution . Readers should experiment with their process simulators to infer how gaseous species are treated by comparing multiple solvents and models

For H2: ln(γ ∞) = [3 .15 − ln(Mwsolv )] (1 − Tcsolv/T )

(4-210)

Example 4-13 Solubility of Hydrogen in Hydrocarbons Estimate the mass fraction of hydrogen in n-hexadecane and n-triacontane at 50°C and 100 bar . Solution At these conditions, we can ignore the composition of the solvent in the vapor phase . Applying the pseudocritical constants in Eq . (4-209), 1/Tr = 42/323 .15 = 0 .447, f iL = (19)10[7(1−0 .447)/3−3exp(−14 .1(0 .447))] = 674 bar . By Eq . (4-210), γ ∞ = exp[(3 .15 − ln 226) (1−723/323 .15)] = 16 .6; fi = 100 = 674(16 .6)xi . Solving gives xi = 100/(674 ⋅ 16 .6) = 0 .0089 . Converting to mass fraction, we obtain 82 ppmw . Repeating for triacontane, we obtain g ∞ = 106 and 6 .6 ppmw . The value of 82 for hexadecane compares to 54 ppmw estimated by the method of Trinh et al, J . Chem . Eng . Data 61: 19 (2016) . An alternative to using a hypothetical liquid fugacity such as the Prausnitz and Shair approach is to examine the bubble pressure in the dilute limit using an EOS approach . An estimate of Henry’s constant can be inferred by effectively simulating the experimental conditions using an EOS model . Generally, this approach would be most amenable to the Lewis-Randall perspective . It has been observed that EOS models can reproduce the observed maximum in Henry’s constant for gaseous components, at least qualitatively . LIQUID/LIQUID AnD VAPOR/LIQUID/ LIQUID EQUILIBRIA Equation (4-127) is the basis for both liquid/liquid equilibria (LLE) and vapor/liquid/liquid equilibria (VLLE) . Thus for LLE with superscripts α and b denoting the two phases, Eq . (4-127) is written as ˆf α = ˆf β i i

i = 1, 2, …, N

(4-211)

Using modified Raoult’s law for fugacities and canceling the Pisat values gives x iα γiα = x iβ γβi

i = 1, 2, …, N

(4-212)

For most LLE applications, the effect of pressure on g i can be ignored, and Eq . (4-212) then constitutes a set of N equations relating equilibrium compositions to one another and to temperature . For a given temperature, solution of these equations requires a single expression for the composition dependence of G E suitable for both liquid phases . Not all expressions for G E suffice, even in principle, because some cannot represent liquid/liquid phase splitting . The UNIQUAC equation is suitable, and therefore prediction is possible by UNIFAC models . A special table of parameters for LLE calculations is given by Magnussen et al . [Ind . Eng . Chem . Process Des . Dev . 20: 331–339 (1981)] . A comprehensive treatment of LLE is given by Sorensen et al . [Fluid Phase Equilibr . 2: 297–309 (1979); 3: 47–82 (1979); 4: 151–163 (1980)] . Data for LLE are collected in a three-part set compiled by Sorensen and Arlt [LiquidLiquid Equilibrium Data Collection, Chemistry Data Series, vol . 5, parts 1–3, DECHEMA, Frankfurt am Main, 1979–1980] . For vapor/liquid/liquid equilibria, Eq . (4-127) becomes ˆf α = ˆf β = ˆf υ i i i

i = 1, 2, …, N

(4-213)

where α and b designate the two liquid phases . With activity coefficients applied to the liquid phases and fugacity coefficients to the vapor phase, the 2N equilibrium equations for subcritical VLLE are  x iα γiα f i α = y i φˆ i P   x iβ γβi f i β = y i φˆ i P 

all i

(4-214)

As for LLE, an expression for G E capable of representing liquid/liquid phase splitting is required; as for VLE, a vapor-phase equation of state for ˆ is also needed . computing the φ i

4-28

THERMODYnAMICS

TREnDS In PHASE BEHAVIOR Thermophysical properties usually and fortunately fall into regular patterns within and among families of compounds, and these patterns are useful to fill gaps in measurements, to identify outliers that are likely in error, and to educate chemical engineers to anticipate expected behaviors. This idea is especially attractive today because large databases of thermophysical properties are widely available. These databases can easily generate patterns, but also should be tested to identify errors and outliers. The patterns of behavior are more evident for fluid properties than for solid properties. This section provides representative examples of property patterns for the phase behavior of pure fluids and mixtures. PURE FLUIDS Figure 4-5 presents a plot of vapor pressures for the 1-alcohols from methanol to 1-docosanol (C22H46O), where the data have been taken from the DIPPR 801 database [R. L. Rowley et al., DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, 2006]. Korsten [Ind . Eng . Chem . Res . 39: 813 (2000)] relates the slopes to the molecular weight within each functional class, and suggests that log P sat versus 1/T1.3 is linear, though deviation is evident in Fig. 4-5. Although patterns are evident for fluid properties like the critical points, a pattern is usually not evident for solid properties like the triple point. Extrapolation of the vapor pressures above the critical temperature suggests that they meet at the “infinite point,” which was first suggested by Cox [Ind . Eng . Chem. 15: 592 (1923)]. The infinite point remains useful as a visualization tool for the vapor pressures of a family of compounds since it illustrates and explains the rule of thumb that “experimental vapor pressures of a family of compounds do not cross.” The extrapolated vapor pressures cross at a hypothetical temperature higher than all the critical temperatures of the members of the family. The pattern is useful to interpolate for missing family members. Another useful pattern is illustrated in the Othmer plot [Ind . Eng . Chem. 32: 841 (1940)] of vapor-pressure ratios. Figure 4-6 presents the ratio of the vapor pressure of the 1-alcohols to that of water plotted against the vapor pressure of water. For each point on the curve, the same temperature is

used to calculate the vapor pressure of the 1-alcohol and water. The chart provides useful education about relative vapor pressures and enthalpies of vaporization (related to the slope of the vapor-pressure curve by the Clausius-Clapeyron equation). Methanol and ethanol have higher vapor pressures than water, and the slopes of their Othmer curves are negative, which means that their enthalpies of vaporization are lower than that of water. The vapor pressure of 1-propanol is very close to that of water, and so is its enthalpy of vaporization. The higher alcohols exhibit successively decreasing vapor pressures and also successively increasing enthalpies of vaporization. The Othmer chart also provides the relative volatility under the ideal solution assumption. MIXTURES Solvents such as dimethyl formamide (DMF) and acetonitrile (ACN) are used in extractive-distillation processes that recover 1,3-butadiene from steam-cracker hydrocarbons. Extractive distillation requires accurate correlation of the activity coefficients because the vapor pressures of the hydrocarbons in the feed mixture are very close, which facilitates azeotrope formation, and the basis of extractive distillation is the varying activity coefficients of the different hydrocarbons in the polar solvents. Table 4-5 presents experimental data for the infinite-dilution activity coefficients of various hydrocarbons in DMF and ACN at 313 K, which has been chosen as a representative value since it is typical of temperatures encountered in butadiene extractive-distillation columns. The infinite-dilution activity coefficients have been reported here since at plant conditions the solubility of the hydrocarbons in the liquid phase is relatively low. Table 4-5 demonstrates that the data fall into the pattern expected from “thermodynamic intuition.” The infinite-dilution activity coefficients progressively decrease as the hydrocarbon class goes from paraffin to olefin to diolefins to triple bond to olefin plus triple bond. This, of course, is the reason why DMF and ACN are effective as extractive solvents, but the fact that the activity coefficients fall into the expected pattern provides confidence in the experimental data and offers a method to fill in data gaps. Figure 4-7 graphically illustrates

1E+04

1E+02

C1

Liquid vapor pressure (bar)

1E+00

1E–02

Infinite point

C3 C5

C12

C8

C18

1E–04

C14 C20

1E–06

C22

1E–08

1E–10 1500 K

1E–12 0.0000

500 K

0.0002

0.0004

300 K

0.0006

200 K

0.0008

0.0010

150 K

0.0012

0.0014

0.0016

1/T1.3(K–1.3) FIG. 4-5

Vapor pressures of the 1-alcohols, including the critical points (solid circles î) and triple points (open squares ▫).

TREnDS In PHASE BEHAVIOR 10 10°C

50°C

100°C

4-29

150°C

1 2 3

Vapor-pressure ratio alcohol:water

1

4 5 6

0.1

7 8 9

0.01

10 11 12 0.001

0.0001 0.01

0.1

1

10

P sat, Water (bar) FIG. 4-6 Ratio of vapor pressure of the 1-alcohols to that of water plotted versus the vapor pressure of

water. The numbers on each curve show the carbon number of the alcohol. The temperatures at the top of the chart correspond to the water saturation temperature.

TABLE 4-5 Infinite-Dilation Activity Coefficients at 313 K of Hydrocarbons in DMF and ACn

Vinyl acetylene

0.84

1-Propyne

1.09

1-Butyne

γ ∞ in ACN 1.78

Olefin and triple bond

1.95

Triple bond

2.98

1,3-Butadiene

2.38

1,2-Butadiene

2.8

3.73

Diolefin Olefin

cis-2-Butene

4.51

7.44

1-Butene

4.97

7.22

Isobutene

5.21

trans-2-butene

6.46

Butane

10.4

10.4

Isobutane

13.5

12.2

DMF

Class of hydrocarbon

Paraffin

Ethanol

8 ln(γ ∞) – HC in second solvent

Compound

γ ∞ in DMF

10

Water

6

4

2

0

–2

the relationship among the infinite-dilution activity coefficients of hydrocarbons in DMF, ethanol, and water compared to that in ACN. Clearly, the regularity of the data itself—without any theoretical model—reveals a simple, clear pattern that helps to evaluate the consistency of the various data sources and also to fill in data gaps as needed. As an example, it is easy to estimate the infinite-dilution activity coefficient of 1-butyne in DMF, and of 1,2-butadiene, isobutene, and trans-2-butene in ACN. For 1-butyne in DMF, taking the value of ln(2.98) = 1.1 from Table 4-5, the y-axis indicates a value of 0.7 for the log value, or 2.0 for the activity coefficient. Figure 4-8 graphically presents Harvey’s correlation [AIChE J . 42: 1491 (1996)] for Henry constants of 12 solutes in hexadecane. Solutes with large Henry constants (low solubility) typically have a negative slope with temperature, which means that the heat of solution is endothermic. As Henry’s constant of a solute decreases, the slope becomes increasingly positive, which relates to exothermic absorption. At a sufficiently high temperature, close to the critical temperature of the solvent, most curves have negative slopes, and hence the solutes with low Henry’s constants go through a maximum. Figure 4-9 studies the pattern of Henry’s constants of various solutes in hexadecane (a variation on Fig. 4-8) by plotting the Henry constant, at a representative temperature of 350 K, versus the solute normal boiling point. (Note that

0.0

0.5

1.0

1.5

2.0

2.5

ln(γ ∞) – HC in ACN FIG. 4-7 Correlation between hydrocarbon infinite-dilution activity coefficients in

dimethyl formamide (DMF), ethanol, and water compared to those in acetonitrile (ACN). All activity coefficients are at 313 K. The dashed lines are best-fit straight lines.

CO2 is a solid when its vapor pressure is atmospheric, hence an “effective” liquid normal boiling point of 183.7 K was estimated by extrapolating the liquid vapor pressure down to a vapor pressure of 1 atm.) Figure 4-9 indicates that for nonpolar compounds the logarithm of Henry constants at 350 K varies approximately linearly with the normal boiling point. Henry constants of the polar compounds (CO2, HCl, H2S, NH3, and SO2) are higher than the value based upon the nonpolar estimate, which indicates that they have relatively higher positive deviations from ideality in the nonpolar solvent, hexadecane. Hydrogen is another exception to the simple pattern, and this is likely because of quantum effects in its boiling behavior. Figure 4-10 presents the aqueous infinite-dilution activity coefficients in water of substances from several families of organic compounds plotted versus their respective normal boiling temperatures. A temperature of 348 K

4-30

THERMODYnAMICS

100

100 CO

H2

N2

h (MPa) @ 350 K

H2

h (MPa)

CH4 CO2 NH3

10

HCl C2H6

H2S

SO2

N2 CO

CH4 CO2

10

NH3

HCl C2H6

H2S SO2

C3H8 C3H8 n-C4H10 1 300

350

1

400 Temperature (K)

450

0

50

100

150

500

200

250

300

Tb (K) FIG. 4-9

Henry’s constants at 350 K of various solutes in hexadecane. The line is based upon the nonpolar solutes and assumes that the logarithm of Henry’s constant at 350 K varies linearly with the normal boiling temperature.

FIG. 4-8 Henry’s constants for various solutes in hexadecane.

1.E+8 Alkanes

Cycloalkanes

1.E+7 1.E+6

Alkylbenzenes Acetates

1.E+5 γ ∞ at 348 K

Alcohols 1.E+4 1.E+3

Mercaptans

1.E+2

Nitrosamines Alkyl sulfides

1.E+1 1.E+0

Ketones Organic acids

1.E–1 250

300

350

400 Tb (K)

450

500

550

FIG. 4-10 Infinite-dilution activity coefficients at 348 K of substances from various families of compounds in water. The lines are best fits for each compound, assuming that ln γ ∞ varies linearly with the solute normal boiling point .

has been chosen to represent separations where the water concentration is fairly high and the pressure is close to atmospheric; however, the patterns are relatively insensitive to temperature. These patterns help chemical engineers estimate the nonideality of the organic-water pair of particular interest and also identify data that may be in error. The variation of infinite-dilution activity coefficients is extremely large, ranging from organic acids that form nearly ideal mixtures with water to alkane-water mixtures where the activity coefficients are more than 7 orders of magnitude higher. The patterns accentuated by Fig. 4-10 are useful to develop correlations for aqueous separations in emerging biotechnology processes and to evaluate predictive techniques. The results in Fig. 4-10 may be used to calculate relative volatilities in water at infinite dilution, which is approximately equal to the activity coefficient multiplied by the ratio of the solute and water vapor pressures. These

results are very useful in biofuels and biochemical processes since the initial separations are typically performed where the liquid concentrations are dominated by water (i.e., fermentation processes usually occur in relatively dilute aqueous solutions). Figure 4-11 presents relative volatilities at infinite dilution of various families of compounds in water. These results may be surprising and unexpected even to experienced chemical engineers. The relative volatility of most compounds at infinite dilution in water is greater than unity, and the relative volatility increases with the boiling point of the solute. The latter result occurs because as the size or molecular weight of the member of a particular family increases (recall that vapor pressures within a family rarely cross), its vapor pressure at the reference temperature (348 K) decreases, but the activity coefficient increases to a greater extent such that the relative volatility rises.

TEMPERATURE DEPEnDEnCE OF InFInITE-DILUTIOn ACTIVITY COEFFICIEnTS

4-31

1.E+7 Alkanes

Relative volatility wrt water at 348 K

1.E+6 Cycloalkanes

1.E+5 Alkylbenzenes

1.E+4

Mercaptans

Acetates

1.E+3 Alkyl sulfides

1.E+2 1.E+1

Alcohols Ketones

Nitrosamines

1.E+0 Organic acids

1.E–1 250

300

350 400 450 Boiling point (K)

500

550

FIG. 4-11

Relative volatilities with respect to (wrt) water for various families of compounds at infinite dilution in water . The relative volatilities have been calculated using the infinite-dilution activity coefficients from Fig . 4-10 .

TEMPERATURE DEPEnDEnCE OF InFInITE-DILUTIOn ACTIVITY COEFFICIEnTS FUnDAMEnTAL RELATIOnSHIPS Most activity coefficient models are concerned primarily with the effect of composition, giving only a rough approximation of the temperature dependence. However, the effect of temperature often is a critical factor in conceptual and process design. Fundamentally, the temperature dependence of γ ∞ij is given by a version of the Gibbs-Helmholtz equation: E ,∞

 ∂ln γ ij∞  H ij   = R  ∂(1/T )  P ,x

(4-215)

where γ ∞ij is evaluated at some constant composition for solute iE ,in solvent j . ∞ Equation (4-215) is a version of Eq . (4-149) . In cases where H ij is known and its value is fairly constant over the temperature range of interest, integration allows convenient calculation: γ ij∞

at T2

≈ γ ij∞

E ,∞ ij

at T1

H  1 1  exp   −   R  T2 T1  

(4-216)

Compilations of available enthalpy of mixing data are given elsewhere (Onken, Rarey-Nies, and Gmehling, Int . J . Thermophys . 10(3): 739–747 (1989); DDBST GmbH, http://www .ddbst .com; Christensen, Hanks, and Izatt, Handbook of Heats of Mixing, Wiley, New York, 1982); and Christensen, Rowley, and Izatt, Handbook of Heats of Mixing, Supplemental Volume, Wiley, New York, 1988)] . Equations (4-215) and (4-216) are the basis for many correlations of activity coefficient temperature dependence . Methods involving correlation of partial molar excess enthalpy are available for specific classes of compounds [Sherman et al ., J . Phys . Chem . 99(28): 11239–11247 (1995)] . Another method involves combining an excess Gibbs energy expression with an equation of state [Kontogeorgis and Coutsikos, Ind . Eng . Chem . Res . 51: 4119–4142 (2012)] . An alternative approach to estimating γ ∞ij as a function of temperature involves use of a power-law expression (or stretched exponential), given by ln γ ij∞ = aij (Tref /T )

θij

(4-217)

where T is temperature in Kelvin and aij is a constant given by a known reference point, aij = ln γ ij∞ at T = Tref [Frank, Arturo, and Holden, AIChE J . 60: 3675–3690 (2014)] . The exponent θij is related to the partial molar excess enthalpy and entropy of mixing, such that θij =

1 E ,∞

E ,∞

1 − (T S ij / H ij )

(4-218)

In certain cases, Eq . (4-217) may be used to correlate data with a constant value of θij . In doing so, one assumes that the ratio of entropic to enthalpic terms is constant over the temperature range of interest . According to Frank et al . [AIChE J . 60: 3675–3690 (2014)], a constant value of θij is able to correlate γ ∞ij for many binary types over a reasonably wide temperature span of 50°C to 80°C or more—at normal process conditions far from the critical point . Exceptions (in addition to near-critical mixtures) include a number of hydrogen bonding organic + water binaries such as C4 to C7 alcohols dissolved in water, 2-butanone in water, and acetonitrile in water . Water is included in the classification scheme as a solvent but not as a solute because of the many varied and difficult-to-predict ways water can form hydrogen bonds . CLASSIFICATIOn SCHEME It is apparent from Eq . (4-218) that very different types of temperature dependence are possible depending on the signs and relative magnitudes of partial molar excess enthalpy and entropy . With this in mind, Frank et al . [AIChE J . 60: 3675–3690 (2014)] have classified solute-solvent binary pairs E ,∞ E ,∞ into seven types corresponding to distinct domains of H ij , S ij , γ ij∞ , and E ,∞ θij shown in Table 4-6 . Specific interactions that can affect H ij include static dipole-dipole (polarity effects), induced dipole-dipole, hydrogen bonding (proton donor and proton acceptor interactions), and electron donor/ E ,∞

acceptor interactions . Factors affecting S ij include segregation resulting from these interactions, molecular size differences, and the hydrophobic effect for organic + water mixtures . In modeling phase equilibrium using the standard activity coefficient correlation equations, it is common practice to represent the effect of temperature for a given binary interaction parameter by using empirical expressions with two or more correlation constants . Typical expressions have the form ln A or A = a + b/T + c ln T, where A is a model parameter and a, b, and c are correlation constants determined by fitting data, an expression derived from E ,∞ Eq . (4-215) assuming H ij is a linear function of temperature . As an alternative, Frank et al . have proposed incorporating the parameter θij directly into an excess Gibbs energy expression as shown in Table 4-7 . In principle, suitable θij values may be estimated via Eq . (4-218) by using molecular modeling methods E ,∞ E ,∞ to estimate the dimensionless ratio of T S ij /H ij , or θij may be treated as adjustable model parameters in fitting data . The range of possible θij values is bounded by the range of values given in Table 4-6 (at normal conditions) . For nonaqueous binaries containing specific classes of compounds, estimates may be obtained from molecular structure using characteristic θij values for various classes of compounds, as summarized in Table 4-8 . Though developed

4-32

THERMODYnAMICS TABLE 4-6

Classification of Activity Coefficient Temperature Dependence Excess enthalpy and entropy

Mixture type

E ,∞

E ,∞

Typical characteristics

h ij

s ij

I

Chemically similar, small molecules (nearly ideal)

≈0

≈0

II

Regular-solution-like

Pos.

Pos.

Typical γ ij∞ values∗ and change with temperature

Typical θij values†

γ∞ij ≈ 1 γ ij∞ ≈ 1

θij ≈ 0

γ ij∞ > 1 1.2 < γ ij∞ < 1000 ∂γ ij∞ ∂T III

Endothermic with negative excess entropy

Pos.

Neg.

∂γ

∂T IV

Exothermic with negative excess entropy

Neg.

Neg.

2 ∞ ij

∂T

0.15 < θij < 1

2 ∂γ ij∞

1 < θij < 5

−3 < θij < −0.3

>0

γ∞ij < 1 V

VI

VII

Net attractive interactions with negative excess entropy

Neg.

Net attractive interactions with positive excess entropy

Neg.

Chemically similar, wide molecular size distribution

Pos.

Neg.

0.2 < γij∞ < 1

1 < θij < 5

∞ ij

∂γ >0 ∂T Pos.

0.2 < γ ij∞ < 1

0.3 < θij < 1

∞ ij

∂γ >0 ∂T Pos.

0.6 < γij∞ < 1

−5 < θij < −0.5

∂γ 1, the surface temperature T(R) = T∞. Two- and Three-Dimensional Conduction Application of the law of conservation of energy to a three-dimensional solid, with the heat flux given by Eq. (5-1) and volumetric source term S (W/m3), results in the following equation for steady conduction in rectangular coordinates.

kAc

and

5-5

tanh βL βL

1/2

(5-17) (5-18) (5-19)

For a surface that is covered with fins of efficiency h f , the total surface efficiency is given by Aηt = ( A − A f ) + η f A f

(5-20)

where A is the total area for heat transfer and Af is the surface area of the fins. The total efficiency becomes q

1 hc

= Q˙ / A

T1

T2 ∆ xD

∆xB

∆xS

kD

kB

kS

ηt = 1 − Tsur

FIG. 5-4 Thermal circuit for Example 5-1. Steady conduction in a furnace wall with heat losses from the outside surface by convection (hC) and radiation (hR) to the surroundings at temperature Tsur. The thermal conductivities kD, kB, and kS are constant. The heat flux q has units of W/m2.

A

(1 − η f )

(5-21)

The thermal resistance, based on the total area for heat transfer, becomes R=

1 hR

Af

1 hc Aηt

(5-22)

Mills (Heat Transfer, 2d ed., Prentice-Hall, Upper Saddle River, N.J., 1999, p. 104) provides fin efficiencies for a variety of fin shapes. UnSTEADY COnDUCTIOn Application of the law of conservation of energy to a three-dimensional solid, with the heat flux given by Eq. (5-1) and volumetric source term

5-6

HEAT AnD MASS TRAnSFER

S (W/m3), results in the following equation for unsteady conduction in rectangular coordinates. rc

∂T ∂  ∂T  ∂  ∂T  ∂  ∂T  + k  +S = k  + k ∂t ∂ x  ∂ x  ∂ y  ∂ y  ∂ z  ∂ z 

(5-23)

The energy storage term is on the left-hand side, and ρ and c are, respectively, the density (kg/m3) and specific heat [J/(kg ⋅ K)]. Solutions to Eq. (5-23) are generally obtained numerically (see General References and Sec. 3). The one-dimensional form of Eq. (5-23), with constant k and no source term, is ∂2 T ∂T =α 2 ∂x ∂t

(5-24)

where a = k/(ρc) is the thermal diffusivity (m2/s). One-Dimensional Conduction: Lumped and Distributed Analysis The one-dimensional transient conduction equations in rectangular (b = 1), cylindrical (b = 2), and spherical (b = 3) coordinates, with constant k, initial uniform temperature Ti, S = 0, and convection at the surface with heattransfer coefficient h and fluid temperature T∞, are α ∂  b − 1 ∂T  ∂T = r  ∂r  ∂t r b − 1 ∂ r  T = Ti

(initial temperature)

At r = 0,

∂T =0 ∂r

(symmetry condition)

At r = R,

−k

(5-25)

The solutions to Eq. (5-25) can be compactly expressed by using dimensionless variables: (1) temperature θ/θi = [T(r, t) - T∞]/(Ti - T∞); (2) heat loss fraction Q/Qi = Q/[ρcV(Ti −T∞)], where V is volume; (3) distance from center ζ = r/R; (4) time Fo = at/R2; and (5) Biot number Bi = hR/k. The temperature and heat loss are functions of ζ, Fo, and Bi. When the Biot number is small, Bi < 0.1, the temperature of the solid is nearly uniform and a lumped analysis is acceptable. The solution to the lumped analysis of Eq. (5-25) is and

 hA  Q t = 1 − exp  − Qi  ρcV 

(5-26)

where A is the active surface area and V is the volume. The time scale for the lumped problem is τ=

ρcV hA

Q θ = A1 exp(−δ12 Fo)S1 (δ1ζ) and = 1 − B1 exp(−δ12 Fo) Qi θi

(5-28)

where the first Fourier coefficients A1 and B1 and the spatial functions S1 are given in Table 5-1. The first eigenvalue d1 is given by Eq. (5-29) in conjunction TABLE 5-1 Fourier Coefficients and Spatial Functions for Use in Eq. (5-28) B1

A1

S1

Plate

2sin δ1 δ1 + sin δ1 cos δ1

2Bi 2 δ ( Bi + Bi + δ12 )

cos ( δ1ζ )

Cylinder

2 J 1 (δ1 ) δ1  J 02 (δ1 ) + J 12 (δ1 ) 

4Bi 2 δ ( δ12 + Bi 2 )

J 0 ( δ1ζ )

Sphere

2Bi δ12 + (Bi − 1)2 

6Bi 2 δ12 ( δ12 + Bi 2 − Bi )

sin ( δ1ζ ) δ1ζ

(δ

2 1

+ Bi − Bi ) 2

2 1

1/2

2

2 1

Bi → ∞

n

Foc 0.24

Plate

δ1 → Bi

δ1 → π / 2

2.139

Cylinder

δ1 → 2Bi

δ1 → 2.4048255

2.238

0.21

Sphere

δ1 → 3Bi

δ1 → π

2.314

0.18

with Table 5-2. The one-term solutions are accurate to within 2 percent when Fo > Foc . The values of the critical Fourier number Foc are given in Table 5-2. The first eigenvalue is accurately correlated by Yovanovich (Chap. 3 of Rohsenow, Hartnett, and Cho, Handbook of Heat Transfer, 3d ed., McGraw-Hill, New York, 1998, p. 3.25) δ1,∞ 1/n

1 + (δ1,∞ / δ1,0 )n 

(5-29)

Equation (5-29) gives values of d1 that differ from the exact values by less than 0.4 percent, and it is valid for all values of Bi. The values of d1,∞, d1,0, n, and Foc are given in Table 5-2.

δ1 =

π/2 1 + {(π/2)/( 5)}2.139 

1/2.139

= 1.312

The tabulated value is 1.3138.

Example 5-3 One-Dimensional, Unsteady Conduction Calculation As an example of the use of Eq. (5-28), Table 5-1, and Table 5-2, consider the cooking time required to raise the center of a spherical, 8-cm-diameter dumpling from 20 to 80°C. The initial temperature is uniform. The dumpling is heated with saturated steam at 95°C. The heat capacity, density, and thermal conductivity are estimated to be c = 3500 J/(kg ⋅ K), ρ = 1000 kg/m3, and k = 0.5 W/(m ⋅ K), respectively. Because the heat-transfer coefficient for condensing steam is of order 104, the Bi → ∞ limit in Table 5-2 is a good choice and d1 = π. Because we know the desired temperature at the center, we can calculate θ/θ i and then solve Eq. (5-28) for the time. θ T (0, t ) − T∞ 80 − 95 = = = 0.200 Ti − T∞ 20 − 95 θi

(5-27)

The time scale is the time required for most of the change in Q/Qi or θ/θi to occur. When t = t, θ/θi = exp(-1) = 0.368 and roughly two-thirds of the possible change has occurred. When a lumped analysis is not valid (Bi > 0.1), the single-term solutions to Eq. (5-25) are convenient:

Geometry

Bi → 0

Example 5-2 Correlation of First Eigenvalues by Eq. (5-29) As an example of the use of Eq. (5-29), suppose that we want d1 for the flat plate with Bi = 5. From Table 5-2, d1,∞ = π/2, d1,0 = Bi = 5 , and n = 2.139. Equation (5-29) gives

∂T = h(T − T∞ ) ∂r

 hA  θ = exp  − t θi  ρcV 

Geometry

δ1 =

 b = 1, plate, thickness 2 R   b = 2, cylinder, diameter 2 R  b = 3, sphere, diameter 2 R 

For t < 0,

TABLE 5-2 First Eigenvalues for Bi ã 0, Bi ã Ç, Correlation Parameter n, where the Single-Term Approximations Apply Only If Fo ê Foc

For Bi → ∞, A1 in Table 5-1 is 2 and for ζ = 0, S1 in Table 5-1 is 1. Equation (5-28) becomes θ αt = 2exp (−π 2 Fo) = 2exp  −π 2 2   θi R  Solving for t gives the desired cooking time. t =−

(0.04 m)2 R2 θ 0.2 ln =− ln = 43.5 min 2 απ 2 θi 1.43 × 10 −7 (m 2 /s)π 2 2

The one-term approximation is applicable in this case because calculation of Fo gives 0.23, which is greater than Foc = 0.18 from Table 5-2.

Example 5-4 Rule of Thumb for Time Required to Diffuse a Distance R

A general rule of thumb for estimating the time required to diffuse a distance R is obtained from the one-term approximations. Consider the equation for the temperature of a flat plate of thickness 2R in the limit as Bi → ∞. From Table 5-2, the first eigenvalue is d1 = π/2, and from Table 5-1,  π 2 αt  θ = A1 exp  −   2  cos δ1ζ θi   2 R 

When t = R2/a, the temperature ratio at the center of the plate (ζ = 0) has decayed to exp(-π2/4), or 8 percent of its initial value. We conclude that diffusion through

HEAT TRAnSFER BY COnVECTIOn a distance R takes roughly R2/a units of time, or alternatively, the distance diffused in time t is about (at)1/2. More generally, the time scale for Eq. (5-25) for any Bi is approximately 2

τ≈

R 1 1   +  bα  2 Bi 

One-Dimensional Conduction: Semi-infinite Plate Consider a semi-infinite plate with an initial uniform temperature Ti. Suppose that the temperature of the surface is suddenly raised to T∞; that is, the heat-transfer coefficient is infinite. The unsteady temperature of the plate is T ( x , t ) − T∞  x  = erf   2 αt  Ti − T∞

(5-30)

If the heat-transfer coefficient is finite,  x  hx h 2αt  T ( x , t ) − T∞ h αt   x  + = erf  + exp  + 2  erfc    2 αt   k Ti − T∞ k  k   2 αt

(5-31)

Equations (5-30) and (5-31) are applicable to finite plates provided that their half-thickness is greater than (12at)1/2. Two- and Three-Dimensional Conduction The one-dimensional solutions discussed above can be used to construct solutions to multidimensional problems. The unsteady temperature of a rectangular, solid box of height, length, and width 2H, 2L, and 2W, respectively, with governing equations in each direction as in Eq. (5-25), is  θ  θ  i

where erf(z) is the error function. The depth to which the heat penetrates in time t is approximately (12at)1/2.

5-7

2 H × 2 L× 2W

 θ  θ  θ =       θi  2 H  θi  2 L  θi  2 W

(5-32)

Similar products apply for solids with other geometries, e.g., semi-infinite, cylindrical rods.

HEAT TRAnSFER BY COnVECTIOn COnVECTIVE HEAT-TRAnSFER COEFFICIEnT Convection is the transfer of energy by conduction and radiation in moving, fluid media. The motion of the fluid is an essential part of convective heat transfer. A key step in calculating the rate of heat transfer by convection is the calculation of the heat-transfer coefficient. This section focuses on the estimation of heat-transfer coefficients for natural and forced convection. The conservation equations for mass, momentum, and energy, as presented in Sec. 6, can be used to calculate the rate of convective heat transfer. Our approach in this section is to rely on correlations. In many cases of industrial importance, heat is transferred from one fluid, through a solid wall, to another fluid. The transfer occurs in a heat exchanger. Section 11 introduces several types of heat exchangers, design procedures, overall heat-transfer coefficients, and mean temperature differences. Section 3 introduces dimensional analysis and the dimensionless groups associated with the heat-transfer coefficient. Individual Heat-Transfer Coefficient The local rate of convective heat transfer between a surface and a fluid is given by Newton’s law of cooling q = h(Tsurface - Tfluid)

(5-33)

where h [W/(m2 ⋅ K)] is the local heat-transfer coefficient and q is the energy flux (W/m2). The definition of h is arbitrary, depending on whether the bulk fluid, centerline, free stream, or some other temperature is used for Tfluid. The heat-transfer coefficient may be defined on an average basis as noted below. Consider a fluid with bulk temperature T, flowing in a cylindrical tube of diameter D, with constant wall temperature Ts . An energy balance on a short section of the tube yields dT = πDh(Ts − T ) (5-34) dx where cp is the specific heat at constant pressure [J/(kg ⋅ K)], m is the mass flow rate (kg/s), and x is the distance from the inlet. If the temperature of the fluid at the inlet is Tin, the temperature of the fluid at a downstream distance L is

where Δx is a short length of tube in the axial direction. Equation (5-37) defines U by using the outside perimeter 2πr2. The inner perimeter can also be used. Equation (5-37) applies to clean tubes. Additional resistances are present in the denominator for dirty tubes (see Sec. 11). For counterflow and parallel flow heat exchanges, with high- and lowtemperature fluids (TH and TC) and flow directions as defined in Fig. 5-5, the total heat transfer for the exchanger is given by Q =UA ∆Tlm

where A is the area for heat exchange and the log mean temperature difference ΔTlm is defined as ∆Tlm =

(TH − TC ) x =0 − (TH − TC ) x = L ln[ (TH − TC ) x =0 /(TH − TC ) x = L ]

(5-39)

Equation (5-39) applies to both counterflow and parallel-flow exchangers with the nomenclature defined in Fig. 5-5. Correction factors to ΔTlm for various heat exchanger configurations are given in Sec. 11. In certain applications, the log mean temperature difference is replaced with an arithmetic mean difference: ∆Tam =

c p m

 h πDL  T ( L) − Ts = exp  −  Tin − Ts  p   mc

(5-38)

(TH − TC ) x = L + (TH − TC ) x =0 2

(5-40)

TH

x=0

(5-35)

TC

x=L

(a) Counterflow.

The average heat-transfer coefficient h is defined by L

h=

1 hdx L ∫0

Overall Heat-Transfer Coefficient and Heat Exchangers A local, overall heat-transfer coefficient U for the cylindrical geometry shown in Fig. 5-2 is defined by using Eq. (5-11): Q = ∆x

Ti − To = 2 πr2U (Ti − To ) 1 ln(r2 /r1 ) 1 + + 2 πr1hi 2 πk 2 πr2 ho

TH

(5-36)

(5-37)

x=0

TC

x=L

(b) Parallel flow. FIG. 5-5 Nomenclature for counterflow and parallel-flow heat exchangers for use with Eqs. (5-38) and (5-39).

5-8

HEAT AnD MASS TRAnSFER

Average heat-transfer coefficients are occasionally reported based on Eqs. (5-39) and (5-40) and are written as hlm and ham . Representation of Heat-Transfer Coefficients Heat-transfer coefficients are usually expressed in two ways: (1) dimensionless equations and (2) dimensional equations. Only the dimensionless approach is used here. The dimensionless form of the heat-transfer coefficient is the Nusselt number. For example, with a cylinder of diameter D in cross flow, the local Nusselt number is defined as NuD = hD/k, where k is the thermal conductivity of the fluid. The subscript D is important because different characteristic lengths can be used to define Nu. The average Nusselt number is written Nu D = hD /k .

procedure outlined in Examples 5-1 and 5-5. A radiative heat-transfer coefficient hR is defined by Eq. (5-12). Mixed Forced and Natural Convection Natural convection is commonly assisted or opposed by forced flow. These situations are discussed, e.g., by Mills [Heat Transfer, 2d ed., Prentice Hall, Upper Saddle River, N.J., 1999, p. 340] and Raithby and Hollands [Chap. 4 of Rohsenow, Hartnett, and Cho, Handbook of Heat Transfer, 3d ed., McGraw-Hill, New York, 1998, p. 4.73]. Enclosed Spaces The rate of heat transfer across an enclosed space is described in terms of a heat-transfer coefficient based on the temperature difference between two surfaces: h=

nATURAL COnVECTIOn Natural convection occurs when a fluid is in contact with a solid surface and their temperatures differ. Temperature differences create the density gradients that drive natural or free convection. In addition to the Nusselt number mentioned above, the key dimensionless parameters for natural convection include the Rayleigh number Rax = β ΔT gx3/na and the Prandtl number Pr = n/a. The properties appearing in Ra and Pr include the volumetric coefficient of expansion β (K−1); the difference ΔT between the surface (Ts) and free stream (Te) temperatures (K or °C); the acceleration of gravity g (m/s2); a characteristic dimension x of the surface (m); the kinematic viscosity n (m2/s); and the thermal diffusivity a (m2/s). The volumetric coefficient of expansion for an ideal gas is β = 1/T, where T is absolute temperature. For a given geometry, Nu x = f (Ra x , Pr)

(5-41)

External Natural Flow for Various Geometries For vertical walls, Churchill and Chu [Int . J . Heat Mass Transfer, 18: 1323 (1975)] recommend, for laminar and turbulent flow on isothermal, vertical walls with height L,   0.387Ra1/6 L Nu L = 0.825 +  [1 + (0.492/Pr)9/16 ]8/27  

2

(5-42)

where the fluid properties for Eq. (5-42) and Nu L = hL/k are evaluated at the film temperature Tf = (Ts + Te)/2. This correlation is valid for all Pr and RaL. For vertical cylinders with boundary layer thickness much less than their diameter, Eq. (5-42) is applicable. An expression for uniform heating is available from the same reference. For laminar and turbulent flow on isothermal, horizontal cylinders of diameter D, Churchill and Chu [Int . J . Heat Mass Transfer, 18: 1049 (1975)] recommend 0.387Ra1/6   D Nu L = 0.60 +  [1 + (0.559/Pr)9/16 ]8/27  

(5-43)

Fluid properties for Eq. (5-43) should be evaluated at the film temperature Tf = (Ts + Te)/2. This correlation is valid for all Pr and RaD. For long, horizontal, flat plates, the characteristic dimension for the correlations is the width L. With constant surface temperature and hot surfaces facing upward, or cold surfaces facing downward, Lloyd and Moran recommend [ASME Paper 74-WA/HT-66 (1974)] Nu L = 0.54Ra1/4 (laminar) L

10 5 < Ra L < 10 7

(5-44)

7 9 Nu L = 0.15Ra1/3 L ( turbulent ) 10 < Ra L < 10

(5-45)

and for hot surfaces facing downward, or cold surfaces facing upward, for laminar and turbulent flow, Nu L = 0.27Ra1/4 L

10 5 < Ra L < 1010

(5-46)

Fluid properties for Eqs. (5-44) to (5-46) should be evaluated at the film temperature, Tf = (Ts + Te)/2

(5-47)

Simultaneous Heat Transfer by Radiation and Convection Simultaneous heat transfer by radiation and convection is treated per the

(5-48)

For rectangular cavities, the plate spacing between the two surfaces L is the characteristic dimension that defines the Nusselt and Rayleigh numbers. The temperature difference in the Rayleigh number RaL = β ΔT gL3/na is ΔT = TH - TC. For a horizontal rectangular cavity heated from below, the onset of advection requires RaL > 1708. Globe and Dropkin [ J . Heat Transfer, 81: 24–28 (1959)] propose the correlation 0.074 Nu L = 0.069Ra1/3 L Pr

3 × 10 5 < Ra L < 7 × 10 9

(5-49)

All properties in Eq. (5-49) are calculated at the average temperature (TH + TC)/2. For vertical rectangular cavities of height H and spacing L, with Pr ≈ 0.7 (gases) and 40 < H/L < 110, the equation of Shewen et al. [ J . Heat Transfer, 118: 993–995 (1996)] is recommended:   0.0665Ra1/3  L Nu L = 1 +  1.4    1 + (9000/Ra L ) 

2

1/2

  

Ra L < 10 6

(5-50)

All properties in Eq. (5-50) are calculated at the average temperature (TH + TC)/2. Example 5-5 Comparison of the Relative Importance of Natural Convection and Radiation at Room Temperature Estimate the heat losses by

natural convection and radiation for an undraped person standing in still air. The temperatures of the air, surrounding surfaces, and skin are 19, 15, and 35°C, respectively. The height and surface area of the person are, respectively, 1.8 m and 1.8 m2. The emissivity of the skin is 0.95. We can estimate the Nusselt number by using Eq. (5-42) for a vertical, flat plate of height L = 1.8 m. The film temperature is (19 + 35)/2 = 27°C. The Rayleigh number, evaluated at the film temperature, is Ra L =

2

Q /A TH − TC

β∆TgL3 (1/300)(35 − 19)9.81(1.8)3 = 8.53 × 10 9 = 1.589 × 10 −5 (2.25 × 10 −5 ) να

From Eq. (5-42) with Pr = 0.707, the Nusselt number is 240 and the average heattransfer coefficient due to natural convection is k 0.0263 W h = Nu L = (240) = 3.50 2 m ⋅K L 1.8 The radiative heat-transfer coefficient is given by Eq. (5-12): 2 2 hR = εskin σ (Tskin + Tsur )(Tskin + Tsur )

= 0.95(5.67 × 10−8)(3082 + 2882)(308 + 288) = 5.71

W m2 ⋅ K

The total rate of heat loss is Q = hA (Tskin − Tair ) + hR A(Tskin − Tsur ) = 3.50(1.8)(35 - 19) + 5.71(1.8)(35 - 15) = 306 W At these conditions, radiation is nearly twice as important as natural convection.

FORCED COnVECTIOn Forced convection heat transfer is probably the most common mode in the process industries. Forced flows may be internal or external. This subsection briefly introduces correlations for estimating heat-transfer coefficients for flows in tubes and ducts; flows across plates, cylinders, and spheres; flows through tube banks; and heat transfer to nonevaporating falling films.

HEAT TRAnSFER BY COnVECTIOn Section 11 introduces several types of heat exchangers, design procedures, overall heat-transfer coefficients, and mean temperature differences. Flow in Round Tubes In addition to the Nusselt (NuD = hD/k) and Prandtl (Pr = n/a) numbers introduced above, the key dimensionless parameter for forced convection in round tubes of inside diameter D is the Reynolds number ReD = 4m /πDμ = ρVD/μ. For internal flow in a tube or duct, the heat-transfer coefficient is defined as q = h(Ts - Tb)

(5-51)

where Tb is the bulk or mean temperature at a given cross section and Ts is the corresponding surface temperature. For laminar flow (ReD < 2100) that is fully developed, both hydrodynamically and thermally, the Nusselt number has a constant value for a uniform wall temperature, NuD = 3.66. For a uniform heat flux through the tube wall, NuD = 4.36. In both cases, the thermal conductivity of the fluid in NuD is evaluated at Tb. The distance x required for a fully developed laminar velocity profile is given by (x/D)/ReD ≈ 0.05. The distance x required for fully developed laminar thermal profiles is obtained from [(x/D)/(ReD Pr)] ≈ 0.05. For a constant wall temperature, a fully developed laminar velocity profile, and a developing thermal profile, the average Nusselt number is estimated by [Hausen, Allg . Waermetech. 9: 75 (1959)] Nu D = 3.66 +

0.0668( D /L)Re D Pr 1 + 0.04[( D /L)Re D Pr]2/3

(5-52)

For large values of L, Eq. (5-52) approaches NuD = 3.66. Equation (5-52) also applies to developing velocity and thermal profile conditions if Pr >> 1. The properties in Eq. (5-52) are evaluated at the bulk mean temperature Tb = (Tb ,in + Tb ,out )/2

D Nu D = 1.86  Re D Pr  L 

1/3

 µb   µ 

0.14

(5-54)

s

The properties, except for μs, are evaluated at the bulk mean temperature per Eq. (5-53) and 0.48 < Pr < 16,700 and 0.0044 < μb/μs < 9.75. For fully developed flow in the transition region between laminar and turbulent flow, and for fully developed turbulent flow, Gnielinski’s [Int . Chem . Eng. 16: 359 (1976)] equation is recommended: Nu D =

( f /8)(Re D − 1000)Pr K 1 + 12.7( f /8)1/2 (Pr 2/3 − 1)

(5-55)

where 0.5 < Pr < 105, 3000 < ReD < 106, K = (Prb/Prs)0.11 for liquids (0.05 < Prb/ Prs < 20), and K = (Tb/Ts)0.45 for gases (0.5 < Tb/Ts < 1.5). The factor K corrects for variable property effects. For smooth tubes, the Fanning friction factor f for use with Eq. (5-55) is given by f = (0.790 ln ReD - 1.64)−2

where 0.7 < Pr < 16,700, ReD < 10,000, and L/D > 10. Equations (5-55) and (5-57) apply to both constant temperature and uniform heat flux along the tube. The properties are evaluated at the bulk temperature Tb, except for μs, which is at the temperature of the tube. For L/D greater than about 10, Eqs. (5-55) and (5-57) provide an estimate of Nu D . In this case, the properties are evaluated at the bulk mean temperature per Eq. (5-53). More complicated and comprehensive predictions of fully developed turbulent convection are available in Churchill and Zajic [AIChE J. 48: 927 (2002)] and Yu, Ozoe, and Churchill [Chem . Eng . Science, 56: 1781 (2001)]. For fully developed turbulent flow of liquid metals, the Nusselt number depends on the wall boundary condition. For a constant wall temperature [Notter and Sleicher, Chem . Eng . Science, 27: 2073 (1972)], 0.93 NuD = 4.8 + 0.0156 Re0.85 D Pr

3000 < ReD < 106

(5-56)

For rough pipes, approximate values of NuD are obtained if f is estimated by the Moody diagram of Sec. 6. Equation (5-55) is corrected for entrance effects per Eq. (5-60) and Table 5-3. Sieder and Tate [Ind . Eng . Chem. 28: 1429 (1936)] recommend a simpler but less accurate equation for fully developed turbulent flow 1/3  µ b  Nu D = 0.027Re 4/5 D Pr  µ 

0.14

(5-57)

s

TABLE 5-3 Effect of Entrance Configuration on the Values C and n in Eq. (5-60) for Pr ò 1 (Gases and Other Fluids with Pr about 1) Entrance configuration

C

n

Long calming section Open end, 90° edge 180° return bend 90° round bend 90° elbow

0.9756 2.4254 0.9759 1.0517 2.0152

0.760 0.676 0.700 0.629 0.614

(5-58)

while for a uniform wall heat flux 0.93 NuD = 6.3 + 0.0167 Re0.85 D Pr

(5-59)

In both cases the properties are evaluated at Tb and 0.004 < Pr < 0.01 and 104 < ReD < 106. Entrance effects for turbulent flow with simultaneously developing velocity and thermal profiles can be significant when L/D < 10. Shah and Bhatti correlated entrance effects for gases (Pr ≈ 1) to give an equation for the average Nusselt number in the entrance region (in Kaka, Shah, and Aung, eds., Handbook of Single-Phase Convective Heat Transfer, Chap. 3, Wiley-Interscience, Hoboken, N.J., 1987). Nu D C = 1+ Nu D ( x /D )n

(5-53)

For a constant wall temperature with developing laminar velocity and thermal profiles, the average Nusselt number is approximated by [Sieder and Tate, Ind . Eng . Chem. 28: 1429 (1936)]

5-9

(5-60)

where NuD is the fully developed Nusselt number and the constants C and n are given in Table 5-3 (Ebadian and Dong, Chap. 5 of Rohsenow, Hartnett, and Cho, Handbook of Heat Transfer, 3d ed., McGraw-Hill, New York, 1998, p. 5.31). The tube entrance configuration determines the values of C and n as shown in Table 5-3. Flow in Noncircular Ducts The length scale in the Nusselt and Reynolds numbers for noncircular ducts is the hydraulic diameter Dh = 4Ac/p, where Ac is the cross-sectional area for flow and p is the wetted perimeter. For a circular annulus, Dh = Do - Di , where Di and Do are the inner and outer diameters. Nusselt numbers for fully developed laminar flow in a variety of noncircular ducts are given by Mills [Heat Transfer, 2d ed., Prentice Hall, Upper Saddle River, N.J., 1999, p. 307]. For turbulent flows, correlations for round tubes can be used with D replaced by Dh. For annular ducts, the accuracy of the Nusselt number given by Eq. (5-55) is improved by the following multiplicative factors [Petukhov and Roizen, High Temp. 2: 65 (1964)]. Inner tube heated

Outer tube heated

D  0.86  i   Do 

−0.16

D  1 − 0.14  i   Do 

0.6

where Di and Do are the inner and outer diameters, respectively. Example 5-6 Turbulent Internal Flow Air at 300 K, 1 bar, and 0.05 kg/s enters a channel of a plate-type heat exchanger (Mills, Heat Transfer, 2d ed., Prentice Hall, Upper Saddle River, N.J., 1999) that measures 1 cm wide, 0.5 m high, and 0.8 m long. The walls are at 600 K, and the mass flow rate is 0.05 kg/s. The entrance has a 90° edge. We want to estimate the exit temperature of the air. Our approach will use Eq. (5-55) to estimate the average heat-transfer coefficient, followed by application of Eq. (5-35) to calculate the exit temperature. We assume ideal gas behavior and an exit temperature of 500 K. The estimated bulk mean temperature of the air is, by Eq. (5-53), 400 K. At this temperature, the properties of the air are Pr = 0.690, μ = 2.301 × 10-5 kg/(m ⋅ s), k = 0.0338 W/(m ⋅ K), and cp = 1014 J/(kg ⋅ K). We start by calculating the hydraulic diameter Dh = 4Ac/p. The cross-sectional area for flow Ac is 0.005 m2, and the wetted perimeter p is 1.02 m. The hydraulic diameter Dh = 0.01961 m. The Reynolds number is Re Dh =

mD  h 0.05(0.01961) = = 8521 Ac µ 0.005(2.301 × 10 -5 )

5-10

HEAT AnD MASS TRAnSFER For an isothermal spherical surface, Whitaker [AIChE, 18: 361 (1972)] recommends

The flow is in the transition region, and Eqs. (5-56) and (5-55) apply: f = 0.25(0.790 ln ReDh - 1.64)-2 = 0.25(0.790 ln 8521 - 1.64)-2 = 0.008235 Nu D =

2/3 0.4  µ e  Nu D = 2 + ( 0.4Re1/2 D + 0.06Re D ) Pr   µ s 

( f /2)(Re D - 1000)( Pr ) K 1 + 12.7( f /2)1/2 (Pr 2/3 - 1)

(0.008235/2)(8521 − 1000)(0.690)  400  =   1 + 12.7(0.008235/2)1/2 (0.690 2/3 − 1)  600 

(5-64)

This equation is based on data for 0.7 < Pr < 380, 3.5 < ReD < 8 × 104, and 1 < μe/μs < 3.2. The properties are evaluated at the free stream temperature Te, with the exception of μs, which is evaluated at the surface temperature Ts . The average Nusselt number for laminar flow over an isothermal flat plate of length x is estimated from [Churchill and Ozoe, J . Heat Transfer, 95: 416 (1973)]

0.45

= 21.68

Entrance effects are included by using Eq. (5-60) for an open-end, 90° edge:    2.4254 C  (21.68) = 25.96 Nu D = 1 + Nu D = 1 + n  0.676   ( x /D )   (0.8/0.01961) 

Nu x =

The average heat-transfer coefficient becomes h=

1/4

k 0.0338 W Nu D = (25.96) = 44.75 2 Dh 0.01961 m ⋅K

1.128Pr 1/2 Re1/2 x [1 + (0.0468/Pr)2/3 ]1/4

(5-65)

This equation is valid for all values of Pr as long as Rex Pr > 100 and Rex < 5 × 105. The fluid properties are evaluated at the film temperature (Te + Ts)/2, where Te is the free stream temperature and Ts is the surface temperature. For a uniformly heated flat plate, the local Nusselt number is given by [Churchill and Ozoe, J . Heat Transfer, 95: 78 (1973)]

The exit temperature is calculated from Eq. (5-35):  hpL  T ( L) = Ts − (Ts − Tin )exp  −  P   mc

Nu x =

 44.75(1.02)0.8  = 600 − (600 − 300)exp  −  = 450 K  0.05(1014) 

0.886Pr 1/2 Re1/2 x 1 + ( 0.0207 / Pr )2/3 

1/4

(5-66)

We conclude that our estimated exit temperature of 500 K is too high. We could repeat the calculations, using fluid properties evaluated at a revised bulk mean temperature of 375 K.

where again the properties are evaluated at the film temperature. The average Nusselt number for turbulent flow over a smooth, isothermal flat plate of length x is given by [Mills, Heat Transfer, 2d ed., Prentice Hall, Upper Saddle River, N.J., 1999, p. 315]

Coiled Tubes For turbulent flow inside helical coils, with tube inside radius a and coil radius R, the Nusselt number for a straight tube Nus is related to that for a coiled tube Nuc by [Rohsenow, Hartnett, and Cho, Handbook of Heat Transfer, 3d ed., McGraw-Hill, New York, 1998, p. 5.90]

  Re  0.8  1/3 0.43 Nu x = 0.664Re1/2 + 0.036Re0.8 1 −  cr   cr Pr x Pr   Re x  

Nu C a a = 1.0 + 3.6  1 −     R R Nu S

0.8

The critical Reynolds number Recr is typically taken as 5 × 105, Recr < Rex < 3 × 107, and 0.7 < Pr < 400. The fluid properties are evaluated at the film temperature (Te + Ts)/2, where Te is the free-stream temperature and Ts is the surface temperature. Equation (5-67) also applies to the uniform heat flux boundary condition provided h is based on the average temperature difference between Ts and Te. Flow-through Tube Banks Aligned and staggered tube banks are sketched in Fig. 5-6. The tube diameter is D, and the transverse and longitudinal pitches are ST and SL. The fluid velocity upstream of the tubes is V∞. To estimate the overall heat-transfer coefficient for the tube bank, Mills [Heat Transfer, 2d ed., Prentice-Hall, 1999, p. 348] proceeds as follows. The Reynolds number for use in Eq. (5-63) is recalculated with an effective average velocity in the space between adjacent tubes:

(5-61)

where 2 × 104 < ReD < 1.5 × 105 and 5 < R/a < 84. For lower Reynolds numbers (1.5 × 103 < ReD < 2 × 104), the same source recommends Nu c a = 1.0 + 3.4 Nu s R

(5-62)

External Flows For a single cylinder in cross flow, Churchill and Bernstein [ J . Heat Transfer, 99: 300 (1977)] recommend Nu D = 0.3 +

1/3   Re D  5/8  0.62Re1/2 D Pr 1+    2/3 1/4  [1 + (0.4/Pr) ]   282,000  

4/5

(5-63)

V ST = V∞ ST − (π /4) D

where Nu D = hD /k . Equation (5-63) is for all values of ReD and Pr, provided that ReD Pr > 0.4. The fluid properties are evaluated at the film temperature (Te + Ts)/2, where Te is the free-stream temperature and Ts is the surface temperature. Equation (5-63) also applies to the uniform heat flux boundary condition provided h is based on the perimeter-averaged temperature difference between Ts and Te.

ST

10+

1

Nu D =Φ Nu D

D ST

SL SL (a)

(b)

FIG. 5-6 (a) Aligned and (b) staggered tube bank configurations. The fluid velocity upstream of

the tubes is V∞.

(5-68)

The heat-transfer coefficient increases from row 1 to about row 5 of the tube bank. The average Nusselt number for a tube bank with 10 or more rows is

D V∞

(5-67)

(5-69)

HEAT TRAnSFER WITH CHAnGE OF PHASE 1

where F is an arrangement factor and Nu D is the Nusselt number for the first row, calculated by using the velocity in Eq. (5-68). The arrangement factor is calculated as follows. Define dimensionless pitches as PT = ST/D and PL/D and calculate a factor y as follows.  π  1− 4 Pt  Ψ=  1− π  4 PT PL 

Φaligned = 1 +

if PL < 1

(5-71)

2 3 PL

(5-72)

1 + ( N − 1)Φ 1 Nu D N

q 280  4 ρ2l gkl3  = Ts − Tb 141  3µ 2l 

where C0 = 0.029 and m = 0.533 for Red > 1600, C0 = 0.212 × 10−3 and m = 1.2 for 1600 < Red < 3200, and C0 = 0.181 × 10−2 and m = 0.933 for Red > 3200. Equation (5-75) provides an average heat-transfer coefficient, and the value of the film thickness d for Red < 1600 is given by  3µ Γ  δ =  2l   ρl g 

 δ 3ρl2 g   µ 2 

(5-73)

1/3

(5-76)

0.5

= 0.137Reδ0.75

(5-77)

l

where N is the number of rows. The fluid properties for gases are evaluated at the average mean film temperature [(Tin + Tout)/2 + Ts]/2. For liquids, properties are evaluated at the bulk mean temperature (Tin + Tout)/2, with Nu D from Eq. (5-73) being multiplied by a Prandtl number correction (Prs/Prb)−0.11 for cooling and (Prs/Prb)−0.25 for heating. Heat Transfer to Nonevaporating Falling Films When a subcooled liquid flows in a thin layer down a vertical surface, there is little or no evaporation and the heat-transfer coefficient is defined by q/(Ts −Tb) where Ts is the surface temperature and Tb is the bulk fluid temperature. For laminar flow (Red < 20–30) the heat-transfer coefficient is given by the equation of Hewitt [Rohsenow, Hartnett, and Cho, Handbook of Heat Transfer, 3d ed., McGraw-Hill, New York, 1998, chap. 15]: h=

(5-75)

and for Red > 1600 by

If there are fewer than 10 rows, Nu D =

hδ = C 0 Reδm Prl0.344 kl

(5-70)

0.7 S L /ST − 0.3 Ψ1.5 (S L /ST + 0.7)2

Φstaggered = 1 +

where the Reynolds number of the falling film is defined as Red = 4Γ/μl and Γ is the mass rate of flow of liquid per unit length normal to the direction of flow [kg/(s ⋅ m)]. To account for wavy laminar (30–50 < Red < 1600) and turbulent (Red > 1600) flow, Wilkie [Rohsenow, Hartnett, and Cho, Handbook of Heat Transfer, 3d ed., McGraw-Hill, New York, 1998, chap. 15] recommends

if PL ≥ 1

The arrangement factors are

5-11

1/3

Reδ−1/3

(5-74)

JACKETS AnD COILS OF AGITATED VESSELS See Secs. 11 and 18. nOnnEWTOnIAn FLUIDS Many real fluids are nonnewtonian. Section 6 introduces the dynamics of nonnewtonian fluids in laminar and turbulent regimes. Heat transfer is reviewed by Hartnett and Cho [Rohsenow, Hartnett, and Cho, Handbook of Heat Transfer, 3d ed., McGraw-Hill, New York, 1998, chap. 13]. They provide equations, tables, and charts for estimating the Nusselt number in laminar and turbulent internal flow and refer to the literature for external convection, free convection, boiling, suspensions and surfactants, and flow of food products.

HEAT TRAnSFER WITH CHAnGE OF PHASE In any process in which a material changes phase, the addition or removal of heat is required to balance the latent heat of the change of phase plus any other sensible heating or cooling that occurs. Heat may be transferred by any one of or a combination of conduction, convection, and radiation. Change of phase involves simultaneous mass and heat transfer. COnDEnSATIOn Condensation Mechanisms Condensation occurs when a saturated vapor comes in contact with a surface whose temperature is below the saturation temperature. A film of condensate forms on the surface, and the thickness of the film increases as the liquid flows down the surface. This is called film-type condensation. Another type of condensation, called dropwise, occurs when the wall is not uniformly wetted by the condensate, with the result that the condensate appears in many small droplets on the surface. The individual droplets grow, coalesce, and finally form a rivulet. Film-type condensation is more common and more dependable. Dropwise condensation normally needs to be promoted by introducing an impurity into the vapor stream. Substantially higher (6 to 18 times) coefficients are obtained for dropwise condensation of steam, but it is difficult to maintain. The equations below are for the film type only. For additional details, see Rohsenow, Hartnett, and Cho, Handbook of Heat Transfer, 3d ed., McGraw-Hill, New York, 1998 and Bergman, Lavine, Incropera, and DeWitt, Fundamentals of Heat and Mass Transfer, 7th ed., Wiley, Hoboken, N.J., 2011. The Reynolds number of the condensate film ( falling film) is defined as Red = 4Γ/μl, where Γ is the mass rate of flow of condensate per unit length normal to the direction of flow [kg/(s ⋅ m)] and μl is the liquid viscosity. For Red < 30 the flow is laminar and free of waves. When 30 < Red < 1800, the

flow is wavy and rippled. At Red > 1800 the flow is turbulent. The Reynolds number can also be written as Reδ =

4 m 4ρl umδ = µl µl

(5-78)

where d is the film thickness. Condensation Coefficients Vertical Tubes and Plates For a Reynolds number < 30, the average Nusselt number for laminar condensate films is 1/4

Nu L =

 ρl g (ρl − ρv )h lfg L3  hL L = 0.943   kl  µ l kl (Tsat − Ts ) 

(5-79)

where L is the length of the cooled surface and h lfg = h fg + 0.68c p ,l (Tsat − Ts )

(5-80)

The liquid properties in Eqs. (5-79) and (5-80) are evaluated at the film temperature, Tf = (Tsat + Ts)/2, and ρv and hfg are at Tsat. The vapor density in Eq. (5-79) is frequently neglected relative to the liquid density. The total rate of heat transfer to the surface at temperature Ts is given by Q = hL A (Tsat − Ts )

(5-81)

5-12

HEAT AnD MASS TRAnSFER where

and the rate of condensation is m =

Q h lfg

Retr = 5800Prl0.65

(5-82)

To estimate average Nusselt numbers for laminar, wavy, and turbulent flow, Bergman et al. (2011) recommend the following procedure. A dimensionless parameter P is defined by combining Eqs. (5-82) and (5-78) to give 1/3 an average modified Nusselt number with characteristic length ( ν2l /g ) :

Liquid properties in Eqs. (5-88) to (5-92) can be approximated by evaluation at the film temperature: Tf = (Tsat + Ts)/2 with hfg at Tsat. An energy balance for a vertical surface of length L is

( ν /g )

1/3

Reδ = 4 P P=

(5-83)

kl L(Tsat − Ts )

1/3

kl

= 0.943 P −1/4

1/3

Nu L =

hL ( νl2 /g ) kl

1/3

Nu L =

hL ( νl2 /g ) kl

=

=

( P ≤ 15.8)

(5-84)

1 (0.68 P + 0.89)0.82 (15.8 ≤ P ≤ 2530) P

(5-85)

4/3 1 ( P ≥ 2530, Prl ≥ 1) (5-86) (0.024 P − 53)Prl1/2 + 89  P

Equations (5-84) and (5-79) are identical if ρl >> ρv. The fluid properties for Eqs. (5-84), (5-85), and (5-86) are evaluated as described below Eq. (5-80). Horizontal Smooth Tubes For laminar film condensation on horizontal smooth tubes the average Nusselt number is given by

Jal =

Prl L d Re 4 Ja l Re∫0 Nu

(5-94)

 ρl g (ρl − ρv )h lfg D 3  hD D = 0.729   kl  µ l kl (Tsat − Ts ) 

(5-87)

The fluid properties for Eq. (5-87) are evaluated as described below Eq. (5-80). Banks of Horizontal Tubes In the idealized case of N tubes in a vertical row where the total condensate flows smoothly from one tube to the one beneath it, without splashing, and still in laminar flow on the tube, the mean condensing coefficient hN for the entire row of N tubes is related to the condensing coefficient for the top tube h1 by hN = h1N −s

(5-88)

c pl (Ts − Tsat )

(5-95)

h fg

The use of Eqs. (5-88) to (5-95) to estimate an evaporation rate is illustrated by Example 5-7 which is based on an example in Mills [Heat Transfer, 2d ed., Prentice Hall, Upper Saddle River, N.J., 1999, pp. 684–685]. Example 5-7 Evaporating Falling Film Water is fed to the outer surface of a single, vertical, 5-cm outer-diameter (OD) tube at the rate of 0.01 kg/s. The tube is 5 m long, and its surface is kept at 311 K by condensing steam on the inside. The saturation temperature at the pressure outside the tube is 308 K. Estimate the evaporation rate. We start by recalling that the liquid properties are approximated at the film temperature [Tf = (Ts + Tsat)/2 = (311 + 308)/2 = 310 K] and that the enthalpy of vaporization hfg is evaluated at the saturation temperature. At 308 K, hfg = 2.418 × 106 J/kg. At the film temperature, kl = 0.628 W/(m ⋅ K), ρl = 993 kg/m3, cpl = 4174 J/(kg ⋅ K), μl = 6.95 × 10-4 kg/(m ⋅ s), nl = 0.700 × 10-6 m2/s, and Prl = 4.6. The film Reynolds number at the top of the tube is Re0 =

1/4

Nu D =

=-

where L is the length of the surface in the direction of flow and the Jakob number for the liquid is defined as

µ l h lfg ( νl2 /g )

1/3

hL ( νl2 /g )

1/3

= 4 P Nu L

kl

The modified average Nusselt numbers for Reδ < 30, 30 < Reδ < 1800, and Reδ > 1800 become Nu L =

Re

L

2 l

hL ( νl2 /g )

(5-93)

4 Γ 0 4 m 0 4(0.01) = = = 366 µl πDµ l π(0.05)6.95 × 10 −4

The Reynolds number for transition from wavy laminar to turbulent flow is

Retr = 5800Prl−1.06 = 5800(4.6)−1.06 = 1151 Because this is greater than 366 we will assume that we remain in the wavy laminar regime and will check ReL by using Eq. (5-94). L

( ν /g ) 2 l

1/3

=-

Prl 4 Ja l

Rel

d Re Pr =- l Nu 4 Ja l Re0

∫

Rel

d Re

∫ 0.822Re

-0.22

Re0

Integrating and solving for ReL give Re1.22 L =−

The standard Nusselt theory gives s = 1/4 but others recommend s = 1/6.

4.01 L Ja l + Re1.22 0 = 730 ( νl2 /g )1/3 Prl

where

EVAPORATInG LIQUID FILMS On VERTICAL WALLS Mills’ presentation of heat transfer to evaporating falling films [Heat Transfer, 2d ed., Prentice Hall, Upper Saddle River, N.J., 1999, pp. 681–685] is given here, with minor modifications. The Reynolds number of the evaporating falling film is defined as Reδ = 4Γ/µl and the Nusselt number for evaporation is 1/3

Nu L =

hL ( νl2 /g ) kl

(5-89)

0 < Reδ < 30, laminar

30 < Reδ < Retr , wavy laminar

Nu = 0.0038Reδ-0.4 Prl0.65

h fg 1/3

=

4174(311 − 308) = 5.18 × 10 −3 2.418 × 10 6 1/3

 (0.700 × 10 −6 )2  =  9.81  

= 3.68 × 10 −5 m

We conclude that the film is entirely in the wavy laminar regime. Solving the film Reynolds number for the mass flow rate at L gives πDµ l Re L π(0.05)6.95 × 10 −4 (222) = = 6.07 × 10 −3 kg/s 4 4

The evaporation rate is

−1/3

(5-90)

For wavy laminar and turbulent flows, the correlations of experimental data for water by Chun and Seban [ J . Heat Transfer, 93: 391–396 (1971)] give Nu = 0.822Reδ-0.22

c pl (Ts − Tsat )

 ν2l   g 

m L =

For laminar flow the local Nusselt number is 3 Nu =  Reδ  4 

Ja l =

Retr < Reδ , turbulent

(5-91) (5-92)

m vap = m 0 − m L = 0.01 − 0.00607 = 0.0039 kg/s

POOL BOILInG Pool boiling refers to the type of boiling experienced when the heating surface is surrounded by a large body of fluid which is not flowing at any appreciable velocity and is agitated only by the motion of the bubbles and by natural convection currents. Two types of pool boiling are possible: subcooled pool boiling, in which the bulk fluid temperature is below the saturation

HEAT TRAnSFER BY RADIATIOn temperature, resulting in collapse of the bubbles before they reach the surface, and saturated pool boiling, with the bulk temperature equal to the saturation temperature, resulting in net vapor generation. The following presentation draws heavily from Mills [Heat Transfer, 2d ed. (1999)]. In the general shape of the curve relating the heat-transfer coefficient to ΔT = Ts - Tsat, the difference between the surface temperature and the saturation temperature is reasonably well understood. The familiar boiling curve was originally demonstrated experimentally by Nukiyama [ J . Soc . Mech . Eng . ( Japan), 37: 367 (1934)]. This curve points out one of the great dilemmas for boiling-equipment designers. They are faced with at least four heat-transfer regimes in pool boiling: natural convection (+), nucleate boiling (+), transition to film boiling (-), and film boiling (+). The signs indicate the sign of the derivative dq/(d ΔT) . In the transition to film boiling, the heat-transfer rate decreases with ΔT. Here we consider nucleate boiling, the peak heat flux, and film boiling. Nucleate boiling occurs in kettle-type and natural-circulation reboilers commonly used in the process industries. High rates of heat transfer are obtained as a result of bubble formation at the liquid-solid interface. The heat-transfer coefficient is defined by q = h(Ts − Tsat )

TABLE 5-4 The Constant Cnb and Exponent m for Use with Rohsenow Eq. (5-97) Liquid Water Water Water Ethanol n-Pentane

Surface Copper, scored Copper, polished Stainless steel, mechanically polished Chromium Chromium

m

0.0068 0.013 0.013 0.0027 0.015

2.0 2.0 2.0 4.1 4.1

Table 5-4. Equations (5-96) and (5-97b) imply that the rate of heat transfer is proportional to ΔT 3. Errors of 100 percent in q and 25 percent in ΔT are possible with Eq. (5-97b). The designer of heat-transfer equipment is usually more concerned with not exceeding the peak heat flux qmax rather than in knowing accurate values of q and ΔT . The peak heat flux may be predicted by the Kutateladse-Zuber [Trans . ASME, 80: 711 (1958)] relationship: 1/4

1/2

  σ Lc =    (ρl − ρv ) g 

(5-97a)

qmax = C max h fg  σρv2 (ρl − ρv ) g 

Ja 2 hL Nu = c = 3 l m kl C nb Prl

1/4

 (ρl − ρv ) gh lfg kv3  h = C fb    νv L(Ts − Tsat ) 

(5-100a)

(5-97b) where L is a characteristic length. For spheres and horizontal cylinders it is the diameter D. The constant Cf b is 0.62 for a horizontal cylinder, 0.67 for a sphere, and 0.71 for a planar vertical surface. The modified latent heat is

The Jakob number is defined as c pl (Ts − Tsat )

(5-99)

where Cmax is approximately 0.15. All properties in Eq. (5-99) are evaluated at Tsat. For laminar film boiling, Bromley’s [Chem . Eng . Prog . 46: 221 (1950)] correlation may be used:

and the Nusselt number is given by Rohsenow [Trans . ASME, 74: 969 (1952)] as

h fg

Cnb

(5-96)

where Tsat is at the system pressure. The characteristic length used to define the Nusselt number is

Ja l =

5-13

(5-98)

All properties in Eq. (5-97b), including the vapor density, are evaluated at Tsat. Typical values for the constant Cnb and the exponent m are given in

h lfg = h fg + 0.35c pv (Ts − Tsat )

(5-100b)

In Eqs. (5-99) and (5-100a), hfg, ρl, and s are evaluated at Tsat; all other properties are at the mean film temperature.

HEAT TRAnSFER BY RADIATIOn General References: Baukal, C. E., ed., The John Zink Combustion Handbook, CRC Press, Boca Raton, Fla., 2001. Blokh, A. G., Heat Transfer in Steam Boiler Furnaces, 3d ed., Taylor & Francis, New York, 1987. Brewster, M. Quinn, Thermal Radiation Heat Transfer and Properties, Wiley, New York, 1992. Goody, R. M., and Y. L. Yung, Atmospheric Radiation—Theoretical Basis, 2d ed., Oxford University Press, London, 1995. Hottel, H. C., and A. F. Sarofim, Radiative Transfer, McGraw-Hill, New York, 1967. Howell, John, M. Pinar Mengüç, and Robert Siegel, Thermal Radiative Heat Transfer, 6th ed., CRC Press, Boca Raton, Fla., 2015. Modest, Michael F., Radiative Heat Transfer, 3d ed., Academic Press, New York, 2013. Noble, James J., “The Zone Method: Explicit Matrix Relations for Total Exchange Areas,” Int . J . Heat Mass Transfer, 18: 261–269 (1975). Rhine, J. M., and R. J. Tucker, Modeling of Gas-Fired Furnaces and Boilers, British Gas Association with McGraw-Hill, New York, 1991. Sparrow, E. M., and R. D. Cess, Radiation Heat Transfer, 3d ed., Taylor & Francis, New York, 1988. Stultz, S. C., and J. B. Kitto, Steam: Its Generation and Use, 40th ed., Babcock and Wilcox, Barkerton, Ohio, 1992. InTRODUCTIOn Heat transfer by thermal radiation involves the transport of electromagnetic (EM) energy from a source to a sink. In contrast to other modes of heat transfer, radiation does not require the presence of an intervening medium, e.g., as in the irradiation of the earth by the sun. Most industrially important applications of radiative heat transfer occur in the near infrared portion of the EM spectrum (0.7 through 25 μm) and may extend into the far infrared region (25 to 1000 μm). For very high temperature sources, such as solar radiation, relevant wavelengths encompass the entire visible region (0.4 to 0.7 μm) and may extend down to 0.2 μm in the ultraviolet

(0.01- to 0.4-μm) portion of the EM spectrum. Radiative transfer can also exhibit unique action-at-a-distance phenomena that do not occur in other modes of heat transfer. Radiation differs from conduction and convection with regard to not only mathematical characterization but also its fourth power dependence on temperature. Thus it is usually dominant in hightemperature combustion applications. The temperature at which radiative transfer accounts for roughly one-half of the total heat loss from a surface in air depends on such factors as surface emissivity and the convection coefficient. For pipes in free convection, radiation is important at ambient temperatures. For fine wires of low emissivity, it becomes important at temperatures associated with bright red heat (1300 K). Combustion gases at furnace temperatures typically lose more than 90 percent of their energy through radiative emission from constituent carbon dioxide, water vapor, and particulate matter. Radiative transfer methodologies are important in myriad engineering applications. These include semiconductor processing, illumination theory, and gas turbines and rocket nozzles, as well as furnace design. THERMAL RADIATIOn FUnDAMEnTALS In a vacuum, the wavelength λ, frequency n, and wave number h for electromagnetic radiation are interrelated by λ = c/n = 1/h, where c is the speed of light. Frequency is independent of the index of refraction of a medium n, but both the speed of light and the wavelength in the medium vary according to cm = c/n and λm = λ/n. When a radiation beam passes into a medium of different refractive index, not only does its wavelength change but also its direction does (Snell’s law) as well as the magnitude of its intensity. In most engineering heat-transfer calculations, wavelength is usually employed to

5-14

HEAT AnD MASS TRAnSFER

characterize radiation while wave number is often used in gas spectroscopy. For a vacuum, air at ambient conditions, and most gases, n ≈ 1.0. For this reason this presentation sometimes does not distinguish between λ and λm. Dielectric materials exhibit 1.4 < n < 4, and the speed of light decreases considerably in such media.   In radiation heat transfer, the monochromatic intensity I λ ≡ I λ r, Ω, λ , is a fundamental (scalar) field variable which characterizes EM energy transport. Intensity defines the radiant energy flux passing through an infinitesimal area dA, oriented normal to a radiation beam of arbitrary direction   Ω . At steady  state, the monochromatic intensity is 2a function of position r, direction Ω , and wavelength and has units of W/(m ⋅ sr ⋅ μm). In the general case of an absorbing-emitting and scattering medium, characterized by some  absorption coefficient K(m−1), intensity in the direction Ω will be modified by attenuation and by scattering of radiation into and out of the beam. For the special case of a nonabsorbing (transparent), nonscattering medium of constant refractive index, the radiation intensity is constant and indepen dent of position in a given direction Ω. This circumstance arises in illumination theory where the light intensity in a room is constant in a given direction but may vary with respect to all other directions. The basic conservation law for radiation intensity is termed the equation of transfer or radiative transfer equation. The equation of transfer is a directional energy balance and mathematically is an integrodifferential equation. The relevance of the transport equation to radiation heat transfer is discussed in many sources; see, e.g., Modest, Michael F., Radiative Heat Transfer, 3d ed., Academic Press, New York, 2013, or Howell, John, M. Pinar Mengüç, and Robert Siegel, Thermal Radiative Heat Transfer, 6th ed., CRC Press, Boca Raton, Fla., 2015. Introduction to Radiation Geometry Consider a homogeneous medium of constant refractive index n . A pencil of radiation originates at differentialarea element dAi and is incident on differential area element dAj.  Designate n i and n j as the unit vectors normal to dAi and dAj, and let r, with unit direction vector Ω, define the distance of separation between the area  elements. Moreover, φi and φ j denote the  confined angles between   Ω and n i  and n j , respectively [i.e., cos φi ≡ cos(Ω, ri ) and cos φ j ≡ cos(Ω, r j )]. As the beam travels toward dAj, it will diverge and subtend a solid angle

(

dΩ j =

cos φ j r2

)

The hemispherical emissive power∗ E is defined as the radiant flux density (W/m2) associated with emission from an element of surface area dA into a surrounding unit hemisphere whose base is coplanar with dA. If the  monochromatic intensity I λ (Ω, λ) of emission from the surface is isotropic  (independent of the angle of emission Ω), then Eq. (5-101) may be integrated over the 2π sr of the surrounding unit hemisphere to yield the simple relation Eλ = πI λ , where Eλ ≡ Eλ (λ) is defined as the monochromatic or spectral hemispherical emissive power. Blackbody Radiation Engineering calculations involving thermal radiation normally employ the hemispherical blackbody emissive power as the thermal driving force analogous to temperature in the cases of conduction and convection. A blackbody is a theoretical idealization for a perfect theoretical radiator; i.e., it absorbs all incident radiation without reflection and emits isotropically. In practice, soot-covered surfaces sometimes approximate blackbody behavior. Let Eb ,λ = Eb ,λ (T , λ) denote the monochromatic blackbody hemispherical emissive power frequency function defined such that Eb,λ (T , λ) d λ represents the fraction of blackbody energy lying in the wavelength region from λ to λ + d λ . The function Eb ,λ = Eb ,λ (T , λ ) is given by Planck’s law Eb ,λ (T , λ) c1 (λT )−5 = c2 /λT (5-102) −1 n 2T 5 e where c1 = 2πhc2 and c2 = hc/k are defined as Planck’s first and second constants, respectively. Integration of Eq. (5-102) over all wavelengths yields the Stefan-Boltzmann law for the hemispherical blackbody emissive power ∞

∫E

λ= 0

Eb , λ (T , λ) n 2T 5

b,λ

(T , λ) d λ = n 2 σT 4

(5-103)

∗In the literature the emissive power is variously called the emittance, total hemispherical intensity, or radiant flux density.

≅ c1 (λT )−5 e − c2 /λT

(5-104)

The error introduced by use of the Wien equation is less than 1 percent when λT < 3000 μm ⋅ K. The Wien equation has significant practical value in optical pyrometry for T < 4600 K when a red filter (λ = 0.65 μm) is employed. The long-wavelength asymptotic approximation for Eq. (5-102) is known as the Rayleigh-Jeans formula, which is accurate to within 1 percent for λT > 778,000 μm ⋅ K. The Raleigh-Jeans formula is of limited engineering utility since a blackbody emits over 99.9 percent of its total energy below the value of λT = 53,000 μm ⋅ K. The blackbody fractional energy distribution function is defined by

Fb (λT ) =

∫ ∫

λ

λ=0 ∞

λ=0

Eb ,λ (T , λ) d λ

(5-105)

Eb ,λ (T , λ) d λ

The function Fb(λT) defines the fraction of total energy in the blackbody spectrum which lies below λT and is a unique function of λT. For purposes of digital computation, the following series expansion for Fb(λT) proves especially useful.

in steradian (sr) units

dA j

 by at dAi. Moreover, the projected area of dAi in the direction of Ω is given    cos(Ω, r j ) dAi = cosfi dAi. Multiplication of the intensity I λ ≡ I λ (r , Ω, λ) by d Ω j and the apparent area of dAi then yields an expression for the (differential) net monochromatic radiant energy flux dQi,j originating at dAi and intercepted by dAj.  dQi , j ≡ I λ (Ω, λ)cos φi cos φ j dAi dA j /r 2 (5-101)

Eb (T ) =

where s = c1(π/c2)4/15 is the Stephan-Boltzmann constant. Since a blackbody is an isotropic emitter, it follows that the intensity of blackbody emission is given by the simple formula Ib = Eb/π = n2sT 4/π. The intensity of radiation emitted over all wavelengths by a blackbody is thus uniquely determined by its temperature. In this presentation, all references to hemispherical emissive power shall be to the blackbody emissive power, and the subscript b may be suppressed for expediency. For short wavelengths λT → 0, the asymptotic form of Eq. (5-102) is known as the Wien equation

Fb (λT ) =

15 ∞ e − kξ  3 3 ξ 2 6 ξ 6  ξ + + 2 + 3 ∑ k k k  π 4 k =1 k 

where

ξ=

c2 λT

(5-106)

Equation (5-106) converges rapidly and is due to Lowan (1941) as referenced in Chang and Rhee [Int . Comm . Heat Mass Transfer, 11: 451–455 (1984)]. Numerically, in the preceding, h = 6.6260693 × 10−34 J ⋅ s is the Planck constant; c = 2.99792458 × 108 m/s is the velocity of light in vacuum; and k = 1.3806505 × 10−23 J/K is the Boltzmann constant. These data lead to the following values of Planck’s first and second constants: c1 = 3.741771 × 10−16 W ⋅ m2 and c2 = 1.438775 × 10−2 m ⋅ K, respectively. Numerical values of the Stephan-Boltzmann constant s in several systems of units are as follows: 5.67040 × 10−8 W/(m2 ⋅ K4); 1.3544 × 10−12 cal/(cm2 ⋅ s ⋅ K4); 4.8757 × 10−8 kcal/ (m2 ⋅ h ⋅ K4); 9.9862 × 10−9 CHU/( ft2 ⋅ h ⋅ K4); and 0.17123 × 10−8 Btu/( ft2 ⋅ h ⋅ °R4) (CHU = Celsius heat unit; 1.0 CHU = 1.8 Btu). Blackbody Displacement Laws The blackbody energy spectrum is plotted logarithmically in Fig. 5-7 as Eb,λ (λT ) W × 1013 2 n 2T 5 m ⋅µm ⋅ K 5 versus λT μm ⋅ K. For comparison, a companion inset is provided in cartesian coordinates. The upper abscissa of Fig. 5-7 also shows the blackbody energy distribution function Fb(λT). Figure 5-7 indicates that the wavelength-temperature product for which the maximum intensity occurs is λmaxT = 2898 μm ⋅ K. This relationship is known as Wien’s displacement law, which indicates that the wavelength for maximum intensity is inversely proportional to the absolute temperature. Blackbody displacement laws are useful in engineering practice to estimate wavelength intervals appropriate to relevant system temperatures. The Wien displacement law can be misleading, however, because the wavelength for maximum intensity depends on whether the intensity is defined in terms of frequency or wavelength interval. Two additional useful displacement laws are defined in terms of either the value of λT corresponding to the maximum energy per unit fractional change in wavelength or frequency, that is, λT = 3670 μm ⋅ K, or to the value of λT corresponding to one-half of the blackbody energy, that is, λT = 4107 μm ⋅ K. Approximately one-half of the blackbody energy lies within the twofold λT range geometrically centered on λT = 3670 μm ⋅ K, that is, 3670/ 2 < λT < 3670 2 μm ⋅ K. Some 95 percent of the blackbody energy lies in the interval 1662.6 < λT < 16,295 μm ⋅ K. It thus follows that for the temperature range between ambient (300 K) and flame temperatures (2000 K or 3140°F), wavelengths of engineering heat-transfer importance are bounded between 0.83 and 54.3 μm.

HEAT TRAnSFER BY RADIATIOn

5-15

nomenclature and Units—Radiative Transfer a, ag, ag,1 C p , C P ,Prod ij = si s j A, Ai c c1, c2 dp, rp Eb,λ = Eb,λ(T, λ) En(x) E Eb = n 2 σT 4 fυ f b(λT) Fi,j Fi,j Fi , j h hi Hi H H F   I λ ≡ I λ (r , Ω , λ ) k kλ,p K LM, LM0 m n M, N MS, MF pk P Qi Qi,j T U V W

WSGG spectral model clear plus gray weighting constants Heat capacity per unit mass, J ⋅ kg-1 ⋅ K-1 Shorthand notation for direct exchange area Area of enclosure or zone i, m2 Speed of light in vacuum, m/s Planck’s first and second constants, W ⋅ m2 and m ⋅ K Particle diameter and radius, μm Monochromatic, blackbody emissive power, W/(m2 ⋅ μm) Exponential integral of order n, where n = 1, 2, 3, … Hemispherical emissive power, W/m2 Hemispherical blackbody emissive power, W/m2 Volumetric fraction of soot Blackbody fractional energy distribution Direct view factor from surface zone i to surface zone j Refractory augmented black view factor; F-bar Total view factor from surface zone i to surface zone j Planck’s constant, J ⋅ s Heat-transfer coefficient, W/(m2 ⋅ K) Incident flux density for surface zone i, W/m2 Enthalpy rate, W Enthalpy feed rate, W Monochromatic radiation intensity, W/(m2 ⋅ μm ⋅ sr) Boltzmann’s constant, J/K Monochromatic line absorption coefficient, (atm ⋅ m)-1 Gas absorption coefficient, m-1 Average and optically thin mean beam lengths, m Mass flow rate, kg/h-1 Index of refraction Number of surface and volume zones in enclosure Number of source/sink and flux zones in enclosure where M = MS + MF Partial pressure of species k, atm Number of WSGG gray gas spectral windows Total radiative flux originating at surface zone i, W Net radiative flux between zone i and zone j, W Temperature, K Overall heat-transfer coefficient in WSCC model Enclosure volume, m3 Leaving flux density (radiosity), W/m2 Greek characters

a, a1,2 ag,1, εg, tg,1 β ∆Tge ≡ Tg − Te ε εg (T, r) ελ(T, Ω, λ) h = 1/λ λ = c/n n ρ=1-ε s Σ tg = 1 - εg Ω F Ψ(3)(x) w

Surface absorptivity or absorptance; subscript 1 refers to the surface temperature while subscript 2 refers to the radiation source Gas absorptivity, emissivity, and transmissivity Dimensionless constant in mean beam length equation, LM = β⋅LM0 Adjustable temperature fitting parameter for WSCC model, K Gray diffuse surface emissivity Gas emissivity with path length r Monochromatic, unidirectional surface emissivity Wave number in vacuum, cm-1 Wavelength in vacuum, μm Frequency, Hz Diffuse reflectivity Stefan-Boltzmann constant, W/(m2 ⋅ K4) Number of unique direct surface-to-surface direct exchange areas Gas transmissivity Solid angle, sr (steradians) Equivalence ratio of fuel and oxidant Pentagamma function of x Albedo for single scatter Dimensionless quantities

Deff = N CR =

N FD (S1G R /A1 ) + N CR h 3

4 σT g ,1 4 = H f /σTRef ⋅ A1

N FD ηg η′g = ηg (1 − Θo ) Θi = Ti /TRef   n and n j i r Ω

Effective firing density Convection-radiation number Dimensionless firing density Gas-side furnace efficiency Reduced furnace efficiency Dimensionless temperature Vector notation Unit vectors normal to differential area elements dAi and dAj Position vector Arbitrary unit direction vector Matrix notation

IM I = [di,j]

Column vector, all of whose elements are unity [M × 1] Identity matrix, where di, j is the Kronecker delta; that is, δ i , j = 1 for i = j and δ i , j = 0 for i ≠ j

aI = [ai ⋅ di,j]

Diagonal matrix of WSGG gray gas surface zone a-weighting factors [M × M] Diagonal matrix of gray gas WSGG volume zone a-weighting factors [N × N] Arbitrary nonsingular square matrix Transpose of A Inverse of A Arbitrary diagonal matrix

a g I = [ a g ,i ⋅δ i , j ] A = [ Ai , j ] A T = [ A j ,i ] A −1 = [ Ai , j ]−1 DI = [ Di · δ i , j ] DI −1 = [δ i , j /Di ] CDI = CI · DI = [Ci · Di · δ i , j ]

Inverse of diagonal matrix Product of two diagonal matrices

AI = [ Ai · δ i , j ] εI = [ εi · δ i , j ] ρI = [ρi ⋅δ i , j ]

Diagonal matrix of surface zone areas, m2 [M × M] Diagonal matrix of diffuse zone emissivities [M × M] Diagonal matrix of diffuse zone reflectivities [M × M]

E = [ Ei ] =  σTi 4 

Column vector of surface blackbody hemispherical emissive powers, W/m2 [M × 1] Diagonal matrix of surface blackbody emissive powers, W/m2 [M × M]

EI = [ Ei · δ i , j ] =  σTi 4 · δ i , j  E g = [ E g ,i ] =  σTg4,i  E g I = [ E g ,i · δ i , j ] =  σTg4,i · δ i , j  H = [Hi ] W = [Wi] Q = [Qi] R = [AI − ss ⋅ρI]−1 KI p = [δ i , j · K p ,i ] KI S′ ss = [ si s j ] T

Column vector of gas blackbody hemispherical emissive powers, W/m2 [N × 1] Diagonal matrix of gas blackbody emissive powers, W/m2 [N × N] Column vector of surface zone incident flux densities, W/m2 [M × 1] Column vector of surface zone leaving flux densities, W/m2 [M × 1] Column vector of surface zone fluxes, W [M × 1] Inverse multiple-reflection matrix, m-2 [M × M] Diagonal matrix of WSGG Kp,i values for the ith zone and pth gray gas component, m-1 [N × N] Diagonal matrix of WSGG-weighted gray gas absorption coefficients, m-1 [N × N] Column vector for net volume absorption, W [N × 1] Array of direct surface-to-surface exchange areas, m2  [M × M]

sg = [ si g j ] = gs

Array of direct gas-to-surface exchange areas, m2 [M × N]

gg = [ g i g j ]

Array of direct gas-to-gas exchange areas, m2 [N × N]

SS = [ Si S j ]

Array of total surface-to-surface exchange areas, m2  [M × M]

SG = [ SiG j ]

Array of total gas-to-surface exchange areas, m2  [M × N]

T

GS = GS GG = [GiG j ]

Array of total surface-to-gas exchange areas, m2  [N × M] Array of total gas-to-gas exchange areas, m2 [N × N]

SS = [ Si S i ]

Array of directed surface-to-surface exchange areas, m2 [M × M]

SG = [ SiG j ]

Array of directed gas-to-surface exchange areas, m2 [M × N]

T

GS ≠ SG GG = [GiG j ] VI = [Vi · δ i , j ] FSQ SSb = [SSbi , j ] SSR = [SSR i , j ]

Array of directed surface-to-gas exchange areas, m2 [N × M] Array of directed gas-to-gas exchange areas, m2 [N × N] Diagonal matrix of zone volumes, m3 [N × N] Array of flux fractions in SSR model, dimensionless MS × MS Array of total refractory-aided exchange areas for black source/sink zones in SSR model, m2 MS × MS Array of total refractory-aided exchange areas for nonblack source/sink zones in SSR model, m2 MS × MS Subscripts

b f h i, j n p r s λ Ref

Blackbody or denotes a black surface zone Flux surface zone Hemispherical surface emissivity Zone number indices Normal component of surface emissivity Index for pth gray gas window Refractory surface zone Source-sink surface zone Monochromatic variable Reference quantity Abbreviations

CFD DEA, TEA DO, FV EM RTE LPFF SSR WSCC WSGG

Computational fluid dynamics Direct exchange area and total exchange area Discrete ordinate and finite volume methods Electromagnetic Radiative transfer equation; equation of transfer Long plug flow furnace Source-sink refractory Well-stirred combustion chamber Weighted sum of gray gases

5-16

HEAT AnD MASS TRAnSFER

FIG. 5-7 Spectral dependence of monochromatic blackbody hemispherical emissive power.

RADIATIVE PROPERTIES OF OPAQUE SURFACES Emittance and Absorptance The ratio of the total radiating power of any surface to that of a black surface at the same temperature is called the emittance or emissivity ε of the surface.∗ In general, the monochromatic emissivity isa function of temperature, direction, and wavelength, that is, ελ = ελ(T, Ω, λ). The subscripts n and h are sometimes used to denote the normal and hemispherical values, respectively, of the emittance or emissivity. If radiation is incident on a surface, the fraction absorbed is called the absorptance (absorptivity). Two subscripts are usually appended to the absorptance a1,2 to distinguish between the temperature of the absorbing surface T1 and the spectral energy distribution of the emitting surface T2. According to Kirchhoff ’s law, the emissivity and absorptivity of a surface exposed to surroundings at its own temperature are the same for both monochromatic and total radiation. When the temperatures of the surface and its surroundings differ, the total emissivity and absorptivity of the surface are often found to be unequal; but because the absorptivity is substantially independent of irradiation density, the monochromatic emissivity and absorptivity of surfaces are equal for all practical purposes. The difference between total emissivity and absorptivity depends on the variation of ελ with wavelength and on ∗In the literature, emittance and emissivity are often used interchangeably. NIST (the National Institute of Standards and Technology) recommends use of the suffix -ivity for pure materials with optically smooth surfaces, and -ance for rough and contaminated surfaces. Most real engineering materials fall into the latter category.

the difference between the temperature of the surface and the effective temperature of the surroundings. Consider radiative exchange between a real surface of area A1 at temperature T1 with black surroundings at temperature T2. The net radiant interchange is given by ∞

Q1,2 = A1

∫ [ε

λ

(T1 , λ ) ⋅ Eb ,λ (T1 , λ) − α λ (T1 , λ ) ⋅ Eb ,λ (T2 , λ)]d λ

(5-107a)

λ=0

or

Q1,2 = A1 ( ε1σT14 − α1,2 σT24 )

∞

where

ε1 (T1 ) =

∫ε

λ

(T1 , λ) ⋅

λ= 0

and since

Eb ,λ (T1 , λ) dλ Eb (T1 )

(5-107b)

(5-108)

α λ (T , λ) = ε λ (T , λ)

∞

α1,2 (T1 ,T2 ) =

∫ε

λ=0

λ

(T1 , λ) ⋅

Eb ,λ (T2 , λ) dλ Eb (T2 )

(5-109)

HEAT TRAnSFER BY RADIATIOn For a gray surface ε1 = a1,2 = ελ. A selective surface is one for which ελ(T, λ) exhibits a strong dependence on wavelength. If the wavelength dependence is monotonic, it follows from Eqs. (5-107) to (5-109) that ε1 and a1,2 can differ markedly when T1 and T2 are widely separated. For example, in solar energy applications, the nominal temperature of the earth is T1 = 294 K, and the sun may be represented as a blackbody with radiation temperature T2 = 5800 K. For these temperature conditions, a white paint can exhibit ε1 = 0.9 and a1,2 = 0.1 to 0.2. In contrast, a thin layer of copper oxide on bright aluminum can exhibit ε1 as low as 0.12 and a1,2 greater than 0.9. The effect of radiation source temperature on low-temperature absorptivity for a number of representative materials is shown in Fig. 5-8. Polished aluminum (curve 15) and anodized (surface-oxidized) aluminum (curve 13) are representative of metals and nonmetals, respectively. Figure 5-8 thus demonstrates the generalization that metals and nonmetals respond in opposite directions with regard to changes in the radiation source temperature. Since the effective solar temperature is 5800 K (10,440°R), the extreme right-hand side of Fig. 5-8 provides surface absorptivity data relevant to solar energy applications. The dependence of emittance and absorptance on the real and imaginary components of the refractive index and on the geometric structure of the surface layer is quite complex. However, a number of generalizations concerning the radiative properties of opaque surfaces are possible. These are summarized in the following discussion. Polished Metals 1. In the infrared region, the magnitude of the monochromatic emissivity ελ is small and is dependent on free-electron contributions. Emissivity is also a function of the ratio of resistivity to wavelength r/λ, as depicted in Fig. 5-9. At shorter wavelengths, bound-electron contributions become significant, ελ is larger in magnitude, and it sometimes exhibits a maximum value.

FIG. 5-8 Variation of absorptivity with temperature of radiation source. (1) Slate composition roofing. (2) Linoleum, red brown. (3) Asbestos slate. (4) Soft rubber, gray. (5) Concrete. (6) Porcelain. (7) Vitreous enamel, white. (8) Red brick. (9) Cork. (10) White Dutch tile. (11) White chamotte. (12) MgO, evaporated. (13) Anodized aluminum. (14) Aluminum paint. (15) Polished aluminum. (16) Graphite. The two dashed lines bound the limits of data on gray paving brick, asbestos paper, wood, various cloths, plaster of Paris, lithopone, and paper. To convert degrees Rankine to kelvins, multiply by (5.556)(10-1).

5-17

FIG. 5-9 Hemispherical and normal emissivities of metals and their ratio. Dashed lines: monochromatic (spectral) values versus r/λ. Solid lines: total values versus rT. To convert ohmcentimeter-kelvins to ohm-meter-kelvins, multiply by 10-2.

In the visible spectrum, common values for ελ are 0.4 to 0.8 and ελ decreases slightly as temperature increases. For 0.7 < λ < 1.5 μm, ελ is approximately independent of temperature. For λ > 8 μm, ελ is approximately proportional to the square root of temperature since ελ ∝ r and r ∝ T. Here the Drude or Hagen-Rubens relation applies, that is, ελ, n ≈ 0.0365 r /λ, where r has units of ohm-meters and λ is measured in micrometers. 2. Total emittance is substantially proportional to absolute temperature, and at moderate temperatures εn = 0.058T rT , where T is measured in kelvins. 3. The total absorptance of a metal at temperature T1 with respect to radiation from a black or gray source at temperature T2 is equal to the emissivity evaluated at the geometric mean of T1 and T2. Figure 5-9 gives values of ελ and ελ,n, and their ratio, as a function of the product rT (solid lines). Although Fig. 5-9 is based on free-electron contributions to emissivity in the far infrared, the relations for total emissivity are remarkably good even at high temperatures. Unless extraordinary efforts are taken to prevent oxidation, a metallic surface may exhibit an emittance or absorptance which may be several times that of a polished specimen. For example, the emittance of iron and steel depends strongly on the degree of oxidation and roughness. Clean iron and steel surfaces have an emittance from 0.05 to 0.45 at ambient temperatures and from 0.4 to 0.7 at high temperatures. Oxidized and/or roughened iron and steel surfaces have values of emittance ranging from 0.6 to 0.95 at low temperatures to 0.9 to 0.95 at high temperatures. Refractory Materials For refractory materials, the dependence of emittance and absorptance on grain size and impurity concentrations is quite important. 1. Most refractory materials are characterized by 0.8 < ελ < 1.0 for the wavelength region 2 < λ < 4 μm. The monochromatic emissivity ελ decreases rapidly toward shorter wavelengths for materials that are white in the visible range but demonstrates high values for black materials such as FeO and Cr2O3. Small concentrations of FeO and Cr2O3, or other colored oxides, can cause marked increases in the emittance of materials that are normally white. The sensitivity of the emittance of refractory oxides to small additions of absorbing materials is demonstrated by the results of calculations presented in Fig. 5-10. Figure 5-10 shows the emittance of a semi-infinite absorbing-scattering medium as a function of its albedo w ≡ KS/(Ka + KS), where Ka and KS are the scatter and absorption coefficients, respectively. These results are relevant to the radiative properties of fibrous materials, paints, oxide coatings, refractory materials, and other particulate media. They demonstrate that over the relatively small range 1 - w = 0.005 to 0.1, the hemispherical emittance εh increases from approximately 0.15 to 1.0. For refractory materials, ελ varies little with temperature, with the exception of some white oxides which at high temperatures become good emitters in the visible spectrum as a consequence of the induced electronic transitions. 2. For refractory materials at ambient temperatures, the total emittance ε is generally high (0.7 to 1.0). Total refractory emittance decreases

5-18

HEAT AnD MASS TRAnSFER It is desired to compute the fraction of radiant energy, per unit emissive power E1, leaving A1 in all directions which is intercepted and absorbed by A2. The required quantity is defined as the direct view factor and is assigned the notation F1,2 . Since the net radiant energy interchange Q1,2 = A1 F1,2 E1 − A2 F2,1 E2 between surfaces A1 and A2 must be zero when their temperatures are equal, it follows thermodynamically that A1 F1,2 = A2 F2,1 . The product of area and view factor s1 s 2 ≡ A1 F1,2 which has the dimensions of area is termed the direct surface-to-surface exchange area [DEA] for finite black surfaces. Clearly, direct exchange areas are symmetric with respect to their subscripts, that is, si s j = s j s i , but view factors are not symmetric unless the associated surface areas are equal. This property is referred to as the symmetry or reciprocity relation for direct exchange areas. The shorthand notation s1 s 2 ≡ 12 = 21 for direct exchange areas is often found useful in mathematical developments. Equation (5-101) may also be restated as ∂ 2 si s j ∂ Ai ∂ A j

FIG. 5-10 Hemispherical emittance εh and the ratio of hemispherical to normal emittance εh/εn for a semi-infinite absorbing-scattering medium.

Q1,2 = (1 + m/4)εaυ A1σ (T14 − T24 )

(5-110)

where εaυ is evaluated at the arithmetic mean of T1 and T2. For metals m ≈ 0.5 while for nonmetals m is small and negative. Table 5-5 illustrates values of emittance for materials encountered in engineering practice. It is based on a critical evaluation of early emissivity data. Table 5-5 demonstrates the wide variation possible in the emissivity of a particular material due to variations in surface roughness and thermal pretreatment. With few exceptions the data in Table 5-5 refer to emittances εn normal to the surface. The hemispherical emittance εh is usually slightly smaller, as demonstrated by the ratio εh/εn depicted in Fig. 5-10. More recent data support the range of emittance values given in Table 5-5 and their dependence on surface conditions. An extensive compilation is provided by Goldsmith, Waterman, and Hirschorn (Thermophysical Properties of Matter, Purdue University, Touloukian, ed., Plenum, New York, 1970–1979). For opaque materials the reflectance ρ is the complement of the absorptance. The directional distribution of the reflected radiation depends on the material, its degree of roughness or grain size, and, if a metal, its state of oxidation. Polished surfaces of homogeneous materials are specular reflectors. In contrast, the intensity of the radiation reflected from a perfectly diffuse or Lambert surface is independent of direction. The directional distribution of reflectance of many oxidized metals, refractory materials, and natural products approximates that of a perfectly diffuse reflector. A better model, adequate for many calculation purposes, is achieved by assuming that the total reflectance is the sum of diffuse and specular components ρD and ρS, as discussed in a subsequent section. VIEW FACTORS AnD DIRECT EXCHAnGE AREAS Consider radiative interchange between two finite black surface area elements A1 and A2 separated by a transparent medium. Since they are black, the surfaces emit isotropically and totally absorb all incident radiant energy.

cos ϕ i cos ϕ j

(5-111)

πr 2

which leads directly to the required definition of the direct exchange area as a double surface integral si s j =  ∫∫  ∫∫

with increasing temperature, such that a temperature increase from 1000 to 1570°C may result in a 20 to 30 percent reduction in ε. 3. Emittance and absorptance increase with increase in grain size over a grain size range of 1 to 200 μm. 4. The ratio εh/εn of hemispherical to normal emissivity of polished surfaces varies with refractive index n; e.g., the ratio decreases from a value of 1.0 when n = 1.0 to a value of 0.93 when n = 1.5 (common glass) and increases back to 0.96 at n = 3.0. 5. As shown in Fig. 5-10, for a surface composed of particulate matter which scatters isotropically, the ratio εh/εn varies from 1.0 when w < 0.1 to about 0.8 when w = 0.999. 6. The total absorptance exhibits a decrease with an increase in temperature of the radiation source similar to the decrease in emittance with an increase in the emitter temperature. Figure 5-8 shows a regular variation of a1,2 with T2. When T2 is not very different from T1, a1,2 = ε1(T2/T1)m. It may be shown that Eq. (5-107b) is then approximated by

=

Ai

Aj

cos ϕ i cos ϕ j πr 2

(5-112)

dA j dAi

All terms in Eq. (5-112) have been previously defined. Suppose now that Eq. (5-112) is integrated over the entire confining surface of an enclosure which has been subdivided into M finite area elements. Each of the M surface zones must then satisfy certain conservation relations involving all the direct exchange areas in the enclosure M

∑s s

j

= Ai for 1 ≤ i ≤ M

(5-113a)

i, j

= 1 for 1 ≤ i ≤ M

(5-113b)

i

j =1

or in terms of view factors M

∑F j =1

Contour integration is commonly used to simplify the evaluation of Eq. (5-112) for specific geometries; see Modest (Radiative Heat Transfer, 3d ed., Academic Press, New York, 2013, chap. 4) or Siegel and Howell (Thermal Radiation Heat Transfer, 4th ed., Taylor and Francis, London, 2001, chap. 5). Two particularly useful view factors are those for perpendicular rectangles of area XZ and YZ with common edge Z and equal parallel rectangles of area XY and distance of separation Z . The formulae for these quantities are given as follows. For perpendicular rectangles with common dimension Z

(π ⋅ X ) ⋅ FX ,Y = X tan −1

1 1 1 + Y tan −1 − X 2 + Y 2 tan −1 (X 2 +Y 2) X Y

1  (1 + X 2 )(1 + Y 2 )  X 2 (1 + X 2 + Y 2 )   Y 2 (1 + X 2 + Y 2 )  + ln  4  1 + X 2 + Y 2  (1 + X 2 )( X 2 + Y 2 )   (1 + Y 2 )( X 2 + Y 2 )   X2

Y2

  

(5-114a) and for parallel rectangles, separated by distance Z, 2 2  π⋅ X ⋅Y  ⋅ F = 1 ⋅ ln  (1 + X )(1 + Y )  + X 1 + Y 2 tan −1 X   X ,Y   2 2 2 2 1+Y 2   1+ X +Y Y + Y 1 + X 2 tan −1 − X tan −1 X − Y tan −1 Y 1+ X 2

(5-114b)

In Eqs. (5-114) X and Y are normalized whereby X = x /z and Y = y /z , and the corresponding dimensional direct surface areas are given by s x s y = x ⋅ z ⋅ FX ,Y and s x s y = x y FX ,Y , respectively. The exchange area between any two area elements of a sphere is independent of their relative shape and position and is simply the product of the areas, divided by the area of the entire sphere; i.e., any spot on a sphere has equal views of all other spots.

HEAT TRAnSFER BY RADIATIOn

5-19

TABLE 5-5 normal Total Emissivity of Various Surfaces A. Metals and Their Oxides Surface Aluminum Highly polished plate, 98.3% pure Polished plate Rough plate Oxidized at 1110°F Aluminum-surfaced roofing Calorized surfaces, heated at 1110°F Copper Steel Brass Highly polished: 73.2% Cu, 26.7% Zn 62.4% Cu, 36.8% Zn, 0.4% Pb, 0.3% Al 82.9% Cu, 17.0% Zn Hard rolled, polished: But direction of polishing visible But somewhat attacked But traces of stearin from polish left on Polished Rolled plate, natural surface Rubbed with coarse emery Dull plate Oxidized by heating at 1110°F Chromium; see Nickel Alloys for Ni-Cr steels Copper Carefully polished electrolytic copper Commercial, emeried, polished, but pits remaining Commercial, scraped shiny but not mirrorlike Polished Plate, heated long time, covered with thick oxide layer Plate heated at 1110°F Cuprous oxide Molten copper Gold Pure, highly polished Iron and steel Metallic surfaces (or very thin oxide layer): Electrolytic iron, highly polished Polished iron Iron freshly emeried Cast iron, polished Wrought iron, highly polished Cast iron, newly turned Polished steel casting Ground sheet steel Smooth sheet iron Cast iron, turned on lathe Oxidized surfaces: Iron plate, pickled, then rusted red Completely rusted Rolled sheet steel Oxidized iron Cast iron, oxidized at 1100°F Steel, oxidized at 1100°F Smooth oxidized electrolytic iron Iron oxide Rough ingot iron

t, °F ∗

Emissivity∗

440–1070 73 78 390–1110 100

0.039–0.057 0.040 0.055 0.11–0.19 0.216

390–1110 390–1110

0.18–0.19 0.52–0.57

476–674 494–710 530

0.028–0.031 0.033–0.037 0.030

70 73 75 100–600 72 72 120–660 390–1110 100–1000

0.038 0.043 0.053 0.096 0.06 0.20 0.22 0.61–0.59 0.08–0.26

176

0.018

66

0.030

72 242

0.072 0.023

77 390–1110 1470–2010 1970–2330

0.78 0.57 0.66–0.54 0.16–0.13

440–1160

0.018–0.035

350–440 800–1880 68 392 100–480 72 1420–1900 1720–2010 1650–1900 1620–1810

0.052–0.064 0.144–0.377 0.242 0.21 0.28 0.435 0.52–0.56 0.55–0.61 0.55–0.60 0.60–0.70

68 67 70 212 390–1110 390–1110 260–980 930–2190 1700–2040

0.612 0.685 0.657 0.736 0.64–0.78 0.79 0.78–0.82 0.85–0.89 0.87–0.95

Surface Sheet steel, strong rough oxide layer Dense shiny oxide layer Cast plate: Smooth Rough Cast iron, rough, strongly oxidized Wrought iron, dull oxidized Steel plate, rough High temperature alloy steels (see Nickel Alloys) Molten metal Cast iron Mild steel Lead Pure (99.96%), unoxidized Gray oxidized Oxidized at 390°F Mercury Molybdenum filament Monel metal, oxidized at 1110°F Nickel Electroplated on polished iron, then polished Technically pure (98.9% Ni, + Mn), polished Electroplated on pickled iron, not polished Wire Plate, oxidized by heating at 1110°F Nickel oxide Nickel alloys Chromnickel Nickelin (18–32 Ni; 55–68 Cu; 20 Zn), gray oxidized KA-2S alloy steel (8% Ni; 18% Cr), light silvery, rough, brown, after heating After 42 hr. heating at 980°F NCT-3 alloy (20% Ni; 25% Cr.), brown, splotched, oxidized from service NCT-6 alloy (60% Ni; 12% Cr), smooth, black, firm adhesive oxide coat from service Platinum Pure, polished plate Strip Filament Wire Silver Polished, pure Polished Steel, see Iron. Tantalum filament Tin—bright tinned iron sheet Tungsten Filament, aged Filament Zinc Commercial, 99.1% pure, polished Oxidized by heating at 750°F Galvanized sheet iron, fairly bright Galvanized sheet iron, gray oxidized

t, °F ∗

Emissivity∗

75 75

0.80 0.82

73 73 100–480 70–680 100–700

0.80 0.82 0.95 0.94 0.94–0.97

2370–2550 2910–3270

0.29 0.28

260–440 75 390 32–212 1340–4700 390–1110

0.057–0.075 0.281 0.63 0.09–0.12 0.096–0.292 0.41–0.46

74

0.045

440–710

0.07–0.087

68 368–1844 390–1110 1200–2290

0.11 0.096–0.186 0.37–0.48 0.59–0.86

125–1894

0.64–0.76

70

0.262

420–914 420–980

0.44–0.36 0.62–0.73

420–980

0.90–0.97

520–1045

0.89–0.82

440–1160 1700–2960 80–2240 440–2510

0.054–0.104 0.12–0.17 0.036–0.192 0.073–0.182

440–1160 100–700

0.0198–0.0324 0.0221–0.0312

2420–5430 76

0.194–0.31 0.043 and 0.064

80–6000 6000

0.032–0.35 0.39

440–620 750 82 75

0.045–0.053 0.11 0.228 0.276

260–1160

0.81–0.79

1900–2560 206–520 209–362

0.526 0.952 0.959–0.947

B. Refractories, Building Materials, Paints, and Miscellaneous Asbestos Board Paper Brick Red, rough, but no gross irregularities Silica, unglazed, rough Silica, glazed, rough Grog brick, glazed See Refractory Materials below.

74 100–700

0.96 0.93–0.945

70 1832 2012 2012

0.93 0.80 0.85 0.75

Carbon T-carbon (Gebr. Siemens) 0.9% ash (this started with emissivity at 260°F of 0.72, but on heating changed to values given) Carbon filament Candle soot Lampblack-waterglass coating

5-20

HEAT AnD MASS TRAnSFER

TABLE 5-5

normal Total Emissivity of Various Surfaces (Continued ) B. Refractories, Building Materials, Paints, and Miscellaneous (Continued ) Surface

t, °F ∗

Emissivity∗

t, °F ∗

Surface

Emissivity∗

Same 260–440 0.957–0.952 Oil paints, sixteen different, all colors 212 0 .92–0 .96 Thin layer on iron plate 69 0 .927 Aluminum paints and lacquers Thick coat 68 0 .967 10% Al, 22% lacquer body, on rough or 212 0 .52 Lampblack, 0 .003 in . or thicker 100–700 0 .945 smooth surface Enamel, white fused, on iron 66 0 .897 26% Al, 27% lacquer body, on rough or 212 0 .3 Glass, smooth 72 0 .937 smooth surface Gypsum, 0 .02 in . thick on smooth or Other Al paints, varying age and Al 212 0 .27–0 .67 blackened plate 70 0 .903 content Marble, light gray, polished 72 0 .931 Al lacquer, varnish binder, on rough plate 70 0 .39 Oak, planed 70 0 .895 Al paint, after heating to 620°F 300–600 0 .35 Oil layers on polished nickel (lube oil) 68 Paper, thin Polished surface, alone 0 .045 Pasted on tinned iron plate 66 0 .924    +0 .001-in . oil 0 .27 On rough iron plate 66 0 .929    +0 .002-in . oil 0 .46 On black lacquered plate 66 0 .944    +0 .005-in . oil 0 .72 Plaster, rough lime 50–190 0 .91 Infinitely thick oil layer 0 .82 Porcelain, glazed 72 0 .924 Oil layers on aluminum foil (linseed oil) Quartz, rough, fused 70 0 .932 Al foil 212 0 .087† Refractory materials, 40 different 1110–1830    +1 coat oil 212 0 .561 poor radiators 0 .65 - 0 .75    +2 coats oil 212 0 .574 0 .70 Paints, lacquers, varnishes good radiators 0 .80 - 0 .85 Snowhite enamel varnish or rough iron 0 .85 - 0 .90 plate 73 0 .906 Roofing paper 69 0 .91 Black shiny lacquer, sprayed on iron 76 0 .875 Rubber Black shiny shellac on tinned iron sheet 70 0 .821 Hard, glossy plate 74 0 .945 Black matte shellac 170–295 0 .91 Soft, gray, rough (reclaimed) 76 0 .859 Black lacquer 100–200 0 .80–0 .95 Serpentine, polished 74 0 .900 Flat black lacquer 100–200 0 .96–0 .98 Water 32–212 0 .95–0 .963 White lacquer 100–200 0 .80–0 .95 ∗When two temperatures and two emissivities are given, they correspond, first to first and second to second, and linear interpolation is permissible . °C = (°F - 32)/1 .8 . † Although this value is probably high, it is given for comparison with the data by the same investigator to show the effect of oil layers . See Aluminum, Part A of this table .

} }{

Figure 5-11, curves 1 through 4, shows view factors for selected parallel opposed disks, squares, and 2:1 rectangles and parallel rectangles with one infinite dimension as a function of the ratio of the smaller diameter or side to the distance of separation. Curves 2 through 4 of Fig. 5-11, for opposed rectangles, can be computed with Eq. (5-114b). The view factors for two finite coaxial coextensive cylinders of radii r ≤ R and height L are shown in Fig. 5-12. The direct view factors for an infinite plane parallel to a system of rows of parallel tubes are given as curves 1 and 3 of Fig. 5-13. The view factors for this two-dimensional geometry can be readily calculated by using the crossed-strings method . The crossed-strings method, due to Hottel (Radiative Transfer, McGrawHill, New York, 1967), is stated as follows: “The exchange area for twodimensional surfaces, A1 and A2, per unit length (in the infinite dimension) is given by the sum of the lengths of crossed strings from the ends of A1 to the ends of A2 less the sum of the uncrossed strings from and to the same points all divided by 2.” The strings must be drawn so that all the flux from one surface to the other must cross each of a pair of crossed strings and neither of the pair of uncrossed strings. If one surface can see the other around both sides of an obstruction, two more pairs of strings are involved. The calculation procedure is demonstrated by evaluation of the tube-to-tube view factor for one row of a tube bank, as illustrated in Example 5-8. Example 5-8 The Crossed-Strings Method Figure 5-14 depicts the transverse cross section of two infinitely long, parallel circular tubes of diameter D and

center-to-center distance of separation C . Use the crossed-strings method to formulate the tube-to-tube direct exchange area and view factor, st s t and Ft ,t , respectively. Solution The circumferential area of each tube is At = πD per unit length in the infinite dimension for this two-dimensional geometry. Application of the crossed-strings procedure then yields simply st s t = and

2( EFGH − HJ ) = D ⋅[sin −1 (1/R ) + R 2 − 1 − R ] 2

Ft ,t = st s t /At = [sin −1 (1/R ) + R 2 − 1 − R ]/π

where EFGH and HJ = C are the indicated line segments and R ≡ C/D ≥ 1. Curves 1 and 5, respectively, of Fig. 5-13 can be calculated from Ft,t with the relations Fp ,t = π ⋅ (0.5 − Ft ,t )/R and F p ,t = Fp ,t (2 − Fp ,t ). Here F p ,t is defined as the refractory augmented view factor from the black plane to the black tubes, as explained in the following section on the zone method.

The Yamauti principle [Yamauti, Res . Electrotech . Lab . (Tokyo), 148 (1924); 194 (1927); 250 (1929)] is stated as follows: The exchange areas between two pairs of surfaces are equal when there is a one-to-one correspondence for all sets of symmetrically positioned pairs of differential elements in the two surface combinations. Figure 5-15 illustrates the Yamauti principle applied to surfaces in perpendicular planes having a common edge. With reference to Fig. 5-15, the Yamauti principle states that the diagonally opposed exchange areas are equal, that is, (1)(4) = (2)(3) . Figure 5-15 also shows a more complex geometric construction for displaced cylinders for which the Yamauti principle also applies. Collectively the three terms reciprocity or symmetry principle, conservation principle, and Yamauti principle are referred to as view factor or exchange area algebra. Example 5-9 Illustration of Exchange Area Algebra Figure 5-15 shows a graphical construction depicting four perpendicular opposed rectangles with a common edge. Numerically evaluate the direct exchange areas and view factors for the diagonally opposed (shaded) rectangles A1 and A4, that is, (1)(4) as well as (1)(3 + 4). The dimensions of the rectangular construction are shown in Fig. 5-15 as x = 3, y = 2, and z = 1. Solution Using shorthand notation for direct exchange areas, the conservation principle yields (1 + 2)(3 + 4) = (1 + 2)(3) + (1 + 2)(4) = (1)(3) + (2)(3) + (1)(4) + (2)(4)

FIG. 5-11 Radiation between parallel planes, directly opposed.

Now by the Yamauti principle we have (1)(4) ≡ (2)(3). The combination of these two relations yields the first result (1)(4) = (1 + 2)(3 + 4) − (1)(3) − (2)(4)  /2. For (1)(3 + 4), again conservation yields (1)(3 + 4) = (1)(3) + (1)(4), and substitution of the expression

HEAT TRAnSFER BY RADIATIOn

FIG. 5-12 View factors for a system of two concentric coaxial cylinders of equal length. (a) Inner surface of outer cylinder to inner cylinder. (b) Inner surface of outer cylinder to itself.

FIG. 5-13 Distribution of radiation to rows of tubes irradiated from one side. Dashed lines: direct view factor F from plane to tubes. Solid lines: total view factor F for black tubes backed by a refractory surface.

FIG. 5-14 Direct exchange between parallel circular

tubes.

FIG. 5-15

Illustration of the Yamauti principle.

5-21

5-22

HEAT AnD MASS TRAnSFER

for (1)(4) just obtained yields the second result, that is, (1)(3 + 4) = [(1 + 2)(3 + 4) + (1)(3) − (2)(4)]/2.0. All three required direct exchange areas in these two relations are readily evaluated from Eq. (5-114a). Moreover, these equations apply to opposed parallel rectangles as well as rectangles with a common edge oriented at any angle. Numerically it follows from Eq. (5-114a) for X = 1/3, Y = 2/3, and z = 3 that (1 + 2)(3 + 4) = 0.95990; for X = 1, Y = 2, and z = 1 that (1)(3) = 0.23285; and for X = 1/2, Y = 1, and z = 2 that(2)(4) = 0.585747. Since A1 = 1.0, this leads to s1 s 4 = F1,4 = (0.95990 − 0.23285 − 0.584747)/2.0 = 0.07115 and

  s1 s 3+ 4 = F1,3+ 4 = (0.95990 + 0.23285 − 0.584747)/2.0 = 0.30400

Many literature sources document closed-form algebraic expressions for view factors. Particularly comprehensive references include the compendia by Modest (Radiative Heat Transfer, 3d ed., Academic Press, New York, 2013, app. D) and Howell, Mengüç, and Siegel (Thermal Radiative Heat Transfer, 6th ed., CRC Press, Boca Raton, Fla., 2015, app. C). The appendices for both of these textbooks also provide a wealth of resource information for radiative transfer. Appendix F of Modest, for example, references an extensive listing of Fortran computer codes for a variety of radiation calculations which include view factors. These codes are archived in the dedicated Internet website maintained by the publisher. The textbook by Howell, Mengüç, and Siegel has also included an extensive database of view factors archived on a CD-ROM and includes a reference to an author-maintained Internet website. Other historical sources for view factors include Hottel and Sarofim (Radiative Transfer, McGraw-Hill, New York, 1967, chap. 2) and Hamilton and Morgan (NACA-TN 2836, December 1952). RADIATIVE EXCHAnGE In EnCLOSURES—THE ZOnE METHOD Total Exchange Areas When an enclosure contains reflective surface zones, allowance must be made for not only the radiant energy transferred directly between any two zones but also the additional transfer attendant to however many multiple reflections which occur among the intervening reflective surfaces. Under such circumstances, it can be shown that the net radiative flux Qi , j between all such surface zone pairs Ai and Aj, making full allowance for all multiple reflections, may be computed from  Qi , j = Ai

i, j

σ T j4 − A j

j ,i

σTi 4

(5-115a)

or Qi , j = S i S j ⋅ Ei − S j S i ⋅ E j

(5-115b)

Here i , j is defined as the total surface-to-surface view factor from Ai to Aj, and the quantity Si S j ≡ Ai ⋅i , j is defined as the corresponding total (surfaceto-surface) exchange area [TEA]. In analogy with the direct exchange areas, the total surface-to-surface exchange areas are also symmetric and thus obey reciprocity, that is,  Ai ⋅ i , j  = A j ⋅ j ,i or Si S j = S j S i . When applied to an enclosure, total exchange areas and total view factors also must satisfy appropriate conservation relations. Total exchange areas are functions of the geometry and radiative properties of the entire enclosure . They are also independent of temperature if all surfaces and any radiatively participating media are gray. The following subsection presents a general matrix method for the explicit evaluation of total exchange areas from direct exchange areas and other enclosure parameters. In what follows, conventional matrix notation is strictly employed as in A = [Ai .j] wherein the scalar subscripts always denote the row and column indices, respectively, and all matrix entities defined here are denoted by boldface notation. Section 3 of this handbook, “Mathematics,” provides an especially convenient reference for introductory matrix algebra and matrix computations. General Matrix Formulation The zone method is perhaps the simplest numerical quadrature of the governing integral equations for radiative transfer. It may be derived from first principles by starting with the equation of transfer for radiation intensity. The zone method always conserves radiant energy since the spatial discretization utilizes macroscopic energy balances involving spatially averaged radiative flux quantities. Because large sets of linear algebraic equations can arise in this process, matrix algebra provides the most compact notation and the most expeditious methods of solution. The mathematical approach presented here is a matrix generalization of the original (scalar) development of the zone method due to Hottel and Sarofim (Radiative Transfer, McGraw-Hill, New York, 1967). The present matrix development is abstracted from that introduced by Noble [Noble, J. J., Int . J . Heat Mass Transfer, 18: 261–269 (1975)]. Consider an arbitrary three-dimensional enclosure of total volume V and surface area A which confines an absorbing-emitting medium (gas). Let the

enclosure be subdivided (zoned) into M finite surface area Ai and N finite volume elements Vi, each small enough that all such zones are substantially isothermal. The mathematical development in this section is then restricted by the following conditions and/or assumptions: 1. The gas temperatures are given a priori. 2. Allowance is made for gas-to-surface radiative transfer. 3. Radiative transfer with respect to the confined gas is either monochromatic or gray. The gray gas absorption coefficient is denoted here by K [m−1]. In subsequent sections the monochromatic absorption coefficient is denoted by Kλ(λ). 4. All surface emissivities are assumed to be gray and thus independent of temperature. 5. Surface emission and reflection are isotropic or diffuse. 6. The gas does not scatter. Noble [Noble, J. J., Int . J . Heat Mass Transfer, 18: 261–269 (1975)] has extended the present matrix methodology to the case where the gaseous absorbingemitting medium also scatters isotropically. In matrix notation the blackbody emissive powers for all surface and volume zones comprising the zoned enclosure are designated as E = [ Ei ] = [ σTi 4 ] , an M × 1 vector, and E g = [ E g ,i ] = [ σTg4,i ] , an N × 1 vector, respectively. Moreover, all surface zones are characterized by three M × M diagonal matrices for surface zone areas AI = [ Ai ⋅δ i , j ], diffuse emissivity εI = [ εi ⋅δ i , j ], and diffuse reflectivity, ρI = [(1 − εi ) ⋅δ i , j ], respectively. Here δ i , j is the Kronecker delta (that is, δ i , j = 1 for i = j and δ i , j = 0 for i ≠ j ). Two arrays of direct exchange areas are now defined; i.e., the matrix ss = [ si s j ] is theM × M array of direct surface-to-surface exchange areas, and the matrix sg = [ si g j ] is the M × N array of direct gas-to-surface exchange areas . Here the scalar elements of ss and sg are computed from the integrals si s j =  ∫∫  ∫∫ Ai

and

Aj

e − Kr cos φi cos φ j dA j dAi πr 2

si g j =  ∫∫  ∫∫∫ K Ai

Vj

e − Kr cos φi dV j dAi πr 2

(5-116a)

(5-116b)

Equation (5-116a) is a generalization of Eq. (5-112) for the case K ≠ 0 while si g j is a new quantity, which arises only for the case K ≠ 0. Matrix characterization of the radiative energy balance at each surface zone is then facilitated via definition of three additional M vectors, namely the radiative surface flux Q = [Qi], with units of watts; and the vectors H = [ H i ] and W = [Wi ] both having units of W/m2. The arrays H and W define the incident and leaving flux densities, respectively, at each surface zone. The variable W is also referred to in the literature as the radiosity or exitance. Subject to the above assumptions the zone method can be stated in three matrix equations in terms of the five vector variables Q, W, H, E, and Eg : W = εεI ⋅ E + ρI ⋅ H

(5-117a)

AI ⋅ H = ss ⋅ W + sg ⋅ E g

(5-117b)

Q = AI ⋅[ W − H ]

(5-117c)

Implementation of Eqs. (5-117) requires a priori specification of the gas (temperatures) Eg, and M other pieces of information for the surface zones. Elimination of W between Eqs. (5-117a) and (5-117c) followed by elimination of H then leads to two alternative forms for the surface flux vector Q: Q = εεAI ⋅[ E − H ] = ρI −1 ⋅ εAI[ E − W ]

for ρi ≠ 0

(5-117d,e)

Explicit Matrix Solution for Total Exchange Areas For gray or monochromatic transfer, the primary working relation for zoning calculations via the matrix method is Q = εAI ⋅ E − SS ⋅ E − SG ⋅ E g

[ M × 1]

(5-118)

Equation (5-118) makes full allowance for multiple reflections in an enclosure of any degree of complexity. To apply Eq. (5-118) for design or simulation purposes, the gas temperatures must be known and surface boundary conditions must be specified for each and every surface zone in the form of either Ei or Qi . In application of Eq. (5-118), physically impossible values of Ei may well result if physically unrealistic values of Qi are specified. In Eq. (5-118), SS and SG are defined as the required arrays of total surfaceto-surface exchange areas and total gas-to-surface exchange areas, respectively. The matrices for total exchange areas are calculated explicitly from the

HEAT TRAnSFER BY RADIATIOn corresponding arrays of direct exchange areas and the other enclosure parameters by the following matrix formulas: Surface-to-surface exchange SS = εI ⋅ AI ⋅ R ⋅ ss ⋅ εI

Gas-to-surface exchange

[M × M ]

SG = εI ⋅ AI ⋅ R ⋅ sg

[M × N ]

−1

[M × M ]

(5-118c)

Direct exchange areas

AI ⋅1M = ss ⋅1M + sg ⋅1N

(5-119a)

Total exchange areas

εI ⋅ AI ⋅1M = SS ⋅1M + SG ⋅1N

(5-119b)

Here 1M is an M × 1 column vector all of whose elements are unity. If εI = I or equivalently, ρI = 0 , then Eq. (5-118c) reduces to R = AI −1 with the result that Eqs. (5-118a) and (5-118b) degenerate to simply SS = ss and SS = sg , respectively. Further, while the array SS is always symmetric, the array SG is generally not square. For purposes of digital computation, it is good practice to enter all data for direct exchange surface-to-surface areas ss with a precision of at least five significant figures. This need arises because all the scalar elements of sg can be calculated arithmetically from appropriate direct surface-to-surface exchange areas by using view factor algebra rather than via the definition of the defining integral, Eq. (5-116b). This process often involves small arithmetic differences between two numbers of nearly equal magnitudes, and numerical significance is easily lost. Computer implementation of matrix methods proves straightforward, given the availability of modern software applications. In particular, several especially user-friendly GUI mathematical utilities are available that perform matrix computations using essentially algebraic notation. Many simple zoning problems may be solved with spreadsheets. For large M and N, matrix methodology can involve management of a large amount of data. Error checks based on symmetry and conservation by calculation of the row sums of the four arrays of direct and total exchange areas then prove indispensable. Zone Methodology and Conventions For a transparent medium, no more than Σ = M ( M − 1)/2 of the M 2 elements of the ss array are unique. Further, surface zones are characterized into two generic types. Source-sink zones are defined as those for which temperature is specified and whose radiative flux Qi is to be determined. For flux zones, conversely, these conditions are reversed. When both types of zone are present in an enclosure, Eq. (5-118) may be partitioned to produce a more efficient computational algorithm. Let M = MS + MF represent the total number of surface zones where MS is the number of source-sink zones and MF is the number of flux zones. The flux zones are the last to be numbered . Equation (5-118) is then partitioned as follows: 0   E1   SS1,1 SS1,2 ⋅ − εAI2 ,2   E2   SS2 ,1 SS2 ,2  

−1

=  εAI2 ,2 − SS2 ,2  ⋅ SS2 ,1 ⋅ E1 + SG2 ⋅ E g + Q 2  E2 =

(5-120a)

= εεAI1,1 ⋅ E1 − SS1,1 ⋅ E1 − SS1,2 ⋅ E2 − SG1 ⋅ E g Q1 =

(5-120b)

(5-118b)

While the R matrix is generally not symmetric, the matrix product ρI ⋅ R is always symmetric. This fact proves useful for error checking. The most computationally significant aspect of the matrix method is that the inverse reflectivity matrix R always exists for any physically meaningful enclosure problem. More precisely, R always exists provided that K ≠ 0. Moreover, for a transparent medium, R exists provided that there formally exists at least one surface zone Ai such that εi ≠ 0. An important computational corollary of this statement for transparent media is that the matrix [ AI − ss] is always singular and demonstrates matrix rank M − 1 [Noble, J. J., Int . J . Heat Mass Transfer, 18: 261–269 (1975)]. Finally, the four matrix arrays ss, sg , SS, and SG of direct and total exchange areas must satisfy matrix conservation relations (row sums), i.e.,

Q 1   εAI1,1 Q  = 0  2  

MS × 1 vector of unknown source-sink fluxes, and E2, the MF × 1 vector of unknown emissive powers for the flux zones, i.e.,

(5-118a)

where in Eqs. (5-118a and b), R is the explicit inverse reflectivity or multiple reflection matrix, defined as R =  AI − ss ⋅ ρI 

5-23

  E1   SG1  ⋅ −   ⋅ Eg   E2   SG2  (5-120)

Here the dimensions of the submatrices εAI1,1 and SS1,1 are both MS × MS and SG1 has dimensions MS × N, where N is the number of volume zones. Partition algebra then yields the following two matrix equations for Q1, the

The inverse matrix in Eq. (5-120a) formally does not exist if there is at least one flux zone such that εi = 0. However, well-behaved results are usually obtained with Eq. (5-120a) by utilizing a notional zero, say, εi ≈ 10−5, to simulate εi = 0. Computationally, E2 is first obtained from Eq. (5-120a) and then substituted into either Eq. (5-120b) or Eq. (5-118). Surface zones need not be contiguous . For example, in a symmetric enclosure, zones on opposite sides of the plane of symmetry may be “lumped” into a single zone for computational purposes. Lumping nonsymmetrical zones is also possible as long as the zone temperatures and emissivities are equal. An adiabatic refractory surface with surface area AR and emissivity ε R , for which QR = 0 , proves quite important in practice. A nearly radiatively adiabatic refractory surface occurs when differences between internal conduction and convection and external heat losses through the refractory wall are small compared with the magnitude of the incident and leaving radiation fluxes. Mathematically, sufficient conditions to model an adiabatic refractory surface are the a priori requirements QR = 0 for 0 < ε R ≤ 1 or simply ε R = 0 . Formally, these two conditions imply somewhat different mathematical consequences. First, from Eqs. (5-117) we may write QR = AR (WR − H R ) = ε R AR ( E R − H R ) such that the requirement QR = 0 directly implies E R = WR = H R. Alternatively, if one specifies ε R = 0 , it follows from the definition of radiosity that WR = H R and thus QR ≡ 0 . In this case the value of E R is not defined and is found to be entirely immaterial to the enclosure calculations. Indeed all the total exchange areas for an adiabatic refractory vanish, to wit Si S R = 0 for all 1 ≤ i ≤ M . Thus the value of E R never even enters the zoning equations. Nonetheless when ε R = 0 , it is customary to use E R = WR = H R to estimate refractory temperatures. A surface zone for which ε R = 0 is termed a perfect diffuse mirror . An adiabatic surface zone is thus also a perfect diffuse mirror. As will be shown, matrix methods automatically deal with all options for flux and adiabatic refractory surfaces. Consider an enclosure with a single (lumped) refractory where εR ≠ 0 and MR = 1 and any number of source/sink and volume zones. The (scalar) refractory emissive power may be calculated from Eq. (5-120a) as a weighted sum of all other known blackbody emissive powers which characterize the enclosure, i.e., M

ER =

∑S j =1

N

R

S j ⋅ E j + ∑ S RG k ⋅ E g , k + Q R k =1

M

∑S j =1

N

R

S j + ∑ S RG k

with j ≠ R and ε R ≠ 0

(5-121)

k =1

Equation (5-121) specifically includes those zones which may not have a direct view of the refractory. When QR = 0 , the refractory surface is said to be in radiative equilibrium with the entire enclosure. Again, note that Eq. (5-121) is indeterminate if ε R = 0 . The Limiting Case of a Transparent Medium For the special case of a transparent medium for which K = 0, many practical engineering applications can be modeled with the zone method. These include combustionfired muffle furnaces and electrical resistance furnaces. When K → 0, sg → 0 and SG → 0. Equations (5-118) through (5-119) then reduce to three simple matrix relations

with again

Q = εI ⋅ AI ⋅ E − SS ⋅ E

(5-122a)

SS = εI ⋅ AI ⋅ R ⋅ ss ⋅ εI

(5-122b)

−1

R = [ AI − ss ⋅ εI ]

(5-122c)

The radiant surface flux vector Q, as computed from Eq. (5-122a), always M

satisfies the (scalar) conservation condition ∑Qi = 0 [or 1TM ⋅ Q = 0] which i =1

is a statement of the overall radiant energy balance. The matrix conservation relations also simplify to AI ⋅1M = ss ⋅ I M

(5-123a)

5-24

HEAT AnD MASS TRAnSFER

and

(5-123b)

εI ⋅ AI ⋅1M = SS ⋅1M

And the M × M arrays for all the direct and total view factors can be readily computed from F = AI −1 ⋅ ss

(5-124a)

−1

 = AI ⋅ SS

and

leads to the even simpler result that S1S 2 = ε1 A1. This simple result has widespread engineering utility. 2. Two parallel plates of equal area are large compared to their distance of separation (infinite parallel plates). Case 2 is a limiting form of case 1 with A1 = A2. Algebraic manipulation then results in  (ε1 + ε 2 − 2 ε1ε 2 ) ⋅ A1 SS =  ε1ε 2 Α1 

(5-124b)

where the following matrix conservation relations must also be satisfied

 ε1ε 2 A1  (ε1 + ε 2 − 2 ε1ε 2 ) A1  

[ ε1 + ε 2 + ε1 ε 2 ]

and in particular

and

F ⋅1M = 1M

(5-125a)

 ⋅1M = εI ⋅1M

(5-125b)

The Two-Zone Enclosure Figure 5-16 depicts four simple enclosure geometries which are particularly useful for engineering calculations characterized by only two surface zones. For M = 2, the reflectivity matrix R is readily evaluated in closed form since an explicit algebraic inversion formula is available for a 2 × 2 matrix. In this case knowledge of only Σ = 1 direct exchange area is required. Direct evaluation of Eqs. (5-122) then leads to  ε A −S S 1 1 1 2 SS =   S1 S 2 

S1 S 2 ε 2 A2 − S1S 2

   

S1 S 2 =

(5-127b)

3. Concentric spheres or cylinders where A2 > A1. Case 3 is mathematically identical to case 1. 1  A1 A2    4. A speckled enclosure has two surface zones. Here F = A1 + A2  A1 A2  2 1  A1 such that ss = A1 + A2  A1 A2 produce 

 ε2 A 2 1 1 SS =   ε1ε 2 A1 A2 

(5-126)

where

A1 1/ε1 + 1/ε 2 − 1

A1 A2   and Eqs. (5-126) and (5-127) then A22   ε1ε 2 A1 A2   ε 22 A22  

[ ε1 A1 + ε 2 A2 ]

with the particular result S1 S 2 =

1  ρ1 1  ρ2  ε A + ε A + s s  1 1 2 2 1 2

(5-127)

Equation (5-127) is of general utility for any two-zone system for which εi ≠ 0. The total exchange areas for the four geometries shown in Fig. 5-16 follow directly from Eqs. (5-126) and (5-127). 1. A planar surface A1 is completely surrounded by a second surface A2 > A1. Here F1,1 = 0, F1,2 = 1, and s1 s 2 = A1 result in   ε 2 A + ε1 (ρ2 − ε 2 ) A1 A2  

 ε ρA 2 + ε ρ A A 1 1 2 1 1 2 SS =   ε1ε 2 A1 A2 

ε1ε 2 A1 A2

2 2

S1 S 2 =

and in particular

[ ε1ρ2 A1 + ε 2 A2 ]

A1 1/ε1 + ( A1 /A2 ) ⋅ (ρ2 /ε 2 )

(5-127a)

In the limiting case, where A1 has no negative curvature and is completely surrounded by a very much larger surface A2 such that A1 A1.

F=

0

1

A1 / A2 1 – A1 / A2

Two infinite parallel plates where A1 = A2.

F=

A1 A2

A2

G

0

1

1

0

(5-127c)

Physically, a two-zone speckled enclosure is characterized by the fact that the view factor from any point on the enclosure surface to the sink zone is identical to that from any other point on the bounding surface. This is only possible when the two zones are “intimately mixed.” The seemingly simplistic concept of a speckled enclosure provides a surprisingly useful default option in engineering calculations when the actual enclosure geometries are quite complex. The Generalized Source/Sink Refractory (SSR) Model M ê 3 The major numerical effort involved in implementation of the zone method is the evaluation of the inverse multiple reflection matrix R. For M = 3, explicit closed-form algebraic formulas do indeed exist for the nine scalar elements of the inverse of any arbitrary nonsingular matrix. These formulas are so algebraically complex, however, that it generally proves impractical to present universal closed-form expressions for the total exchange areas, as has been done for the case M = 2. For M = 3, a notable exception, which is amenable to hand calculation, is an enclosure comprised of two source/sink zones and one flux zone. Here this method is called the classical SSR model and requires inversion of one 2 × 2 matrix. The generalization of this method to multizone enclosures with M ≥ 3 follows.

Case 2

G

1 1/(ε1 A1 ) + 1/(ε 2 A2 )

G

Concentric spheres or infinite cylinders where A1 < A2. Identical to Case 1.

F=

0

1

A1 / A2 1 – A1 / A2

G A1

A1 A2

A speckled enclosure with two surface zones.

F=

A1 A2 1 (A1 + A2 ) A A 1 2

FIG. 5-16 Four enclosure geometries characterized by two surface zones and one volume zone. (Marks’ Standard Handbook for Mechanical

Engineers, McGraw-Hill, New York, 1999, p. 4-73, Table 4.3.5).

HEAT TRAnSFER BY RADIATIOn Consider an arbitrary multizone enclosure that confines a transparent medium. The bounding surface is comprised of MS source/sink and MF flux zones such that M = MS + MF. The MS source/sink zones are numbered first, and MF flux zones are numbered last. We then partition the zoning equations exactly per the conventions employed in Eqs. (5-120). Assume now that all the surface source/sink zones are black and all the flux zones are adiabatic. The partitioned flux equations for this simple black enclosure are then given as  Q 1   AI1,1  =  0   0

0   E1   ss1,1 ss1,2 ⋅ −  AI2 ,2   E2   ss2 ,1 ss2 ,2    

  E1  ⋅    E2 

where

or

S1 S 2 =

1,2 =

1 ρ1 ρ2 1 + + ε1 A1 ε 2 A2 SSb1,2 1 ρ1  A1  ρ2 1 + + ε1  A2  ε 2 F 1,2

(5-128a) and

SSb1,2 = s1 s 2 +

and the solution to Eq. (5-128a) then readily follows as

where and

Q 1 =  AI1,1 − SSb  ⋅ E1

(5-128b)

SSb = ss1,1 + ss1,2 ⋅ R22 ⋅ ss2 ,1

(5-128c)

R22 =  AI2 ,2 − ss2 ,2 

−1

(5-128d)

Equation (5-128c) states that SSb is the sum of the direct radiation between all black source/sink zones plus radiation absorbed and reemitted (reflected) from all the adiabatic flux zones. It then may be shown that if the source/sink zones are nonblack Q 1 = εAI1 ⋅ E1 − SSR ⋅ E1 − FSQ ⋅ Q 2

(5-129a)

where SSR and FSQ are specialized total exchange areas defined as follows

with

SSR = εAI1,1 ⋅ R11b ⋅ SSb ⋅ εI1,1

(5-129b)

FSQ = εAI1,1 ⋅ R11b ⋅ ss1,2 ⋅ R22

(5-129c)

R11b =  AI1,1 − SSb ⋅ ρI1,1 

−1

(5-129d)

which satisfy the following conservation relations SSb ⋅1MS = AI1,1 ⋅1MS

(5-130e)

SSR ⋅1MS = εAI1,1 ⋅1MS

(5-130f)

T

(5-130g)

FSQ ⋅1MS = 1MF

The solution sequence for all the enclosure surface vectors then follows as W1 = E1 − ρ ρI1,1 ⋅ εAI1-,11 ⋅ Q 1 W2 = R22 ⋅ ss2 ,1 ⋅ W1 + Q 2  Q 1   W1  W=  Q=  Q 2   W1  H = W − AI -1 ⋅ Q

(5-131)

E2 = W2 + ρI2 ,2 ⋅ εAI2-1,2 ⋅ Q 2

εi ≠ 0

For the special case Q 2 = 0 it may also be shown that E2 = FSQ T⋅ E1. The terminology in Hottel and Sarofim defines SSb as the refractory augmented exchange area for black source/sink zones, and SSR is termed the refractory augmented exchange area for nonblack source/sink zones . It is of paramount importance here to notice that Eqs. (5-131) lead to the fact that the zoning solution for W, H, and Q is always independent of the emissivities of all the flux zones. Moreover, E2 is also independent of dI2,2, provided that Q2 = 0. In other words, if all the flux zones are adiabatic refractories, then the refractory emissivity is entirely immaterial to the zoning calculations. One might first find this consequence counterintuitive since solution of the same problem via the conventional TEA route [Eqs. (5-120)] does indeed require a priori specification of dI2,2 even if Q2 = 0. Note further that in contrast to Eqs. (5-120) this procedure permits dI2,2 = 0. The Classical Three-Zone SSR Model Set M = 3 and let zones 1 and 2 be the source/sink zones and zone 3 the flux zone with Q3 = 0. Then the general expressions for SSR reduce to  ε A −S S 1 1 1 2 SSR =   S1 S 2 

S1 S 2 ε 2 A2 − S1S 2

   

(5-132)

s1 s 3 ⋅ s 3 s 2 ≡ A1 ⋅ F 1,2 s1 s 3 + s 2 s 3

5-25 (5-132a)

(5-132b)

(5-132c)

where εi ≠ 0. Notice that Eq. (5-132a) appears deceptively similar to Eq. (5-127). Moreover Eq. (5-132c) is the scalar analog of Eq. (5-128c). Further, if s1 s 1 = s 2 s 2 = 0, Eq. (5-132c) then reduces to

SSb1,2 =

A1 A2 − ( s1 s 2 )2 A1 + A2 − 2 ⋅ s1 s 2

(5-132d)

which necessitates the evaluation of only one direct exchange area. A consequence of Eq. (5-132d) is that the classic SSR model with M = 3 cannot distinguish the shape of the refractory. Collectively, Eqs. (5-132) along with formulas to compute F 1,2 (F-bar) are sometimes called the three-zone source/sink refractory model. Refractory Augmented Black View Factors F i , j In the older zoning literature, the following definition is employed: SSbi , j = Ai F i , j , where F i , j is called the refractory augmented black view factor, or F-bar. This quantity is especially convenient to archive results for a particular enclosure geometry when the enclosure contains only one source/sink pair and any number of refractory zones. The refractory augmented view factor F i , j is documented for a few geometrically simple cases and can be calculated or approximated for others. If A1 and A2 are equal parallel disks, squares, or rectangles, connected by nonconducting but reradiating refractory surfaces, then F i , j is given by Fig. 5-11 in curves 5 to 8. Let A1 represent an infinite plane and A2 represent one or two rows of infinite parallel tubes. If the only other surface is an adiabatic refractory surface located behind the tubes, then F 2,1 is given by curve 5 or 6 of Fig. 5-13. The classic zoning literature thus contains a hierarchy of three distinct surface-to-surface view factors, denoted by Fi , j , F i , j , and i , j . Accuracy of the Zone Method Experience has shown that despite its limitations even the simple SSR model with M = 3 can yield quite useful results for a host of practical engineering applications without resorting to digital computation. The error due to representation of the source and sink by single zones is often small, even if the views of the enclosure from different parts of the same zone are dissimilar, provided the surface emissivities are near unity. The error is also small if the temperature variation of the refractory is small. Any degree of accuracy can, of course, be obtained via matrix methodologies for arbitrarily large M by using a digital computer. From a computational viewpoint, when M ≥ 4, matrix methods must be used. Matrix methods must also be used for finer-scale calculations such as more detailed wall temperature and flux density profiles. The Electrical Network Analog At each surface zone, the total radiant flux is proportional to the difference between Ei and Wi, as indicated by the εA equation Qi = i i ( Ei - Wi ) . The net flux between zones i and j is also given ρi M by Qi , j = si s j (Wi − W j ) where Qi = ∑Qi , j for all 1 ≤ i ≤ M is the total heat flux i =1

leaving each zone. These relations suggest a visual electrical analog in which Ei and Wi are analogous to voltage potentials. The quantities εi Ai /ρi and si s j are analogous to conductances (reciprocal impedances), and Qi or Qi , j is analogous to electric currents. Such an electrical analog has been developed by Oppenheim [Oppenheim, A. K., Trans . ASME, 78: 725–735 (1956)]. Figure 5-17 illustrates a generalized electrical network analogy for a three-zone enclosure consisting of one refractory zone and two gray zones A1 and A2. The potential points Ei and Wi are separated by conductances εi Ai /ρi . The emissive powers E1 and E2 represent potential sources or sinks, while W1, W2, and Wr are internal node points. In this construction, the nodal point representing each surface is connected to that of every other surface it can see directly. Figure 5-17 can be used to formulate the total exchange area S1S 2 for the SSR model virtually by inspection. The refractory zone is first characterized by a floating potential such that Er = Wr. Next, the resistance for the parallel “current paths” between the internal nodes W1 and W2

5-26

HEAT AnD MASS TRAnSFER Example 5-10 Radiation Pyrometry A long tunnel furnace is heated by electrical resistance coils embedded in the ceiling. The stock travels on a floor-mounted conveyer belt and has an estimated emissivity of 0.7. The sidewalls are unheated refractories with emissivity 0.55, and the ceiling emissivity is 0.8. The furnace cross section is rectangular with height 1 m and width 2 m. A total radiation pyrometer is sighted on the walls and indicates the following apparent temperatures: ceiling 1340°C, sidewall readings average about 1145°C and the load indicates about 900°C. (a) What are the true temperatures of the furnace walls and stock? (b) What is the net heat flux at each surface and each zone pair? (c) Compare the adiabatic SSR and TEA matrix models.

Er Ar ∋r r

1r E1

W1

Wr 12

rr 2r W2

A1∋1 1

E2 A2 ∋2

11

22

2

FIG. 5-17 Generalized electrical network analog for a three-zone enclosure. Here A1

and A2 are gray surfaces and Ar is a radiatively adiabatic surface (Hottel, H. C., and A. F. Sarofim, Radiative Transfer, McGraw-Hill, New York, 1967, p. 91).

M = 3 Zones Zone 1 Source (top) Zone 2 Sink (bottom) Zone 3 Refractory (lumped sides) Physical constants: σ ≡ 5.6704 × 10 −8

T0 ≡ 273.15°C

W m2 ⋅ K

Enclosure input parameters:

1 is defined by ≡ A1 F1,2

1

which is identical to Eq. (5-132c).  1 1  + s1 s 2 + 1/    s1 s r s 2 s r  Finally, the overall impedance between the source E1 and the sink E2 is represented simply by three resistors in series and is thus given by

or

ρ 1 1 ρ = 1 + + 2 S1S 2 ε1 A1 A1 F1,2 ε 2 A2 1 S1 S 2 = ρ1 ρ2 1 + + ε1 A1 ε 2 A2 A1 F1,2

(5-133)

This result is identically the same as for the SSR model obtained previously in Eq. (5-132a). This equation is also valid for Mr ≥ 1 as long as Mb = 2. The electrical network analog methodology can be generalized for enclosures having M > 3. Some Examples from Furnace Design The theory of the past several subsections is best understood in the context of two engineering examples involving furnace modeling. The engineering idealization of the equivalent gray plane concept is introduced first. Figure 5-18 depicts a common furnace configuration in which the heating source is two refractory-backed, internally fired tube banks. Clearly the overall geometry for even this common furnace configuration is too complex to be modeled in an expeditious manner by anything other than a simple engineering idealization. Thus the furnace shown in Fig. 5-18 is modeled in Example 5-10, by partitioning the entire enclosure into two subordinate furnace compartments. First, the approach defines an imaginary gray plane A2, located on the inward-facing side of the tube assemblies. Second, the total exchange area between the tubes to this equivalent gray plane is calculated, making full allowance for the reflection from the refractory tube backing. This plane-to-tube view factor is then defined to be the emissivity of the required equivalent gray plane whose temperature is further assumed to be that of the tubes. This procedure guarantees continuity of the radiant flux into the interior radiant portion of the furnace arising from a moderately complicated external source. Example 5-10 demonstrates classical zoning calculations for radiation pyrometry in furnace applications. Example 5-11 is a classical furnace design calculation via zoning an enclosure with a diathermanous atmosphere and M = 5. The latter calculation can only be addressed with matrix methods. The results of Example 5-11 demonstrate the relative insensitivity of zoning to M > 3 and the engineering utility of the generalized SSR model.

H = 1.0 m

W = 2.0 m

L = 1.0 m

Compute direct exchange areas using crossed strings method ∑ = 3   ss 4 =   

0.0000 1.2361 0.3820 0.3820

1.2361 0.0000 0.3820 0.3820

0.3820 0.3820 0.0000 0.2361

  2  m  

0.3820 0.3820 0.2361 0.0000

Lump the four-zone enclosure into a three-zone enclosure by combining rows and columns 3 and 4. Then  ss  1 1 ss =  s 2 s1   s 3 s1

s1 s 2 s2 s2 s3 s2

s1 s 3   0 1.2361 0.7639   2 s 2 s 3  =  1.2361 0 0.7639  m    0.7639 0.7639 0.4721  s 3 s 3  

 1  0 

( AI − ss ) ⋅  1 =  0      1  0 

 A1  AI =  0  0   ε1  εI =  0  0 

0 ε2 0

0 A2 0

0   W ⋅L 0 0  0 = 0 0 W ⋅L  0 2⋅H ⋅L A3   0 

 ρ1 0   0.8 0 0    ρI =  0 0  =  0 0.7 0     0 0 0.55  ε 3   0  

  2.0 0 0  =  0 2.0 0   0 2.0   0 0 ρ2 0

  m2  

0   0.2 0 0   0  =  0 0.3 0    0 0 0.45 ρ 3    

Compute Radiosities W from Pyrometer Temperature Readings  1340.0  TW =  900.0  °C    1145.0 

 384.0  W = σ ⋅[ TW + 273.15]4 =  107.4  kW/m2    229.4 

All matrix wall flux density quantities and heat fluxes can then be directly calculated from the radiosity (leaving flux density) vector W. H = AI −1 ⋅ ss ⋅ W

Q = [ AI − ss ] ⋅ W

q = AI −1 ⋅ Q

E = εεI −1 ⋅[ W − ρI ⋅ H ]

leading to the final results W H  ZONE  1      154.0 384.0   2   107.4   324.9       3   229.4   241.8

q    

E

 230.0   441.5  −217.5   14.2     −12.5   219.1

   2   kW/m   

 460.0  Q =  −435.0  kW    −25.0 

and

Here the sidewalls act as near-adiabatic surfaces since the heat loss through each sidewall is only about 2.7 percent of the total heat flux originating at the source. Part (a): Actual Wall Temperatures versus Pyrometer Readings

FIG. 5-18 Furnace chamber cross section. To convert feet to meters, multiply by

0.3048.

 E T =    σ 

0.25

 1397.3   − 273.15  =  434.1  °C   1128.9 

 1340.0  TW =  900.0  °C    1145.0 

HEAT TRAnSFER BY RADIATIOn Demonstrate relationships between SSR and TEA models Assume Q3 = 0; then from Eq. (5-121) we have

[ k = 1, 3]  Wk    ε min k = 1 − Hk  

%Ref k = ρk ⋅

 8.0  %Ref =  90.8     47.4 

 NA  ε min =  0.669     0.052 

Hk Wk

The (low) estimated sink emissivity, ε2 = 0.7, is the dominant parameter in this example. First, the marked disparity in actual and measured sink temperature arises because the sink radiosity is comprised of 90.8 percent reflected energy, that is, ρ2 ⋅ H2/W2 = 0.9075. Moreover, when a surface flux is negative, W < H and a minimum allowable surface emissivity is defined by εmin = 1 − W/H. Thus if the sink emissivity is less than ε 2 = 1 − 107.4/324.9 = 0.6694, the sink temperature becomes imaginary. Lastly if the sink were black, E2 = W2 = 107.4 kW/m 2, the pyrometer and sink temperatures would be equal with T2 = 900°C. Part (b): Radiant Heat Flux at Each Surface  384  0 WI 4 =   0  0

Define

0 107.4 0 0

  Q = Q P ⋅  

leading to

1 1 1 1

kW m2

   kW  

  460.0    −435.0   kW  =   −12.5    −12.5 

E2 = 14.2

kW m2

Q3 = 25.0 kW

Compute total exchange areas R ≡ [ AI − ss ⋅ ρI]−1  0.2948 0.8284 0.4769  SS = εI ⋅ AI ⋅ R ⋅ ss ⋅ εI =  0.8284 0.1761 0.3955     0.4769 0.3955 0.2277  E3 =

(SS 3,1 ⋅ E1 + SS 3,2 ⋅ E2 + Q3 ) kW = 219.10 2 m SS 3,1 + SS 3,2

 A1 0  AI1 =   0 A2 

SSR 1,2 =

see Eq. (5-121)

ε 2 ⋅ A2 − SSR 1,2

   

Example 5-11 Furnace Simulation via Zoning The furnace chamber depicted in Fig. 5-18 is heated by combustion gases passing through 20 vertical radiant tubes which are backed by refractory sidewalls. The tubes have an outside diameter of D = 5 in (12.7 cm) mounted on C = 12-in (4.72-cm) centers and a gray body emissivity of 0.8. The interior (radiant) portion of the furnace is a 6 × 8 × 10 ft rectangular parallelepiped with a total surface area of 376 ft2 (34.932 m2). A 50-ft2 (4.645-m2) sink with emissivity 0.9 is positioned centrally on the floor of the furnace. The tube and sink temperatures are measured with embedded thermocouples as 1500 and 1200°F, respectively. The gray refractory emissivity may be taken as 0.5. While all other refractories are assumed to be radiatively adiabatic, the roof of the furnace is estimated to lose heat to the surroundings with a flux density (W/m2) equal to 5 percent of the source and sink emissive power difference. An estimate of the radiant flux arriving at the sink is required, as well as estimates for the roof and average refractory temperatures in consideration of refractory service life. Part (a): Equivalent Gray Plane Emissivity Algebraically compute the equivalent gray plane emissivity for the refractory-backed tube bank idealized by the imaginary plane A2, depicted in Fig. 5-18. Solution Let zone 1 represent one tube and zone 2 represent the effective plane, that is, the unit cell for the tube bank. Then A1 = πD and A2 = C are the corresponding zone areas, respectively (per unit vertical dimension). Also set ε1 = 0.8 with ε2 = 1.0 and define R = C/D = 12/5 = 2.4. For R = 2.4, curves 1 and 5 of Fig. 5-13 yield, respectively, Fp ,t = 0.57 and Fp ,t = 0.81. Using notation consistent with Example 5-8, more accurate values are calculated as follows: Ft ,t = [sin −1 (1/R ) + R 2 − 1 − R ]/π = 0.06733 Fp ,t = (0.5 − Ft ,t ) . π/R = 0.56637 F2,1 = Fp ,t = Fp ,t (1 − Fp ,t ) = 0.81196

To make allowance for nonblack tubes, application of Eq. (5-132b) with ε2 = 0.8 then yields 2,1 =

0  ε 2 

ss1,3 ⋅ ss 3,2 = 1.618 m 2 ss1,3 + ss 2,3

SSR 1,2

SS 3,1 = 0.5466 SS 3,1 + SS 3,2

Thus SSR1,2 = SS12 is the refractory-aided total exchange area between nonblack zones 1 and 2. Perhaps counterintuitive, this result is independent of ε3. Note further that if we recompute the total exchange areas with ε3 = 0 to obtain SS0, then SSR can be directly evaluated from the (upper) source/sink portion of SS0 as shown below.

and

1 = 1.0446 m 2 1 ρ1 ρ2 + + ε1 ⋅ A1 ε 2 ⋅ A2 ssb1,2

 ε1 ⋅ A1 − SSR 1,2 SSR =   SSR 1,2

E30 − E2 = 0.5466 E1 − E2

SS12 = SS1,2 + SS 2,3 ⋅Θ 3 = 1.0446 m 2

1   0 

[Use Eqs. (5-128a) and (5-130).] ssb1,2 = ss1,2 +

Θ 30 =

with the result that Θ3 = Θ30 and

1   0 

 ε1 εI1 =  0

Θ3 =

and we define

[ εI ⋅ AI − SS]⋅ 1 =  0 

 E1   460.0  Q 3 = (εI ⋅ AI − SS) ⋅  E 2  =  -435.0  kW      E 3   - 25.0  Compute SSR matrix for M = 3

(SS 3,1 ⋅ E1 + SS 3,2 ⋅ E2 ) kW = 247.8 2 SS 3,1 + SS 3,2 m

(This example was developed as a MATHCAD 15 worksheet. MATHCAD is a registered trademark of Parametric Technology Corporation.)

where Qp defines the heat flux between all zone pairs and Q is the total heat flux at each surface. Part (c): Compare the Adiabatic SSR and TEA Matrix Approaches Both approaches require the a prioi specification of three unknowns. Here we shall assume as in part (a) that E1 = 441.5

E30 =

 0.5554 1.0446 0 SS0 =  1.0446 0.3554 0  0 0 0 

0 0  0 0  kW  229.4 0  m2 0 229.4 

 0 341.9 59.1 59.1  −341.9 −46.6 −46.6 0 Q P = WI 4 ⋅ ss 4 − ss 4 ⋅ WI 4 =  0 0  −59.1 46.6  −59.1 46.6 0 0

and

5-27

  0.5554 1.0446  m2  =   1.0446 0.3554 

 E1   446.3   Q1   Q  = (εI1 ⋅ AI1 − SSR ) ⋅  E  =  -446.3  kW 2 2 Thus the adiabatic SSR model produces Q1 = 446.3 kW versus the measured value of Q1 = 460.0 with a discrepancy of about 3.0 percent. Mathematically the adiabatic SSR model assumes a value of Q3 = 0 which precludes the sidewall heat loss of Q3 = −25.0 kW/m2. This assumption accounts for all the difference between the two values.

1 = 0.70295 0 /1 + (2.4/π) ⋅ (0.2/0.8) + 1/F2,1

Part (b): Radiant Furnace Chamber with Roof Heat Loss M = 5 zones Zone 1 = Sink (bottom) Zone 2 = Source (lumped sides) Zone 3 = Refractory (roof) Zone 4 = Refractory (lumped ends) Zone 5 = Refractory (lumped floor strips) Boundary conditions: Five pieces of information are required for M = 5.  1200.0  T1F =  °F  1500.0 

 648.9  5 T1C = (T1F − 32) =  °C 9  815.6 

 E1   40.98  4 E1 =  kW/m2  = σ ⋅[ T1C + 273.15] =   79.66   E2  Q3 = −0.5 ⋅[ E2 − E1 ]⋅ A3 /10.76391 = −14.374 kW  Q3   −14.374     kW Q 2 =  Q4  =  0    Q5   0   

Q4 = Q5 = 0

5-28

HEAT AnD MASS TRAnSFER

Enclosure input parameters:

 εI11 εI =   OT

 ρI11 ρI =  T  O

   O   = εI22           =     

O ρI22

  0 0.9 0 0 0.70295   0  0  0   0

0 0 0

0 0

 0.5  0   0

   

0 0.5 0

  0 0.1 0 0 0.29705   0  0  0   0

0 0 0

   

 0.5  0   0

 −110.88    125.25      Q1  Q =   =  −14.37   kW   Q 2   0         0  

    0   0   0.5  

0  0 

0 0 0 0.5 0

 −23.87   11.23    kW q = AI −1 ⋅ Q =  −1.93  2   m  0   0 

 43.636  kW ρI11 ⋅ ( εI11 ⋅ AI11 )-1 ⋅ Q 1 =  W1 = E1 − ρ  74.915  m 2

    0  0   0.5  

0  0 

 43 ⋅ 64    74.91      W1   kW W =   =  62 ⋅ 69   2  m  W2     64 ⋅ 87      68 ⋅ 88  

 62.694  kW W2 = R22(ss21 ⋅ W1 + Q 2 ) =  64 ⋅ 874  2  68 ⋅ 879  m

A1 = 50 ft 2 A2 = 120 ft 2 A3 = 80 ft 2 A4 = 96 ft 2 A5 = 30 ft 2

 AI11 AI =   OT

O   AI22 

 4.6452   0 0 0 0     0 0 11.1484 0 0     =  7.4322 0 0 0    0    0 0 8.9187 0 0      0 2.7871 0 0 0   

   

    m2    

Compute direct exchange areas: There are Σ = 10 nonzero direct exchange areas. These are obtained from Eqs. (5-114) and view factor algebra. The final (partitioned) array of direct exchange areas is

 ss11 ss12 ss =   ss21 ss22

 0   1.559   =     1.5747  1.5115  0 

 1  0   1  0      ( AI − ss) ⋅  1 =  0       1  0   1  0 

1.559   1.5747 2.0777   2.8391 2.8391 3.3925 1.2802

   

 0  2.2421   0.7763

 0.1553 R22 = ( AI22 − ss22 )−1 =  0.0494   0.0562

  0  1.2802    2 0.7763   m 0.7306    0 

1.5115 3.3925 2.2421 1.0419 0.7306

0.0494 0.1459 0.052

0.0562 0.052 0.3881

Compute SSR total exchange areas:

 0.222 0.0273  1 R11b = ( AI11 − SSb ⋅ ρI11 )−1 =  2  0.0092 0.1131  m  1.1751 3.0055  2 SSR = εI11 ⋅ AI11 ⋅ R11b ⋅ SSb ⋅ εI11 =  m  3.0055 4.8312  0.3568 0.6432

0.2500  2 m 0.7500 

Check row-sum conservation:  1  0  ( AI11 − SSb) ⋅   =    1  0   1  0   1  0      ( εI11 ⋅ AI11 − SSR ) ⋅  1 =  0       1  0   1  0 

 0 0  1 ρI11 ⋅ R11b − R11bT ⋅ρI11 =   0 0  m 2  1  1 FSQ T ⋅   =  1  1    1

Compute wall fluxes and radiosity for source/sink zones:  -110.88  Q 1 = εI11 ⋅ AI11 ⋅ E1 − SSR ⋅ E1 − FSQ ⋅ Q 2 =  kW  125.25 

 40 ⋅ 98    79.66      E1   kW E =   =  60 ⋅ 76   2  m  E2     64 ⋅ 87      68 ⋅ 88  

 648.9  815.6    TC = (E/σ )0.25 − 273.15 = 744.3  °C   761.1  776.7 

H = AI −1 ⋅ ss ⋅ W

Summary of computed results: A 5 percent roof heat loss is consistent with practical measurement errors. Sensitivity testing was also performed with M = 3, 4, and 5 with and without heat loss. The classic adiabatic SSR model corresponds to M = 3 with no roof heat loss. For M = 4, the ends (zone 4) and floor strips (zone 5) were lumped together into one noncontiguous refractory zone. The results are summarized in the following tables. With the exception of the temperature of the floor strips, the computed results for Q are seen to be remarkably insensitive to M. 5% ROOF HEAT LOSS Computed results for W, H, Q, and E are wholly independent of refractory emissivity except the roof emissive power, E3, because Q3 ≠ 0.          

 0.9537 3.6915  2 SSb = ss11 + ss12 ⋅ R22 ⋅ ss21 =  m  3.6915 7.4569 

 0.3739 FSQ = εI11 ⋅ AI11 ⋅ R11b ⋅ SS12 ⋅ R22 =   0.6261

  1  m2 

 60 ⋅ 76  kW E2 = W2 + ρ ρI22 ⋅ ( εΙ 22 ⋅ AI22 )−1 . Q 2 =  64 ⋅ 87  2    68 ⋅ 88  m

ZONE

W

H

Q

E

1   2    3    4  5 

 43.64   74.91     62.69     64.87   68.88 

 67.50   63.68     64.63     64.87   68.88 

 −23.87   11.23     −1.93     0   0 

 40.98   79.66     60.76     64.87   68.88 

   −110.88    125.25      kW/m2 and Q =  −14.37  kW    0       0  

ADIABATIC ROOF Computed results for W, H, Q, and E are wholly independent of the refractory emissivity.  ZONE W  1     43.76    2   75.26    3   65.20        4   65.86    5   69.99 

H  68.79   64.83   65.20     65.86   69.99 

Q  −25.03   10.43   0     0   0 

E  40.98   79.66   65.20     65.86   69.99 

  −116.25     116.25   2  0  kW  kW/m and Q =   0      0  

Effect of zone numbers: Heat Flux Computations [kW] 5% Roof Heat Loss  ZONE M =3   −112.600   1  126.974    2       −14.374      3 

M =4  −111.869   126.242     −14.374 

M =5  −110.876   125.250     −14.374 

      

HEAT TRAnSFER BY RADIATIOn

[ρS 1 = ρS 2 = 0 or ρ1 = ρ D 1 with ρ2 = ρ D 2 ], Eq. (5-134) results in a formula identical to Eq. (5-127a),

Adiabatic Roof [ SINK ZI (−117.657) (−117.275) (−116.251)] Computed Temperatures [°C] 5% Roof Heat Loss  ZONE M = 3    3   756.2    4   NA         5   NA  

M =4  743.9   764.5     NA 

M =5  744.3   761.1     776.7 

M =3  765.8   NA     NA 

M =4  762.0   768.4     NA 

      

M =5  762.4   765.0     780.9 

S1 S 2 =

QTubes 1  1 − ε Enc  ATubes ( E2 − E1 ) −   .   . QTubes  R   ε Enc 

where QTubes = Q2 = 125.25 km and R = AEnc /ATubes = 376/157.1 = 2.394 . For εEnc = 0.50 there results εTubes = 0.2446 while for a black surround

The insensitivity of Eq. (5-127a) for R >1 thus demonstrates its significant engineering utility. [This example was developed as a MATHCAD 15 worksheet. MATHCAD is a registered trademark of Parametric Technology Corporation.]

Allowance for Specular Reflection If the assumption that all surface zones are diffuse emitters and reflectors is relaxed, the zoning equations become much more complex. Here, all surface parameters become functions of the angles of incidence and reflection of the radiation beams at each surface. In practice, such details of reflectance and emission are seldom known. When they are, the Monte Carlo method of tracing a large number of beams emitted from random positions and in random initial directions is probably the best way of obtaining a solution. Howell, Mengüç, and Siegel, Thermal Radiative Heat Transfer, 6th ed., CRC Press, Boca Raton, Fla., 2015, chap. 7) and Modest (Radiative Heat Transfer, 3d ed., Academic Press, New York, 2013, chap. 21) review the utilization of the Monte Carlo approach to a variety of radiant transfer applications. Among these is the Monte Carlo calculation of direct exchange areas for very complex geometries. Monte Carlo techniques are generally not used in practice for simpler engineering applications. A simple engineering approach to specular reflection is the diffuse plus specular reflection model . Here the total reflectivity ρi = 1 − ε i = ρSi + ρDi is represented as the sum of a diffuse component ρSi and a specular component ρDi . The method yields analytical results for a number of two-surface zone geometries. In particular, the following equation is obtained for exchange between concentric spheres or infinitely long coaxial cylinders for which A1 < A2: A1 ρS 2 1 ρ2 A1 + ⋅ + (1 − A1 /A2 ) ε1 ε 2 A2 (1 − ρS 2 )

(5-134)

For ρ D 1 = ρ D 2 = 0 (or equivalently ρ1 = ρS 1 with ρ2 = ρS 2 ), Eq. (5-134) yields the limiting case for wholly specular reflection Specular limit

S1 S 2 =

A1 1 1 + -1 ε1 ε 2

ε12 ⋅ρs 2 ⋅ A1 1 − ρ1 ⋅ρs 2

and

(5-134b)

(5-134a)

which is independent of the area ratio A1/A2. It is important to notice that Eq. (5-134a) is similar to Eq. (5-127b), but the emissivities here are defined as ε1 ≡ 1 − ρs 1 and ε 2 ≡ 1 − ρs 2. When surface reflection is wholly diffuse

S1 S 2 =

ε1 (1 − ρs 2 ) ⋅ A1 1 − ρ1 ⋅ρs 2

(5-134c,d)

which again exhibits diffuse and specular limits . The diffuse plus specular reflection model becomes significantly more complex for geometries with M ≥ 3 where digital computation is usually required . An Exact Solution to the Integral Equations—The Hohlraum Exact solutions of the fundamental integral equations for radiative transfer are available for only a few simple cases . One of these is the evaluation of the emittance from a small aperture, of area A1, in the surface of an isothermal spherical cavity of radius R . In German, this geometry is termed a hohlraum for hollow space . For this special case the radiosity W is constant over the inner surface of the cavity . It then follows that the ratio W/E is given by W /E =

Q2 ε Tubes = = 0.2219 ATubes ( E2 − E1 )

S1 S 2 =

A1  1  A1  ρ2   +    ε1  A2  ε 2 

For the case of (infinite) parallel flat plates where A1 = A2, Eq. (5-134) leads to a general formula similar to Eq. (5-134a) but with the stipulation here that ε1 ≡ 1 − ρ D 1 − ρS 1 and ε 2 ≡ 1 − ρ D 2 − ρS 2 . Another particularly interesting limit of Eq. (5-134) occurs when A2 >> A1 , which might represent a small sphere irradiated by infinite surroundings which can reflect radiation originating at A1 back to A1. That is, even though A2 → ∞, the “self ” total exchange area does not necessarily vanish, to wit

Part (c): Auxiliary Calculations for Tube Area and Effective Tube Emissivity Suppose the heating tubes were totally surrounded by an enclosure at the temperature of the sink and the emissivity of the refractory. Calculate the effective emissivity of the tubes for this idealization. Make reference to Eq. (5-127a). Solution: With D = 5 in and H = 6 ft, the total surface area of the tubes is calculated as ATubes = 20 ⋅π ⋅ D ⋅ H = 157.1 ft 2 = 14.59 m2. Equation (5-127a) may be employed to yield ε Tubes =

S1 S 2 =

Diffuse limit

Adiabatic Roof ZONE  3  4    5 

5-29

ε 1 − ρ⋅[1 − A1 /(4 πR 2 )]

(5-135)

where ε and ρ = 1 − ε are the diffuse emissivity and reflectivity of the interior cavity surface, respectively . The ratio W/E is the effective emittance of the aperture as sensed by an external narrow-angle receiver (radiometer) viewing the cavity interior . Assume that the cavity is constructed of a rough material whose (diffuse) emissivity is ε = 0 .5 . As a point of reference, if the cavity is to simulate a blackbody emitter to better than 98 percent of an ideal theoretical blackbody, Eq . (5-135) then predicts that the ratio of the aperture to sphere areas A1 /(4 πR 2 ) must be less than 2 percent . Equation (5-135) has practical utility in the experimental design of calibration standards for laboratory radiometers . RADIATIOn FROM GASES AnD SUSPEnDED PARTICULATE MATTER Introduction Flame radiation originates as a result of emission from water vapor and carbon dioxide in the hot gaseous combustion products and from the presence of particulate matter . The latter includes emission both from burning of microscopic and submicroscopic soot particles and from large suspended particles of coal, coke, or ash . Thermal radiation owing to the presence of water vapor and carbon dioxide is not visible . The characteristic blue color of clean natural gas flames is due to chemiluminescence of the excited intermediates in the flame which contribute negligibly to the radiation from combustion products . Gas Emissivities Radiant transfer in a gaseous medium is characterized by three quantities: the gas emissivity, gas absorptivity, and gas transmissivity . Gas emissivity refers to radiation originating within a gas volume that is incident on some reference surface . Gas absorptivity and gas transmissivity, however, refer to the absorption and transmission of radiation from some external surface radiation source characterized by some radiation temperature T1 . The sum of the gas absorptivity and transmissivity must, by definition, be unity . Gas absorptivity may be calculated from an appropriate gas emissivity . The gas emissivity is a function of only the gas temperature Tg while the absorptivity and transmissivity are functions of both Tg and T1 . The standard hemispherical monochromatic gas emissivity is defined as the direct volume-to-surface exchange area for a hemispherical gas volume to an infinitesimal area element located at the center of the planar base . Consider monochromatic transfer in a black hemispherical enclosure of radius R that confines an isothermal volume of gas at temperature Tg . The temperature of the bounding surfaces is T1 . Let A2 denote the area of the finite hemispherical surface and dA1 denote an infinitesimal element of area located at the center of the planar base . The (dimensionless) monochromatic direct

HEAT AnD MASS TRAnSFER

exchange area for exchange between the finite hemispherical surface A2 and dA1 then follows from direct integration of Eq. (5-116a) as ∂( s1 s 2 )λ π/2 e − K λ R cos ϕ1 2 πR 2 sin ϕ1 d ϕ1 = e − K λ R = ∫ ∂ A1 πR 2 ϕ1 = 0

(5-136a)

and from conservation there results ∂( s1 g )λ = 1 − e− Kλ R ∂ A1

(5-136b)

Note that Eq. (5-136b) is identical to the expression for the gas emissivity for a column of path length R . In Eqs. (5-136) the gas absorption coefficient is a function of gas temperature, composition, and wavelength, that is, K λ = K λ (T , λ). The net monochromatic radiant flux density at dA1 due to irradiation from the gas volume is then given by q1 g ,λ =

∂( s1 g )λ ( E1,λ − E g ,λ ) ≡ α g ,1,λ E1,λ − ε g ,λ E g ,λ ∂ A1

(5-137)

In Eq. (5-137), ε g ,λ (T , λ) = 1 − exp(− K λ R ) is defined as the monochromatic or spectral gas emissivity and α g ,λ (T , λ) = ε g ,λ (T , λ) . If Eq. (5-137) is integrated with respect to wavelength over the entire EM spectrum, an expression for the total flux density is obtained q1, g = α g ,1 E1 − ε g E g ∞

where

ε g (Tg ) =

∫ε

λ

(Tg , λ ) ⋅

λ= 0

Eb ,λ (Tg , λ ) Eb (Tg )

∞

α g ,1 (T1 , Tg ) =

and

∫α

λ= 0

g ,λ

(5-138)

(Tg , λ) ⋅

dλ

Eb ,λ (T1 , λ) dλ Eb (T1 )

(5-138a)

(5-138b)

define the total gas emissivity and absorptivity, respectively. The notation used here is analogous to that used for surface emissivity and absorptivity as previously defined. For a real gas εg = αg,1 only if T1 = Tg, while for a gray gas mass of arbitrarily shaped volume ε g = α g ,1 = ∂( si g )/ ∂ A1 is independent of temperature. Because K λ (T , λ) is also a function of the composition of the radiating species, it is necessary in what follows to define a second absorption coefficient kp,λ, where K λ = k p ,λ p . Here p is the partial pressure of the radiating species, and kp,λ, with units of (atm ⋅ m)−1, is referred to as the monochromatic line absorption coefficient. Mean Beam Lengths It is always possible to represent the emissivity of an arbitrarily shaped volume of gray gas (and thus the corresponding direct gas-to-surface exchange area) with an equivalent sphere of radius R = LM. In this context the hemispherical radius R = LM is referred to as the mean beam length of the arbitrary gas volume. Consider, e.g., an isothermal gas layer at temperature Tg confined by two infinite parallel plates separated by distance L . Direct integration of Eq. (5-116a) and use of conservation yield a closedform expression for the requisite surface-gas direct exchange area ∂( s1 g ) ∂ A1 ∞

1.0

= [1 − 2 E3 ( KL)]

(5-139a)

− z⋅t

e dt is defined as the nth-order exponential integral which tn t =1 is readily available. Employing the definition of gas emissivity, the mean beam length between the plates LM is then defined by the expression

where En ( z ) =

∫

Use of the optically thin value of the mean beam length yields values of gas emissivities or exchange areas that are too high . It is thus necessary to introduce a dimensionless constant β ≤ 1 and define some new average mean beam length such that KLM ≡ β⋅ KLM 0 . For the case of parallel plates, we now require that the mean beam length exactly predict the gas emissivity for a third value of KL . In this example we find β = − ln[2E3 ( KL)]/2KL and for KL = 0.193095 there results β = 0.880 . The value β = 0.880 is not wholly arbitrary . It also happens to minimize the error defined by the so-called shape correction factor φ = [ ∂( si g )/ ∂ A1 ]/(1 − e − KLM ) for all KL > 0 . The required average mean beam length for all KL > 0 is then taken simply as LM = 0.88LM 0 = 1.76L . The error in this approximation is less than 5 percent . For an arbitrary geometry, the average mean beam length is defined as the radius of a hemisphere of gas which predicts values of the direct exchange area s1 g /A1 = [1 − exp(− KLM )], subject to the optimization condition indicated above . It has been found that the error introduced by using average mean beam lengths to approximate direct exchange areas is sufficiently small to be appropriate for many engineering calculations . When it is evaluated for a large number of geometries, it is found that 0 .8 < β < 0 .95 . It is recommended here that β = 0 .88 be employed in lieu of any further geometric information . For a single-gas zone, all the requisite direct exchange areas can be approximated for engineering purposes in terms of a single appropriately defined average mean beam length . Emissivities of Combustion Products Absorption or emission of radiation by the constituents of gaseous combustion products is determined primarily by vibrational and rotational transitions between the energy levels of the gaseous molecules . Changes in both vibrational and rotational energy states give rise to discrete spectral lines . Rotational lines accompanying vibrational transitions usually overlap, forming a so-called vibration-rotation band . These bands are thus associated with the major vibrational frequencies of the molecules . Each spectral line is characterized by an absorption coefficient kp,λ which exhibits a maximum at some central characteristic wavelength or wave number h0 = 1/λ0 and is described by a Lorentz∗ probability distribution . Since the widths of spectral lines are dependent on collisions with other molecules, the absorption coefficient will also depend upon the composition of the combustion gases and the total system pressure . This brief discussion of gas spectroscopy is intended as an introduction to the factors controlling absorption coefficients and thus the factors which govern the empirical correlations to be presented for gas emissivities and absorptivities . Figure 5-19 shows computed values of the spectral emissivity εg,λ ≡ εg,λ(T, pL, λ) as a function of wavelength for an equimolar mixture of carbon dioxide and water vapor for a gas temperature of 1500 K, partial pressure of 0 .18 atm, and a path length L = 2 m . Three principal absorption-emission bands for CO2 are seen to be centered on 2 .7, 4 .3, and 15 μm . Two weaker bands at 2 and 9 .7 μm are also evident . Three principal absorption-emission bands for water vapor are also identified near 2 .7, 6 .6, and 20 μm with lesser bands at 1 .17, 1 .36, and 1 .87 μm . The total emissivity εg and total absorptivity ag,1 are calculated by integration with respect to the wavelength of the spectral emissivities, using Eqs . (5-138) in a manner similar to the development of total surface properties .

ε g = [1 − 2 ⋅ E3 ( KL)] ≡ 1 − e

− KLM

(5-139b)

Solution of Eq. (5-139b) yields KLM = − ln[2 E3 ( KL)], and it is apparent that KLM is a function of KL. Since En (0) = 1/(n − 1) for n > 1, the mean beam length approximation also correctly predicts the gas emissivity as zero when K = 0 and K → ∞. In the limit K → 0, power series expansion of both sides of Eq . (5-139b) leads to KLM → 2 KL ≡ KLM 0, where LM ≡ LM 0 = 2 L . Here LM 0 is defined as the optically thin mean beam length for radiant transfer from the entire infinite planar gas layer to a differential element of surface area on one of the plates . The optically thin mean beam length for two infinite parallel plates is thus simply twice the plate spacing L . In a similar manner it may be shown that for a sphere of diameter D, LM0 = ⅔D, and for an infinitely long cylinder LM 0 = D . A useful default formula for an arbitrary enclosure of volume V and area A is given by LM 0 = 4V /A . This expression predicts LM 0 = 8 9 R for the standard hemisphere of radius R because the optically thin mean beam length is averaged over the entire hemispherical enclosure .

Spectral Emissivity of Gaseous Species ελ

5-30

0.9 0.8 0.7 H2O

0.6 0.5

CO2

0.4 0.3 0.2 0.1 0.0 0

2

4

6

8 10 12 Wavelength λ [µm]

14

16

18

20

FIG. 5-19 Spectral emittances for carbon dioxide and water vapor after RADCAL .

pcL = pwL = 0 .36 atm ⋅ m, Tg = 1500 K .

∗ Spectral lines are conventionally described in terms of wave number h = 1/λ, with each line having a peak absorption at wave number h0 . The Lorentz distribution is bc defined as kη /S = where S is the integral of kh over all wave numbers . π[bc2 + ( η− η0 )2 ] The parameter S is known as the integrated line intensity, and bc is defined as the collision line half-width, i .e ., the half-width of the line is one-half of its peak centerline value . The units of kh are m−1 atm−1 .

HEAT TRAnSFER BY RADIATIOn Spectral Emissivities Highly resolved spectral emissivities can be generated at ambient temperatures from the HITRAN database (highresolution transmission molecular absorption) that has been developed for atmospheric models [Rothman, L. S., K. Chance, and A. Goldman, eds., J . Quant . Spectroscopy & Radiative Trans . 82(1–4): 2003]. This database includes the chemical species H2O, CO2, O3, N2O, CO, CH4, O2, NO, SO2, NO2, NH3, HNO3, OH, HF, HCl, HBr, ClO, OCS, H2CO, HOCl, N2, HCN, CH3C, HCl, H2O2, C2H2, C2H6, PH3, COF2, SF6, H2S, and HCO2H. These data have been extended to high temperature for CO2 and H2O, allowing for the changes in the population of different energy levels and in the line half width [Denison, M. K., and B. W. Webb, Heat Transfer, 2: 19–24 (1994)]. The resolution in the single-line models of emissivities is far greater than that needed in engineering calculations. A number of models are available that average the emissivities over narrow-wavelength regimes or over the entire band. An extensive set of measurements of narrowband parameters performed at NASA (Ludwig, C., et al., Handbook of Infrared Radiation from Combustion Gases, NASA SP-3080, 1973) has been used to develop the RADCAL computer code to obtain spectral emissivities for CO2, H2O, CH4, CO, and soot (Grosshandler, W. L., “RADCAL,” NIST Technical Note 1402, 1993). The exponential wideband model is available for emissions averaged over a band for H2O, CO2, CO, CH4, NO, SO2, N2O, NH3, and C2H2 [Edwards, D. K., and Menard, W. A ., Appl . Optics, 3: 621–625 (1964)]. The line and band models have the advantages of being able to account for complexities in determining emissivities of line broadening due to changes in composition and pressure, exchange with spectrally selective walls, and greater accuracy in formulating fluxes in gases with temperature gradients. These models can be used to generate the total emissivities and absorptivies that will be used in this

TABLE 5-6

5-31

section. RADCAL is a command-line FORTRAN code which is available in the public domain on the Internet. Total Emissivities and Absorptivities Total emissivities and absorptivities for water vapor and carbon dioxide at present are still based on data embodied in the classical Hottel emissivity charts . These data have been adjusted with the more recent measurements in RADCAL and used to develop the correlations of emissivities given in Table 5-6. Two empirical correlations which permit hand calculation of emissivities for water vapor, carbon dioxide, and four mixtures of the two gases are presented in Table 5-6. The first section of Table 5-6 provides data for the two constants b and n in the empirical relation ε g Tg = b[ pL − 0.015]n

(5-140a)

while the second section of Table 5-6 utilizes the four constants in the empirical correlation log(ε g Tg ) = a0 + a1 log ( pL) + a2 log 2 ( pL) + a3 log 3 ( pL)

(5-140b)

In both cases the empirical constants are given for the three temperatures of 1000, 1500, and 2000 K. Table 5-6 also includes six values for the partial pressure ratios pW/pC of water vapor to carbon dioxide, namely, 0, 0.5, 1.0, 2.0, 3.0, and ∞. These ratios correspond to composition values of pC/(pC + pW) = 1/(1 + pW /pC) of 0, 1/3, 1/2, 2/3, 3/4, and unity. For emissivity calculations at other temperatures and mixture compositions, linear interpolation of the constants is recommended.

Emissivity-Temperature Product for CO2-H2O Mixtures, ε g Tg Limited range for furnaces, valid over 25-fold range of pw + cL, 0.046–1.15 m ⋅ atm (0.15–3.75 ft ⋅ atm)

pw /pc

0

½

1

2

3

∞

pw pw + pc

0

⅓(0 .3–0 .42)

½(0 .42–0 .5)

⅔(0 .6–0 .7)

¾(0 .7–0 .8)

1

Corresponding to CH4, covering natural gas and refinery gas

Corresponding to (CH6)x, covering future high H2 fuels

H2O only

CO2 only

Corresponding to (CH)x, covering coal, heavy oils, pitch

Corresponding to (CH2)x, covering distillate oils, paraffins, olefines

Constants b and n of ε g Tg = b( pL - 0 .015)n, pL = m ⋅ atm, T = K

Section 1   T, K

b

n

b

n

b

n

b

n

b

n

b

n

1000 1500 2000

188 252 267

0 .209 0 .256 0 .316

384 448 451

0 .33 0 .38 0 .45

416 495 509

0 .34 0 .40 0 .48

444 540 572

0 .34 0 .42 0 .51

455 548 594

0 .35 0 .42 0 .52

416 548 632

0 .400 0 .523 0 .640

Constants b and n of ε g Tg = b(pL - 0 .05)n, pL = ft ⋅ atm, T = °R T, °R

b

n

b

n

b

n

b

n

b

n

b

n

1800 2700 3600

264 335 330

0 .209 0 .256 0 .316

467 514 476

0 .33 0 .38 0 .45

501 555 519

0 .34 0 .40 0 .48

534 591 563

0 .34 0 .42 0 .51

541 600 577

0 .35 0 .42 0 .52

466 530 532

0 .400 0 .523 0 .640

Full range, valid over 2000-fold range of pw + cL, 0 .005–10 .0 m ⋅ atm (0 .016–32 .0 ft ⋅ atm) Constants of log10 ε g Tg = a0 + a1 log pL + a2 log2 pL + a3 log3 pL

Section 2   pw pc

pw pw + pc

0

0

½

⅓

1

½

2

⅔

3

¾

∞

1

pL = m ⋅ atm, T = K

pL = ft ⋅ atm, T = °R

T, K

a0

a1

a2

a3

T, °R

a0

a1

a2

a3

1000 1500 2000 1000 1500 2000 1000 1500 2000 1000 1500 2000 1000 1500 2000 1000 1500 2000

2 .2661 2 .3954 2 .4104 2 .5754 2 .6451 2 .6504 2 .6090 2 .6862 2 .7029 2 .6367 2 .7178 2 .7482 2 .6432 2 .7257 2 .7592 2 .5995 2 .7083 2 .7709

0 .1742 0 .2203 0 .2602 0 .2792 0 .3418 0 .4279 0 .2799 0 .3450 0 .4440 0 .2723 0 .3386 0 .4464 0 .2715 0 .3355 0 .4372 0 .3015 0 .3969 0 .5099

-0 .0390 -0 .0433 -0 .0651 -0 .0648 -0 .0685 -0 .0674 -0 .0745 -0 .0816 -0 .0859 -0 .0804 -0 .0990 -0 .1086 -0 .0816 -0 .0981 -0 .1122 -0 .0961 -0 .1309 -0 .1646

0 .0040 0 .00562 -0 .00155 0 .0017 -0 .0043 -0 .0120 -0 .0006 -0 .0039 -0 .0135 0 .0030 -0 .0030 -0 .0139 0 .0052 0 .0045 -0 .0065 0 .0119 0 .00123 -0 .0165

1800 2700 3600 1800 2700 3600 1800 2700 3600 1800 2700 3600 1800 2700 3600 1800 2700 3600

2 .4206 2 .5248 2 .5143 2 .6691 2 .7074 2 .6686 2 .7001 2 .7423 2 .7081 2 .7296 2 .7724 2 .7461 2 .7359 2 .7811 2 .7599 2 .6720 2 .7238 2 .7215

0 .2176 0 .2695 0 .3621 0 .3474 0 .4091 0 .4879 0 .3563 0 .4561 0 .5210 0 .3577 0 .4384 0 .5474 0 .3599 0 .4403 0 .5478 0 .4102 0 .5330 0 .6666

-0 .0452 -0 .0521 -0 .0627 -0 .0674 -0 .0618 -0 .0489 -0 .0736 -0 .0756 -0 .0650 -0 .0850 -0 .0944 -0 .0871 -0 .0896 -0 .1051 -0 .1021 -0 .1145 -0 .1328 -0 .1391

0 .0040 0 .00562 -0 .00155 0 .0017 -0 .0043 -0 .0120 -0 .0006 -0 .0039 -0 .0135 0 .0030 -0 .0030 -0 .0139 0 .0052 0 .0045 -0 .0065 0 .0119 0 .00123 -0 .0165

note: pw/(pw + pc) of ⅓, ½, ⅔, and ¾ may be used to cover the ranges 0 .2–0 .4, 0 .4–0 .6, 0 .6–0 .7, and 0 .7–0 .8, respectively, with a maximum error in εg of 5 percent at pL = 6 .5 m ⋅ atm, less at lower pL’s . Linear interpolation reduces the error generally to less than 1 percent . Linear interpolation or extrapolation on T introduces an error generally below 2 percent, less than the accuracy of the original data .

5-32

HEAT AnD MASS TRAnSFER

The absorptivity can be obtained from the emissivity with aid of Table 5-6 by using the following functional equivalence.  Tg  α g ,1T1 =  ε g T 1 ( pL ⋅T1 / Tg )     T1 

0.5

(5-141)

Verbally, the absorptivity computed from Eq. (5-141) by using the correlations in Table 5-6 is based on a value for gas emissivity εg calculated at a temperature T1 and at a partial-pressure path length product of (pC + pW) LT1/Tg. The absorptivity is then equal to this value of gas emissivity multiplied by (Tg/T1)0.5. It is recommended that spectrally based models such as RADCAL be used particularly when extrapolating beyond the temperature, pressure, or partial-pressure-length product ranges presented in Table 5-6. A comparison of the results of the predictions of Table 5-6 with values obtained via the integration of the spectral results calculated from the narrowband model in RADCAL is provided in Fig. 5-20. Here calculations are shown for pCL = pWL = 0.12 atm ⋅ m and a gas temperature of 1500 K. The RADCAL predictions are 20 percent higher than the measurements at low values of pL and are 5 percent higher at the large values of pL . An extensive comparison of different sources of emissivity data shows that disparities up to 20 percent are to be expected at the current time [Lallemant, N., Sayre, A., and Weber, R., Prog . Energy Combust . Sci. 22: 543–574 (1996)]. However, smaller errors result for the range of the total emissivity measurements presented in the Hottel emissivity tables. This is demonstrated in Example 5-12. Example 5-12 Calculations of Gas Emissivity and Absorptivity

Consider a slab of gas confined between two infinite parallel plates with a distance of separation of L = 1 m. The gas pressure is 101.325 kPa (1 atm), and the gas temperature is 1500 K (2240°F). The gas is an equimolar mixture of CO2 and H2O, each with a partial pressure of 12 kPa ( pC = pW = 0.12 atm). The radiative flux to one of its bounding surfaces has been calculated by using RADCAL for two cases. For case (a) the flux to the bounding surface is 68.3 kW/m2 when the emitting gas is backed by a black surface at an ambient temperature of 300 K (80°F). This (cold) back surface contributes less than 1 percent to the flux. In case (b), the flux is calculated as 106.2 kW/m2 when the gas is backed by a black surface at a temperature of 1000 K (1340°F). In this example, gas emissivity and absorptivity are to be computed from these flux values and compared with values obtained by using Table 5-6. Case (a): The flux incident on the surface is equal to εg ⋅ s ⋅ Tg4 = 68.3 kW/m2; therefore, εg = 68,300/(5.6704 × 10-8 ⋅ 15004) = 0.238. To utilize Table 5-6, the mean beam length for the gas is calculated from the relation LM = 0.88LM0 = 0.88 ⋅ 2L = 1.76 m. For Tg = 1500 K and (pC + pW)LM = 0.24(1.76) = 0.422 atm ⋅ m, the two-constant correlation in Table 5-6 yields εg = 0.230 and the four-constant correlation yields εg = 0.234. These results are clearly in excellent agreement with the predicted value of εg = 0.238 obtained from RADCAL. Case (b): The flux incident on the surface (106.2 kW/m2) is the sum of that contributed by (1) gas emission εg ⋅ s ⋅ Tg4 = 68.3 kW/m2 and (2) emission from the opposing

surface corrected for absorption by the intervening gas using the gas transmissivity, that is, tg,1s ⋅ T41 where tg,1 = 1 − ag,1. Therefore ag,1 = [1 - (106,200 − 68,300)/(5.6704 × 10-8⋅10004)] = 0.332. Using Table 5-6, the two-constant and four-constant gas emissivities evaluated at T1 = 1000 K and pL = 0.4224 × (1000/1500) = 0.282 atm ⋅ m are εg = 0.2654 and εg = 0.2707, respectively. Multiplication by the factor (Tg/T1)0.5 = (1500/1000) 0.5 = 1.225 produces the final values of the two corresponding gas absorptivities ag,1 = 0.325 and ag,1 = 0.332, respectively. Again the agreement with RADCAL is excellent.

Other Gases The most extensive available data for gas emissivity are those for carbon dioxide and water vapor because of their importance in the radiation from the products of fossil fuel combustion. Selected data for other species present in combustion gases are provided in Table 5-7. Flames and Particle Clouds Luminous Flames Luminosity conventionally refers to soot radiation. At atmospheric pressure, soot is formed in locally fuel-rich portions of flames in amounts that usually correspond to less than 1 percent of the carbon in the fuel. Because soot particles are small relative to the wavelength of the radiation of interest in flames (primary particle diameters of soot are of the order of 20 nm compared to wavelengths of interest of 500 to 8000 nm), the incident radiation permeates the particles, and the absorption is proportional to the volume of the particles. In the limit of rp/λ 2. For temperatures above 1500 K, soot burns out rapidly (in less than 0.1 s) under fuel-lean conditions, F < 1. Because of this rapid soot burnout, soot is usually localized in a relatively small fraction of a furnace or combustor volume. Long, poorly mixed diffusion flames promote soot formation while highly back-mixed combustors can burn soot-free. In a typical flame at atmospheric pressure, maximum volumetric soot concentrations are found to be in the range of 10-7 < fυ < 10−6. This corresponds to a soot formation of about 1.5 to 15 percent of the carbon in the fuel. When fυ is to be calculated at high pressures, allowance must be made for the significant increase in soot formation with pressure and for the inverse proportionality of fυ with respect to pressure. Great progress is being made in the ability to calculate soot in premixed flames. For example, predicted and measured soot concentration has been compared in a well-stirred reactor operated over a wide range of temperatures and equivalence ratios [Brown, N. J., Revzan, K. L., and Frenklach, M., Twenty-seventh Symposium (International) on Combustion, pp. 1573–1580, 1998]. Moreover, computational fluid dynamics (CFD) and population dynamics modeling have been used to simulate soot formation in a turbulent non-premixed ethylene-air flame [Zucca et al., Chem . Eng . Sci . 61: 87–95 (2006)]. The importance of soot radiation varies widely between combustors. In large boilers the soot is confined to small volumes and is of only local importance. In gas turbines, cooling the combustor liner is of primary importance so that only small incremental soot radiation is of concern. In high-temperature glass tanks, the presence of soot adds 0.1 to 0.2 to emissivities of oil-fired flames. In natural gas-fired flames, efforts to augment flame emissivities with soot generation generally have been unsuccessful. The contributions of soot to the radiation from pool fires often dominates, and thus the presence of soot in such flames directly impacts the safe separation distances from dikes around oil tanks and the location of flares with respect to oil rigs. Clouds of Large Black Particles The emissivity εM of a cloud of black particles with a large perimeter-to-wavelength ratio is ε M = 1 − exp[ − ( a /υ ) L ]

(5-144)

where a/υ is the projected area of the particles per unit volume of space. If the particles have no negative curvature (the particle does not “see” any of itself) and are randomly oriented, a = a′/4, where a′ is the actual surface area. If the particles are uniform, a/υ = cA = cA′/4, where A and A′ are the projected and total areas of each particle, respectively, and c is the number concentration of particles. For spherical particles this leads to ε M = 1 − exp[ −(π/4)cd p2 L ] = 1 − exp(−1.5 f υ L/d p )

(5-145)

As an example, consider a heavy fuel oil (CH1.5, specific gravity of 0.95) atomized to a mean surface particle diameter of dp burned with 20 percent excess

air to produce coke-residue particles having the original drop diameter and suspended in combustion products at 1204°C (2200°F). The flame emissivity due to the particles along a path of L m, with dp measured in micrometers, is εM = 1 - exp(-24.3L/dp)

(5-146)

For 200-μm particles and L = 3.05 m, the particle contribution to emissivity is calculated as 0.31. Clouds of Nonblack Particles For nonblack particles, emissivity calculations are complicated by multiple scatter of the radiation reflected by each particle. The emissivity εM of a cloud of gray particles of individual emissivity ε1 can be estimated by the use of a simple modification Eq. (5-144), i.e., εM = 1 - exp[-ε1(a/υ)L]

(5-147)

Equation (5-147) predicts that εM → 1 as L → ∞. This is impossible in a scattering system, and use of Eq. (5-147) is restricted to values of the optical thickness (a/υ)L < 2. Instead, the asymptotic value of εM is obtained from Fig. 5-12 as εM = εh (lim L → ∞), where the albedo w is replaced by the particlesurface reflectance w = 1 - ε1. Particles with perimeter-to-wavelength ratios of 0.5 to 5.0 can be analyzed, with significant mathematical complexity, by use of the the Mie equations (Bohren, C. F., and Huffman, D. R., Absorption and Scattering of Light by Small Particles, Wiley, Hoboken, N.J., 1998). Combined Gas, Soot, and Particulate Emission In a mixture of emitting species, the emission of each constituent is attenuated on its way to the system boundary by absorption by all other constituents. The transmissivity of a mixture is the product of the transmissivities of its component parts. This statement is a corollary of Beer’s law. For present purposes, the transmissivity of “species k” is defined as tk = 1 - εk. For a mixture of combustion products consisting of carbon dioxide, water vapor, soot, and oil coke or char particles, the total emissivity εT at any wavelength can therefore be obtained from (1 − εT )λ = (1 − εC )λ (1 − εW )λ (1 − ε S )λ (1 − ε M )λ

(5-148)

where the subscripts denote the four flame species. The total emissivity is then obtained by integrating Eq. (5-148) over the entire EM energy spectrum, taking into account the variability of εC, εW, and εS with respect to wavelength. In Eq. (5-148), εM is independent of wavelength because absorbing char or coke particles are effectively blackbody absorbers. Computer programs for spectral emissivity, such as RADCAL, perform the integration with respect to wavelength for obtaining total emissivity. Corrections for the overlap of vibration-rotation bands of CO2 and H2O are automatically included in the correlations for εg for mixtures of these gases. The monochromatic soot emissivity is higher at shorter wavelengths, resulting in higher attenuations of the bands at 2.7 μm for CO2 and H2O than at longer wavelengths. The following equation is recommended for calculating the emissivity εg+S of a mixture of CO2, H2O, and soot ε g + S = ε g + ε S − M ⋅ε g ε S

(5-149)

where M can be represented with acceptable error by the dimensionless function M = 1.12 − 0.27 ⋅ (T /1000) + 2.7 × 10 5 f υ · L

(5-150)

5-34

HEAT AnD MASS TRAnSFER

In Eq. (5-150), T has units of kelvins and L is measured in meters. Since coke or char emissivities are gray, their addition to those of the CO2, H2O, and soot follows simply from Eq. (5-148) as εT = ε g + S + ε M − ε g + S ε M

(5-151)

good one. The zone method is now further generalized to make allowance for nongray radiative transfer via incorporation of the weighted sum of gray gas (WSGG) spectral model. Hottel has shown that the emissivity εg (T, L) of an absorbing-emitting gas mixture containing CO2 and H2O of known composition can be approximated by a weighted sum of P gray gases P

ε g (T , L) ≈ ∑ a p (T )[1 − e

with the definition 1 − ε g + S ≡ (1 − εC )(1 − εW )(1 − ε S ).

Energy Balances for Volume Zones—The Radiation Source Term Reconsider a generalized enclosure with N volume zones confining a gray gas. When the N gas temperatures are unknown, an additional set of N equations is required in the form of radiant energy balances for each volume zone. These N equations are given by the definition of the N-vector for the net radiant volume absorption S′ = [ S ′j ] for each volume zone [ N × 1]

(5-152)

The radiative source term is a discretized formulation of the net radiant absorption for each volume zone which may be incorporated as a source term into numerical approximations for the generalized energy equation . As such, it permits formulation of energy balances on each zone that may include conductive and convective heat transfer. For K → 0, GS → 0, and GG → 0 leading to S′ → 0 N . When K ≠ 0 and S′ = 0 N , the gas is said to be in a state of radiative equilibrium . In the notation usually associated with the discrete ordinate (DO) and finite volume (FV) methods, see Modest (Radiative Heat Transfer, 3d ed., Academic Press, New York, 2013, chap. 17), one would  write S ′i /Vi = K [G − 4· E g ] = −∇⋅ q r . Here H g = G/4 is the average flux density incident on a given volume zone from all other surface and volume zones. The DO and FV methods are currently available options as “RTE-solvers” in complex simulations of combustion systems using computational fluid dynamics (CFD).∗ Implementation of Eq. (5-152) necessitates the definition of two additional symmetric N × N arrays of exchange areas, namely, gg = [ g i g j ] and GG = [GiG j ]. In Eq. (5-152) VI = [Vi ·δ i , j ] is an N × N diagonal matrix of zone volumes. The total exchange areas in Eq. (5-151) are explicit functions of the direct exchange areas as follows: Surface-to-gas exchange GS = SG

T

[N × M ]

(5-153a)

Gas-to-gas exchange T

GG = gg + sg ⋅ρI ⋅ R ⋅ sg

[N × M ]

Total exchange areas:

4 K ⋅ VI·1N = gs·1M + gg ·1N

4 K ⋅ VI·1N = GS·1M + GG·1N

P

∑a

Vi

Vj

(T ) = 1.0

ε g = a1 (1 − e − K1 LM ) + a2 (1 − e − K 2 LM )

(5-156b)

(5-157)

In Eq. (5-157) if K1 = 0 and a2 ≠ 0, the limiting value of gas emissivity is εg(T, ∞) → a2. Put K1 = 0 in Eq. (5-157), ag = a2, and define τg = e−K2LM as the gray gas transmissivity. Equation (5-157) then simplifies to ε g = a g (1 − τ g )

(5-158)

It is important to note in Eq. (5-158) that 0 ≤ ag, τg ≤ 1.0 while 0 ≤ εg ≤ ag. Equation (5-158) constitutes a two-parameter model which may be fitted with only two empirical emissivity data points. To obtain the constants ag and τg in Eq. (5-158) at fixed composition and temperature, denote the two emissivity data points as ε g ,2 = ε g (2 pL) > ε g ,1 = ε g ( pL) and recognize that ε g ,1 = a g (1 − τ g ) and ε g ,2 = a g (1 − τ 2g ) = a g (1 − τ g )(1 + τ g ) = ε g ,1 (1 + τ g ) . These relations lead directly to the final emissivity fitting equations τg =

ε g ,2 ε g ,1

−1

(5-159a)

and ag =

(5-154a)

(5-154b)

p

In Eqs. (5-156), Kp is some gray gas absorption coefficient and L is some appropriate path length. In practice, Eqs. (5-156) usually yield acceptable accuracy for P ≤ 3. For P = 1, Eqs. (5-156) degenerate to the case of a single gray gas. The Clear Plus Gray Gas WSGG Spectral Model In principle, the emissivity of all gases approaches unity for infinite path length L . In practice, however, the gas emissivity may fall considerably short of unity for representative values of pL . This behavior results because of the band nature of real gas spectral absorption and emission whereby there is usually no significant overlap between dominant absorption bands. Mathematically, this physical phenomenon is modeled by defining one of the gray gas components in the WSGG spectral model to be transparent. For P = 2 and path length LM, Eqs. (5-156) yield the following expression for the gas emissivity

ε g ,1 2 − ε g ,2 / ε g ,1

(5-159b)

The clear plus gray WSGG spectral model also readily leads to values for gas absorptivity and transmissivity, with respect to some appropriate surface radiation source at temperature T1, for example,

The formal integral definition of the direct gas-gas exchange area is 2 gi g j =  ∫∫∫  ∫∫∫ K

(5-156a)

p =1

(5-153b)

The matrices gg = [ g i g j ]and GG = [GiG j ] must also satisfy the following matrix conservation relations: Direct exchange areas:

]

where

RADIATIVE EXCHAnGE WITH PARTICIPATInG MEDIA

S′ = GS ⋅ E + GG ⋅ E g − 4 K ⋅ VI ⋅ E g

− K pL

p =1

α g ,1 = a g ,1 (1 − τ g )

(5-160a)

τ g ,1 = a g ,1 ·τ g

(5-160b)

- Kr

e dVj dVi πr 2

(5-155)

Clearly, when K = 0, the two direct exchange areas involving a gas zone g i s j and g i g j vanish . Computationally it is never necessary to make resort to Eq. (5-155) for calculation of g i g j . This is so because, si g j , si g j , and g i g j may all be calculated arithmetically from appropriate values of si s j by using associated conservation relations and view factor algebra. Weighted Sum of Gray Gas (WSGG) Spectral Model Even in simple engineering calculations, the assumption of a gray gas is almost never a ∗ To further clarify the mathematical differences between zoning and the DO and FV methods, recognize that (neglecting scatter) the matrix expressions H = AI −1 ⋅ ss ⋅ W + AI −1 ·sg ⋅ E g and 4 K ·H g = VI −1 ·gs·W + VI −1 ·gg ·E g represent spatial discretizations of the integral form(s) of the RTE applied at any point (zone) on the boundary or interior of an enclosure, respectively, for a gray gas.

and

In Eqs. (5-160) the gray gas transmissivity τg is taken to be identical to that obtained for the gas emissivity εg. The constant ag,1 in Eq. (5-160a) is then obtained with knowledge of one additional empirical value for αg,1 which may also be obtained from the correlations in Table 5-6. Notice further in the definitions of the three parameters εg, αg,1, and τg,1 that all the temperature dependence is forced into the two WSGG constants ag and ag,1. The three clear plus gray WSGG constants ag, ag,1, and τg are functions of total pressure, temperature, and mixture composition. It is not necessary to ascribe any particular physical significance to them. Rather, they may simply be visualized as three constants that happen to fit the gas emissivity data. It is noteworthy that three constants are far fewer than the number required to calculate gas emissivity data from fundamental spectroscopic data.

HEAT TRAnSFER BY RADIATIOn The two constants ag and ag,1 defined in Eqs. (5-158) and (5-160) can, however, be interpreted physically in a particularly simple manner. Suppose the gas absorption spectrum is idealized by many absorption bands (boxes), all of which are characterized by the identical absorption coefficient K . The a’s might then be calculated from the total blackbody energy fraction Fb (λT) defined in Eqs. (5-105) and (5-106). That is, ag simply represents the total energy fraction of the blackbody energy distribution in which the gas absorbs. This concept may be further generalized to real gas absorption spectra via the wideband stepwise gray spectral box model (Modest, Radiative Heat Transfer, 3d ed., Academic Press, New York, 2013, chap. 14). When P ≥ 3, exponential curve-fitting procedures for the WSGG spectral model become significantly more difficult for hand computation but are quite routine with the aid of a variety of readily available mathematical software utilities. The clear plus gray WSGG fitting procedure is demonstrated in Example 5-13. The Zone Method and Directed Exchange Areas Spectral dependence of real gas spectral properties is now introduced into the zone method via the WSGG spectral model. It is still assumed, however, that all surface zones are gray isotropic emitters and absorbers. General Matrix Representation We first define a new set of four directed exchange areas SS, SG, GS, and GG, which are denoted by an overarrow. The directed exchange areas are obtained from the total exchange areas for gray gases by simple matrix multiplication using weighting factors derived from the WSGG spectral model. The directed exchange areas are denoted by an overarrow to indicate the “sending” and “receiving” zone. The a-weighting factors for transfer originating at a gas zone ag,i are derived from WSGG gas emissivity calculations, while those for transfers originating at a surface zone ai are derived from appropriate WSGG gas absorptivity calculations. Let a g I p = [ a p , g ,i ⋅δ i , j ] and aI p = [ a p ,i ⋅δ i , j ] represent the P [M × M] and [N × N] diagonal matrices comprised of the appropriate WSGG a constants. The directed exchange areas are then computed from the associated total gray gas exchange areas via simple diagonal matrix multiplication. P

SS = ∑ SS p ⋅ aI p

[M × M]

(5-161a)

p =1 P

SG = ∑ SG p ⋅ a g I p

[M × N]

(5-161b)

p =1

5-35

It may be proved that the Q and S′ vectors computed from Eqs. (5-162) and (5-163) always exactly satisfy the overall (scalar) radiant energy balance 1TM ⋅ Q = 1TN ⋅ S′ . In words, the total radiant gas emission for all gas zones in the enclosure must always exactly equal the total radiant energy received at all surface zones which comprise the enclosure. In Eqs. (5-162) and (5-163), the following definitions are employed for the four forward-directed exchange areas SS = SS SG = GS

T

T

GS = SG GG = GG

T

(5-164a,b,c,d)

such that formally there are some eight matrices of directed exchange areas. The four backward-directed arrays of directed exchange areas must satisfy the following conservation relations:   SS ⋅1M + SG ⋅1N = εI ⋅ AI ⋅1M

(5-165a)

   4 KI ⋅ VI ⋅1N = GS ⋅1M + GG ⋅1N

(5-165b)

Subject to the restrictions of no scatter and diffuse surface emission and reflection, the above equations are the most general matrix statement possible for the zone method. When P = 1, the directed exchange areas all reduce to the total exchange areas for a single gray gas. If, in addition, K = 0, the much simpler case of radiative transfer in a transparent medium results. If, in addition, all surface zones are black, the direct, total, and directed exchange areas are all identical. Allowance for Flux Zones As in the case of a transparent medium, we now distinguish between source and flux surface zones. Let M = Ms + Mf represent the total number of surface zones where Ms is the number of sourcesink zones and Mf is the number of flux zones. The flux zones are the last to be numbered . To accomplish this, partition the surface emissive power and Q 1   E1  flux vectors as E =   and Q =   , where subscript 1 denotes surface E Q 2   2 source/sink zones whose emissive power E1 is specified a priori and subscript 2 denotes surface flux zones of unknown emissive power vector E2 and known radiative flux vector Q 2 . Suppose the radiative source vector S′ is known. Appropriate partitioning of Eqs. (5-162) then produces

P

GS = ∑ GS p ⋅ aI p

[M × N]

(5-161c)

p =1 P

GG = ∑ GG p ⋅ a g I p

[N × N]

(5-161d)

p =1

 Q 1   εAI1,1 =   Q 2   0

KI = ∑ KI p ⋅ a g I p

[N × N]

S′ = GG ⋅ E g + GS1

(5-161e)

p =1

In contrast to the total exchange areas which are always independent of temperature, the four directed arrays SS, SG, GS, and GG are dependent on the temperatures of each and every zone, i.e., as in ap,i = ap(Ti). Moreover, in contrast to total exchange areas, the directed arrays SS and GG are genT erally not symmetric and GS   ≠ SG . Finally, since the directed exchange areas are temperature-dependent, iteration may be required to update the aI p and a g I p arrays during the course of a calculation. There is a great deal of latitude with regard to fitting the WSGG a constants in these matrix equations, especially if N > 1 and composition variations are to be allowed for in the gas. An extensive discussion of a fitting for N > 1 is beyond the scope of this presentation. Details of the fitting procedure, however, are presented in Example 5-13 in the context of a single-gas zone. Once the directed exchange areas are formulated, the governing matrix equations for the radiative flux equations at each surface zone and the radiant source term are then given as follows: Q = εAI · E − SS · E − SG · E g

(5-162a)

S′   = GG · E g + GS · E − 4 ⋅ KI · VI · E g

(5-162b)

or the alternative forms Q = [ EI · SS   −SS · EI  · 1M +  EI ·  SG − SG ⋅ E g I ] · 1N

(5-163a)

S′   = −[ E g I · GS − GS · EI]· 1M − [ E g I · GG − GG · E g I]· 1 N

(5-163b)

(5-166a)

and

P

with

0   E1   SS1,1 SS1,2   E1   SG1  ⋅ −  ⋅   ⋅E εAI2,2   E2   SS2,1 SS2,2   E2   SG2  g        

 E1  GS2  ⋅   − 4⋅KI ⋅ VI ⋅ E g  E2 

(5-166b)

where the definitions of the matrix partitions follow the conventions with respect to Eq. (5-120). Simultaneous solution of the two unknown vectors in Eqs. (5-166) then yields E2 = RP ⋅[ SS2 ,1 + SG2 ⋅ PP ⋅ GS1 ] ⋅ E1 + RP ⋅ Q 2 − SG2 ⋅ PP ⋅ S′ 

(5-167a)

and E g = PP ⋅GS1

 E1  GS2  ⋅   − PP ⋅ S′  E2 

(167b)

where two auxiliary inverse matrices RP and PP are defined as −1

PP = [ 4⋅KI ⋅ VI − GG ]

RP =  εAI2,2 − SS2,2 − SG2 ⋅ PP ⋅ GS2 

(5-168a) −1

(5-168b)

The emissive power vectors E and E g are then both known quantities for purposes of subsequent calculation. Algebraic Formulas for a Single-Gas Zone As shown in Fig. 5-16, the three-zone system with M = 2 and N = 1 can be employed to simulate a surprisingly large number of useful engineering geometries. These include two infinite parallel plates confining an absorbing-emitting medium, any two-surface zone system where a nonconvex surface zone is completely surrounded by a second zone (this includes concentric spheres and cylinders),

5-36

HEAT AnD MASS TRAnSFER

and the speckled two-surface enclosure. As in the case of a transparent medium, the inverse reflectivity matrix R is capable of explicit matrix inversion for M = 2. This allows derivation of explicit algebraic equations for all the required directed exchange areas for the clear plus gray WSGG spectral model with M = 1 and 2 and N = 1. The Limiting Case M = 1 and N = 1 The directed exchange areas for this special case correspond to a single well-mixed gas zone completely surrounded by a single-surface zone A1. Here the reflectivity matrix is a 1 × 1 scalar quantity which follows directly from the general matrix equations as R = 1/( A1 − s1 s 1 ⋅ρ1 ). There are two WSCC clear plus gray constants a1 and ag and only one unique direct exchange area which satisfies the conservation relation s1 s 1 + s1 g = A1. The only two physically meaningful directed exchange areas are those between the surface zone A1 and the gas zone S1G = GS 1 =

a g ⋅ε1 A1 ⋅ s1 g

(5-169a)

ε1 ⋅ A1 + ρ1 ⋅ s1 g a1 ⋅ε1 A1 ⋅ s1 g ε1 ⋅ A1 + ρ1 ⋅ s1 g

(5-169b)

 ε1 A1[( A2 − ρ2 ⋅ s 2 s 2 ) ⋅ s1 g + ρ2 ⋅ s1 s 2 ⋅ s 2 g ] SG =   ) ⋅ s g + ρ1 ⋅ s1 s 2 ⋅ s1 g  (  ε 2 A2  A1 − ρ1 ⋅ s1 s 1 2 GS = [GS 1 GS 1 ]

and

(5-169)

Directed Exchange Areas for M = 2 and N = 1 For this case there are four WSGG constants, a1, a2, ag, and tg. There is one required value of K that is readily obtained from the equation K = − ln(τ g )/Lm , where τ g = exp(− KLm ). For an enclosure with M = 2, N = 1, and K ≠ 0, only three unique direct exchange areas are required because conservation stipulates A1 = s1 s 1 + s1 s 2 + s1 g and A2 = s 2 s 1 + s 2 s 2 + s 2 g . For M = 2 and N = 1, the matrix Eqs. (5-118) readily lead to the general gray gas matrix solution for SS and SG with K ≠ 0 as   ε 2 A2 − S1S 2 − S 2G  

 ε A −S S −S G 1 1 1 2 1 SS =   S 1 S1 

S1 S 2

(5-170a)

where S1S 2 = ε1ε 2 A1 A2 s1 s 2 /det R −1

(5-170b)

 ε1 A1 ( A2 − ρ2 ⋅ s 2 s ) ⋅ s1 g + ρ2 ⋅ s1 s ⋅ s 2 g  2 2   SG =    ε 2 A2 ( A2 − ρ2 ⋅ s 2 s 2 ) ⋅ s 2 g + ρ1 ⋅ s1 s 2 ⋅ s1 g 

and

  /det R −1 (5-170c)  

S1G R = S1G +

(5-170d)

For the WSGG clear gas components we denote SS]K =0 ≡ SS0 and SG]K =0 ≡ SG 0 = 0. Finally the WSGG arrays of directed exchange areas are computed simply from a-weighted sums of the gray gas total exchange areas as  1 − a1 0 SS = SS0 ⋅  1 − a2  0

  a1  + SS ⋅    0

E2 =

 a1 GS = GS ⋅   0

0  T  ≠ SG a2  

and finally 1  GG = a g ⋅ 4 KV − GS ⋅   1 

(5-171d)

The results of this development may be further expanded into algebraic form with the aid of Eq. (5-127) to yield S2S 1 =

ε1ε 2 A1 A2 ⋅ s 2 s 1 ]0 (1 − a1 ) ε ε A A s s ⋅a + 1 2 1 2 −21 1 1 ε1ε 2 A1 A2 + (ε1 A1ρ2 + ε 2 A2ρ1 ) ⋅ s 2 s 1 ]0 det R

(5-171e)

S 2 S 1 ⋅ E1 + S 2G ⋅ E g S 2 S 1 + S 2G

 A1 ⋅ F1,1 ss = τ g   A2 ⋅ F2,1

A1 ⋅ F1,2   A2 ⋅ F2,2  

 A1  sg = (1 − τ g )    A2 

with

(5-172b)

(5-173a)

(5-173b)

and for the particular case of a speckled enclosure ss =

(5-171a,b,c)

(5-172a)

In this circumstance, all the radiant energy originating in the gas volume is transferred to the sole sink zone A1. Equation (5-172a) is thus tantamount to the statement that Q1 = S′ or that the net emission from the source ultimately must arrive at the sink. Notice that if ε1 = 0, Eq. (5-172a) leads to a physically incongruous statement since all the directed exchange areas would vanish and no sink would exist. Even for the simple case of M = 2 and N = 1, the algebraic complexity of Eqs. (5-171) suggests that numerical matrix manipulation of directed exchange areas is preferred rather than calculations using algebraic formulas. Engineering Approximations for Directed Exchange Areas Use of the preceding equations for directed exchange areas with M = 2 and N = 1 and the WSGG clear plus gray gas spectral approximation requires knowledge of three independent direct exchange areas. It also formally requires evaluation of three WSGG weighting constants a1, a2, and ag with respect to the three temperatures T1, T2, and Tg. Further simplifications may be made by assuming that radiant transfer for the entire enclosure is characterized by the single mean beam length LM = 0.88⋅4 ⋅ V/A. The requisite direct exchange areas are then approximated by

0   a2  

SG = SG ⋅ a g

S1S 2 ⋅ S 2G S1S 2 + S 2G

Assuming radiative equilibrium, the emissive power of the refractory may also be calculated from the companion equation

T

2

(5-171g)

ρ2 ⋅ s1 s 2 ⋅ s 2 g  a1 /det R −1 and GS 2 ≡ ε 2 A2 ( A1 − ρ1 ⋅ s1 s 1 ) ⋅ s 2 g + ρ1 ⋅ s1 s 2 ⋅ s1 g  a2 / detR-1. Derivation of the scalar (algebraic) forms for the directed exchange areas here is done primarily for illustrative purposes. Computationally, the only advantage is to obviate the need for a digital computer to evaluate a [2 × 2] matrix inverse. Allowance for an Adiabatic Refractory with N = 1 and M = 2 Set N = 1 and M = 2, and let zone 2 represent the refractory surface. Let Q2 = 0 and ε2 ≠ 0; it then follows that we may define a refractory-aided directed exchange area S1G R by

with GS = SG and the indicated determinate of R−1 is evaluated algebraically as det R −1 = ( A1 − s1 s 1 ⋅ρ1 ) ⋅ ( A2 − s 2 s 2 ⋅ρ2 ) − ρ1 ⋅ρ2 ⋅ s1 s 2

(5-171f )

whose matrix elements are given by GS 1 ≡ ε1 A1 ( A2 − ρ2 ⋅ s1 s 1 ) ⋅ s1 g +

The total radiative flux Q1 at surface A1 and the radiative source term Q1 = S are given by   Q1 = GS 1 ⋅ E1 − S1G ⋅ E g

  ⋅ a g /det R −1  

also with

 A2  1 A1 + A2  A1 ⋅ A2  τg

A1 ⋅ A2   A22  

 A1  sg = (1 − τ g )    A2 

(5-174a)

(5-174b)

where again tg is obtained from the WSGG fit of gas emissivity. These approximate formulas clearly obviate the need for exact values of the direct exchange areas and may be used in conjunction with Eqs. (5-171). For engineering calculations, an additional simplification is sometimes warranted. Again characterize the system by a single mean beam length LM = 0.88⋅4⋅V/A and employ the identical value of tg = KLM for all surface-gas transfers. The three a constants might then be obtained by a WSGG datafitting procedure for gas emissivity and gas absorptivity which utilizes the three different temperatures Tg, T1, and T2. For engineering purposes we choose a simpler method, however. First calculate values of εg and ag1 for gas temperature Tg with respect to the dominant (sink) temperature T1. The net radiative flux between an isothermal gas mass at temperature Tg and a

HEAT TRAnSFER BY RADIATIOn black isothermal bounding surface A1 at temperature T1 (the sink) is given by Eq. (5-138) as Q1, g = A1σ α g ,1T 14 − ε g T g4

(

)

(5-175)

It is clear that transfer from the gas to the surface and transfer from the surface into the gas are characterized by two different constants of proportionality, εg and αg,1, respectively. To allow for the difference between gas emissivity and absorptivity, it proves convenient to introduce a single mean gas emissivity defined by

(

σ  ε g Tg4 − α g ,1T14  = ε m σ Tg4 − T 14

or

εm =

)

(5-176a)

ε g − α g ,1 (T1 /Tg ) 4

(5-176b)

1 − (T1 /Tg ) 4

The calculation then proceeds by computing two values of εm at the given Tg and T1 temperature pair and the two values of pLM and 2pLM. We thereby obtain the expression εm = αm(1 − τm). It is then assumed that a1 = a2 = ag = am for use in Eqs. (5-171). This simplification may be used for M > 2 as long as N = 1. This simplification is illustrated in Example 5-13.

εg1 = εgF (1500, pLM, 540, 0.42)

εg1 = 0.3048

εg2 = εgF (1500, 2pLM, 540, 0.42)

εg2 = 0.4097

ag11 = ag1F (1500, 1000, pLM, 444, 0.34)

ag11 = 0.4124

ag12 = ag1F (1500, 1000, 2pLM, 444, 0.34)

ag12 = 0.5250

5-37

Case (a): Compute Flux Density Using Exact Values of the WSGG Constants τg =

εg2 εg1

−1

tg = 0.3442

ag =

εg1 1− τg

ag = 0.4647

α g 11

ε g = a g ⋅ (1 − τ g )

ag1 =

εg = 0.3048

ag1 = 0.6289

1− τg

and the WSGG gas absorption coefficient (which is necessary for calculation of direct exchange areas) is calculated as K1 =

−(ln τ g ) LM

K 1 = 0.3838

or

1 m

Compute directed exchange areas: = 124.61 m2

s1g = (1 - tg) ⋅ A1

Given

Eqs. (5-169) yield

Example 5-13 WSGG Clear Plus Gray Gas Emissivity Calculations

Methane is burned to completion with 20 percent excess air (50 percent relative humidity at 298 K or 0.0088 mol water/mol dry air) in a furnace chamber of floor dimensions 3 × 10 m and height 5 m. The entire surface area of the enclosure is a gray sink with emissivity of 0.8 at 1000 K. The confined gas is well stirred at 1500 K. Evaluate the clear plus gray WSGG constants and the mean effective gas emissivity, and calculate the average radiative flux density to the enclosure surface. Two-zone model, M = 1, N = 1: A single volume zone completely surrounded by a single sink surface zone. Function definitions: Gas emissivity: εgF(Tg, pL, b, n) = b ⋅ (pL − 0.015)n ÷ Tg

α g 1 F (Tg ,T1 , pL , b , n ) =

Gas absorptivity:

Eq. (5-140a)

DS1G =

a g ⋅ε1 ⋅ A1 ⋅ s1 g

DS1G = 49.75 m2

Q1 = DGS1⋅E1 - DS1G⋅Eg

0.5

T1 τm =

ε g − α g ⋅ (T1 /Tg ) 4

s ≡ 5.670400 × 10−8

Enclosure input parameters: Tg = 1500 K T1 = 1000 K ε1 = 0.8 E1 = s ⋅ T14

1 − (T1 /Tg )

tm = 0.3701

W m2 ⋅ K 4

A1 = 190 m ρ1 = 0.2 kW E1 = 56.70 m2

V = 150 m

3

Eg = 287.06

MW

Moles in

CH4 O2 N2 CO2 H2O Totals

16.04 32.00 28.01 44.01 18.02 138.08

1.00000 2.40000 9.02857 0.00000 0.10057 12.52914

Mass in

Moles out

16.04 76.80 252.93 0.00 1.81 347.58

0.00000 0.40000 9.02857 1.00000 2.10057 12.52914

pC = 0.07981 atm

p = pW + pC

Y out 0.00000 0.03193 0.72061 0.07981 0.16765 1.00000

p = 0.2475 atm

The mean beam length is approximated by LM = 0.88⋅4 ⋅ V ÷ A1 pLM = p ⋅ LM

ε gm1

εgm2 = εgm(εg2, ag12, Tg, T1)

εgm2 = 0.3813

LM = 2.7789 m

pLM = 0.6877 atm ⋅ m

am =

−1

ε gm1

ε gm = am ⋅ (1 − τ m )

1 − τm

am = 0.4418

ε ⋅a ⋅s g ⋅ A S1Gm = 1 m 1 m 1 ε1 ⋅ A1 + ρ1 ⋅ s1 g m

εgm = 0.2783 S1Gm = 45.68 m2

SIG m ⋅ ( E1 − E g ) A1

q1m = -55.38

s1gm = (1 - tm) ⋅ A1 s1gm = 119.67 m2

kW m2

The computed flux densities are nearly equal because there is a single sink zone A1. (This example was developed as a MATHCAD 15 worksheet. MATHCAD is a registered trademark of Parametric Technology Corporation.)

Mole Table: Basis 1.0 mol Methane

and

ε gm 2

εgm1 = 0.2783

kW compared with Q1 = -55.07 2 m A1

kW m2

Stoichiometry yields the following mole table:

Species

kW Q1 = -55.07 2 m A1

εgm1 = εgm(εg1, ag11, Tg, T1)

q1m = 2

ρ1 = 1 - ε1 Eg = s ⋅ Tg4

pW = 0.16765 atm pW ÷ pC = 2.101

Q1 = -10,464.0 kW

4

Eq. (5-176a) Physical constants:

DGS1 = 67.32 m2

Case (b): Compute the Flux Density Using Mean Effective Gas Emissivity Approximation

ε g F (T1 , pL ⋅T1 /Tg , b , n ) ⋅T1 ⋅ (Tg /T1 )

ε gm (ε g , α g , Tg , T1 ) =  

a g 1 ⋅ε1 ⋅ A1 ⋅ s1 g ε1 ⋅ A1 + ρ1 ⋅ s1 g

And finally the gas to sink flux density is computed as

Eq. (5-141) Mean effective gas emissivity:

DGS1 =

ε1 ⋅ A1 + ρ1 ⋅ s1 g

pLM = 0.6877

The gas emissivities and absorptivities are then calculated from the two-constant correlation in Table 5-6 (column 5 with pW/pC = 2.0) as follows:

EnGInEERInG MODELS FOR FUEL-FIRED FURnACES Modern digital computation has evolved methodologies for the design and simulation of fuel-fired combustion chambers and furnaces which incorporate virtually all the transport phenomena, chemical kinetics, and thermodynamics studied by chemical engineers. Nonetheless, there still exist many furnace design circumstances where such computational sophistication is not always appropriate. Indeed, a practical need still exists for simple engineering models for purposes of conceptual process design, cost estimation, and the correlation of test performance data. In this section, the zone method is used to develop perhaps the simplest computational template available to address some of these practical engineering needs. Input/Output Performance Parameters for Furnace Operation The term firing density is typically used to define the basic operational input parameter for fuel-fired furnaces. In practice, firing density is often defined as the input fuel feed rate per unit area (or volume) of furnace heat-transfer surface. Thus defined, the firing density is a dimensional quantity. Since the feed enthalpy rate H f is proportional to the feed rate, we employ the sink 4 area A1 to define a dimensionless firing density as N FD = H f /σTRef · A1 where TRef is some characteristic reference temperature. In practice, gross furnace

5-38

HEAT AnD MASS TRAnSFER

output performance is often described by using one of several furnace efficiencies. The most common is the gas or gas-side furnace efficiency ηg , defined as the total enthalpy transferred to furnace internals divided by the total available feed enthalpy. Here the total available feed enthalpy is defined to include the lower heating value (LHV) of the fuel plus any air preheat above an arbitrary ambient datum temperature. Under certain conditions the definition of furnace efficiency reduces to some variant of the simple equation ηg = (TRef − Tout )/(TRef − T0 ) where again TRef is some reference temperature appropriate to the system in question. The Long Plug Flow Furnace (LPFF) Model If a combustion chamber of cross-sectional area Aduct and perimeter Pduct is sufficiently long in the direction of flow, compared to its mean hydraulic radius L >> Rh = Aduct/ Pduct, then the radiative flux from the gas to the bounding surfaces can sometimes be adequately characterized by the local gas temperature. The physical rationale for this is that the magnitudes of the opposed upstream and downstream radiative fluxes through a cross section transverse to the direction of flow are sufficiently large as to substantially balance each other. Such a situation is not unusual in engineering practice and is referred to as the long furnace approximation. As a result, the radiative flux from the gas to the bounding surface may then be approximated using two-dimensional   ∂(S1G ) directed exchange areas S1G /A1 ≡ , calculated using methods as ∂ A1 described previously. Consider a duct of length L and perimeter P, and assume plug flow in the direction of flow z . Further assume high-intensity mixing at the entrance end of the chamber such that combustion is complete as the combustion products enter the duct. The duct then acts as a long heat exchanger in which heat is transferred to the walls at constant temperature T1 by the combined effects of radiation and convection. Subject to the long furnace approximation, a differential energy balance on the duct then yields  dTg  S G mC ɺ p = P  1 σ Tg4 − T14 + h(Tg − T1 )  (5-177) A dz   1

(

 (Tg , in − Tg , out ) ⋅T1   T12 + Tg , in ⋅Tg , out 

(

)

 4 =− Deff  

(5-178)

The long plug flow furnace (LPFF) model is described by only two dimensionless parameters, namely, an effective firing density and a dimensionless sink temperature N Deff =  FD and   Θ1 = T1 /Tg , in  S1G  + N CR  A  1

(5-178a,b)

Here the dimensionless firing density NFD and a dimensionless convectionradiation (CR) namber NCR are defined as N FD =

mC  p σ ⋅T13 A1

h and N CR = 3 4 σT g ,1

(5-178c,d)

where A1 = PL is the duct surface area (the sink area), and Tg,1 = (Tg + T1 )/2 is treated as a constant. This definition of the effective dimensionless firing density Deff clearly delineates the relative roles of radiation and convective heat transfer since radiation and convection are identified as parallel (electrical) conductances. In analogy with a conventional heat exchanger, Eq. (5-178) displays two asymptotic limits. First define ηf =

Tg , in − Tg ,out Tg ,in − T1

= 1−

Tg ,out − T1 Tg ,in − T1

(5-179)

as the efficiency of the long furnace. The two asymptotic limits with respect to firing density are then given by Deff > 1

Tg,out → Tg,in

(5-179a)

4 R −1 R −1 Deff 1 − − 2 2  R +1   R +1

(5-179b)

where R ≡ Tg ,in /T1 = 1/Θ1. For low firing rates, the exit temperature of the furnace gases approaches that of the sink; i.e., sufficient residence time is provided for nearly complete heat removal from the gases. When the combustion chamber is overfired, only a small fraction of the available feed enthalpy heat is removed within the furnace. The exit gas temperature then remains essentially that of the inlet temperature, and the furnace efficiency tends asymptotically to zero. It is important to recognize that the two-dimensional exchange area S1G ∂(S1G ) in the definition of Deff can represent a lumped two≡ ∂ A1 A1 dimensional exchange area of somewhat arbitrary complexity. This quantity also contains all the information concerning furnace geometry and gas and surface emissivities. To compare the relative importance of radiation with respect to convection, suppose h = 10 Btu/(h ⋅ ft2 ⋅ °R) = 0.057 kW/(K ⋅ m2) and Tg ,1 = 1250 K, which leads to the numerical value NCR = 0.128; or, in general, NCR is of order 0.1 or less. The importance of the radiation contribution is estimated by bounding the magnitude of the dimensionless directed exchange area. For the case of a single-gas zone completely surrounded by a black enclosure, Eq. (5-169) reduces to simply S1G /A1 = ε g ≤ 1.0 , and it is evident that the magnitude of the radiation contribution never exceeds unity. At high temperatures, radiative effects can easily dominate other modes of heat transfer by an order of magnitude or more. When mean beam length calculations are employed, use LM/D = 0.94 for a cylindrical cross section of diameter D, and LM 0 =

)

where m is the mass flow rate and C p is the heat capacity per unit mass. Equation (5-177) is nonlinear with respect to temperature. To solve Eq. (5-177), first linearize the convective heat-transfer term in the right-hand side with the approximation ∆T = T2 − T1 ≈ (T24 − T14 )/4T1,23 where T 1,2 = (T1 + T2 )/2. This linearization underestimates ΔT by no more than 5 percent when T2/T1 < 1.59. Integration of Eq. (5-177) then leads to the solution  (Tg , out − T1 )(Tg , in + T1 )  −1 ln   + 2.0tan  (Tg , out + T1 )(Tg , in − T1 ) 

ηf →

2 H ⋅W H +W

for a rectangular duct of height H and width W . The Well-Stirred Combustion Chamber (WSCC) Model Many combustion chambers utilize high-momentum feed conditions with associated high-intensity mixing. The well-stirred combustion chamber (WSCC) model assumes a single-gas zone and high-intensity mixing. Moreover, combustion and heat transfer are visualized to occur simultaneously within the combustion chamber. The WSCC model is characterized by some six temperatures which are listed in rank order as T0, Tair, T1, Te, Tg, and Tf . Even though the combustion chamber is well mixed, it is arbitrarily assumed that the gas temperature within the enclosure Tg is not necessarily equal to the gas exit temperature Te. Rather the two temperatures are related by the simple relation ΔTge ≡ Tg - Te, where ΔTge ≈ 170 K (as a representative value) is introduced as an adjustable parameter for the purposes of data fitting and to make allowance for nonideal mixing. In addition, T0 is the ambient temperature, Tair is the air preheat temperature, and Tf is a pseudoadiabatic flame temperature, as will be explained in the following development. The condition ΔTge ≡ 0 is intended to simulate a perfect continuous well-stirred reactor (CSTR). Dimensional WSCC Approach A macroscopic enthalpy balance on the well-stirred combustion chamber is written as −∆H = H in − H out = Qrad + Qcon + Qref

(5-180)

 Here Qrad = S1G R σ Tg4 − T14 represents radiative heat transfer to the sink (with due allowance for the presence of any refractory surfaces). And the two terms Qcon = h1 A1 (Tg − T1 ) and Qref = UAR (Tg − T0 ) formulate the convective heat transfer to the sink and through the refractory, respectively. Formulation of the left-hand side of Eq. (5-180) requires representative thermodynamic data and information on the combustion stoichiometry. In particular, the former includes the lower heating value of the fuel, the temperature-dependent molal heat capacity of the inlet and outlet streams, and the air preheat temperature Tair. It proves especially convenient now to introduce the definition of a pseudoadiabatic flame temperature Tf , which is not the true adiabatic flame temperature, but rather is an adiabatic flame temperature based on the average heat capacity of the combustion products over the temperature interval T0 < T < Te . The calculation of Tf does not allow for dissociation of chemical species and is a surrogate for the total enthalpy content of the input fuel-air mixture. It also proves to be an especially convenient system reference temperature. Details for the calculation of Tf are illustrated in Example 5-14. In terms of this particular definition of the pseudoadiabatic flame temperature Tf, the total enthalpy change and gas efficiency are given simply as

(

)

∆H = H f − m ⋅C P ,Prod (Te − T0 ) = mC  P ,Prod (T f − Te )

(5-181a,b)

HEAT TRAnSFER BY RADIATIOn where H f ≡ m ⋅C P ,Prod (T f − T0 ) and Te = Tg − ΔTge. This particular definition of Tf leads to an especially convenient formulation of furnace efficiency: ηg = Q /H f =

m ⋅C P ,Prod (T f − Te )

=

 is the total mass flow rate and C P ,Prod [ J/(kg · K)] is defined In Eq. (5-182), m as the average heat capacity of the product stream over the temperature interval T0 < T < Te . The final overall enthalpy balance is then written as  mɺ ⋅C P ,Prod (T f − Te ) = S1G R σ Tg4 − T14 + h1 A1 (Tg − T1 ) + UAR (Tg − T0 )

)

(5-183)

with Te = Tg − ΔTge . Equation (5-183) is a nonlinear algebraic equation which may be solved by a variety of iterative methods. The sole unknown quantity, however, in Eq. (5-183) is the gas temperature Tg. It should be recognized, in particular, that Tf, Te, C P ,Prod , and the directed exchange area are all explicit functions of Tg. The method of solution of Eq. (5-183) is demonstrated in detail in Example 5-14. Dimensionless WSCC Approach In Eq. (5-183), assume the convective heat loss through the refractory is negligible, and linearize the convective heat transfer to the sink. These approximations lead to the result  mɺ ⋅C P ,Prod (T f − Tg + ∆Tge ) = S1G R σ T g4 - T 14 + h1 A1 T g4 - T 14 /4Tg3,1

(

)

(

)

(5-184)

where Tg ,1 = (Tg + T1 )/2 is some characteristic average temperature which is taken as constant. Now normalize all temperatures based on the pseudoadiabatic temperature as in Θi = Ti/Tf . Equation (5-184) then leads to the dimensionless equation Deff (1 − Θ g + ∆ ∗ ) = (Θ 4g   − Θ14 )

(5-185)

 where again Deff = N FD /(S1G R /A1 + N CR ) is defined exactly as in the case of the LPFF model, with the proviso that the WSCC dimensionless firing density is defined here as N FD =   mC  P ,Prod / σT f3 · A1 . The dimensionless furnace efficiency follows directly from Eq. (5-182) as

(

ηg =

)

∗ 1 − Θe 1 − Θ g + ∆ = 1 − Θ0 1 − Θ0

(5-186b)

(5-182)

m ⋅C P ,Prod (T f − T0 ) T f − T0

(

We also define a reduced furnace efficiency η′g as η′g ≡ (1 − Θ 0 ) ⋅η g = 1 − Θ g + ∆ ∗

T f − Te

5-39

(5-186a)

Since Eq. (5-186b) may be rewritten as Θ g = (1 + ∆ ∗ − η′g ) combination of Eqs. (5-185) and (5-186b) yields the final result Deff ⋅ η′g = (1 + ∆ ∗ − η′g ) 4 − Θ14

(5-187)

Equation (5-187) provides an explicit relation between the modified furnace efficiency and the effective firing density directly in which the gas temperature is eliminated. Equation (5-187) has two asymptotic limits Deff 1000) in low-molecular-weight solvents or where the molar volume of the solute is greater than 500 cm3/ mol (Reddy and Doraiswamy, Ind . Eng . Chem . Fundam . 6: 77 (1967); Wilke and Chang [21]). Despite its intellectual appeal, this equation is seldom used “as is.” Rather, the following principles have been identified: (1) The diffusion coefficient is inversely proportional to the size rA  V A1/3 of the solute

molecules. Experimental observations, however, generally indicate that the exponent of the solute molar volume is larger than one-third. (2) The term DAB μB/T is approximately constant only over a 10 to 15 K interval. Thus, the dependence of liquid diffusivity on properties and conditions does not generally obey the interactions implied by that grouping. For example, Robinson, Edmister, and Dullien [Ind . Eng . Chem . Fundam . 5: 75 (1966)] found that ln DAB ∝ −1/T. (3) Finally, pressure does not affect liquid-phase diffusivity much, since μB and VA are only weakly pressure-dependent. Pressure does have an impact at very high levels. Another advance in the concepts of liquid-phase diffusion was provided by Hildebrand [Science 174: 490 (1971)] who adapted a theory of viscosity to self-diffusivity. He postulated that DA′A = B(V − Vms)/Vms, where DA′A is the selfdiffusion coefficient, V is the molar volume, and Vms is the molar volume at which fluidity is zero (i.e., the molar volume of the solid phase at the melting temperature). The difference V − Vms can be thought of as the free volume, which increases with temperature; and B is a proportionality constant. Ertl and Dullien (AIChE J . 19: 1215 (1973)) found that Hildebrand’s equation could not fit their data with B as a constant. They modified it by applying an empirical exponent n (a constant greater than unity) to the volumetric ratio. The new equation is not generally useful, however, since there is no means for predicting n . The theory does identify the free volume as an important physical variable, since n > 1 for most liquids implies that diffusion is more strongly dependent on free volume than is viscosity. Dilute Binary Nonelectrolytes: General Mixtures These correlations are outlined in Table 5-14. Wilke-Chang [22] This correlation for D°AB, which is an empirical modification of the Stokes-Einstein equation, is one of the most widely used. It is not very accurate, however, for water as the solute. Otherwise, it applies to diffusion of very dilute A in B . The average absolute error for 251 different systems is about 10 percent; fB is an association factor of solvent B that accounts for hydrogen bonding. Component B

fB

Water Methanol Ethanol Propanol Others

2.26 1.9 1.5 1.2 1.0

The value of fB for water was originally stated as 2.6, although when the original data were reanalyzed, the empirical best fit was 2.26. Random comparisons of predictions with 2.26 versus 2.6 show no consistent advantage for either value, however. Kooijman [Ind . Eng . Chem . Res . 41: 3326 (2002)] suggests replacing VA with θAVA, in which θA = 1 except when A = water, θA = 4.5. This modification leads to an overall error of 8.7 percent for 41 cases he compared. He suggests retaining fB = 2.6 when B = water. It has been suggested to replace the exponent of 0.6 with 0.7 and to use an association factor of 0.7 for systems containing aromatic hydrocarbons. These modifications, however, are not recommended by Umesi and Danner [Ind . Eng . Chem . Process Des . Dev . 20: 662 (1981)], who developed an equation for nonaqueous solvents with nonpolar and polar solutes. The average absolute deviation was 16 percent, compared with 26 percent for the Wilke-Chang equation. Lees and Sarram [ J . Chem . Eng . Data 16: 41 (1971)] compare the association parameters. The average absolute error for 87 different solutes in water is 5.9 percent. Tyn-Calus [19] This correlation requires data in the form of molar volumes and parachors yi = Visi1/4 (a property which, over moderate temperature ranges, is nearly constant), measured at the same temperature (not necessarily the temperature of interest). The parachors for the components may also be evaluated at different temperatures from one another. Quale [Chem . Rev . 53: 439 (1953)] compiled values of yi for many chemicals. Group contribution methods are available for estimation purposes (Poling et al.). The following suggestions were made by Poling et al.: The correlation is constrained to cases in which μB < 30 cP. If the solute is water or if the solute is an organic acid and the solvent is not water or a short-chain alcohol, then dimerization of solute A should be assumed for purposes of estimating its volume and parachor. For example, the appropriate values for water as solute at 25°C are VW = 37.4 cm3/mol and yW = 105.2 cm3g1/4/s1/2 mol. Finally, if the solute is nonpolar, the solvent volume and parachor should be multiplied by 8μB. According to Kooijman [Ind . Eng . Chem . Res . 41: 3326 (2002)], if the Brock-Bird method (described in Poling et al.) is used to estimate the surface tension, the error is only increased by about 2 percent, relative to employing experimentally measured values. Siddiqi-Lucas [17] In an impressive empirical study, these authors examined 1275 organic liquid mixtures. Their equation yielded an average absolute deviation of 13.1 percent, which was less than that for the WilkeChang equation (17.8 percent). Note that Eq. (5-216) does not encompass aqueous solutions, which are correlated in Eq. (5-218).

MASS TRAnSFER TABLE 5-14

5-51

Correlations for Diffusivities of Dilute, Binary Mixtures of nonelectrolytes in Liquids

Authors∗

Equation

Error

1. General Mixtures Wilke-Chang [21]

o = D AB

Tyn-Calus [19]

o = D AB

Siddiqi-Lucas [17]

o D AB =

7.4 × 10 −8 (φ B M B )1/2 T µ BV A0.6

(5-214)

20%

(5-215)

10%

(5-216)

13%

(5-217)

6%

o D AW = 2.98 × 10 −7 V A−0.5473 µw−1.026T

(5-218)

13%

Hayduk-Minhas [10]

o V A − 0.791) −0.71 D AB = 13.3 × 10 −8 T 1.47 µ (10.2/ VA B

(5-219)

5%

Matthews-Akgerman [15]

o = 32.88 M A−0.61VD−1.04T 0.5 (VB − VD ) D AB

(5-220)

5%

8.93 × 10 −8 (VA / VB2 )1/6 ( ψ B /ψA )0.6 T µB 9.89 × 10 −8 (VB0.265 )T V A0.45 µ 0.907 B

2. Gases in Low-Viscosity Liquids Chen-Chen [6]

o D AB = 2.018 × 10 −9

(βVC B )2/3 ( RTC B )1/2 M

1/6 A

1/3

( M BVC A )

 T  (Vr − 1)    TC B 

1/2

3. Aqueous Solutions Siddiqi-Lucas [17] 4. Hydrocarbon Mixtures

∗References are listed at the beginning of the Mass Transfer subsection.

Binary Mixtures of Gases in Low-Viscosity, Nonelectrolyte Liquids Sridhar and Potter [AIChE J . 23: 4, 590 (1977)] derived an equation for predicting gas diffusion through liquid by combining existing correlations. Hildebrand had postulated the following dependence of the diffusivity for a gas in a liquid: D°AB = DB′B(VcB/VcA)2/3, where DB′B is the solvent self-diffusion coefficient and Vci is the critical volume of component i, respectively. To correct for minor changes in volumetric expansion, Sridhar and Potter multiplied the resulting equation by VB/VmlB, where VmlB is the molar volume of the liquid B at its melting point. They compared experimentally measured diffusion coefficients for 27 data points of 11 binary mixtures. Their average absolute error was 13.5 percent. This correlation demonstrates the usefulness of self-diffusion as a means to assess mutual diffusivities and the value of observable physical property changes, such as molar expansion, to account for changes in conditions. Chen-Chen [6] Their correlation was based on diffusion measurements of 50 combinations of conditions with 3 to 4 replicates each and exhibited an average error of 6 percent. In this correlation, Vr = VB/[0.9724(VmlB + 0.04765)] and VmlB = the liquid molar volume at the melting point, as discussed previously. Their association parameter β [which is different from the definition of that symbol in Eq. (5-221)] accounts for hydrogen bonding of the solvent. Values for acetonitrile and methanol are β = 1.58 and 2.31, respectively. Dilute Binary Mixtures of a Nonelectrolyte in Water The correlations that were suggested previously for general mixtures, unless specified otherwise, may also be applied to diffusion of miscellaneous solutes in water. The following correlations are restricted to aqueous systems. Hayduk and Laudie [AIChE J . 20: 3, 611 (1974)] presented a simple correlation for the infinite dilution diffusion coefficients of nonelectrolytes in water. It has about the same accuracy as the Wilke-Chang equation (about 5.9 percent). There is no explicit temperature dependence, but the variation in water viscosity compensates for the absence of temperature. Siddiqi and Lucas [17] These authors examined 658 aqueous liquid mixtures in an empirical study. They found an average absolute deviation of 19.7 percent. In contrast, the Wilke-Chang equation gave 35.0 percent and the Hayduk-Laudie correlation gave 30.4 percent. Dilute Binary Hydrocarbon Mixtures Hayduk and Minhas [10] presented an accurate correlation for normal paraffin mixtures that was developed from 58 data points consisting of solutes from C5 to C32 and solvents from C5 to C16. The average error was 3.4 percent for the 58 mixtures. Matthews and Akgerman [15] The free-volume approach of Hildebrand was shown to be valid for binary, dilute liquid paraffin mixtures (as well as self-diffusion), consisting of solutes from C8 to C16 and solvents of C6 and C12. The term they referred to as the “diffusion volume” was simply correlated with the critical volume, as VD = 0.308Vc. We can infer from Table 5-11

that this is approximately related to the volume at the melting point as VD = 0.945Vm. Their correlation was valid for diffusion of linear alkanes at temperatures up to 300°C and pressures up to 3.45 MPa. Matthews, Rodden, and Akgerman [ J . Chem . Eng . Data 32: 317 (1987)] and Erkey and Akgerman [AIChE J . 35: 443 (1989)] completed similar studies of diffusion of alkanes, restricted to n-hexadecane and n-octane, respectively, as the solvents. Riazi and Whitson [Ind . Eng . Chem . Res . 32: 3081 (1993)] presented a generalized correlation in terms of viscosity and molar density that was applicable to both gases and liquids. The average absolute deviation for gases was only about 8 percent, while for liquids it was 15 percent. Their expression relies on the Chapman-Enskog correlation [Eq. (5-200)] for the low-pressure diffusivity and correlations for low-pressure viscosity. Dilute Binary Mixtures of Nonelectrolytes with Water as the Solute Olander [AIChE J . 7: 175 (1961)] modified the Wilke-Chang equation to adapt it to the infinite dilution diffusivity of water as the solute. The modification he recommended is simply the division of the right-hand side of the Wilke-Chang equation by 2.3. Unfortunately, neither the Wilke-Chang equation nor that equation divided by 2.3 fit the data very well. A reasonably valid generalization is that the Wilke-Chang equation is accurate if water is very insoluble in the solvent, such as pure hydrocarbons, halogenated hydrocarbons, and nitro-hydrocarbons. On the other hand, the Wilke-Chang equation divided by 2.3 is accurate for solvents in which water is very soluble, as well as those that have low viscosities. Such solvents include alcohols, ketones, carboxylic acids, and aldehydes. Neither equation is accurate for higher-viscosity liquids, especially diols. Dilute Dispersions of Macromolecules in Nonelectrolytes The Stokes-Einstein equation predicts accurately the diffusion coefficient of spherical latex particles and globular proteins. Corrections to Stokes-Einstein for molecules approximating spheroids are given by Tanford [Physical Chemistry of Macromolecules, Wiley, New York, 1961]. Since solute-solute interactions are ignored in this theory, it applies in the dilute range only. Hiss and Cussler [AIChE J . 19: 698 (1973)] Their basis is the diffusion of a small solute in a fairly viscous solvent of relatively large molecules, which is the opposite of the Stokes-Einstein assumptions. The large solvent molecules investigated were not polymers or gels but were of moderate molecular weight so that the macroscopic and microscopic viscosities were the same. The major conclusion is that D°AB μ2/3 = constant at a given temperature and for a solvent viscosity from 5 × 10−3 to 5 Pa ⋅ s or greater (5 to 5 × 103 cP). This observation is useful if D°AB is known in a given high-viscosity liquid (oils, tars, etc.). Use of the usual relation of D°AB ∝ 1/μ for such an estimate could lead to large errors. Concentrated Binary Mixtures of Nonelectrolytes Since the infinite dilution values D°AB and D°BA are generally unequal, even a thermodynamically

5-52

HEAT AnD MASS TRAnSFER

ideal solution like gA = gB = 1 will exhibit concentration dependence of the diffusivity. In addition, nonideal solutions require the following thermodynamic correction factor because the true “driving force” is the chemical potential gradient, not the composition gradient. βA = 1+

∂ ln γ A ∂ ln x A

(5-221)

Darken [Trans . Am . Inst . Mining Met . Eng . 175: 184 (1948)] observed that solid-state diffusion in metallurgical applications followed a simple relation. His equation related the tracer diffusivities and mole fractions to the mutual diffusivity: DAB = (xADB + xBDA)βA

(5-222)

Several correlations that predict the composition dependence of DAB are summarized in Table 5-15. Most are based on known values of D°AB and D°BA. In fact, a rule of thumb states that, for many binary systems, D°AB and D°BA bound the DAB vs. xA curve. Caldwell and Babb [4]  used virtually Darken’s equation to evaluate the mutual diffusivity for concentrated mixtures of common liquids . Van Geet and Adamson [ J . Phys . Chem . 68: 238 (1964)] tested that equation for the n-dodecane (A) and n-octane (B) system and found the average deviation of DAB from experimental values to be -0 .68 percent . Additional tests showed Eq . (5-223) can be expected to be fairly accurate for nonpolar hydrocarbons of similar molecular weight . For systems that depart significantly from thermodynamic ideality, such as polar-polar mixtures, it breaks down, sometimes by a factor of 8 . Siddiqi, Krahn, and Lucas [ J . Chem . Eng . Data 32: 48 (1987)] found that this relation was superior to those of Vignes and Leffler and Cullinan for a variety of mixtures . Umesi and Danner [Ind . Eng . Chem . Process Des . Dev . 20: 662 (1981)] found an average absolute deviation of 13 .9 percent for 198 data points . Rathbun and Babb [16] suggested that Darken’s equation could be improved by raising the thermodynamic correction factor βA to a power n less than unity . They looked at systems exhibiting negative deviations from Raoult’s law and found n = 0 .3 . Furthermore, for polar-nonpolar mixtures, they found n = 0 .6 . Siddiqi and Lucas [17] followed those suggestions and found an average absolute error of 3 .3 percent for nonpolar-nonpolar mixtures, 11 .0 percent for polar-nonpolar mixtures, and 14 .6 percent for polarpolar mixtures . Siddiqi, Krahn, and Lucas [ J . Chem . Eng . Data 32: 48 (1987)] examined a few other mixtures and found that n = 1 was probably best . Thus, this approach is, at best, highly dependent on the type of components . Vignes [20] empirically correlated mixture diffusivity data for 12 binary mixtures . Later Ertl, Ghai, and Dollon [AIChE J . 20: 1 (1974)] evaluated

122 binary systems, which showed an average absolute deviation of only 7 percent . None of the latter systems, however, was very nonideal . Leffler and Cullinan [13] modified Vignes’ equation using theoretical arguments to arrive at Eq . (5-226), which the authors compared to Eq . (5-225) for the 12 systems mentioned above . The average absolute maximum deviation was only 6 percent . Umesi and Danner [Ind . Eng . Chem . Process Des . Dev . 20: 662 (1981)], however, found an average absolute deviation of 11 .4 percent for 198 data points . For normal paraffins, it is not very accurate . In general, the accuracies of the two equations are not much different, and since Vignes’ equation is simpler to use, it is suggested . The application of either should be limited to nonassociating systems that do not deviate much from ideality (0 .95 < βA < 1 .05) . Cussler [8] showed that in concentrated associating systems it is the size of diffusing clusters rather than diffusing solutes that controls diffusion . Do is a reference diffusion coefficient discussed hereafter; aA is the activity of component A; and K is a constant . By assuming that Do could be predicted by Eq . (5-225) with β = 1, K was found to be equal to 0 .5 based on five binary systems and validated with a sixth binary mixture . The limitations of Eq . (5-227) using Do and K defined previously have not been explored, so caution is warranted . Gurkan [AIChE J . 33: 175 (1987)] showed that K should actually be closer to 0 .3 (rather than 0 .5) and discussed the overall results . Cullinan [7] presented an extension of Cussler’s cluster diffusion theory that contains no adjustable constants, does not use diffusivity values at infinite dilution, and relates transport properties and solution thermodynamics . His method accurately accounts for composition and temperature dependence of diffusivity; however, it requires accurate density, viscosity, and activity coefficient data . This equation has been tested for six very different mixtures by Rollins and Knaebel [AIChE J . 37: 470 (1991)], and it was found to agree remarkably well with data for most conditions, considering the absence of empirical parameters (including diffusivity values) . In the dilute region (of either A or B), there are systematic errors probably caused by the breakdown of certain implicit assumptions (that nevertheless appear to be generally valid at higher concentrations) . Asfour and Dullien [1] developed a relation for predicting alkane diffusivities at moderate concentrations that employs  V fm  ζ=   Vfx A V fx B 

Equation o o D AB = ( x A D BA + x B D AB )β A

(5-223)

Rathbun-Babb [16]

o o D AB = ( x A D BA )βnA + x B D AB

(5-224)

Vignes [20]

ox B ox A D AB = D AB D BA βA

(5-225)

Leffler-Cullinan [13]

o o D AB µ mix = ( D AB µ B ) x B ( D BA µ A )x A β A

(5-226)

Cussler [8]

 K  ∂ ln x A   − 1  D AB = D0 1 +   x A x B  ∂ ln a A  

Cullinan [7]

D AB =

Asfour-Dullien [1]

 Do  D AB =  AB   µB 

−1/2

(5-227) 1/2

  kT 2 πx A x B β A   2 πµ mix (V / A )1/3  1 + β A (2 πx A x B − 1)  xB

(5-228)

xA

o  D BA   µ  ζµβ A

(5-229)

A

Siddiqi-Lucas [17]

o o D AB = (C B V B D AB + C A V A DBA )βA

Bosse and Bart no . 1 [2]

 g  ∞ XB ∞ XA D AB = ( D AB ) ( D AB ) exp  −  RT 

Bosse and Bart no . 2 [2]

 g  ∞ XB ∞ XA µD AB = (µβD AB ) (µ A D BA ) exp  −  RT 

(5-230)

E

(5-231) E

(5-232)

Relative errors for the correlations in this table are very dependent on the components of interest and are cited in the text . ∗See the beginning of the Mass Transfer subsection for references .

(5-233a)

Mm

 x 2 2x x x2  Vmlm =  A + A B + B   Vml A Vml AB Vml B 

and

Caldwell-Babb [4]

M xA M xB

where Vfxi = Vfixi; the fluid free volume is Vfi = Vi − Vmli for i = A, B, and m, in which Vmli is the molar volume of the liquid at the melting point and

TABLE 5-15 Correlations of Diffusivities for Concentrated, Binary Mixtures of nonelectrolyte Liquids Authors∗

2/3

 Vml1/3 + Vml1/3B  Vml AB =  A  2  

−1

(5-233b)

3

(5-233c)

and m is the mixture viscosity, Mm is the mixture mean molecular weight, and βA is defined by Eq . (5-221) . The average absolute error of this equation is 1 .4 percent, while the Vignes equation and the Leffler-Cullinan equation give 3 .3 percent and 6 .2 percent, respectively . Siddiqi and Lucas [17] suggested that component volume fractions might be used to correlate the effects of concentration dependence . They found an average absolute deviation of 4 .5 percent for nonpolar-nonpolar mixtures, 16 .5 percent for polar-nonpolar mixtures, and 10 .8 percent for polar-polar mixtures . Bosse and Bart [2] added a term to account for excess Gibbs free energy, involved in the activation energy for diffusion, which was previously omitted . Doing so yielded minor modifications of the Vignes and LefflerCullinan equations [Eqs . (5-225) and (5-226), respectively] . The UNIFAC method was used to assess the excess Gibbs free energy . Comparing predictions of the new equations with data for 36 pairs and 326 data points yielded relative deviations of 7 .8 percent and 8 .9 percent, respectively, but which were better than the closely related Vignes (12 .8 percent) and LefflerCullinan (10 .4 percent) equations . Binary Electrolyte Mixtures When electrolytes are added to a solvent, they dissociate to a certain degree . It would appear that the solution contains at least three components: solvent, anions, and cations . If the solution is to remain neutral in charge at each point (assuming the absence of any applied electric potential field), the anions and cations diffuse effectively as a single component, and diffusion can thus be treated as a binary mixture .

MASS TRAnSFER Nernst-Haskell The theory of dilute diffusion of salts is well developed and has been experimentally verified. For dilute solutions of a single salt, the well-known Nernst-Haskell equation (Poling et al.) is applicable:

D

° AB

1 1 + RT n+ n− = 8.9304 × 10 −10 T F2 1 + 1 λ +0 λ −0

1 1 + n+ n− 1 1 + λ +0 λ −0

(5-234)

(z

−

z+ + z− /D+ ) + ( z + /D− )

1 µ B  ln γ ±  1+  C BV B µ  ln m 

(5-235)

(5-236)

o where D AB is given by the Nernst-Haskell equation . References that tabulate γ± as a function of m, as well as other equations for DAB, are given by Poling et al . Morgan, Ferguson, and Scovazzo [Ind . Eng . Chem . Res . 44: 4815 (2005)] studied diffusion of gases in ionic liquids having moderate to high viscosity (up to about 1000 cP) at 30°C . Their range was limited, and the empirical equation they found was

  1 D AB = 3.7 × 10 −3  0.59  µ B V A ρ2B 

(5-237)

which yielded a correlation coefficient of 0 .975 . Of the estimated diffusivities 90 percent were within ±20 percent of the experimental values . The exponent for viscosity approximately confirmed the observation of Hiss and Cussler [AIChE J . 19: 698 (1973)] . Example 5-15 Diffusivity Estimation

a . Estimate the diffusivity of naphthalene (A) in nitrogen (B) at 30°C and 1 atm (abs) . 1 . Chapman-Enskog equation (refer to Table 5-11, Eqs . (5-200), (5-210), and (5-211a), and Table 5-12) . We will use properties of naphthalene (MA = 128 .17) at its melting point (353 .5 K, ρLA = 0 .973 g/cm3), and nitrogen (MB = 28 .01) at its boiling point (77 .4 K, ρLB = 0 .804 g/cm3) for estimation of parameters: εA/k = 1 .92 × 353 .5 = 678 .72 K, σ A = 1.222 (128.17/0.973)1/3 = 6.22 Å εB/k = 1 .15 × 77 .4 = 89 .01 K, σ B = 1.18 (28.01/0.804)1/3 = 3.85 Å Note that Svehla’s (Svehla, R . A ., NASA Tech . Rep . R-132, Lewis Research Ctr ., Cleveland, Ohio, 1962) values for air are εB/k = 78 .6 K and sB = 3 .711 Å . 1/2

1/2

εAB/k = (εAεB) /k = (678 .72 × 89 .01) = 245 .79 K sAB = (6 .22 + 3 .85)/2 = 5 .04 Å T ∗ = kT/εAB = 303 .2/245 .79 = 1 .234 ΩD = (44 .54T ∗−4 .909 + 1 .911T ∗−1 .575)0 .10 = 1 .056 D AB =

0 .0000 0 .1960 0 .4919 0 .7991 1 .0000

0 .6529 1 .5578 1 .3509 0 .8768 0 .7143

ρ (kg/m3) 992 .214 984 .062 962 .324 940 .222 929 .435

xDMF

DAB (105 cm2/s)

0 .05013 0 .5064 0 .9581

1 .653 1 .482 2 .751

VA = 73 .09/0 .9294 = 78 .64 cm3/gmol

where |z±| represents the magnitude of the ionic charge and where the cationic or anionic diffusivities are D± = 8.9304 × 10−10 Tλ±/|z±| cm2/s and λ± are the infinite dilution conductances of cation and anion. In practice, the equivalent conductance of the ion pair of interest would be obtained and supplemented with conductances of permutations of those ions and one independent cation and anion. This would allow determination of all the ionic conductances and hence the diffusivity of the electrolyte solution. According to Gordon [ J . Phys . Chem. 5: 522 (1937)] typically, as the concentration of a salt increases from infinite dilution, the diffusion coefficient decreases rapidly from D°AB . As concentration is increased further, however, DAB rises steadily, often becoming greater than D°AB . Gordon proposed the following empirical equation, which is applicable up to concentrations of 2N: o D AB = D AB

μ (cP)

1 . ξB = 2 .26, MA = 73 .09 g/mol, MB = 18 .016 g/mol, μB = 0 .6529 cP

where D°AB = diffusivity based on molarity rather than normality of dilute salt A in solvent B, cm2/s. The previous equations can be interpreted in terms of ionic-species diffusivities and conductivities. The latter are easily measured and depend on temperature and composition. The resulting equation of the electrolyte diffusivity is D AB =

xDMF

5-53

0.001858 × 303.2 3/2 × [(1/128.17) + (1/29.0)]1/2 = 0.06066 cm 2 /s 1 × σ 2AB × Ω D

b . Estimate the diffusivities of dimethylformamide (DMF = C3H7NO = A) in water (B) at 40°C (313 .15 K) using the Wilke and Chang method (Table 5-14, Eq . (5-214)) and the following property data .

DAB =1 .17 × 10−13 (ξB MB)1/2 T/(μB (ϕVA)0 .6) = 1 .651 × 10−5 cm2/s The experimental value is 1 .65 × 10−5 cm2/s . 2 . H2O in DMF ( following Kooijman’s suggestions): ξB = 2 .6 MA = 18 .016 g/mol MB = 73 .09 g/mol μB = 0 .7143 cP ϕVA = 4 .5 × 18 .016/0 .9922 = 78 .64 cm3/gmol DAB =1 .17 × 10−13 (ξBMB)1/2 T/(μBVA0 .6) = 3 .185 × 10−5 cm2/s The experimental value is 2 .75 × 10−5 cm2/s .

MAXWELL-STEFAn AnALYSIS Fick’s law was originally developed for dilute binary diffusion based on analogy to Fourier’s law, and then it was successfully extended to concentrated solutions . Although Fick’s law has been extended to ternary mixtures, the resulting equations, except for a few special cases, are complex and require additional diffusivity values, some of which may be negative to fit experimental data . The Maxwell-Stefan (M-S) and Fickian analyses give identical results for binary systems, and the choice of which to use becomes one of personal preference . For multicomponent gas systems, the M-S method has clear advantages that are outlined in this section . Curtis and Bird [Ind . Eng . Chem . Res . 38: 2515 (1999)] reconciled the multicomponent Fick’s law approach with the more elegant M-S theory . In the late 1800s, the development of the kinetic theory of gases led to a method developed by Maxwell and Stefan for calculating multicomponent gas diffusion (e .g ., the flux of each species in a mixture) . The M-S diffusion equations for Nc components in a reference system moving at the average molar velocity are simpler in principle than extensions of Fick’s law since they employ binary diffusivities: Nc

∇x i = ∑ j =1

1 (xi N j − x j N i ) cDij

(5-238)

For ideal gases, the values Dij of this equation are equal to the binary diffusivities for the ij pairs, which are identical to the Fickian diffusivities, Equation (5-238) can be solved for Nc - 1 independent fluxes . An additional equation (called a “bootstrap” equation) based on the movement of the reference system or the reaction stoichiometry is needed to determine all Nc fluxes . For example, for equimolar counterdiffusion this Nc

expression is

∑( N ) = 0 . j

j =1

A study of ternary gas diffusion showed that the M-S equations predicted the experimental results within the experimental error [Duncan and Toor, AIChE J . 8: 38 (1962)] . These predictions include a zero component flux despite the presence of that component’s concentration gradient, a finite component flux with no component concentration gradient, and flux of a component in the direction opposite the component’s concentration gradient . Simplified solutions for ternary diffusion of ideal gases with equimolal counterdiffusion are shown later in Examples 5-15 and 5-16 . For nonideal systems the generalized form of the driving forces is based on the derivative of the chemical potential μi (see Taylor and Krishna, Wesselingh and Krishna, Datta and Vilekar [Chem . Eng . Sci . 65: 5976 (2010)] and Krishna and Wesselingh [Chem . Eng . Sci . 52: 861 (1997)]): xi ∇µ i RT

Nc

T,p

1 (xi N j − x j N i ) cD j =1 ij

=∑

(5-239)

For liquids activity coefficients are included in the M-S equations Nc  x i ∂γ i  1  1 + γ ∂ x  ∇x i = ∑ cD ( x i N j − x j N i ) j =1 i i ij

(5-240)

Although in principle extension of the M-S equations to nonideal liquid systems is straightforward, in practice the need for extensive activity coefficient data and the variability of the Dij can prove daunting .

5-54

HEAT AnD MASS TRAnSFER

Almost all reported diffusivities are based on the Fickian model. The relationship between binary Fickian and M-S diffusivities is Dij =

Dij x i ∂γ i 1+ γ i ∂xi

(5-241)

The Fickian and M-S binary diffusivities are equal at the infinite dilution limit and for ideal systems. The generalized form of the M-S equations in terms of the gradient of the chemical potential can include electromagnetic effects and thermal and pressure diffusion. Since electroneutrality can be included, the M-S method may be applied to electrolyte diffusion [Kraaijeveld, Wesselingh, and Kuiken, Ind . Eng . Chem . Res . 33: 750 (1994)]. Ordinary molecular diffusion and pressure and thermal diffusion in multicomponent mixtures have been studied [Ghorayeb and Firoozabadi, AIChE J . 46: 883 (2000)]. Approximate solutions have been developed by linearization [Toor, H. L., AIChE J . 10: 448 and 460 (1964); Stewart and Prober, Ind . Eng . Chem . Fundam . 3: 224 (1964)]. Those differ in details but yield about the same accuracy as Smith and Taylor [Ind . Eng . Chem . Fundam . 22: 97 (1983)] . More recently, efficient algorithms for solving the equations exactly have been developed; see Benitez, Taylor and Krishna, Krishnamurthy and Taylor [Chem . Eng . J . 25: 47 (1982)] and Taylor and Webb [Comput . Chem . Eng . 5: 61 (1981)]. Amundson, Pan, and Paulson [AIChE J . 48: 813 (2003)] presented numerical methods for coping with mixtures having four or more components, which are nearly intractable via the analytical M-S method. An even simpler approach than solving the M-S differential equations is to use difference equations (see Wesselingh and Krishna, and Wankat [114]). For a ternary system with mass transfer in the z direction the difference equation is  x A ∂γ A  ∆x A x B N A ,z − x A N B ,z xC N A ,z − x A N C ,z −  1 + γ ∂ x  ∆z = − cD AB cD AC A A

(5-242)

with equivalent equations for the other components. The bars indicate evaluation of the terms at the average conditions. For ideal gases this equation simplifies to c

y N − y A N B ,z y C N A ,z − y A N C ,z ∆y A = − B A ,z − D AB D AC ∆z

(5-243)

Although difference equation solutions are approximate, they show typical multicomponent behavior. The solutions can be made more exact by including additional ∆z segments. The M-S equations are often used for multicomponent gas mixtures because each Dij is practically independent of composition by itself and in a multicomponent mixture. This procedure is illustrated with the difference equation formulation in Example 5-16. Example 5-16 Maxwell-Stefan Diffusion Without a Gradient Two identical large glass bulbs are filled with gases and connected by a capillary tube that is d = 0.0090 m long. Bulb 1 at z = 0 contains the following mole fractions: yair = 0.620, yH2 = 0.380, and yNH3 = 0.000. Bulb 2 at z = δ contains yair = 0.620, yH2 = 0.000, and yNH3 = 0.380. Operation is assumed to be at pseudo- (or quasi-) steady state. The pressure and temperature are uniform at 1.5 atm and 273 K, respectively. Diffusivity values at 1.0 atm and 273 K are Dair-H2 = 0.611, Dair-NH3 = 0.198, and DH2-NH3 = 0.748 cm2/s. Assume the gases are ideal. Estimate the fluxes of the three components using the M-S difference equation formulation. Solution Let A = air, B = hydrogen, and C = ammonia. Since Dp = constant, D (1.5 atm) = D (1 atm)/(1.5 atm). At pseudo-steady state, mole fractions at the boundaries are constant (e.g., yair = 0.620 at z = 0 and yair = 0.620 at z = δ so that ∆yair = 0.00). Since temperature and pressure are constant and the molar densities of ideal gases are equal, the system has equimolar counterdiffusion and the total flux is zero, NC = −NA − NB. Substitute this expression into Eq. (5-243) and the equivalent equation for B.  y  y ρm ∆y A y y  y  = − B + C + A  N A +  A - A  N B ∆z  D AB D AC D AC   D AB D AC 

(5-244a)

 y ρm ∆y B  y B y  y y  = − B NA − A + C + B  NB ∆z  DBA DBC   DBA DBC DBC 

(5-244b)

Determine NB from the first equation and NA from the second. ρm ∆y A  y B y y  + + C + A NA ∆z  D AB D AC D AC  NB =  yA yA   D − D  AB AC

(5-245a)

ρm ∆y B  y A y y  + + C + B NB ∆z  D BA DBC DBC  NA =  yB yB   D − D  BA BC

(5-245b)

Input these equations and the values for mole fractions at the boundaries, diffusivities, ρm from ideal gas law, and ∆z = δ into a spreadsheet. Guess a value for NA,guess, calculate NA,calc and NB,calc, and use Goal Seek to make NA,guess − NA,calc = 0 by changing the value of NA,guess. Then NC = −(NA + NB). Results Nair = −5.846 × 10-5, NH2 = 1.216 × 10-4, and NNH3 = -6.312 × 10−5 kmol/(m2s). The transfer rates = N × (area of capillary tube). As expected, hydrogen diffuses in the positive direction and ammonia in the negative direction. The surprise is the substantial negative diffusion rate of air despite a Fickian driving force of zero. The air diffusion is caused by the friction of the ammonia.

Example 5-17 Maxwell-Stefan Diffusion Counter to Gradient Repeat Example 5-16, but bulb 2 at z = d contains yair = 0.610, yH2 = 0.010, and yNH3 = 0.380. Solution The solution approach is identical to that of Example 5-16, and the same spreadsheet is used with different mole fractions in bulb 2. Results Nair = -5.561 × 10-5, NH2 = 1.1850 × 10-4, and NNH3 = -6.289 × 10-5 kmol/(m2s). Since air and hydrogen have gradients in the same direction, extrapolation of binary Fickian diffusion would lead us to expect diffusion of these gases in the same direction. However, because of friction with ammonia, the diffusion of air is in the same direction as the ammonia. The spreadsheet can be used for other ideal gas, ternary diffusion systems with equimolal counterdiffusion that are at either steady state or pseudosteady state. Kmit and Shah [Chem . Eng . Educ . 30(1): 14 (1996)] have a detailed discussion of when pseudo-steady state is valid. Multicomponent Liquid Mixtures Most liquid mixtures are not ideal, and each Dij can be strongly composition-dependent in binary mixtures; moreover, the binary Dij are strongly affected in a multicomponent mixture (see Taylor and Krishna). Several theories have been developed for predicting multicomponent liquid-diffusion coefficients, but the necessity for extensive activity data, pure component and mixture volumes, mixture viscosity data, and tracer and binary diffusion coefficients has significantly limited the utility of the theories (see Poling et al.). One particular case of multicomponent liquid diffusion that is somewhat tractable is the dilute diffusion of a solute in a homogeneous mixture (e.g., of A in B + C). Umesi and Danner [Ind . Eng . Chem . Process Des . Dev . 20: 662 (1981)] compared the three equations given below for 49 ternary systems. All three equations were equivalent, giving average absolute deviations of 25 percent. Perkins and Geankoplis [Chem . Eng . Sci . 24: 1035 (1969)] suggested the following empirical equation as an extension of the Caldwell-Babb [4] equation, in order to take into account variations in viscosity in multicomponent mixtures. n

o 0.8 Damµ 0.8 m = ∑ x j D Aj µ j

(5-246)

j =1 j≠ A

Cullinan [Can . J . Chem . Eng . 45: 377 (1967)] extended Vignes’ equation to multicomponent systems: n

( )

Dam = ∏ D Ajo j =1 j≠ A

xj

(5-247)

Leffler and Cullinan [13]  extended their binary relation to an arbitrary multicomponent mixture: n

(

Damµ m = ∏ D Ajo µ j j =1 j≠ A

)

xj

(5-248)

where DAj is the dilute binary diffusion coefficient of A in j ; Dam is the dilute diffusion of a through m; xj is the mole fraction; μj is the viscosity of component j; and μm is the mixture viscosity . Dilute multicomponent diffusion of gases in aqueous electrolyte solutions is of significant practical interest because many gas absorption processes use electrolyte solutions . Akita [Ind . Eng . Chem . Fundam . 10: 89 (1981)] presents experimentally tested equations for this case . Multicomponent diffusion of electrolytes is important in ion exchange . Graham and Dranoff [Ind . Eng . Chem . Fundam . 21: 360, 365 (1982)] found that the M-S interaction coefficients reduce to limiting ion tracer diffusivities of each ion . Pinto and Graham [AIChE J . 32: 291 (1986) and 33: 436 (1987)] corrected for solvation effects in multicomponent diffusion in electrolyte solutions . They achieved excellent results for 1-1 electrolytes in water at 25°C up to concentrations of 4M .

MASS TRAnSFER DIFFUSIOn OF FLUIDS In POROUS SOLIDS Diffusion in porous solids is usually the most important factor controlling mass transfer in adsorption, ion exchange, drying, heterogeneous catalysis, leaching, and many other applications. Some of the applications of interest are outlined in Table 5-16. Applications of these equations are found in Secs. 16, 22, and 23. Diffusion within the largest cavities of a porous medium is assumed to be similar to ordinary or bulk diffusion except that it is hindered by the pore walls [see Eq. (5-249)]. The tortuosity τ that expresses this hindrance was originally estimated from geometric arguments. Unfortunately, measured values are often an order of magnitude greater than those estimates. Thus, the effective diffusivity Deff (and hence τ) is normally determined by comparing a diffusion model to experimental measurements. The normal range of tortuosities for silica gel, alumina, and other porous solids is 2 ≤ τ ≤ 6, but for activated carbon, 5 ≤ τ ≤ 65. In small pores and at low pressures, the mean free path  of the gas molecule (or atom) is significantly greater than the pore diameter dpore. Its magnitude may be estimated from =

3.2µ  RT    P  2 πM 

1/2

m

(5-261)

As a result, collisions with the wall occur more frequently than with other molecules. This is referred to as the Knudsen mode of diffusion and is

5-55

contrasted with ordinary or bulk diffusion, which occurs by intermolecular collisions. At intermediate pressures, both ordinary diffusion and Knudsen diffusion may be important [see Eqs. (5-252) and (5-253)]. For gases and vapors that adsorb on the porous solid, surface diffusion may be important, particularly at high surface coverage [see Eqs. (5-254) and (5-257)]. The mechanism of surface diffusion may be viewed as molecules hopping from one surface site to another. Thus, if adsorption is too strong, surface diffusion is impeded, while if adsorption is too weak, surface diffusion contributes insignificantly to the overall rate. Surface diffusion and bulk diffusion usually occur in parallel [see Eqs. (5-258) and (5-259)]. Although Ds is expected to be less than Deff, the solute flux due to surface diffusion may be larger than that due to bulk diffusion if ∂qi/∂z >> ∂Ci/∂z . This can occur when a component is strongly adsorbed and the surface coverage is high. For all that, surface diffusion is not well understood. The references in Table 5-15 should be consulted for further details. For multicomponent diffusion in porous media the M-S formulation should be employed for combinations of ordinary, Knudsen, and surface diffusion (see Krishna, Gas Separ . Purific . 7(2): 91 (1993)). InTERPHASE MASS TRAnSFER Transfer of material between phases is important in most separation processes in which two phases are involved. In this section, mass transfer between gas and liquid phases is discussed. The principles are easily applied to other phases. When one phase is pure, mass transfer in the pure phase

TABLE 5-16 Relations for Diffusion in Porous Solids Mechanism

Equation εpD

Bulk diffusion in pores

Deff =

Knudsen diffusion

T DK = 48.5 d pore    M

τ

DK eff =

in m 2 /s

(5-250)

Dilute (low pressure) gases in small pores. NKn = /dpore > 10

Geankoplis, [25, 26]

dCi dz

(5-251)

" "

" "

(5-252)

" "

" "

−1

NB NA −1

NA = NB

(5-254)

Adsorbed gases or vapors

τ

(5-255)

" "

DSθ=0 (1 − θ)

(5-256)

θ = fractional surface coverage ≤ 0.6

−E DS = DS′ (q ) exp  S   RT 

(5-257)

" "

" "

dp dq   J = −  Deff  i  + DSeff ρ p  i    dz    dz  

(5-258)

" "

" "

dp J = − Dapp  i   dz 

(5-259)

" "

" "

 dq  Dapp = Deff + DSeff ρ p  i   dpi 

(5-260)

" "

" "

dq J si = − DSeff ρ p  i   dz 

DSθ =

Geankoplis, [23, 26]

NA ≠ NB

(5-253)

DSeff =

Parallel bulk and surface diffusion

[24]

τ

 1 1  Deff =  +  Deff DKeff  Surface diffusion

Gases or liquids in large pores. NKn = /dpore < 0.01

1/2

 1 − αx A 1  Deff =  + DKeff   Deff α =1+

(5-249)

ε p DK

N i = − DK

Combined bulk and Knudsen diffusion

References∗

Applies to

ε p DS

[23, 25, 26]

" "

[25]

∗Author names refer to the General References list at the beginning of the Mass Transfer subsection (pp. 5-41, 5-42). Bracketed numbers refer to the table reference lists (p. 5-42).

5-56

HEAT AnD MASS TRAnSFER where LM = molar liquid velocity, GM = molar gas velocity, HL = height of 1 transfer unit based on liquid-phase resistance, Eq. (5-283), and HG = height of 1 transfer unit based on gas-phase resistance, Eq. (5-281). The interfacial mole fractions yi and xi can be determined by solving Eq. (5-265) simultaneously with the equilibrium relation y i* = F (xi) to obtain yi and xi. The rate of transfer may then be calculated from Eq. (5-263). Equation (5-265) may be solved graphically if a plot is made of the equilibrium vapor and liquid compositions and a point representing the bulk concentrations x and y is located on this diagram. This construction is shown in Fig. 5-25, which represents a gas absorption situation. If the equilibrium relation y i* = F (xi) is linear, not necessarily through the origin, the rate of transfer is proportional to the difference between the bulk concentration in one phase and the concentration (in that same phase), which would be in equilibrium with the bulk concentration in the second phase. One such difference is y - y ∗, and another is x ∗ - x . In this case, there is no need to solve for the interfacial compositions, as may be seen from the following derivation. The rate of mass transfer may be defined by the equation

FIG. 5-24 Concentration gradients near a gas-liquid interface.

NA = KG( y - y ∗) = kG( y - yi) = kL(xi - x) = KL(x ∗ - x) is not involved. For example, when a pure liquid is being evaporated into a gas, only the gas-phase mass transfer need be calculated. When phases are not pure, the gas phase consists of an insoluble carrier gas plus solute A, and the liquid phase consists of a nonvolatile solvent plus solute A. Thus, mass transfer in each phase is binary. When the resistance to mass transfer is much larger in one phase than in the other, mass transfer in the phase with low resistance may be neglected even though pure components are not involved. Understanding the nature and magnitudes of these resistances is one of the keys to performing reliable mass-transfer analyses. Mass-Transfer Principles: Dilute Systems When material is transferred from one phase to another across an interface that separates the two, the resistance to mass transfer in each phase causes a concentration gradient in each, as shown in Fig. 5-24 for a gas-liquid interface. The concentrations of the diffusing material in the two phases immediately adjacent to the interface generally are unequal, even if expressed in the same units, but usually are assumed to reach equilibrium almost immediately when a gas and a liquid are brought into contact. For systems with dilute solute concentrations in the gas and liquid phases, the rate of mass transfer is proportional to the difference between the solute’s bulk concentration and its concentration at the gas-liquid interface. Thus NA = k′G(p - pi) = k′L(ci - c)

(5-262)

where NA = mass-transfer rate, k′G = gas-phase mass-transfer coefficient, k′L = liquid-phase mass-transfer coefficient, p = solute partial pressure in bulk gas, pi = solute partial pressure at interface, c = solute concentration in bulk liquid, and ci = solute concentration in liquid at the interface. The mass-transfer coefficients k′G and k′L by definition are equal to the ratios of the molal mass flux NA to the concentration driving forces p − pi and ci - c, respectively. An alternative expression for the rate of transfer in dilute systems is given by NA = kG(y - yi) = kL(xi - x)

(5-263)

(5-266)

where KG = overall gas-phase mass-transfer coefficient, KL = overall liquidphase mass-transfer coefficient, y ∗ = vapor composition in equilibrium with x, and x ∗ = liquid composition in equilibrium with vapor of composition y . This equation can be rearranged to the formula 1 1  y − y ∗  1 1  yi − y ∗  1 1  yi − y ∗  = + = + = K G kG  y − y i  kG kG  y − y i  kG kL  x i − x 

(5-267)

in view of Eq. (5-265). Comparison of the last term in parentheses with the diagram of Fig. 5-25 shows that it is equal to the slope of the chord connecting the points (x, y ∗) and (xi, yi). If the equilibrium curve is a straight line, then this term is the slope m . Thus 1/KG = 1/kG + m/kL

(5-268)

When Henry’s law is valid (pA = HxA or pA = H′CA), the slope m is m = H/pT = H′ ρL /pT

(5-269)

where m is defined in terms of mole-fraction driving forces in Eq. (5-263). If it is desired to calculate the rate of transfer from the overall concentration difference based on bulk-liquid compositions x ∗ - x, the appropriate overall coefficient KL is related to the individual coefficients by the equation 1/KL = 1/kL + 1/(mkG)

(5-270)

Conversion of these equations to a k′G, k′L basis can be accomplished readily by direct substitution of Eqs. (5-264a) and (5-264b). Occasionally one will find k′L or K′L values reported in units (SI) of meters per second. The correct units for these values are kmol/[(s ⋅ m2)(kmol/m3)],

where kG = gas-phase mass-transfer coefficient, kL = liquid-phase mass-transfer coefficient, y = mole-fraction solute in bulk-gas phase, yi = mole-fraction solute in gas at interface, x = mole-fraction solute in bulk-liquid phase, and xi = molefraction solute in liquid at interface. The mass-transfer coefficients defined by Eqs. (5-262) and (5-263) are related to each other as follows: kG = kG′ pT

(5-264a)

kL = kL′ρL

(5-264b)

where pT = total system pressure employed during the experimental determinations of k′G values and ρL = average molar density of the liquid phase. The coefficient kG is relatively independent of the total system pressure and therefore is more convenient to use than k′G, which is inversely proportional to the total system pressure. The above equations may be used for finding the interfacial concentrations corresponding to any set of values of x and y provided the ratio of the individual coefficients is known. Thus (y - yi)/(xi - x) = kL/kG = k′L ρL /k′GpT = LMHG/GMHL

(5-265)

FIG. 5-25

tower.

Identification of concentrations at a point in a countercurrent absorption

MASS TRAnSFER and Eq. (5-264b) is the correct equation for converting them to a molefraction basis. When k′G and K′G values are reported in units (SI) of kmol/[(s ⋅ m2)(kPa)], one must be careful, in converting them to a mole-fraction basis, to multiply by the total pressure actually employed in the original experiments and not by the total pressure of the system to be designed. This conversion is valid for systems in which Dalton’s law of partial pressures (p = ypT) is valid. Comparison of Eqs. (5-268) and (5-270) shows that for systems in which the equilibrium line is straight, the overall mass-transfer coefficients are related to one another by the equation (5-271)

KL = mKG

When the equilibrium curve is not straight, there is no strictly logical basis for the use of an overall transfer coefficient, since the value of m will be a function of position in the apparatus, as can be seen from Fig. 5-25. In such cases the rate of transfer should be calculated by solving for the interfacial compositions as described above. Experimentally observed rates of mass transfer often are expressed in terms of overall transfer coefficients even when the equilibrium lines are curved. This procedure is approximate, since the rates of transfer may not vary in direct proportion to the overall bulk concentration differences y - y ∗ and x ∗ - x at all concentration levels even though the rates may be proportional to the concentration difference in each phase taken separately, that is, xi - x and y - yi. In most types of separation equipment such as packed or spray towers, the interfacial area that is effective for mass transfer cannot be accurately determined. For this reason it is customary to report experimentally observed rates of transfer in terms of transfer coefficients based on a unit volume of the apparatus rather than on a unit of interfacial area. Such volumetric coefficients are designated as KGa, kLa, etc., where a represents the interfacial area per unit volume of the apparatus. Experimentally observed variations in the values of these volumetric coefficients with variations in flow rates, type of packing, etc., may be due as much to changes in the effective value of a as to changes in k . Calculation of the overall coefficients from the individual volumetric coefficients is done by means of the equations 1/(KGa) = 1/(kGa) + m/(kLa)

(5-272a)

1/(KLa) = 1/(kLa) + 1/(mkGa)

(5-272b)

Because of the wide variation in equilibrium, the variation in the values of m from one system to another can have an important effect on the overall coefficient and on the selection of the type of equipment to use. For example, if m is large, the liquid-phase part of the overall resistance might be extremely large where kL might be relatively small. This kind of reasoning must be applied with caution, however, since species with different equilibrium characteristics are separated under different operating conditions. Thus, the effect of changes in m on the overall resistance to mass transfer may partly be counterbalanced by changes in the individual specific resistances as the flow rates are changed. Mass-Transfer Principles: Concentrated Systems When solute concentrations in the gas and/or liquid phases are large, the equations derived above for dilute systems no longer are applicable. The correct equations to use for concentrated systems are as follows:

= KˆG ( y − y ∗ )/y ∗BM = kˆL ( x ∗ − x )/x ∗BM

For concentrated systems the gas-phase kˆG and liquid-phase kˆL mass-transfer coefficients and the overall gas-phase KˆG and liquid-phase Kˆ L mass-transfer coefficients are defined later in Eqs. (5-278) to (5-280). The factors yBM and xBM arise because in the diffusion of a solute through a stationary layer of fluid the resistance to diffusion varies in proportion to the concentration of the stationary fluid, approaching zero as the concentration of the fluid approaches zero. See Eq. (5-198). The factors y *BM and x *BM cannot be justified on the basis of mass-transfer theory since they are based on overall resistances. These factors therefore are included in the equations by analogy with the corresponding film equations. In dilute systems the logarithmic-mean insoluble-gas and nonvolatileliquid concentrations approach unity, and Eq. (5-273) reduces to the dilute system formula, Eq. (5-266). For equimolar counterdiffusion (e.g., binary distillation), the log-mean factors are omitted. See Eq. (5-197). Substitution of Eqs. (5-274) and (5-275) into Eq. (5-273) results in the following simplified formula: NA = kˆG ln [(1 - yi)/(1 - y)] = KˆG ln [(1 - y ∗)/(1 - y)] = kˆL ln [(1 - x)/(1 - xi)] = Kˆ L ln [(1 - x)/(1 - x ∗)]

( y − y i )/( x i − x ) = kˆL y BM /kˆG x BM = LM H G y BM /G M H L x BM = kL /kG

where NB = 0. In these and following equations, yB represents the insoluble carrier gas in the gas phase and xB represents the nonvolatile solvent in the liquid. Hence, yA = y and xA = x represent the solute in the gas and liquid phases, respectively. Thus, for example, it is understood that 1 - x = xB.

(5-277)

This equation is identical to Eq . (5-265) for dilute systems since kˆG = kG yBM and kˆL = kL xBM, and yBM and xBM are both 1 in dilute systems . Note, however, that when kˆG and kˆL are given, the equation must be solved by trial and error, since xBM contains xi and yBM contains yi . The overall gas-phase and liquid-phase mass-transfer coefficients for concentrated systems are computed from y 1 1 x BM 1  y i − y ∗  = BM + KˆG y BM ∗ kˆG y BM ∗ kˆL  x i − x 

(5-278)

1 x BM 1 y BM 1  x ∗ − x i  = + Kˆ L x ∗BM kˆL x ∗BM kˆG  y − y i 

(5-279)

When the equilibrium curve is a straight line, the terms in parentheses can be replaced by the slope m or 1/m as before . In this case, the overall masstransfer coefficients for concentrated systems are related to one another by the equation

(

(5-273)

(5-276)

Note that the units of kˆG , KˆG , kˆL , and Kˆ L are identical, i .e ., kmol/(s ⋅ m2) in SI units . The interfacial gas and liquid compositions in concentrated systems can be determined from

∗ /y BM ∗ Kˆ L = mKˆG x BM

NA = kˆG (y - yi)/yBM = kˆL (xi - x)/xBM

5-57

)

(5-280)

All these equations reduce to their dilute system equivalents as the inert concentrations approach unity in terms of mole fractions of inert concentrations in the fluids . Height Equivalent to 1 Transfer Unit (HTU) In packed beds used for distillation, absorption, stripping, and extraction, it is convenient to represent mass transfer as the height of apparatus required to accomplish a separation of standard difficulty . The gas-phase HTU is the ratio of gas flow rate to gas-phase mass-transfer coefficient, and the liquid-phase HTU is the ratio of the liquid flow rate to liquid-phase coefficient . The following relations between the transfer coefficients and the values of HTU apply:

y BM =

(1 − y ) − (1 − y i ) ln[ (1 − y )/(1 − y i ) ]

(5-274a)

y ∗BM =

(1 − y ) − (1 − y ∗ ) ln[(1 − y )/(1 − y ∗ )]

(5-274b)

x BM =

(1 − x ) − (1 − x i ) ln[(1 − x )/(1 − x i )]

(5-275a) (5-275b)

Frequently the HTU values are closer to constant than the mass-transfer coefficients .

x ∗BM =

∗

(1 − x ) − (1 − x ) ln[(1 − x )/(1 − x ∗ )]

HG = GM/(kGa yBM) = GM/(kˆG a)

(5-281)

HOG = GM/(KGa y ∗BM) = GM/(KˆG a)

(5-282)

HL = LM/(kLa xBM) = LM/(kˆL a)

(5-283)

HOL = LM/(KLa x∗BM) = LM/(Kˆ L a)

(5-284)

5-58

HEAT AnD MASS TRAnSFER

The equations that express the addition of individual resistances in terms of HTUs, applicable to either dilute or concentrated systems, are mG M x BM y BM HL HG + LM y ∗BM y ∗BM

(5-285)

L y x H OL = ∗BM H L + M ∗BM H G mG M x BM x BM

(5-286)

H OG =

These equations are strictly valid only when the slope m of the equilibrium curve is constant, as noted previously. Example 5-18 Conversion of Overall Mass Transfer Coefficient An overall mass-transfer coefficient was experimentally measured for SO2 in water at 30°C and 1 atm, and it was found to be K′G = 0.40 kmol/(h ⋅ m2 ⋅ atm). Linear regression of the equilibrium data in Table 2-13 yielded y = 43.727x − 0.0081, R2 = 0.9971. Based on 30 percent of the resistance to mass transfer residing in the liquid phase, find the value of the alternative, overall mass-transfer coefficient in the liquid phase KL. Solution K′G = 0.4 kmol/(h ⋅ m2 ⋅ atm) and P = 1.0 atm, KG = PK′G = 0.4 kmol/(h ⋅ m2). Since resistance = 1/KG, m/kL = 0.3/KG → 1/kL = 0.3/(KGm). From the equilibrium data, m = 43.727 (slope of y versus x). Thus, 1/kL = 0.3/[(0.40)(43.727)] = 0.01715. Similarly, 1/kG = 0.7/KG → kG = 1/1.75 = 0.5714. Then 1/KL = 1/(mkG) + 1/kL = 1/(43.727)(0.5714) + 0.01715 = 0.0572 and KL = 17.49. Note that KL = mKG = 17.49 kmol/(h ⋅ m2). Number of Transfer Units (NTU) The total height of packing is HTU × NTU. The NTU required for a given separation is closely related to the number of theoretical stages or plates required to carry out the same separation in a stage or plate-type apparatus. For equimolal counterdiffusion, such as in a binary distillation, the number of overall gas-phase transfer units NOG required for changing the composition of the vapor stream from y1 to y2 is y1

N OG =

dy ∫y 2 y − y ∗

(5-287)

When diffusion is in one direction only, as in the absorption of a soluble component from an insoluble gas, y1

N OG =

y ∗BM dy

∫ (1 − y )( y − y ∗)

(5-288)

y2

For dilute systems Eq. (5-288) simplifies to Eq. (5-287). If HOG is constant, the total height of packing required is hT = HOG NOG

(5-289)

When it is known that HOG varies appreciably within the tower, this term must be placed inside the integral in Eqs. (5-287) and (5-288) for accurate calculations of hT. For example, the packed-tower design equation in terms of the overall gas-phase mass-transfer coefficient for absorption would be expressed as follows: y ∗BM dy GM  hT = ∫   ∗ (1 y )( y − y ∗) − y 2  K G ay BM  y1

(5-290)

where the first term under the integral can be recognized as the HTU term. Convenient solutions of these equations for special cases are discussed later. Film, Penetration, and Surface-Renewal Theories In certain simple situations, the mass-transfer coefficients can be calculated from first principles. The film, penetration, and surface-renewal theories are attempts to extend these theoretical calculations to more-complex situations. Although these theories are often not accurate, they provide useful physical pictures for variations in the mass-transfer coefficient. For the special case of steady-state unidirectional diffusion of a component through an inert-gas film in an ideal-gas system, the rate of mass transfer is derived as NA =

D AB pT y − y i D AB pT 1 − y i ln = 1− y RT δG y BM RT δG

(5-291)

where dG = the “effective” thickness of a stagnant-gas layer which would offer a resistance to molecular diffusion equal to the experimentally observed resistance and R = the gas constant [Nernst, Z . Phys . Chem . 47: 52 (1904); Whitman, Chem . Mat . Eng . 29: 149 (1923), and Lewis and Whitman, Ind . Eng . Chem . 16: 1215 (1924)]. According to this analysis, one can see that for gas absorption problems, which often exhibit unidirectional diffusion, the most appropriate driving-force expression is of the form (y − yi)/yBM, and the most appropriate

mass-transfer coefficient is therefore  kˆG . This concept recurs for all unidirectional diffusion problems. Comparing Eq. (5-273), NA = kˆG (y - yi)/yBM, to Eq. (5-291), we obtain D p D C kˆG = AB T = AB RT δG δG

(5-292)

where C is the molar concentration of the stagnant gas film. Thus, with the film model the mass-transfer coefficient is inversely proportional to film thickness dG, which depends primarily on the hydrodynamics of the system and hence on the Reynolds (NRe) and Schmidt (NSc) numbers. Thus, the gasphase mass-transfer coefficient  kˆG depends principally upon the transport properties of the fluid (NSc) and the hydrodynamics of the particular system involved (NRe). Correlations have been developed for different geometries in terms of the following dimensionless variables: NSh = kˆG RTd/(pT DAB) = kˆG d/(CDAB) = f (NRe, NSc)

(5-293)

where the Sherwood number NSh and Reynolds number NRe = Gd/μG are based on the characteristic length d appropriate to the geometry of the particular system; and NSc = μG/(ρGDAB) is the Schmidt number . It is sometimes convenient to work in terms of the Stanton number NSt = kˆG /GM = k′G pBM yBM/GM, instead of the Sherwood number . The Sherwood number can be written as NSh = (kˆG /GM)NReNSc = NStNReNSc

(5-294)

Equations (5-293) and (5-294) can now be combined in the alternative functional form NSt = kˆG /GM = g(NRe, NSc)

(5-295)

It is important to recognize that specific mass-transfer correlations can be derived only in conjunction with the investigator’s particular assumptions concerning the numerical values of the effective interfacial area a of the packing . The stagnant-film model assumes a steady state in which the local flux across each element of area is constant; i .e ., there is no accumulation of the diffusing species within the film . For a liquid the film model predicts kˆL = DLC /δ L . Higbie [Trans . Am . Inst . Chem . Eng . 31: 365 (1935)] pointed out that industrial contactors often operate with repeated brief contacts between phases in which the contact times are too short for the steady state to be achieved . Higbie advanced the penetration theory that in a packed tower the liquid flows across each packing piece in laminar flow and is remixed at the points of discontinuity between the packing elements . Thus, a fresh liquid surface is formed at the top of each piece, and as it moves downward, it absorbs gas at a decreasing rate until it is mixed at the next discontinuity . If the velocity of the flowing stream is uniform over a very deep region of liquid (total thickness dT >> Dt ), where the time-averaged liquid-phase mass-transfer coefficient kˆL according to penetration theory is kˆL = 2 ρL x BM DL /(πt )

(5-296)

where DL = liquid-phase diffusion coefficient and t = contact time . In practice, the contact time t is not known except in special cases in which the hydrodynamics are clearly defined . This is somewhat similar to the case of the stagnant-film theory in which the unknown quantity is the thickness of the stagnant layer d . Penetration theory predicts that kˆL should vary by the square root of the molecular diffusivity, as compared with film theory, which predicts a firstpower dependency on D . Various investigators have reported experimental powers of D ranging from 0 .5 to 0 .75, and the Chilton-Colburn analogy uses a ⅔ power . Penetration theory often is used in analyzing absorption with chemical reaction because it makes no assumption about the depths of penetration of the various reacting species, and it gives a more accurate result when the diffusion coefficients of the reacting species are not equal . When the reaction process is very complex, however, penetration theory is more difficult to use than film theory, and the latter method normally is preferred . Danckwerts [Ind . Eng . Chem . 42: 1460 (1951)] proposed an extension of the penetration theory, called the surface renewal theory, which allows for the eddy motion in the liquid to bring masses of fresh liquid continually from the interior to the surface, where they are exposed to the gas for finite lengths of time before being replaced . Danckwerts assumed that every element of fluid has an equal chance of being replaced regardless of its age . The Danckwerts model gives kˆL = ρL x BM DL s

(5-297)

MASS TRAnSFER where s = fractional rate of surface renewal. Both the penetration and the surface renewal theories predict a square-root dependency on DL . Unfortunately, values of the surface renewal rate s generally are not available, which presents the same problems as do d and t in the film and penetration models. The predictions of correlations based on the film model often are nearly identical to predictions based on the penetration and surface renewal models. Thus, in view of its relative simplicity, the film model normally is preferred for purposes of discussion or calculation. Theoretical models have not proved adequate for making a priori predictions of mass-transfer rates in packed towers, and therefore empirical correlations such as those outlined later in Table 5-23 must be employed. Effects of High Solute Concentrations on kˆG and kˆL The stagnantfilm model indicates that kˆG should be independent of yBM and kG should be inversely proportional to yBM. The data of Vivian and Behrman [Am . Inst . Chem . Eng. J. 11: 656 (1965)] for the absorption of ammonia from an inert gas strongly suggest that the film model’s predicted trend is correct. This is another indication that the most appropriate rate coefficient to use in concentrated systems is kˆG and the proper driving-force term is of the form (y − yi)/yBM. The use of the rate coefficient kˆL and the driving force (xi − x)/xBM is also believed to be appropriate. For many practical absorption and stripping situations, the liquid-phase solute concentrations are low, thus making this assumption unimportant. Effects of Total Pressure on kˆG and kˆL The influence of total system pressure on the rate of mass transfer from a gas to a liquid or to a solid has been shown to be the same as would be predicted from stagnant-film theory value of kˆG = DABpT /(RT dG). Since the quantity DABpT is known to be relatively independent of the pressure, it follows that the rate coefficients kˆG , kG yBM, and kG′ pTyBM (= kG′ pBM) do not depend on the total pressure of the system, subject to the limitations discussed later. Investigators of tower packings normally report k′Ga values measured at very low inlet-gas concentrations, so that yBM = 1, and at total pressures close to 100 kPa (~1 atm). Thus, the correct rate coefficient for use in packedtower designs involving the use of the driving force (y − yi)/yBM is obtained by multiplying the reported k′Ga values by the value of pT employed in the actual test unit ( for example, 100 kPa) and not the total pressure of the system to be designed. In other words, one can determine k′Ga in kmol/[(s ⋅ m3)(kPa)] for design pressure pT (in kPa) from k′Ga at design pressure pT = k′Ga at 1 atm × 101.3/pT (5-298) One way to avoid a lot of confusion on this point is to convert the experimentally measured k′Ga values to values of kˆG a straightaway, before beginning the design calculations. A design based on the rate coefficient kˆG a and the driving force (y − yi)/yBM will be independent of the total system pressure with cautions for systems that have significant vapor-phase nonideality, that operate in the vicinity of the critical point, or that have total pressures higher than about 3040 to 4050 kPa (30 to 40 atm). Experimental confirmations of the relative independence of kˆG with respect to total pressure have been widely reported. Deviations do occur at extreme conditions. For example, Bretsznajder (Prediction of Transport and Other Physical Properties of Fluids, Pergamon Press, Oxford, 1971, p. 343) discusses the effects of pressure on the DAB pT product and presents experimental data on the self-diffusion of CO2 which show that the Dp product begins to decrease at a pressure of approximately 8100 kPa (80 atm). For reduced temperatures (Tr) higher than about 1.5, the deviations are relatively modest for pressures up to the critical pressure. However, deviations are large near the critical point. The effect of pressure on the gas-phase viscosity also is negligible for pressures below about 5060 kPa (50 atm). For the liquid-phase mass-transfer coefficient kˆL , the effects of total system pressure can be ignored for all practical purposes. Thus, when kˆG and kˆL are used for the design of gas absorbers or strippers, the primary pressure effects to consider will be those that affect the equilibrium curves and the values of m. However, if pressure changes affect the hydrodynamics, kˆG , kˆL , and a can all change significantly. Effects of Temperature on kˆG and kˆL The Stanton number relationship for gas-phase mass transfer in packed beds, Eq. (5-295), indicates that for a given system geometry the rate coefficient kˆG depends on only the Reynolds number and the Schmidt number. Since the Schmidt number for a gas is approximately independent of temperature, the principal effect of temperature upon kˆG arises from changes in the gas viscosity with changes in temperature. For normally encountered temperature ranges, these effects will be small owing to the fractional powers involved in Reynolds number terms (see Tables 5-16 to 5-23). Thus, for all practical purposes kˆG is independent of temperature and pressure in the normal ranges of these variables. For modest changes in temperature, the influence of temperature upon the interfacial area a may be neglected. For example, in experiments on the absorption of SO2 in water, Whitney and Vivian [Chem . Eng . Prog. 45: 323 (1949)] found no appreciable effect of temperature upon kˆG a over the range from 10 to 50°C.

5-59

Whitney and Vivian found that the effect of temperature upon kˆL a and Sherwood and Holloway [101] (see Table 5-23A) found that the effect of temperature upon HL could be explained entirely by variations in the liquidphase viscosity and diffusion coefficient with temperature. These effects can be very large and therefore must be carefully accounted for when using kˆL or HL data. For liquids, the mass-transfer coefficient kˆL is correlated by Eqs. (5-297) and (5-299). Typically, the general form of the correlation for HL is (see Table 5-23) a H L = bN Re N Sc1/2

(5-299)

where b is a proportionality constant and the exponent a may range from about 0.2 to 0.5 for different packings and systems. The liquid-phase diffusion coefficients may be corrected from a base temperature T1 to another temperature T2 by using the Einstein relation as recommended by Wilke [Chem . Eng . Prog. 45: 218 (1949)]: D2 = D1(T2/T1)(μ1/μ2)

(5-300)

The Einstein relation can be rearranged to relate Schmidt numbers at two temperatures: NSc2 = NSc1(T1/T2)(ρ1/ρ2)(μ2/μ1)2

(5-301)

Substitution of this relation into Eq. (5-299) shows that for a given geometry the effect of temperature on HL can be estimated as HL2 = HL1(T1/T2)1/2(ρ1/ρ2)1/2(μ2/μ1)1-a

(5-302)

In using these relations, note that for equal liquid flow rates HL2/HL1 = (kˆL a )1/(kˆL a )2

(5-303)

Maxwell-Stefan Mass Transfer Equation (5-262) can be obtained by solving Fick’s law for a thin stagnant film and then noting kˆL = DLC / δ L where d is the unknown film thickness. Thus, the usual linear driving-force masstransfer analysis is inherently a Fickian analysis that is excellent for binary mass transfer but can be problematic for multicomponent systems (see Taylor and Krishna). A M-S mass-transfer analysis can be derived by starting with Eq. (5-240), multiplying both sides of the equation by d, and defining the M-S mass-transfer coefficient as k = DC/d (see Wesselingh and Krishna). For ternary mass transfer in the z direction the result is  x A ∂γ A  dx A  1 + γ ∂ x  d ( z /δ) A A x B N A ,z − x A N B ,z xC N A ,z − x A N C ,z =− − k AB k AC

(5-304)

For ideal gases this result simplifies to y N − y A N B ,z y C N A ,z − y A NC , z dx A = − B A ,z − d ( z /δ) k AB k AC

(5-305)

The resulting difference form of the mass-transfer equation for ideal ternary gas systems is ∆y A = −

y B N A ,z − y A N B ,z y C N A ,z − y A N C ,z − k AB k AC

(5-306)

For binary systems the M-S mass-transfer coefficient is related to the Fickian mass-transfer coefficient by k AB =

k AB D AB k AB = x ∂γ D AB 1+ A A γ A ∂x A

(5-307)

For ideal systems and at the infinite dilution limits DAB = DAB and kAB = kAB . Thus, for most gas systems and for dilute liquid systems, the standard masstransfer correlations discussed next can be used to determine kAB which is then used in Eq. (5-305) or (5-306). MASS-TRAnSFER CORRELATIOnS Because of the tremendous importance of mass transfer in chemical engineering, a very large number of studies have determined mass-transfer coefficients. Tables 5-17 to 5-24 summarize a variety of different configurations to provide a sense of the range of correlations available. These

5-60

HEAT AnD MASS TRAnSFER

TABLE 5-17 Mass-Transfer Correlations for a Single Flat Plate or Disk—Transfer to or from Plate to Fluid Situation A. Laminar, local, flat plate, forced flow

Laminar, average, flat plate, forced flow

j factors B. Laminar, local, flat plate, natural convection vertical plate

C. Laminar, stationary disk Laminar, spinning disk

D. Laminar, inclined, plate

k ′x = 0.323 (NRe,x)1/2(NSc)1/3 D Coefficient 0.332 is a better fit. NSh,x =

km′ L = 0.646( N Re,L )1/2 ( N Sc )1/3 D Coefficient 0.664 is a better fit. k′m is mean mass-transfer coefficient for dilute systems. f jD = jH = = 0.664(NRe,L)-1/2 2 N Sh, avg =

NSh,x=

1/2 −1/4 1/4 k ′x = 0.508 N Sc (0.952 + N Sc ) N Gr D

N Gr =

gx 3  ρ∞  −1 (µ/ρ)2  ρ0 

N Sh =

k ′ddisk 8 = π D

k ′ddisk 1/2 N Sc1/3 = 0.879 N Re D N Re 0.6, NRe, x < 3 × 105 [S] Chilton-Colburn analogy. NSc = 1.0, f = drag coefficient. jD is defined in terms of k′m.

Skelland, p. 271

[T] Low MT rates. Dilute systems, Δρ/ρ 0.5 D Entrance effects are ignored. NRe, Cr is transition laminar to turbulent.

Sherwood, Pigford, & Wilke, p. 201

[S] Low solute concentration and low transfer rates. Use arithmetic concentration difference. NGr > 1010 Assumes laminar boundary layer is small fraction of total.

Skelland, p. 225

[E] Entrance turbulent channel For parallel flow and corrugations: NSC = 1483, a = 0.56, c = 0.268 NSC = 4997, a = 0.50, c = 0.395 Corrugations perpendicular to flow: NSC = 1483, a = 0.57, c = 0.368 NSC = 4997, a = 0.52, c = 0.487

[98]

[E] Use arithmetic concentration difference. u = wddisk/2 where w = rotational speed, radians/s. NRe = ρwd2disk/2μ

[42] Sherwood, Pigford, & Wilke, p. 241

MASS TRAnSFER

5-61

TABLE 5-17 Mass-Transfer Correlations for a Single Flat Plate or Disk—Transfer to or from Plate to Fluid (Continued ) Situation

Comments E = Empirical, S = Semiempirical, T = Theoretical

Correlation

J. Mass transfer to a flat-plate membrane in a stirred vessel

k ′d tank b = aN Re N Scc D a depends on system. a = 0.0443 [40]; b is often 0.65 - 0.70 [67].

K. Spiral wound type RO (seawater desalination)

2/3 N Sh = 0.210 N Re N Sc1/4 0.875 N Sc1/4 Or with slightly larger error, N Sh = 0.080 N Re

N Sh =

0.875 N Sh = 0.065 N Re N Sc1/4

References∗

[E] Useful for laboratory dialysis, R.O., U.F., and microfiltration systems. Use arithmetic concentration difference. w = stirrer speed, radians/s. ωd 2 ρ N Re = tank µ b = 0.785 [27]. c is often 0.33 but other values have been reported [67].

[27] [67] p. 965

[E] Polyamide membrane. p = 6.5 MPa and TDS rejection = 99.8%. Recovery ratio 40%.

[108] [103], p. 113

∗Author names refer to the General References list at the beginning of the Mass Transfer subsection (pp. 5-41, 5-42). Bracketed numbers refer to the table reference lists (p. 5-42).

TABLE 5-18 Mass-Transfer Correlations for Falling Films with a Free Surface in Wetted Wall Columns—Transfer between Gas and Liquid Situation A. Laminar, vertical wetted wall column

Comments E = Empirical, S = Semiempirical, T = Theoretical

Correlation N Sh,avg =

km′ x x ≈ 3.41 δ film D

( first term of infinite series)  3µQ  δ film =   wρg 

1/3

= film thickness

4Qρ N Re, film = < 20 wµ

B. Turbulent, vertical wetted wall column

Better fit C. Turbulent, very short column

D. Turbulent, vertical wetted wall column with ripples

km′ dt 0.83 = 0.023 N Re N Sc0.44 D A coefficient 0.0163 has also been reported using NRe′, where υ = υ of gas relative to liquid film. N Sh,avg =

0.790 N Sh,avg = 0.0318 N Rc N Sc0.5

0.5 Sc,g

0.08 Re,liq

N Sh = 0.00283 N Re, g N N NSh = kg(dtube - 2d)/D NReg,g = ρgug (dtube - 2d)/μg NRe, liq = ρliqQliq/[πμ(dtube - 2d)] N Sh,avg =

 4Qρ  km′ dt 0.83 = 0.00814 N Re N Sc0.44   wµ  D

E . Rectification in vertical wetted wall column with turbulent vapor flow, Johnstone and Pigford correlation

km′ dt 0.8 = 0.023 N Re N Sc1/3 D

N Sh,avg =

kG′ dcol pBM = 0.0328( N Re ′ )0.77 N Sc0.33 Dv p

[T] Low rates MT. Use with log-mean concentration difference. Parabolic velocity distribution in films. w = film width (circumference in column) Derived for flat plates, used for tubes if 1/2 ρg rtube   > 3.0. σ = surface tension  2σ  If NRe, film > 20, surface waves and rates increase. An approximate solution Dapparent can be used. Ripples are suppressed with a wetting agent good to NRe = 1200.

Sherwood, Pigford, & Wilke, p. 78

[E] Use with log-mean concentration difference for correlations in B and D. NRe is for gas. NSc for vapor in gas. 2000 < NRe ≤ 35,000, 0.6 ≤ NSc ≤ 2.5. Use for gases, dt = tube diameter.

[51], [57] p.181 Sherwood, Pigford, & Wilke, p. 211 Skelland, p. 265 Taylor & Krishna, p. 212 Treybal, p. 71

Skelland, p. 137 Treybal, p. 50

[S] Reevaluated data

[44]

[E] Evaporation data NSh,g = 11 to 65, NRe,g = 2400 to 9100 NRe,liq = 11 to 480, NSc,g = 0.62 to 1.93 d = film thickness

[43]

[E] For gas systems with rippling.  4Qρ  = 1000 Fits 5-17B for   wµ  [E] “Rounded” approximation to include ripples. Includes solid-liquid mass-transfer data to find ⅓ coefficient on NSc . May use NRe0 .83 . Use for liquids . See also Table 5-19 .

[64]

[E] Use log-mean driving force at two ends of column. Based on four systems with gas-side resistance only. pBM = log-mean partial pressure of nondiffusing species B in binary mixture. p = total pressure Modified form is used for structured packings (see Table 5-24H) .

[63]

0.15

 4Qρ  30 ≤  < 1200  wµ  N Sh,avg =

References∗

3000 < N Re ′ < 40,000, 0.5 < N Sc < 3 d υ ρ N Re ′ = col rel v , υ rel = gel velosity relative to µv 3 liquid film = uavg in film 2

Sherwood, Pigford, & Wilke, p . 213

Sherwood, Pigford, & Wilke, p. 214

[113]

∗Author names refer to the General References list at the beginning of the Mass Transfer subsection (pp . 5-41, 5-42) . Bracketed numbers refer to the table reference lists (p . 5-42) .

5-62

HEAT AnD MASS TRAnSFER

TABLE 5-19 Mass-Transfer Correlations for Flow in Pipes and Ducts—Transfer Is from Wall to Fluid Situation A. Tubes, laminar, fully developed parabolic velocity profile, developing concentration profile, constant wall concentration

Fully developed concentration profile

B. Tubes, approximate solution

N Sh =

N Sh =

0.0668(dt /x ) N Re N Sc k ′dt = 3.66 + 1 + 0.04[(dt /x ) N Re N Sc ]2/3 D

k ′dt = 3.66 D

N Sh,x =

k ′dt d = 1.077  t   x D

N Sh,avg =

C. Tubes, laminar, uniform plug velocity, developing concentration profile, constant wall concentration

Comments E = Empirical, S = Semiempirical, T = Theoretical

Correlation

[T] Use log-mean concentration difference. x/dt For < 0.10, N Re < 2100. N Re N Sc x = distance from tube entrance. Good agreement with experiment at values π dt 10 4 > N Re N Sc > 10 4 x x/dt [T] > 0.1 N Re N Sc

[57] p. 176

[T] For arithmetic concentration difference. W > 400 ρDx

Skelland, p. 166

k ′dt d = 1.615  t   L D

( N Re N Sc )1/3 1/3

( N Re N Sc )1/3

 11 1 ∞ exp[ −λ 2j ( x/rt )/( N Re N Sc )]  N Sh,x =  − ∑  C j λ 4j  48 2 j =1  λ 2j 25.68 83.86 174.2 296.5 450.9

E. Laminar, alternate

F. Laminar, fully developed concentration and velocity profile G. Vertical tubes, laminar flow, forced and natural convection

H. Hollow-fiber extraction inside fibers

N Sh = 4.36 +

N Sh =

Skelland, p. 159 Skelland, p. 165

Leveque’s approximation: Concentration BL is thin. Assume velocity profile is linear. High mass velocity. Fits liquid data well.

∞   −2 a 2j ( x/rt )   −2  1 − 4 ∑ a j exp    N Re N Sc   1 dt j =1 N Re N Sc  N Sh,avg = 2 ∞ 2 L  −2 a j ( x/rt )    1 + 4 ∑ a −j 2 exp     N Re N Sc   j =1

j 1 2 3 4 5

[66] p. 525

1/3

[T] Use arithmetic concentration difference. Fits gas data well, for W < 50 (fit is fortuitous) Dρx N Sh, avg = ( km′ dt )/D , a1 = 2.405, a2 = 5.520,

−1

[T] For arithmetic concentration difference. NRe < 2100

[102] Skelland, p. 167

k ′dt D vd ρ N Re = t µ N Sh, x =

Cj 7.630 × 10-3 2.058 × 10-3 0.901 × 10-3 0.487 × 10-3 0.297 × 10-3

k ′dt . Use log-mean concentration D difference. NRe < 2100

0.023(dt /L) N Re N Sc 1 + 0.0012(dt /L) N Re N Sc

[T] N Sh =

k ′dt 48 = = 4.3636 D 11

( N Gr N Sc d/L)3/4  1/3  N Sh,avg = 1.62 N Gz  1 ± 0.0742 N Gz  

[78] Skelland, p. 150

a3 = 8.654, a4 = 11.792, a5 = 14.931. graphical solution are in reference.

Graetz solution for heat transfer written for MT.

D. Laminar, fully developed parabolic velocity profile, constant mass flux at wall

References∗

1/3

N Sh = 0.5 N Gz , N Gz < 6

[57] p. 176

[T] Use log-mean concentration difference. NRe < 2100

Skelland, p. 167

[T] Approximate solution. Use minus sign if forced and natural convection oppose each other. Good agreement with experiment. g ∆ρd 3 N N d N Gz = Re Sc , N Gr = ρv 2 L

[94]

[E] Use arithmetic concentration difference.

[28]

Use arithmetic concentration difference. Thin concentration polarization layer, not fully developed. NRe < 2000, L = length tube.

[27]

0.5 Gz

N Sh = 1.62 N , N Gz ≥ 6 I. Tubes, laminar, RO systems N Sh,avg =

 ud 2  km′ dt = 1.632  t   DL  D

1/3

J. Tubes and parallel plates, laminar RO

Graphical solutions for concentration polarization. Uniform velocity through walls.

[T]

[100]

K. Rotating annulus for reverse osmosis

For nonvortical flow:

[E,S] NTe = Taylor number = riwd/v

[75]

0.5  d  N Sh = 2.15  N Ta     ri   

0.18

N Sc1/3

For vortical flow:  d N Sh = 1.05  N Ta    ri   L. Fully developed, parallel plates, laminar, parabolic velocity, developing concentration profile, constant wall concentration

N Sh =

k ′(2 h) = 7.6 D

0.5

 1/3  N Sc 

ri = inner cylinder radius w = rotational speed, rad/s d = gap width between cylinders

[T] h = distance between plates. Use log-mean concentration difference N Re N Sc < 20 x/(2 h)

Skelland, p. 177

MASS TRAnSFER

5-63

TABLE 5-19 Mass-Transfer Correlations for Flow in Pipes and Ducts—Transfer Is from Wall to Fluid (Continued ) Situation M. same as 5-19L except constant mass flux at wall.

N. Laminar flow, vertical parallel plates, forced and natural convection

N Sh =

k ′(2 h) = 8.23 D

( N Gr N Sc h/L)3/4  1/3  N Sh,avg = 1.47 N Gz  1 ± 0.0989 N Gz  

O. Parallel plates, laminar, RO systems N Sh,avg = P. Tubes, turbulent

Q. Tubes, turbulent

R. Tubes, turbulent, smooth tubes, Reynolds analogy

S. Tubes, turbulent, smooth tubes, Chilton-Colburn analogy

Comments E = Empirical, S = Semiempirical, T = Theoretical

Correlation

k ′(2 H p ) D

 uH 2p  = 2.354    DL 

1/3

1/3

km′ dt 0.83 = 0.023 N Re N Sc1/3 D 2100 < NRe < 35,000 0.6 < NSc < 3000 k′ d 0.83 N Sh,avg = m t = 0.023 N Re N Sc0.44 D 2100 < NRe < 35,000 0.6 < NSc < 2.5 N Sh,avg =

N Sh =

k ′dt  f  =   N Re N Sc D  2 f = Fanning friction faction

If

Skelland, p. 177

[T] Approximate solution. Use minus sign if forced and natural convection oppose each other. Good agreement with experiment. g ∆ρh 3 N N h N Gz = Re Sc , N Gr = ρv 2 L

[94]

Thin concentration polarization layer. Short tubes, concentration profile not fully developed. Use arithmetic concentration difference.

[27]

[E] Use with log-mean concentration difference at two ends of tube. Good fit for liquids.

[57] p. 181

[E] Evaporation of liquids. Use with log-mean concentration difference. Better fit for gases.

N Sh =

jD = jH ≤

[T] Use log-mean concentration difference. N Re N Sc < 20 x/(2 h)

From wetted wall column and dissolution data—see Table 5-18B.

k ′dt 0.913 = 0.0096 N Re N Sc0.346 D

f 2

f N Sh −0.2 −0.2 , jD = = 0.023 N Re = 0.023 N Re 2 N Re N Sc1/3

k ′dt , see Table 5-17G D jD = jH = F(NRe, geometry and B.C.) N Sh =

( f /2) N Re N Sc k ′dt = D 1 + 5 f /2( N Sc − 1)

N Sh =

[51], [57] p. 181 Kirwan, p. 112 Sherwood, Pigford, & Wilke, p. 211 McCabe, Smith, & Harriott, p. 668

[T] Use arithmetic concentration difference. NSc near 1.0 Turbulent core extends to wall. Of limited utility.

Geankoplis p. 474 [57] p. 171 Skelland, p. 239 Taylor & Krishna, p. 250

[E] Use log-mean concentration difference. Relating jD to f/2 approximate. NPr and NSc near 1.0. Low concentration. Results about 20% lower than experiment. 3 × 104 × NRe × 106

Bird, Stewart, & Lightfoot, pp. 400, 647 [38][40] Skelland, p. 264 Taylor & Krishna, p. 251 Geankoplis, p. 475 Bird, Stewart, & Lightfoot, p. 647

[E] Good over wide ranges.

[38]

[T] Use arithmetic concentration difference. Improvement over Reynolds analogy. Best for NSc near 1.0.

[57] p. 173

f −0.25 = 0.04 N Re 2 U. Tubes, turbulent, smooth tubes, Constant surface concentration, Von Karman analogy

[78], Treybal, p. 72

[E] 430 < NSc < 100,000. Dissolution data. Use for high NSc.

N Sh =

T. Tubes, turbulent, smooth tubes, constant surface concentration, Prandtl analogy

References∗

Skelland, p. 241

{

( f / 2) N Re N Sc

5 1 + 5 f /2 ( N Sc − 1) + ln 1 + ( N Sc − 1)   6 

}

[T] Use arithmetic concentration difference. NSh = k′dt/D. Improvement over Prandtl, NSc < 25.

[57] p. 173 Skelland, p. 243 Taylor & Krishna, p. 250 [111]

f −0.25 = 0.04 N Re 2 V. Turbulent flow, tubes

W. Turbulent flow, noncircular ducts

N St =

N Sh N Sh −0.12 = = 0.0149 N Re N Sc−2/3 N Pe N Re N Sc

[E] Smooth pipe data. Data fits within 4% except at NSc > 20,000, where experimental data is underpredicted. NSc > 100, 105 > NRe > 2100

[80]

deq =

4 cross-sectional area wetted perimeter

Can be suspect for systems with sharp corners. Parallel plates: 2 hw deq = 4 2w + 2 h

Skelland, p. 289

∗Author names refer to the General References list at the beginning of the Mass Transfer subsection (pp. 5-41, 5-42). Bracketed numbers refer to the table reference lists (p. 5-42).

5-64

HEAT AnD MASS TRAnSFER

TABLE 5-20 Mass-Transfer Correlations for Flow Past Submerged Objects Situation A. Single sphere

Correlation N Sh =

kG′ pBLM RTd s 2r = PD r − rs

r/rs 2

5

10

50

Comments E = Empirical, S = Semiempirical, T = Theoretical

References∗

[T] Use with log-mean concentration difference. r = distance from sphere, rs, ds = radius and diameter of sphere. No convection.

Skelland, p. 18

[T] Use with log-mean concentration difference. Average over sphere. Numerical calculations. (NReNSc) < 10,000 NRe < 1.0. Constant sphere diameter. Low mass-transfer rates. [T] Fit to above ignoring molecular diffusion. 1000 < (NReNSc) < 10,000.

[33], Kirwan, p. 114 Sherwood, Pigford, & Wilke, p. 214 [76] p. 80 Sherwood, Pigford, & Wilke, p. 215

∞ (asymptotic limit)

NSh 4.0 2.5 2.22 2.04 2.0 B. Single sphere, creeping flow with forced convection

C. Single spheres, molecular diffusion, and forced convection, low flow rates

k ′d = [4.0 + 1.21( N Re N Sc )2/3 ]1/2 D k ′d N Sh = = a ( N Re N Sc )1/3 D a = 1.00 ± 0.01 N Sh =

b N Sh = 2.0 + AN Re N Scc , b =1/2, c = 1/3 A = 0.5 to 0.62

A = 0.60. A = 0.95. A = 0.95.

Use with arithmetic concentration difference. NSc = 1; 50 ≤ NRe ≤ 350. NSc < 1, NRe < 1. 1.0 ≤ NRe ≤ 48,000, Gases: 0.6 ≤ NSc ≤ 2.7

A = 0.544. A = 0.575, b = 0.5, c = 0.35 A = 0.552, b = 0.53, c = 1/3

D. Single cylinders, perpendicular flow

E. Rotating cylinder in an infinite liquid, no forced flow

k ′d s 1/2 = AN Re N Sc1/3 , A = 0.82 D A = 0.74 A = 0.582 jD = 0.600(NRe)-0.487 k ′dcyl N Sh = D N Sh =

j D′ =

k ′ 0.644 −0.30 N Sc = 0.0791 N Re v

Results presented graphically to NRe = 241,000. N Re = F. Oblate spheroid, forced convection

jD =

vdcyl µ ρ

where v =

ωdcyl 2

[E] Use with log-mean concentration difference. Average over sphere. Frössling Eq. (A = 0.552), 2 ≤ NRe ≤ 800, 0.6 ≤ NSc ≤ 2.7. NSh lower than experimental at high NRe. Ranz and Marshall 2 ≤ NRe ≤ 200, 0.6 ≤ NSc ≤ 2.5. Modifications recommended [83] Liquids 2 ≤ NRe ≤ 2000. Graph Sherwood, Pigford, & Wilke, pp. 217–218. 100 ≤ NRe ≤ 700; 1,200 ≤ NSc ≤ 1525.

= peripheral velocity

N Sh k ′dch −0.5 = 0.74 N Re , N Sh = N Re N Sc1/3 D

d υρ total surface area N Re = ch , dch = perimeter normal to flow µ

[57], p. 194; Kirwan, p. 114 Skelland, p. 276 Bird, Stewart, & Lightfoot, pp. 409, 647 [90] [83] Sherwood, Pigford, & Wilke, p. 217 Skelland, p. 276 [49], Geankoplis, p. 482 Sherwood, Pigford, & Wilke, p. 217 [93], Skelland, p. 276 [60], Skelland, p. 276 [53], Skelland, p. 276 Geankoplis, p. 482

[E] 100 < NRe ≤ 3500, NSc = 1560.

Skelland, p. 276

120 ≤ NRe ≤ 6000, NSc = 2.44. 300 ≤ NRe ≤ 7600, NSc = 1200. Use with arithmetic concentration difference.

Skelland, p. 276 [104]

50 ≤ NRe ≤ 50,000; gases, 0.6 ≤ NSc ≤ 2.6; liquids; 1000 ≤ NSc ≤ 3000. Data scatter ± 30%.

Skelland, p. 276 Geankoplis, p. 486

[E] Used with arithmetic concentration difference. Useful geometry in electrochemical studies.

[46]

112 < NRe ≤ 100,000. 835 < NSc < 11490

Sherwood, Pigford, & Wilke, p. 238

k¢ = mass-transfer coefficient, cm/s; w = rotational speed, radian/s. [E] Used with arithmetic concentration difference. 120 ≤ NRe ≤ 6000; standard deviation 2.1%. Eccentricities between 1:1 (spheres) and 3:1. Oblate spheroid is often approximated by drops.

Skelland, p. 284

[E] Used with arithmetic concentration difference. Agrees with cylinder and oblate spheroid results, ±15%. Assumes molecular diffusion and natural convection are negligible. 500 ≤ NRe,p ≤ 5000. Turbulent.

Kirwan, p. 115 Skelland, p. 285

[104]

e.g., for cube with side length a, dch = 1.27a . G. Other objects, including prisms, cubes, hemispheres, spheres, and cylinders; forced convection Molecular diffusion limits H. Shell side of microporous hollow fiber module for solvent extraction

−0.486 j D = 0.692 N Re, p , N Re, p =

υdch ρ µ

Terms same as in 5-20E.

k ′dch N Sh = =A D 0.6 N Sh = β[ d h (1 − ϕ)/ L ] N Re N Sc0.33

N Sh =

Kd h D

d h υρ , K = overall mass-transfer coefficient µ β = 5.8 for hydrophobic membrane. β = 6.1 for hydrophilic membrane. N Re =

[84] [85]

[T] Hard to reach limits in experiments. Spheres and cubes: A = 2, tetrahedrons: A = 2 6 , octahedrons: 2 2 .

Kirwan, p. 114

[E] Use with log-mean concentration difference.

[87] [103], p. 113

4 × cross-sectional area of flow d h = hydraulic diameter = wetted perimeter ϕ = packing fraction of shell side. L = module length. Based on area of contact according to inside or outside diameter of tubes depending on location of interface between aqueous and organic phases. Can also be applied to gas-liquid systems with liquid on shell side.

See Table 5-23 for flow in packed beds. ∗Author names refer to the General References list at the beginning of the Mass Transfer subsection (pp. 5-41, 5-42). Bracketed numbers refer to the table reference lists (p. 5-42).

MASS TRAnSFER

5-65

TABLE 5-21 Mass-Transfer Correlations for Drops, Bubbles, and Bubble Columns Conditions A. Single liquid drop in immiscible liquid, drop formation, discontinuous (drop) phase coefficient

Comments E = Empirical, S = Semiempirical, T = Theoretical

Correlations  ρ  D  kˆd , f = A  d   d   M d  av  πt f 

1/2

A = 24/7 (penetration theory), A = 1.31 (semiempirical value) 24 A =  (0.8624)  (extension by fresh surface elements) 7  B. Single liquid drop in immiscible liquid, drop formation, continuous phase coefficient

 ρ   D   ρ σg  kL ,c = 0.386 ×  c   c   c c   M c  av  t f   ∆ρgt f µ c 

C. Single liquid drop in immiscible liquid, free rise or fall, discontinuous phase coefficient, stagnant drops

kL ,d , m =

D. Same as 5-21C

E. Same as 5-21C, continuous phase coefficient, stagnant drops, spherical F. Single bubble or drop with surfactant. Stokes flow.

0.5

 6 ∞ 1  − Dd j 2 π 2 t    − d p  ρd  ln  ∑ exp   2   6t  M d  av  π 2 j =1 j 2  (d p / 2)    

β N Sh = 2.0 + αN Pe, N Sh = 2 rk/D 5.49 A α= + A + 6.10 A + 28.64 0.35 A + 17.21 β= A + 34.14 2r = 2 to 50 μm, A = 2.8E4 to 7.0E5 0.0026 < NPe,s < 340, 2.1 < NMa < 1.3E6 NPe = 1.0 to 2.5 × 104, NRe = 2.2 × 10-6 to 0.034

ρ  kL ,c ,m d 3 = 0.74  c  ( N Re,3 )1/2 ( N Sc,c )1/3 Dc  M c  av

N Re,3 =

υ s d 3 ρc µc

 R 1/2 πDd1/2 θ1/2  dp  ρ  kˆL ,d ,circ = −  d  ln 1 −  6θ  M d  av  dp /2 

I. Same as 5-21F N Sh =

kˆL ,d ,circ d p Dd

M. Liquid drops in immiscible liquid, free rise or fall, discontinuous phase coefficient, oscillating drops

 d p υ 2s ρc  −0.125 N Sc, d    σg c 

−0.34

−0.37

1/8 Re,drop

kL′ ,c d p

 µc   µ  d

L. Same as 5-20J, circulating swarm of drops

4D t ρ = 31.4  d   2d   M f  av  d p 

0.072   d p g 1/3  0.484 0.339 N Sc, =  2 + 0.463 N Re,drop c  2/3  Dd  Dc   F = 0.281 + 1.615K + 3.73K2 - 1.874K3

N Sh,c =

K=N K. Same as 5-20J, circulating, single drop

0.148

 ρ  kL ,c ,m dc 1/2 = 0.74  c  N Re ( N Sc )1/3 Dc  M c  av

N Sh =

N Sh =

J. Liquid drop in immiscible liquid, free rise or fall, continuous phase coefficient, circulating single drops

 gt 2f     dp 

 πD 1/2 t 1/2  − d p  ρd  ln 1 − d kˆL ,d ,m =  6t  M d  av  d p / 2 

G. See oblate spheroid

H. Single liquid drop in immiscible liquid, free rise or fall, discontinuous phase coefficient, circulating drops

0.407

N Sh =

kL ,c d p Dc

1/4

 µc υs   σg 

Dd

[E] Average absolute deviation 11% for 20 data points for 3 systems.

Skelland, p. 402 [105] p. 434

[T] Use with log-mean mole fraction differences based on ends of column. t = rise time. No continuous phase resistance. Stagnant drops are likely if drop is very viscous, quite small, or is coated with surface active agent. kL,d,m = mean dispersed liquid MT coefficient.

Skelland, p. 404 [105] p. 435

[S] See 5-21C. Approximation for fractional extractions less than 50%.

Skelland, p. 404 [105] p. 435

[E] N Re = υ s d pρc / µ c , υ S = slip velocity between drop and continuous phase.

Skelland, p. 407 [104][105] p. 436

[T] A = surface retardation parameter A = BΓor/μDs = NMaNPe,s NMa = BΓo/μu = Marangoni no. Γ = surfactant surface concentration, B = -∂s/ ∂Γ = constant NPe,s = surface Peclet number = ur/Ds Ds = surface diffusivity NPe = bulk Peclet number For A >> 1 acts like rigid sphere: β → 0.35, a → 1/2864 = 0.035

[89]

[E] Used with log-mean mole fraction. Differences based on ends of extraction column; 100 measured values ±2% deviation. Based on area oblate spheroid. total drop surface area υ s = slip velocity, d 3 = perimeter normal to flow

Skelland, pp. 285, 406, 407

[E] Used with mole fractions for extraction less than 50%, R ≈ 2.25.

Skelland, p. 405

[E] Used with log-mean mole fraction difference. dp = diameter of sphere with same volume as drop. 856 ≤ NSc ≤ 79,800, 2.34 ≤ s ≤ 4.8 dynes/cm.

[105] p. 435 [106]

[E] Used as an arithmetic concentration difference.

[61]

d p υ s ρc µc

c

ρ 1/2 1/2 = 0.6  c  N Re,drop N Sc, c  M c  av

kL ,d ,osc d p

Skelland, p. 399

Solid sphere form with correction factor F .

 ρ  −0.43 −0.58 kL ,c = 0.725  c  N Re,drop N Sc, c υ s (1 − φ d )  M c  av

N Sh =

[T,S] Use arithmetic mole fraction difference. Fits some, but not all, data. Low mass transfer rate. Md = mean molecular weight of dispersed phase; tf = formation time of drop kL,d = mean dispersed liquid phase MT. coefficient k mole/[s ⋅ m2 (mole fraction)].

N Re,drop =

1/6

References∗

 ρ   4D t  = 0.32  d   2d   M d  av  d p 

−0.14

 σ 3 g c3 ρc2  0.68 N Re,drop  g µ 4 ∆ρ  c

0.10

[E] Used as an arithmetic concentration difference. Low s.

Skelland, p. 407

[E] Used as an arithmetic concentration difference. Low s, disperse-phase holdup of drop swarm. fd = volume fraction dispersed phase.

Skelland, p. 407 [105] p. 436

[E] Used with a log-mean mole fraction difference. Based on ends of extraction column. d p υ s ρc , 411 ≤ NRe ≤ 3114 N Re,drop = µc dp = diameter of sphere with volume of drop. Average absolute deviation from data, 10.5%. Low interfacial tension (3.5–5.8 dyn), μc < 1.35 centipoise.

Skelland, p. 406 [105] p. 435 [106]

5-66

HEAT AnD MASS TRAnSFER

TABLE 5-21 Mass-Transfer Correlations for Drops, Bubbles, and Bubble Columns (Continued ) Conditions N. Same as 5-21M

O. Single liquid drops in gas, gas side coefficient

Correlations kL ,d ,osc =

0.00375 υ s 1 + µ d / µc

kˆg M g d p P Dgas ρ g

1/2 1/3 = 2 + AN Re, g N Sc, g

A = 0.552 or 0.60 d pρg υs N Re, g = µg P. Single water drop in air, liquid side coefficient

D kL = 2  L   πt  kL = 10

Q. Single bubbles of gas in liquid, continuous phase coefficient, very small bubbles R. Same as 5-21Q, medium to large bubbles

Comments E = Empirical, S = Semiempirical, T = Theoretical

References∗

[T] Use with log-mean concentration difference. Based on end of extraction column. No continuous phase resistance. kL,d,osc in cm/s, vs = drop velocity relative to continuous phase.

Sherwood, Pigford, & Wilke, p. 228 Skelland, p. 405

[E] Used for spray drying (arithmetic partial pressure difference).

[68] p. 388 [90]

vs = slip velocity between drop and gas stream. Sometimes written with MgP/rg = RT .

1/2

, short contact times

[T] Use arithmetic concentration difference. Penetration theory. t = contact time of drop. Gives plot for kGa also. Air-water system.

[68] p. 389

DL , long contact times dp

N Sh =

kc′db = 1.0 ( N Re N Sc )1/3 Dc

[T] Solid-sphere Eq. db < 0.1 cm, k¢c is average over entire surface of bubble.

Sherwood, Pigford, & Wilke, p. 214

N Sh =

kc′db = 1.13( N Re N Sc )1/2 Dc

[T] Use arithmetic concentration difference. Droplet equation: db > 0.5 cm.

Sherwood, Pigford, & Wilke, p. 231

N Sh =

  kc′db db = 1.13 ( N Re N Sc )1/2   Dc  0.45 + 0.2 db 

[S] Use arithmetic concentration difference. Modification of above (5-21R), db > 0.5 cm. No effect SAA for dp > 0.6 cm.

[62], Sherwood, Pigford, & Wilke, p. 231

[E] Air-water Luc = unit cell length, Lslug = slug length, dc = capillary i.d. For most data kLa ± 20%.

[110]

[E] Each channel in monolith is a capillary. Results are in expected order of magnitude for capillaries based on 5-21T. kL is larger than in stirred tanks.

[70]

[E] Use with arithmetic concentration difference. Valid for single bubbles or swarms. Independent of agitation as long as bubble size is constant. Recommended by [99]. Note that NRa = NGrNSc.

[34] Geankoplis, p. 451 Kirwan, p. 119 Treybal, p. 156 [99]

[E] Use with arithmetic concentration difference. For large bubbles, k′c is independent of bubble size and independent of agitation or liquid velocity. Resistance is entirely in liquid phase for most gas-liquid mass transfer. Hg = fractional gas holdup, volume gas/total volume.

[34] Geankoplis, p. 452 Kirwan, p. 119 [72] p. 249 [99]

[E] d = bubble diameter Air–liquid. Recommended by [99] and Treybal. For swarms, calculate NRe with slip velocity Vs . ϕG = gas holdup, VG = superficial gas velocity Col. diameter = 0.025 to 1.1 m ρ¢L = 776 to 1696 kg/m3, μL = 0.0009 to 0.152 Pa ⋅ s

[42] [61] Treybal, p. 144

[E] dVs = Sauter mean bubble diameter, NRe = dVsuGρL/μL. Recommended by [36] based on experiments in industrial system.

[36] [97]

S. Same as 5-21R

500 ≤ NRe ≤ 8000 T. Taylor bubbles in single capillaries (square or circular)

 Du  kL a = 4.5  G   Luc 

1/2

1 dc

 u +u  Applicable  G L   Lslug  U. Gas-liquid mass transfer in monoliths

P kL a ≈ 0.1   V 

0.5

> 3( s −0.5 )

1/4

P/V = power/volume (kW/m3), range = 100 to 10,000 V. Rising small bubbles of gas in liquid, continuous phase. Calderbank and Moo-Young correlation

W. Same as 5-21V, large bubbles

X. Bubbles in bubble columns. Hughmark correlation

N Sh =

kc′db = 2 + 0.31( N Gr )1/3 N Sc1/3 , db < 0.25 cm Dc

N Ra =

db3 | ρG − ρL | g = Raleigh number µ L DL

kc′db = 0.42( N Gr )1/3 N Sc1/2 , db > 0.25 cm Dc 6H g Interfacial area =a= volume db

N Sh =

N Sh =

1/3  kL d 0.779  dg = 2 + bN Sc0.546 N Re  D 2/3  D

b = 0.061 single gas bubbles b = 0.0187 swarms of bubbles Vg V − L Vs = ϕG 1 − ϕG Y. Bubbles in bubble column

kL =

0.15 D  v    dVs  D 

1/2 3/4 N Re

0.116

See Table 5-22 for agitated systems. ∗Author names refer to the General References list at the beginning of the Mass Transfer subsection (pp. 5-41, 5-42). Bracketed numbers refer to the table reference lists (p. 5-42).

MASS TRAnSFER

5-67

TABLE 5-22 Mass-Transfer Correlations for Particles, Drops, and Bubbles in Agitated Systems Situation A. Solid particles suspended in agitated vessel containing vertical baffles, continuous phase coefficient

Comments E = Empirical, S = Semiempirical, T = Theoretical

Correlation kLT ′ dp

1/2 1/3 = 2 + 0.6 N Re, T N Sc D Replace vslip with vT = terminal velocity. Calculate Stokes’ law terminal velocity

υ Ts =

d p2 | ρ p − ρc | g

18µ c and correction factor:

N Re,T =

N Re, Ts

1

10

100

1000

υT / υ Ts

0.9

0.65

0.37

0.17

10,000 100,000 0.07

0.023

Approximate: k¢L = 2 k¢LT B. Solid, neutrally buoyant particles, continuous phase coefficient

N Sh =

[S] Use log-mean concentration difference. Modified Frossling equation: υ Ts d p ρc N Re,Ts = µc (Reynolds number based on Stokes’ law.)

kL′ d p

d imp  0.62 0.36  = 2 + 0.47 N Re, p N Sc  D  d tank 

Graphical comparisons are in Ref. 88, p. 116. 0.52 1/3 N Sh = 2 + 0.52 N Re, p N Sc , N Re, p < 1.0

µc (terminal velocity Reynolds number.) kL′ almost independent of dp Harriott [56] suggests different correction procedures. Range k¢L /k¢LT is 1.5 to 8.0.

=

C. Solid particles with significant density difference

N Sh =

kL′ d p D

 d p υslip  = 2 + 0.44   v 

D. Small solid particles, gas bubbles or liquid drops, dp < 2.5 mm. Aerated mixing vessels

N Sh =

E. Highly agitated systems; solid particles, drops, and bubbles; continuous phase coefficient

 ( P / Vtank )µ c g c  kL′ N Sc2/3 = 0.13   ρc2  

F. Gas bubble swarms in sparged tank reactors

G. Same as 5-22F, baffled tank with standard blade Rushton impeller

H. Same as 5-22G, bubbles

D

N Sc0.38

 d p3 | ρ p − ρc |  = 2 + 0.31  µc D  

1/3

1/4

b

a 1/3  P / VL   qG  v   =C    2  4 1/3  (v g ) V g ρ      L  Rushton turbines: C = 7.94 × 10−4, a = 0.62, b = 0.23. Intermig impellers: C = 5.89 × 10−4, a = 0.62, b = 0.19.

 v  kL′ a =  2  g 

1/3

 P kL′ a = 93.37    VL 

2 kL′ ad imp

D I. Surface aerators for airwater contact

kL′ d p

1/2

0.76

uG0.45

2 2 N ρ   d imp N2  d imp = 0.060     µ eff   g 

kL a 0.48 0.82  H  = bN 0.71 p N Fr N Re   d  N

−0.54

V   3  d

0.19

 µ eff uG    σ 

0.6

−1.08

b = 7 × 10−6, Np = P/(ρN3d5) NRe = Nd2ρliq/µliq NFr = N2d/g, P/V = 90 to 400 W/m3

J. Individual drops in LLE. Continuous phase coefficients

ShC,circ ≡ (kC d/DAC) = (2/π0.5) PeC0.5 PeC = (d ut/DAC) ShC,rigid = 2.43 + {0.773 Redrop0.5 + 0.0103 Redrop}ScC0.33 (ShC − ShC,rigid)/(ShC,circ − ShC,rigid) = 1 − exp[−0.00418 PeC0.42]

K. Average drop size in LLE mixers

dP  σ 2 g 2   µC4 g  = 1 + 1.18ϕ D  o 2c   d Po  d P µC g   ∆ρσ 3 g c3 

0.62

 ∆ρ   ρ  C

0.05

[56] Sherwood, Pigford, & Wilke, pp. 220–222 [83]

υT d p ρc

[E] Use log-mean concentration difference. Density unimportant if particles are close to neutrally buoyant. Also used for drops. Geometric effect (dimp/dtank) is usually unimportant. Ref. [77] gives a variety of references on correlations. [E] E = energy dissipation rate per unit mass fluid

0.17

References∗

Pg c Vtank ρc

, P = power, N Re, p =

[56] Kirwan, p. 115 [77] p. 132

Treybal, p. 523

E 1/3 d p4/3 v

[E] Small particles

Kirwan, p. 116

[E] Use log-mean concentration difference. NSh standard deviation 11.1%. vslip calculated by methods given in reference.

[77] [83]

[E] Use log-mean concentration difference g = 9.80665 m/s2. Second term RHS is free-fall or rise term. For large bubbles, see Table 5-21W.

[33] [50] p. 487 [72] p. 249

[E] Use arithmetic concentration difference. Use when gravitational forces overcome by agitation. Up to 60% deviation. Correlation prediction is low [77]. (P/Vtank) = power dissipated by agitator per unit volume liquid.

[34] Geankoplis, p. 489 [83]

[E] Use arithmetic concentration difference. Done for biological system, O2 transfer. htank/Dtank = 2.1; P = power, kW. VL = liquid volume, m3. qG = gassing rate, m3/s. k¢La = s−1. Since a = m2/m3, v = kinematic viscosity, m2/s. Low viscosity system. Better fit claimed with qG/VL than with uG (see 5-22G and H).

[96]

[E] Air-water. Same definitions as 5-22F. 0.005 < uG < 0.025, 3.83 < N < 8.33, 400 < P/VL < 7000 h = Dtank = 0.305 or 0.610 m. VG = gas volume, m3, N = stirrer speed, rpm. Method assumes perfect liquid mixing.

[50] [73]

[E] Use arithmetic concentration difference. O2 into aqueous glycerol solutions. O2 into aqueous millet jelly solutions. Same definitions as 5-22G.

[73] [117]

[E] Three impellers: Pitched blade downflow turbine, pitched blade upflow turbine, standard disk turbine. Baffled cylindrical tanks 1.0- and 1.5-m id and 8.2 × 8.2-m square tank. Submergence optimized all cases. Good agreement with data. N = impeller speed, s−1; d = impeller diameter, m; H = liquid height, m; V = liquid volume, m3; kLa = s−1, g = acceleration gravity = 9.81 m/s2

[86]

[E] Clean circulating drops, Steiner’s results for 10 < Redrop < 1200, 190 < ScC < 241000, and 1000 < PeC < 106, [E] Rigid drops (common in dirty conditions), Steiner’s results, 104 < PeC < 106, Preferred for dirty conditions. [E] Preferred for clean conditions between circulating & rigid. Steiner’s results

[107] [114]

[E] Baffled mixers. LLE data. ∆ρ = ρC − ρD ⋅d Po is from,

Treybal [114]

o3 p

2 C 2 C

d ρ g µ

3 2 Liq-tank C c 3 3 c

V = 29  

4

ρ µ g  

P g

0.32

 σ 3ρC g c3   µ 4 g  C

0.14

See also Table 5-21. ∗Author names refer to the General References list at the beginning of the Mass Transfer subsection (pp. 5-41, 5-42). Bracketed numbers refer to the table reference lists (p. 5-42).

5-68

HEAT AnD MASS TRAnSFER

TABLE 5-23 Mass-Transfer Correlations for Fixed and Fluidized Beds Transfer is to or from particles Situation A. For gases, fixed and fluidized beds, Gupta and Thodos correlation

Comments E = Empirical, S = Semiempirical, T = Theoretical

Correlation jH = jD =

2.06 , 90 ≤ N Re ≤ A 0.575 εN Re

[E]For spheres. N Re =

Equivalent: k ′d s 2.06 0.425 1/3 N Sh = = N Re N Sc D ε For other shapes: εj D = 0.79 (cylinder) or 0.71 (cube) (εj D )sphere B. For gases and liquids, fixed and fluidized beds

jD =

C. For liquids, fixed bed, Wilson and Geankoplis correlation

jD =

0.4548 ,10 ≤ N Re ≤ 2000 0.4069 εN Re k ′d s N Sh , N Sh = jD = D N Re N Sc1/3 1.09 , 0.0016 < N Re < 55 2/3 εN Re

165 ≤ NSc ≤ 70,600, 0.35 < ε < 0.75 Equivalent: 1.09 1/3 1/3 N Sh = N Re N Sc ε 0.25 , 55 < N Re < 1500,165 ≤ N Sc ≤ 10,690 jD = 0.31 εN Re 0.25 0.69 1/3 Equivalent: N Sh = N Re N Sc ε D. For liquids, fixed beds, Ohashi et al. correlation

N Sh =

 E 1/3 d p4/3 ρ  k ′d s = 2 + 0.51   µ D  

0.60

N Sc1/3

E = Energy dissipation rate per unit mass of fluid  υ3  = 50 (1 − ε)ε 2C Do  r  , m 2 /s 3  dp   50 (1 − ε)C D   υsuper  =   d  ε   p  3

General form: 1/3

4/3 p

α

 E d ρ β N Sh = 2 + K   N Sc µ  

E. Electrolytic system. Pall rings. Transfer from fluid to rings.

Full liquid upflow, NRedeu/v = 80 to 550: 0.39 N Sh = kL de /D = 4.1 N Re N Sc1/3 Irrigated liquid downflow (no gas flow): 0.44 N Sh = 5.1 N Re N Sc1/3

F. For liquids, fixed and fluidized beds

G. For gases and liquids, fixed and fluidized beds, Dwivedi and Upadhyay correlation

H. For gases and liquids, fixed bed

εj D =

1.1068 ,1.0 < N Re ≤ 10 0.72 N Re

εjD =

N Sh k ′d s , N Sh = N Re N Sc1/3 D

0.765 0.365 + 0.386 0.82 N Re N Re Gases: 10 ≤ NRe ≤ 15,000. Liquids: 0.01 ≤ NRe ≤ 15,000. d p υsuper ρ k ′d s N Re = , N Sh = µ D εjD =

−0.415 j D = 1.17 N Re ,10 ≤ N Re ≤ 2500

k ′ pBM 2/3 jD = N Sc υ av P

υsuper d p ρ

References∗ [54] [55]

µ A = 2453 (Skelland), A = 4000 [57]. For NRe > 1900, jH = 1.05jD. Heat transfer result is in absence of radiation. Graphical results are available for NRe from 1900 to 10,300. surface area a= = 6(1 − ε)/d p volume For spheres, dp = diameter. For nonspherical : d p = 0.567 Part. Surf. Area

[57], p. 195 Skelland

[E] Packed spheres, deep bed. Average deviation ±20%, NRe = dpvsuperρ/μ. Can use for fluidized beds. 10 ≤ NRe ≤ 4000.

[46] Geankoplis, p. 484

[E] Beds of spheres,

Geankoplis, p. 484

N Re =

d pVsuper ρ

µ Deep beds.

[57], p. 195 Skelland, p. 287 [115]

k ′d s N Sh = D

[S] Applies to single particles, packed beds, two-phase tube flow, suspended bubble columns, and stirred tanks with different definitions of E . Correlates large amount of published data. Compares number of correlations, vr = relative velocity, m/s. In packed bed, vr = vsuper/ε. CDo = single particle drag coefficient at vsuper calculated from −m C Do = AN Re . i N Re

A

m

0 to 5.8

24

1.0

5.8 to 500

10

0.5

> 500

0.44

0

[81]

Ranges for packed bed: E 1/3 d p4/3 ρ < 4600 0.2 < µ Compares different situations versus general correlation. [E] de = diameter of sphere with same surface area as Pall ring. Full liquid upflow agreed with literature values. Schmidt number dependence was assumed from literature values. In downflow, NRe used superficial fluid velocity.

[52]

[E] Spheres:

[45] Geankoplis, p. 484

N Re =

d p υsuper ρ µ

[E] Deep beds of spheres, N Sh jD = N Re N Sc1/3 Best fit correlation at low conc. [39] Based on 20 gas studies and 17 liquid studies.

[45] [57] p. 196 [39]

[E] Spheres: Variation in packing that changes ε not allowed for. Extensive data referenced. 0.5 < NSc < 15,000. Show comparisons with other results. d p υsuper ρ N Re = µ

Sherwood, Pigford, & Wilke, p. 241

MASS TRAnSFER

5-69

TABLE 5-23 Mass-Transfer Correlations for Fixed and Fluidized Beds (Continued ) Situation I. For liquids, fixed and fluidized beds, Rahman and Streat correlation

Comments E = Empirical, S = Semiempirical, T = Theoretical

Correlation

References∗

N Sh =

0.86 N Re N Sc1/3 , 2 ≤ N Re ≤ 25 ε

[E] Can be extrapolated to NRe = 2000. NRe = dpvsuperρ/μ. Done for neutralization of ion exchange resin.

[88]

J. Size exclusion chromatography of proteins

N Sh =

kL d 1.903 1/3 1/3 = N Re N Sc D ε

[E] Slow mass transfer with large molecules. Aqueous solutions. Modest increase in NSh with increasing velocity.

[58]

K. For liquids and gases, Ranz and Marshall correlation

N Sh =

k ′d 1/2 = 2.0 + 0.6 N Sc1/3 N Re D d p υsuper ρ

[E] Based on freely falling, evaporating spheres (see 5-20C). Has been applied to packed beds, prediction is low compared to experimental data. Limit of 2.0 at low NRe is too high. Not corrected for axial dispersion.

[23] p. 214, [90]

[E] Correlate 20 gas studies and 16 liquid studies. Corrected for axial dispersion. Graphical comparison with data shown [23, p. 215], and [112].

[23] p. 214 [112]

N Re = L. For liquids and gases, Wakao and Funazkri correlation

µ

0.6 N Sh = 2.0 + 1 N Sc1.1/3 N Re , 3 < N Re < 10,000

N Sh =

[112] [83]

kfilm ′ dp D

, N Re =

ρ f υsuper d p µ

Daxial is axial dispersion coefficient.

εDaxial = 10 + 0.5 N Sc N Re D M. Semifluidized or expanded bed. Liquid-solid transfer.

N. Mass-transfer structured packing and static mixers. Liquid with or without fluidized particles. Electrochemical

kfilm d p

1/3 N Sc1/3 = 2 + 1.5 (1 − ε L ) N Re D NRe = ρpdpu/μεL; NSc = μ/ρD

N Sh =

Fixed bed: 0.572 j ′ = 0.927 N Re ′ < 219 ′ , N Re -0.435 j ′ = 0.443 N Re , 219 < N Re ′ < 1360 ′ Fluidized bed with particles: −0.885 −0.950 j ′ = 6.02 N Re , or j ′ = 16.40 N Re ′ Natural convection: 0.299 NSh = 0.252(NScNGr) Bubble columns: Structured packing: N St = 0.105 ( N Re N Fr N Sc2 )−0.268

0.023 0.306  ρs − ρ  N Sh = 0.250 N Re N Ga  ρ 

0.282

−0.057 0.332  ρs − ρ  N Sh = 0.304 N Re N Ga  ρ 

N Sc0.410 (ε < 0.85) 0.297

N Sc0.404 (ε > 0.85)

This can be simplified (with slight loss in accuracy at high ε) to 0.323  ρs − ρ  N Sh = 0.245 N Ga  ρ 

P. Liquid film flowing over solid particles with air present, trickle bed reactors, fixed bed

Q. Supercritical fluids in packed bed

0.300

N Sc0.400

kL 1/2 = 1.8 N Re N Sc1/3 , 0.013 < N Re < 12.6 aD two-phases, liquid trickle, no forced flow of gas. 1/2 N Sh = 0.8 N Re N Sc1/3 , one-phase, liquid only. N Sh =

 N 1/2 N 1/3  N Sh = 0.5265  Re Sc1/4  ( N Sc N Gr )1/4  N Sc N Gr )   N 2 N 1/3  + 2.48  Re Sc   N Gr 

R. Co current gas-liquid flow in fixed beds

[48] [116]

k cos β 2/3 N Sc , υ β = corrugation incline angle. NRe′ = v¢ d¢hρ/μ, v¢ = vsuper/(ε cos β), d¢h = channel side width. Particles enhance mass transfer in laminar flow for natural convection. Good fit with correlation of Ray et al., Intl . J . Heat Mass Transfer 41: 1693 (1998). NGr = g Δ ρZ3ρ/μ2, Z = corrugated plate length. Bubble column results fit correlation of Neme et al., Chem . Eng . Technol . 20: 297 (1997) for structured packing. NSt = Stanton number = kZ/D NFr = Froude number = v2super/gz

[35]

[E] Correlate amount of data from literature. Predicts very little dependence of NSh on velocity. Compare large number of published correlations. kL′ d p d p ρυsuper d p3 ρ2 g N Sh = , , N Re = , N Ga = D µ µ2 µ N Sc = ρD 1.6 < NRe < 1320, 2470 < NGa < 4.42 × 106 ρ −ρ 0.27 < s < 1.114, 305 < N Sc < 1595 ρ

[109]

L , irregular granules of benzoic acid, aµ 0.29 ≤ d p ≤ 1.45 cm.

[95]

[E] = Sulzer packings, j ′ =

Static mixer: N St = 0.157 ( N Re N Fr N Sc2 )−0.298 O. Liquid fluidized beds

[E] εL = liquid-phase void fraction, ρp = particle density, ρ = fluid density, dp = particle diameter. Fits expanded bed chromatography in viscous liquids.

1.6808

[E] N Re =

L = superficial liquid flow rate, kg/m2s. a = surface area/col. volume, m2/m3. [E] Natural and forced convection. 0.3 < NRe < 135.

[74]

Literature review and meta-analysis. Analyzed both downflow and upflow. Recommendations for best mass and heat-transfer correlations (see reference).

[71]

1.553

0.6439

− 0.8767

Downflow in trickle bed and up flow in bubble columns.

note: For NRe < 3 convective contributions which are not included may become important. Use with logarithmic concentration difference (integrated form) or with arithmetic concentration difference (differential form). ∗Author names refer to the General References list at the beginning of the Mass Transfer subsection (pp. 5-41, 5-42). Bracketed numbers refer to the table reference lists (p. 5-42).

5-70

HEAT AnD MASS TRAnSFER

TABLE 5-24 Mass-Transfer Correlations for Packed Two-Phase Contactors—Absorption, Distillation, Cooling Towers, and Extractors (Packing Is Inert) Situation A. Absorption, countercurrent, liquid-phase coefficient HL, Sherwood and Holloway correlation for random packings

Comments E = Empirical, S = Semiempirical, T = Theoretical

Correlations n

 L 0.5 2 H L = a L   N Sc, L , L = lb/hr ft  µL  Ranges for 5-23-B (G and L) Packing

aG

b

c

G

L

aL

n

Raschig rings ⅜ inch

2.32

0.45 0.47 200–500

500–1500 0.00182 0.46

1

7.00

0.39 0.58 200–800

400–500

1

6.41

0.32 0.51 200–600

500–4500 —

—

2

3.82

0.41 0.45 200–800

500–4500 0.0125

0.22

½ inch

32.4

0.30 0.74 200–700

500–1500 0.0067

0.28

½

0.811 0.30 0.24 200–800

400–4500 —

—

1

1.97

0.36 0.40 200–800

400–4500 0.0059

0.28

1.5

5.05

0.32 0.45 200–1000 400–4500 0.0062

0.28

0.010

0.22

References∗

[E] From experiments on desorption of sparingly soluble gases from water. Graphs: Sherwood, Pigford, & Wilke, p. 606. Equation is dimensional. Geankoplis states a typical value of n is 0.3 and has constants in kg, m, and s units for use in 5-24A and B with kˆG in kg mole/sm2 and kˆL in kg mole/ sm2 (kg mol/m3). Constants for other packings are given by [79, p. 187] and Treybal, p. 239. L HL = M kˆL a LM = lbmol/hr ft2, kˆL = lbmol/hr ft2, a = ft2/ft3, μL = lb/(h ft). Range for 5-24A is 400 < L < 15,000 lb/h ft2

[79] p. 187 Sherwood, Pigford, & Wilke, p. 606 [101], [114] [113]

[E] Based on ammonia-water-air data in Fellinger’s 1941 MIT thesis. Curves: [79], p. 186 and Sherwood, Pigford, & Wilke, p. 607. Constants given in 5-24A. The equation is dimensional. G = lb/hr ft2, GM = lb mol/hr ft2, kˆG = lbmol/hr ft2.

[79] p. 189 Sherwood, Pigford, & Wilke, p. 607 [114]

[E] Gas absorption and desorption from water and organics plus vaporization of pure liquids for Raschig rings, saddles, spheres, and rods. d¢p = nominal packing size, ap = dry packing surface area/volume, aw = wetted packing surface area/volume. Equations are dimensionally consistent, so any set of consistent units can be used. s = surface tension, dynes/cm. A = 5.23 for packing ≥ 1/2 inch (0.012 m) A = 2.0 for packing < 1/2 inch (0.012 m) k¢G = lbmol/hr ft2 atm [kg mol/s m2 (N/m2)] Critical surface tensions, sC = 61 (ceramic), 75 (steel), 33 (polyethylene), 40 (PVC), 56 (carbon) dynes/cm. L G 4< < 400, 5 < < 1000 aw µ L a P µG

[31]

Berl saddles

B. Absorption countercurrent, gas-phase coefficient HG, for random packing

C. Absorption and and distillation, countercurrent, gas and liquid individual coefficients and wetted surface area, Onda et al. correlation for random packings

b

HG =

0.5

G M aG (G ) N Sc, υ = ( L )c kˆG a

 G  kG′ RT = A  a p DG  a p µG   ρ  kL′  L   µL g 

1/3

0.7 1/3 −2.0 N Sc, G (a p d ′p )

 L  = 0.0051   aw µ L 

2/3 0.4 −1/2 N Sc, L (a p d ′p )

k¢L = lbmol/hr ft2 (lbmol/ft3) [kgmol/s m2 (kgmol/m3)] 0.1 0.75   L   σ  −1.45  c     σ   a pµ L    aw  = 1 − exp  0.2  −0.05 ap  L     L2 a p  ×  2      ρL σa p     ρL g 

D. Distillation and absorption, counter-current, random packings, modification of Onda correlation, Bravo and Fair correlation to determine interfacial area

E. Absorption and distillation, countercurrent gas-liquid flow, random and structured packing. Determine HL and HG

 σ 0.5  ae = 0.489 a p  0.4  ( N Ca ,L N Re,G )0.392 Z  6G Lµ L N Re,G = , N Ca ,L = (dimensionless) a p µG ρL σg c  0.226   N Sc  b  Gx  −0.5  G y  0.35 HG =         f p   0.660   6.782   0.678  0.3 0.5  0.357   N Sc    Gx /µ HL =       f p   372   6.782/0.0008937  Relative transfer coefficients [69], fp values are in table: Ceramic Ceramic Metal Pall Raschig Berl saddles rings Size, in. rings

Metal Intalox

Metal Hypac

0.5 1.0 1.5 2.0

— 1.78 — 1.27

— 1.51 — 1.07

1.58 1.36 — —

— 1.61 1.34 1.14

[82] Taylor & Krishna, p. 355 [113]

Most data ± 20% of correlation, some ± 50%. Graphical comparison with data in [82].

Use Onda’s correlations (5-24C) for k¢G and k¢L. Calculate: G L HG = , HL = , H OG = H G + λH L kG′ ae PM G kL′ ae ρL m λ= LM /G M

1.52 1.20 1.00 0.85

[68] p. 380

Norton Intalox structured: 2T, fp = 1.98; 3T, fp = 1.94.

[E] Used Bolles & Fair [30] database to determine new effective area ae to use with Onda et al. [82] correlation. Same definitions as 5-24C. P = total pressure, atm; MG = gas, molecular weight; m = local slope of equilibrium curve; LM/GM = slope operating line; Z = height of packing in feet. Equation for ae is dimensional. Fit to data for effective area quite good for distillation. Good for absorption at low values of (NCa,L × NRe,G), but correlation is too high at higher values of (NCa,L × NRe,G).

[31]

[S] HG based on NH3 absorption data (5-24B) for which HG, base = 0.226 m with NSc, base = 0.660 at Gx, base = 6.782 kg/(sm2) and Gy, base = 0.678 kg/(sm2) with 1½ in. ceramic Raschig rings. The exponent b on NSc is reported as either 0.5 or as ⅔. H for NH 3 with1 1 2 Raschig rings fp = G H G for NH 3 with desired packing

Geankoplis, pp. 686, 659 Sherwood, Pigford, & Wilke, [113]

HL based on O2 desorption data (5-24A). Base viscosity, μbase = 0.0008937 kg/(ms). HL in m. Gy < 0.949 kg/(sm2), 0.678 < Gx < 6.782 kg/(sm2). Best use is for absorption and stripping. Limited use for organic distillation [113].

MASS TRAnSFER

5-71

TABLE 5-24 Mass-Transfer Correlations for Packed Two-Phase Contactors—Absorption, Distillation, Cooling Towers, and Extractors (Packing Is Inert) (Continued ) Situation F. Absorption, cocurrent downward flow, random packings, Reiss correlation

Comments E = Empirical, S = Semiempirical, T = Theoretical

Correlations Air-oxygen-water results correlated by k′La = 0.12EL0.5. Extended to other systems. 0.5

DL  ∆P  kL′ a = 0.12 E L0.5  υ , E L =  5  ∆L  2-phase L  2.4 × 10  Δp/ΔL = 2-phase flow pressure loss, lbf/( ft2 ⋅ ft) kG′ a = 2.0 + 0.91 EG2/3 for NH 3 , E g = ( ∆p/∆L)2-phase υ g

G. Absorption, stripping, distillation, countercurrent, HL, and HG, random packings, Bolles and Fair correlation

For Raschig rings, Berl saddles, and spiral tile: 0.15 φC 0.5  Z  H L = flood N Sc, L  3.05  3.28 Cflood = 1.0 if below 40% flood—otherwise, use figure in [41] or [114]. 0.5 Aψ (dcol ′ )m Z 0.33 N Sc, G HG = 0.16 1.25 0.8 n   µL   ρ   σ water   Figures for f and y in water L         µ water   ρL   σ L   [42 and 43]. Ranges: 0.02 < f < 0.300; 25 < y < 190 m.

H. Distillation and absorption. Counter-current flow. Structured packings. Gauze-type with triangular flow channels, Bravo, Rocha, and Fair correlation

Equivalent channel: 1 1 +  deq = Bh   B + 2 S 2 S 

References∗

[E] Based on oxygen transfer from water to air 77°F. Liquid film resistance controls. (Dwater @ 77°F = 2.4 × 10-5). Equation is dimensional. Data was for thin-walled polyethylene Raschig rings. Correlation also fit data for spheres. Fit ±25%. See [91] for graph. k¢La = s-1 DL = cm/s, EL = ft, lbf/s ft3 vL = superficial liquid velocity, ft/s; vg = superficial gas velocity, ft/s [E] Ammonia absorption into water from air at 70°F. Gas-film resistance controls. Thin-walled polyethylene Raschig rings and 1-inch Intalox saddles. Fit ±25%. See [91] for fit. Terms defined as above.

[91] [95] p. 217

[E] Z = packed height, m of each section with its own liquid distribution. The original work is reported in English units. Cornell et al. (Ref. 41) review early literature. Improved fit of Cornell’s f values given by Bolles and Fair (Refs. [29], [30]) and [114]. A = 0.017 (rings) or 0.029 (saddles) d¢col = column diameter in m (if diameter > 0.6 m, use d¢col = 0.6) m = 1.24 (rings) or 1.11 (saddles) n = 0.6 (rings) or 0.5 (saddles) L = liquid rate, kg/(sm2), μwater = 1.0 Pa.s, ρwater = 1000 kg/m3, swater = 72.8 mN/m (72.8 dyn/cm). HG and HL will vary from location to location. Design each section of packing separately.

[29, 30, 41] [57] p. 428 [68] p. 381 Skelland, p. 353 [114] [113]

[T] Check of 132 data points showed average deviation 14.6% from theory. Johnstone and Pigford [Ref. 63] correlation (5-18E) has exponent on NRe rounded to 0.8. Assume gauze packing is completely wet. Thus, aeff = ap to calculate HG and HL. Same approach may be used generally applicable to sheet-metal packings, but they will not be completely wet and need to estimate transfer area. Fit to data shown in Ref. [32]. L = liquid flux, kg/s m2, G = vapor flux, kg/s m2.

[32] [47] pp. 310, 326 Taylor & Krishna, pp. 356, 362 [113]

[91]

G L , HL = kυ′ a p ρυ kL′ a p ρL effective velocities HG =

Use modified correlation for wetted wall column (See 5-18E) kυ′ deq 0.8 0.333 N Sh,υ = = 0.0338 N Re, υ N Sc,υ Dυ N Re,υ =

deq ρυ (U υ ,eff + U L ,eff )

µυ Calculate k¢L from penetration model (use time for liquid to flow distance s). k¢L = 2(DLUL,eff/πS)1/2. I . Distillation and absorption, counter-current flow . Structured packing with corrugations . Rocha, Bravo, and Fair correlation .

N Sh,G = uυ ,eff =

U υ ,eff =

kg S Dg

u g ,super

, u L ,eff =

uliq,super εhL sin θ

,

DC u  kL = 2  L E L ,eff    πS H OG = H G + λ H L =

u g ,super k g ae

+

ε sin θ

, U L ,eff =

3 Γ  ρ2L g  2ρL  3µ L Γ 

0.333

Γ=

L Per

Perimeter 4 S + 2 B = Bh Area

[E, T] Modification of Bravo, Rocha, and Fair (5-24H) . Same definitions as in (5-24H) unless defined differently here . Recommended by [113] . hL = fractional hold-up of liquid CE = factor for slow surface renewal CE ~ 0 .9 ae = effective area/volume (1/m) ap = packing surface area/volume (1/m) FSE = surface enhancement factor g = contact angle; for sheet metal, cos g = 0 .9 for s < 0 .055 N/m cos g = 5 .211 × 10-16 .8356, s > 0 .055 N/m m dy λ= ,m= from equilibrium dx L /V

0.8 N Sc0.33 = 0.054 N Re

ε(1 − hL )sin θ

Per =

U υ ,super

λu L ,super k L ae

Interfacial area: ae 29.12(N we N Fr )0.15 S 0.359 = FSE 0.2 0.6 ap N Re,L ε (1 − 0.93 cos γ )(sin θ)0.3 Packing factors: ap

ε

FSE

θ

Flexi-pac 2

233

0 .95

0 .350

45°

Gempak 2A

233

0 .95

0 .344

45°

Intalox 2T

213

0 .95

0 .415

45°

Mellapak 350Y

350

0 .93

0 .350

45°

[92], [113]

5-72

HEAT AnD MASS TRAnSFER

TABLE 5-24 Mass-Transfer Correlations for Packed Two-Phase Contactors—Absorption, Distillation, Cooling Towers, and Extractors (Packing Is Inert) (Continued ) Situation J. Rotating packed bed (Higee)

Comments E = Empirical, S = Semiempirical, T = Theoretical

Correlations kL ad p  V V 1 − 0.93 o − 1.13 i  = 0.65 N Sc0.5 Da  V V  p

t

 L  ×   a pµ 

0.17

t

0.3

 d p3 ρ2 ac   L2   µ 2   ρa σ    p  

0.3

500 ≤ NSc ≤ 1.2 E5; 0.0023 ≤ L/(apμ) ≤ 8.7 3 2 120 ≤ (d p ρac)/ μ2 ≤ 7.0 E7; 3.7 E - 6 ≤ L2/(ρaps) ≤ 9.4 E - 4 9.12 ≤ K. High-voidage packings, cooling towers, splashgrid packings

kL a d p Da p

References∗

[E] Studied oxygen desorption from water into N2. Packing 0.22-mm-diameter stainless-steel mesh ε = 0.954, ap = 829 (1/m), hbed = 2 cm a = gas-liquid area/vol (1/m) L = liquid mass flux, kg/(m2s) ac = centrifugal accel, m2/s Vi, Vo, Vt = volumes inside inner radius, between outer radius and housing, and total, respectively, m3. Coefficient (0.3) on centrifugal acceleration agrees with literature values (0.3–0.38).

[37]

[E] General form . Ga = lb dry air/hr ft2 . L = lb/h ft2, N¢ = number of deck levels . (Ka)H = overall enthalpy transfer coefficient =  lb water  lb/(h)(ft 3 )   lb dry air  Vtower = tower volume, ft3/ft2 . If normal packings are used, use absorption mass-transfer correlations .

[65] [79], p . 220

≤ 2540

 L ( Ka )H Vtower = 0.07 + A ′N ′   L  Ga 

− n′

A¢ and n¢ depend on deck type [ 65], 0.060 ≤  A¢ ≤ 0 .135, 0 .46 ≤ n¢ ≤ 0 .62 . General form fits the graphical comparisons Sherwood, Pigford, & Wilke, p . 286) .

Sherwood, Pigford, & Wilke, p . 286

See also Sec . 14 . ∗Author names refer to the General References list at the beginning of the Mass Transfer subsection (pp . 5-41, 5-42) . Bracketed numbers refer to the table reference lists (p . 5-42) .

correlations include transfer to or from one fluid to either a second fluid or a solid. Many of the correlations are for kL and kG values obtained from dilute systems where xBM ≈ 1.0 and yBM ≈ 1.0. Each table is for a specific geometry or type of contactor, starting with flat plates (Table 5-17); then wetted wall columns (Table 5-18); flow in pipes and ducts (Table 5-19); submerged objects (Table 5-20); drops and bubbles (Table 5-21); agitated systems (Table 5-22); packed beds of particles for adsorption, ion exchange, and chemical reaction (Table 5-23); and finishing with packed bed two-phase contactors for distillation, absorption, and other unit operations (Table 5-24). For simple geometries, one may be able to determine a theoretical (T) form of the mass-transfer correlation. For very complex geometries, only an empirical (E) form can be found. In systems of intermediate complexity, semiempirical (S) correlations in which the form is determined from theory and the coefficients from experiment are often useful. Although the major limitations and constraints in use are usually included in the tables, obviously many details cannot be included in this summary form. Readers are strongly encouraged to check the references including the original paper before using the correlations in important situations. Note that even authoritative sources occasionally have typographical errors in the fairly complex correlation equations. The original papers will often include figures comparing the correlations with data. Although extensive, these tables are not meant to be encyclopedic, and other sources such as Skelland, who extensively surveys older masstransfer correlations, and Benitez, who surveys more recent correlations, should also be consulted. The extensive review of bubble column systems (see Table 5-21) by Shah et al. [AIChE J . 28: 353 (1982)] includes estimation of bubble size, gas holdup, interfacial area kLa, and the liquid dispersion coefficient. For correlations for particle-liquid mass transfer in stirred tanks (part of Table 5-22) see the review by Pangarkar et al. [Ind . Eng . Chem . Res . 41: 4141 (2002)]. Mass-transfer correlations for membrane separators are reviewed by Sirkar [103]. For mass transfer in distillation, absorption, and extraction in packed beds (Table 5-24), see also the appropriate sections in this handbook and the review by Wang, Yuan, and Yu [Ind . Eng . Chem . Res . 44: 8715 (2005)]. Mass transfer and interfacial area for absorption in packed beds for the specific problem of postcombustion carbon dioxide capture are reviewed by Mirzaei, Shamiri, and Aroua [Rev . Chem . Engr . 31: 521 (2015)]. Since often several correlations are applicable, how does one choose the correlation to use? First, the engineer must determine which correlations are closest to the current situation. This involves recognizing the similarity of geometries, which is often challenging, and checking that the range of parameters in the correlation is appropriate. For example, the Bravo, Rocha, and Fair correlation for distillation with structured packings with triangular cross-sectional channels (Table 5-24H) uses the Johnstone and Pigford correlation for rectification in vertical wetted wall columns (Table 5-18E). Recognizing that this latter correlation pertains to a rather different application and geometry was a nontrivial step in the process of developing a correlation. If several correlations appear to be applicable, check to see if the correlations have been compared to one another and to the data. When a

detailed comparison of correlations is not available, the following heuristics may be useful: 1 . Mass-transfer coefficients are derived from models . They must be employed in a similar model . For example, if an arithmetic concentration difference was used to determine k, that k should only be used in a masstransfer expression with an arithmetic concentration difference . 2 . Semiempirical correlations are often preferred to purely empirical or purely theoretical correlations . Purely empirical correlations are dangerous to use for extrapolation . Purely theoretical correlations may predict trends accurately, but they can be several orders of magnitude off in the value of k . 3 . Correlations with broader databases are often preferred . 4 . The analogy between heat and mass transfer holds over wider ranges than the analogy between mass and momentum transfer . Good heattransfer data (without radiation) can often be used to predict mass-transfer coefficients . 5 . More recent data are often preferred to older data, since end effects are better understood, the new correlation often builds on earlier data and analysis, and better measurement techniques are often available . 6 . With complicated geometries, the product of the interfacial area per volume and the mass-transfer coefficient is required . Correlations of kap or of HTU are more accurate than individual correlations of k and ap since the measurements are simpler to determine the product kap or HTU . 7 . Finally, if a mass-transfer coefficient looks too good to be true, it probably is incorrect . Volumetric Mass-Transfer Coefficients Kˆ G a and Kˆ L a Experimental determinations of the individual mass-transfer coefficients kˆG and kˆL and of the effective interfacial area a involve the use of extremely difficult techniques, and therefore such data are not plentiful . More often, column experimental data are reported in terms of overall volumetric coefficients, which normally are defined as follows:

and

° ) K G′ a = n A /(hT S pT ∆y 1m

(5-308)

° ) K L′ a = nA /(hTS ∆x 1m

(5-309)

where K G′ a = overall volumetric gas-phase mass-transfer coefficient, K L′ a = overall volumetric liquid-phase mass-transfer coefficient, nA = overall rate of transfer of solute A, hT = total packed depth in tower, S = tower crosssectional area, pT = total system pressure employed during the experiment, ° and ∆y ° are defined as and ∆x 1m 1m

and

∗ ∆y 1m =

( y − y ∗ )1 − ( y − y ∗ )2 ln [( y − y ∗ )1 /( y − y ∗ )2 ]

(5-310)

∗ ∆x 1m =

( x ∗ − x )2 − ( x ∗ − x )2 ln [( x ∗ − x)2 /( x ∗ − x )1 ]

(5-311)

MASS TRAnSFER where subscripts 1 and 2 refer to the bottom and top of the tower, respectively. Experimental K G′ a and K L′ a data are available for most absorption and stripping operations of commercial interest (see Table 5-24 and Sec. 14). The solute concentrations employed in these experiments normally are very low, so that K L′ a = Kˆ L a and K G′ apT = KˆG a , where pT is the total pressure employed in the actual experimental-test system. Unlike the individual gas-film coefficient kˆG a , the overall coefficient KˆG a will vary with the total system pressure except when the liquid-phase resistance is negligible (i.e., when either m = 0 or Kˆ L a is very large, or both). Extrapolation of K G′ a data for absorption and stripping to conditions other than those for which the original measurements were made can be extremely risky, especially in systems involving chemical reactions in the liquid phase. One therefore would be wise to restrict the use of overall volumetric mass-transfer coefficient data to conditions not too far removed from those employed in the actual tests. The most reliable data for this purpose would be those obtained from an operating commercial unit of similar design. Experimental values of HOG and HOL for a number of distillation systems of commercial interest are also readily available (e.g., see Table 5-24). Extrapolation of the data or the correlations to conditions that differ significantly from those used for the original experiments is risky. For example, pressure has a major effect on vapor density and thus can affect the hydrodynamics significantly. Changes in flow patterns affect both mass-transfer coefficients and interfacial area. Analogies Analogies have been important in the study of mass transfer since Fick modeled his analysis of mass transfer on Fourier’s analysis of heat transfer. If the underlying mechanisms for heat, mass, and momentum transfer are identical (e.g., transfer by eddies in turbulent flow), analogies are useful. If the underlying mechanisms are different (e.g., radiation in heat transfer), analogies do not apply. Reynolds developed an analogy (see Cussler for details) that is most commonly applied to turbulent flow in tubes (Table 5-19R) k′ h f = = v ρc p v 2

(5-312)

where h is the heat-transfer coefficient, cp is the heat capacity, f is the Fanning friction factor, and v is a characteristic velocity. Since the Reynolds analogy is of limited utility, improved analogies for flow in tubes were developed by Prandtl (Table 5-19T) and Von Karman (Table 5-19U). Chilton and Colburn [38] developed an empirical analogy that provided a better fit of experimental data. The general form of their analogy is f h k′ ( N Sc )2/3 = ( N Pr )2/3 = or j D = j H = f /2 2 v ρc p v

(5-313)

Specific applications are included in Tables 5-17A, 5-17E, and 5-19S. The Chilton-Colburn analogy [38, 40, 68] is frequently used to develop estimates of the mass-transfer rates based on heat-transfer data. Extrapolation of experimental jM or jH data obtained with gases to predict liquid systems (and vice versa) should be approached with caution, however. When pressure-drop or friction-factor data are available, one may be able to place an upper bound on the rates of heat and mass transfer of f/2. In distillation columns there are more mass-transfer data than heat-transfer data, and the Chilton-Colburn analogy is used to estimate heat-transfer rates. The Chilton-Colburn analogy can be used for simultaneous heat and mass transfer as long as the concentration and temperature fields are independent [Venkatesan and Fogler, AIChE J. 50: 1623 (2004)]. Effects of System Physical Properties on kˆG and kˆL When one is designing packed towers for nonreacting gas-absorption systems for which no experimental data are available, it is necessary to make corrections for differences in composition between the existing test data and the system in question. For example, ammonia-water test data (see Table 5-24B) can be used to estimate HG, and the oxygen desorption data (see Table 5-24A) can be used to estimate HL. The method for doing this is illustrated in Table 5-24E. There is some conflict on whether the value of the exponent for the Schmidt number is 0.5 or 2/3 [Yadav and Sharma, Chem . Eng . Sci . 34: 1423 (1979)]. Despite this disagreement, this method is extremely useful, especially for absorption and stripping systems. If one is in doubt about the exponent, we recommend using 2/3, the value used in the Chilton-Colburn analogy. Note that the influence of substituting solvents of widely differing viscosities upon the interfacial area a can be very large. One therefore should be cautious about extrapolating kˆL a data to account for viscosity effects between different solvent systems. Influence of Chemical Reactions on kˆG and kˆL When a chemical reaction occurs, the transfer rate may be influenced by the chemical reaction

5-73

as well as by the purely physical processes of diffusion and convection within the two phases. Since this situation is common in gas absorption, gas absorption will be the focus of this discussion. One must consider the impacts of chemical equilibrium and reaction kinetics on the absorption rate in addition to accounting for the effects of gas solubility, diffusivity, and system hydrodynamics. There is no sharp dividing line between pure physical absorption and absorption controlled by the rate of a chemical reaction. Most cases fall in an intermediate range in which the rate of absorption is limited both by the resistance to diffusion and by the finite velocity of the reaction. Even in these intermediate cases the equilibria between the various diffusing species involved in the reaction may affect the rate of absorption. The gas-phase rate coefficient kˆG is not affected by chemical reactions taking place in the liquid phase. If the liquid-phase chemical reaction is extremely fast and irreversible, the rate of absorption may be governed completely by the resistance to diffusion in the gas phase. In this case the absorption rate may be estimated by knowing only the gas-phase rate coefficient kˆG or else the height of 1 gas-phase transfer unit HG = GM/(kˆG a ). Note that the highest possible absorption rates will occur under conditions in which the liquid-phase resistance is negligible and the equilibrium back pressure of the gas over the solvent is zero. Such situations would exist, for instance, for NH3 absorption into an acid solution, for SO2 absorption into an alkali solution, for vaporization of water into air, and for H2S absorption from a dilute-gas stream into a strong alkali solution, provided there is a large excess of reagent in solution to consume all the dissolved gas. This is known as the gas-phase mass-transfer limited condition, when both the liquid-phase resistance and the back pressure of the gas equal zero. Even when the reaction is sufficiently reversible to allow a small back pressure, the absorption may be gas-phase-controlled, and the values of kˆG and HG that would apply to a physical absorption process will govern the rate. The liquid-phase rate coefficient kˆL is strongly affected by fast chemical reactions and generally increases with increasing reaction rate. Indeed, the condition for zero liquid-phase resistance (m/kˆL ) implies that either the equilibrium back pressure is negligible or kˆL is very large, or both. Frequently, even though reaction consumes the solute as it is dissolving, thereby enhancing both the mass-transfer coefficient and the driving force for absorption, the reaction rate is slow enough that the liquid-phase resistance must be taken into account. This may be due either to an insufficient supply of a second reagent or to an inherently slow chemical reaction. In any event the value of kˆL in the presence of a chemical reaction normally is larger than the value found when only physical absorption occurs, kˆL0 . This has led to the presentation of data on the effects of chemical reaction in terms of the reaction factor or enhancement factor, defined as f = kˆL /kˆL0 ≥ 1

(5-314)

where kˆL = mass-transfer coefficient with reaction and kˆL0 = mass-transfer coefficient for pure physical absorption. It is important to understand that when chemical reactions are involved, this definition of kˆL is based on the driving force, defined as the difference between the concentration of unreacted solute gas at the interface and in the bulk of the liquid. A coefficient based on the total of both unreacted and reacted gas could have values smaller than the physical absorption mass-transfer coefficient kˆL0 . When liquid-phase resistance is important, particular care should be taken in employing any given set of experimental data to ensure that the equilibrium data used conform with those employed by the original author in calculating values of kˆL or HL. Extrapolation to widely different concentration ranges or operating conditions should be made with caution, since the mass-transfer coefficient kˆL may vary in an unexpected fashion, owing to changes in the apparent chemical reaction mechanism. Generalized prediction methods for kˆL and HL do not apply when chemical reaction occurs in the liquid phase, and therefore one must use actual operating data for the particular system in question. A discussion of the various factors to consider in designing gas absorbers and strippers when chemical reactions are involved is presented by Astarita, Savage, and Bisio, Gas Treating with Chemical Solvents, Wiley, New York, 1983 and by Kohl and Nielsen, Gas Purification, 5th ed., Gulf Publishing, Houston, Tex., 1997. Effective Interfacial Mass-Transfer Area a To determine the masstransfer rate, one needs the interfacial area in addition to the mass-transfer coefficient. In a packed tower of constant cross-sectional area S the differential change in solute flow per unit time is given by −d(GMSy) = NAa dV = NAaS dh

(5-315)

where a = interfacial area effective for mass transfer per unit of packed volume and V = packed volume. Owing to incomplete wetting of the packing surfaces and to the formation of areas of stagnation in the liquid film,

5-74

HEAT AnD MASS TRAnSFER

the effective area normally is significantly less than the total external area of the packing pieces. For packed beds of particles, a can be estimated as shown in Table 5-23A. For packed beds in distillation, absorption, and so on in Table 5-24, the interfacial area per volume is usually included with the mass-transfer coefficient in the correlations for HTU. For agitated liquid-liquid systems, the interfacial area can be estimated from the dispersed phase holdup and mean drop size correlations. Godfrey, Obi, and Reeve [Chem . Engr . Prog . 85: 61 (Dec. 1989)] summarize these correlations. For many systems, −0.6 3 ddrop /d imp = (const) N We where N We = ρc N 2 d imp /σ

(5-316)

Piché, Grandjean, and Larachi [Ind . Eng . Chem . Res . 41: 4911 (2002)] developed two correlations for reconciling the gas-liquid mass-transfer coefficient and interfacial area in randomly packed towers. The correlation for the interfacial area was a function of five dimensionless groups, and it yielded a relative error of 22.5 percent for 325 data points. That equation, when combined with a correlation for NSh as a function of four dimensionless groups, achieved a relative error of 24.4 percent, for 3455 data points for the product kG′ a. The effective interfacial area depends on a number of factors, as discussed in a review by Charpentier [Chem . Eng . J. 11: 161 (1976)]. Among these factors are (1) the shape and size of packing, (2) the packing material ( for example,

plastic generally gives smaller interfacial areas than either metal or ceramic), (3) the liquid mass velocity, and (4) for small-diameter towers, the column diameter. Whereas the interfacial area generally increases with increasing liquid rate, it apparently is relatively independent of the superficial gas mass velocity below the flooding point. According to Charpentier’s review, it appears valid to assume that the interfacial area is independent of the column height when specified in terms of unit packed volume (i.e., as a). Also, the existing data for chemically reacting gas-liquid systems (mostly aqueous electrolyte solutions) indicate that the interfacial area is independent of the chemical system. However, this situation may not hold true for systems involving large heats of reaction. Rizzuti et al. [Chem . Eng . Sci . 36: 973 (1981)] examined the influence of solvent viscosity upon the effective interfacial area in packed columns and concluded that for the systems studied the effective interfacial area a was proportional to the kinematic viscosity raised to the 0.7 power. Thus, the hydrodynamic behavior of a packed absorber is strongly affected by viscosity effects. Surface-tension effects also are important, as expressed in the work of Onda et al. [82] (see Table 5-24C). Concluding Comment In developing correlations for the masstransfer coefficients kˆG and kˆL , various authors have assumed different but internally compatible correlations for the effective interfacial area a. It therefore would be inappropriate to mix the correlations of different authors unless it has been demonstrated that there is a valid area of overlap.

Section 6

Fluid and Particle Dynamics

James n. Tilton, Ph.D., P.E. DuPont Fellow, Chemical and Bioprocess Engineering, E . I . du Pont de Nemours & Co .; Member, American Institute of Chemical Engineers; Registered Professional Engineer (Delaware)

FLUID DYnAMICS Nature of Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deformation and Stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Viscosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rheology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kinematics of Fluid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Streamlines, Pathlines, and Streaklines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rate of Deformation Tensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vorticity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laminar and Turbulent Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conservation Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Macroscopic and Microscopic Balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Macroscopic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass Balance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Momentum Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total Energy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanical Energy Balance, Bernoulli Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . Microscopic Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass Balance, Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stress Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cauchy Momentum and Navier-Stokes Equations . . . . . . . . . . . . . . . . . . . . . . . . . Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-1 Force Exerted on a Reducing Bend . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-2 Simplified Ejector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-3 Venturi Flowmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-4 Plane Poiseuille Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Incompressible Flow in Pipes and Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanical Energy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Friction Factor and Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laminar and Turbulent Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Velocity Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Entrance and Exit Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Residence Time Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noncircular Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonisothermal Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Open-Channel Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonnewtonian Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drag Reduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Economic Pipe Diameter, Turbulent Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Economic Pipe Diameter, Laminar Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vacuum Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molecular Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slip Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Frictional Losses in Pipeline Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equivalent Length and Velocity Head Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contraction and Entrance Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-5 Entrance Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6-4 6-4 6-4 6-4 6-5 6-5 6-5 6-5 6-5 6-5 6-5 6-5 6-5 6-5 6-7 6-7 6-8 6-8 6-8 6-8 6-8 6-9 6-9 6-9 6-9 6-9 6-10 6-10 6-10 6-11 6-11 6-12 6-12 6-12 6-12 6-13 6-13 6-14 6-14 6-15 6-15 6-15 6-15 6-16 6-16 6-16 6-16

Expansion and Exit Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fittings and Valves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-6 Losses with Fittings and Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Curved Pipes and Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jet Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow Through Orifices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compressible Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mach Number and Speed of Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Isothermal Gas Flow in Pipes and Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adiabatic Frictionless Nozzle Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-7 Flow Through Frictionless Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adiabatic Flow with Friction in a Duct of Constant Cross Section. . . . . . . . . . . Example 6-8 Compressible Flow with Friction Losses . . . . . . . . . . . . . . . . . . . . . . Convergent/Divergent Nozzles (De Laval Nozzles) . . . . . . . . . . . . . . . . . . . . . . . . . Multiphase Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquids and Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gases and Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solids and Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluid Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Perforated-Pipe Distributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-9 Pipe Distributor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slot Distributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Turning Vanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Perforated Plates and Screens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beds of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Flow-Straightening Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluid Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stirred Tank Agitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pipeline Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tube Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beds of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fixed Beds of Granular Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Porous Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tower Packings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluidized Beds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boundary Layer Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flat Plate, Zero Angle of Incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cylindrical Boundary Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuous Flat Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuous Cylindrical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vortex Shedding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Falling Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minimum Wetting Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Turbulent Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Surface Traction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flooding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6-17 6-17 6-18 6-18 6-20 6-20 6-21 6-22 6-22 6-22 6-22 6-23 6-23 6-25 6-25 6-25 6-25 6-29 6-30 6-31 6-31 6-32 6-32 6-32 6-33 6-33 6-33 6-33 6-33 6-34 6-35 6-35 6-35 6-36 6-37 6-37 6-37 6-37 6-37 6-37 6-38 6-38 6-39 6-39 6-39 6-39 6-40 6-40 6-40

6-1

6-2

FLUID AnD PARTICLE DYnAMICS

Hydraulic Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-10 Response to Instantaneous Valve Closing . . . . . . . . . . . . . . . . . . . . Pulsating Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cavitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time Averaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Closure Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eddy Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computational Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dimensionless Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6-40 6-40 6-40 6-41 6-41 6-41 6-41 6-42 6-43 6-43 6-44

PARTICLE DYnAMICS Drag Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Terminal Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spherical Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonspherical Rigid Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hindered Settling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time-Dependent Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gas Bubbles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid Drops in Liquids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid Drops in Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wall Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6-46 6-46 6-46 6-47 6-47 6-48 6-48 6-49 6-50 6-50

FLUID AnD PARTICLE DYnAMICS

6-3

nomenclature and Units* In this listing, symbols used in this section are defined in a general way and appropriate SI units are given. Specific definitions, as denoted by subscripts, are stated at the place of application in the section. Some specialized symbols used in the section are defined only at the place of application. Some symbols have more than one definition; the appropriate one is identified at the place of application.

Symbol

Definition

a A b b c cf C Ca C0 CD d D De E Eo f f

Pressure wave velocity Area Wall thickness Channel width Acoustic velocity Friction coefficient Conductance Capillary number Discharge coefficient Drag coefficient Diameter Diameter Dean number Elastic modulus Eotvos number Fanning friction factor Vortex shedding frequency Force Cumulative residence time distribution Froude number Acceleration of gravity Mass flux Enthalpy per unit mass Liquid depth Ratio of specific heats Kinetic energy of turbulence Power law coefficient Viscous losses per unit mass Length Mass flow rate Mass Mach number Morton number Molecular weight Power law exponent Blend time number Power number Pumping number Pressure Entrained flow rate Volumetric flow rate Throughput (vacuum flow) Heat input per unit mass Radial coordinate Radius Ideal gas universal constant Volume fraction of phase i Reynolds number Density ratio Entropy per unit mass Slope Pumping speed

F F Fr g G h h k k K lv L m M M M Mw n Nb NP NQ p q Q Q δQ r R R Ri Re s s S S

SI units

U.S. Customary System units

m/s m2 m m m/s Dimensionless m3/s Dimensionless Dimensionless Dimensionless m m Dimensionless Pa Dimensionless Dimensionless 1/s

ft/s ft2 in ft ft/s Dimensionless ft3/s Dimensionless Dimensionless Dimensionless ft ft Dimensionless lbf/in2 Dimensionless Dimensionless 1/s

N Dimensionless

lbf Dimensionless

Dimensionless m/s2 kg/(m2 ⋅ s) J/kg m Dimensionless J/kg

Dimensionless ft/s2 lbm/( ft2 ⋅ s) Btu/lbm ft Dimensionless ft ⋅ lbf/lbm

2−n

2−n

kg/(m ⋅ s ) J/kg

lbm/( ft ⋅ s ) ft ⋅ lbf/lbm

m kg/s kg Dimensionless Dimensionless kg/kgmol Dimensionless Dimensionless Dimensionless Dimensionless Pa m3/s m3/s Pa ⋅ m3/s

ft lbm/s lbm Dimensionless Dimensionless lbm/lbmol Dimensionless Dimensionless Dimensionless Dimensionless lbf/in2 ft3/s ft3/s (lbf/in2) ⋅ ft3/s

J/kg m m J/(kgmol ⋅ K)

Btu/lbm ft ft Btu/(lbmol ⋅ °R)

Dimensionless

Dimensionless

Dimensionless Dimensionless J/(kg ⋅ K) Dimensionless m3/s

Dimensionless Dimensionless Btu/(lbm ⋅ °R) Dimensionless ft3/s

Symbol

Definition

S

Surface area per unit volume Strouhal number Time Force per unit area Absolute temperature Internal energy per unit mass Velocity Velocity Velocity Velocity Volume Weber number Rate of shaft work Shaft work per unit mass Cartesian coordinate Cartesian coordinate Cartesian coordinate Elevation

Sr t t T u u U υ V V We W s dWs x y z Z

U.S. Customary System units

SI units l/m

l/ft

Dimensionless s Pa K J/kg

Dimensionless s lbf/in2 °R Btu/lbm

m/s m/s m/s m/s m3 Dimensionless J/s J/kg m m m m

ft/s ft/s ft/s ft/s ft3 Dimensionless Btu/s Btu/lbm ft ft ft ft

Greek Symbols a a b b γ G Gij G d dij ε ε ε q q l m n r s s sij t t tij F f w

Velocity profile factor Included angle Velocity profile factor Bulk modulus of elasticity Shear rate Mass flow rate Components of rate of deformation tensor Magnitude of rate of deformation tensor Boundary layer or film thickness Kronecker delta Pipe roughness Void fraction Turbulent dissipation rate Residence time Angle Mean free path Viscosity Kinematic viscosity Density Surface tension Cavitation number Components of total stress tensor Shear stress Time period Components of deviatoric stress tensor Energy dissipation rate per unit volume Angle of inclination Vorticity

Dimensionless rad Dimensionless Pa

Dimensionless rad Dimensionless lbf/in2

l/s kg/(m ⋅ s) 1/s

l/s lbm/( ft ⋅ s) 1/s

1/s

1/s

m

ft

Dimensionless m Dimensionless J/(kg ⋅ s)

Dimensionless ft Dimensionless ft ⋅ lbf/(lbm ⋅ s)

s rad m Pa ⋅ s m2/s kg/m3 N/m Dimensionless Pa

S rad ft lbm/( ft ⋅ s) ft2/s lbm/ft3 lbf/ft Dimensionless lbf/in2

Pa s Pa

lbf/in2 s lbf/in2

J/(m3 ⋅ s)

ft ⋅ lbf/( ft3 ⋅ s)

rad 1/s

rad 1/s

*Note that with U.S. Customary System units, the conversion factor gc may be required to make equations in this section dimensionally consistent; gc = 32.17 (lbm ⋅ ft)/(lbf ⋅ s2).

FLUID DYnAMICS General References: Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University, Cambridge, UK, 1967; Bird, R. B., W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2d ed., Wiley, New York, 2002; Brodkey, R. S., The Phenomena of Fluid Motions, Addison-Wesley, Reading, Mass., 1967; Denn, M. M., Process Fluid Mechanics, PrenticeHall, Englewood Cliffs, N.J., 1979; Govier, G. W., and K. Aziz, The Flow of Complex Mixtures in Pipes, Krieger, Huntington, N.Y., 1977; Landau, L. D., and E. M. Lifshitz, Fluid Mechanics, 2d ed., Pergamon, Oxford, 1987; Panton, R. L., Incompressible Flow, Wiley, New York, 1984; Schlichting, H., and K. Gersten, Boundary Layer Theory, 8th ed rev., Springer-Verlag, Berlin, 2003; Shames, I. H., Mechanics of Fluids, 3d ed., McGraw-Hill, New York, 1992; Streeter, V. L., Handbook of Fluid Dynamics, McGraw-Hill, New York, 1971; Streeter, V. L., and E. B. Wylie, Fluid Mechanics, 8th ed., McGraw-Hill, New York, 1985; Vennard, J. F., and R. L. Street, Elementary Fluid Mechanics, 5th ed., Wiley, New York, 1975; Whitaker, S., Introduction to Fluid Mechanics, Krieger, Malabar, Fla., 1981.

depends on the history of the rate of deformation, as a result of structure or orientation buildup or breakdown during deformation. A rheogram is a plot of shear stress versus shear rate for a fluid in simple shear flow. Rheograms for several types of time-independent fluids are shown in Fig. 6-2. The newtonian fluid rheogram is a straight line passing through the origin. The slope of the line is the viscosity. For a newtonian fluid, the viscosity is independent of shear rate and depends on temperature and perhaps pressure. By far, the newtonian fluid is the largest class of fluid of engineering importance. Gases and low-molecular-weight liquids are generally newtonian. Newton’s law of viscosity is a rearrangement of Eq. (6-1) in which the viscosity is a constant: t = µ γ = µ

nATURE OF FLUIDS

τ γ

(6-1)

The SI units of viscosity are kg/(m ⋅ s) or Pa ⋅ s (pascal-seconds). The cgs unit for viscosity is the poise (P); 1 Pa ⋅ s = 10 P = 1000 centipoise (cP) or 0.672 lbm/( ft ⋅ s). The terms absolute viscosity and shear viscosity are synonymous with the viscosity as used in Eq. (6-1). Kinematic viscosity n ≡ m/r is the ratio of viscosity to density. The SI units of kinematic viscosity are m2/s. The cgs unit stoke (St) = 1 cm2/s. Rheology In general, fluid flow patterns are more complex than the one shown in Fig. 6-1, as is the relationship between fluid deformation and stress. Rheology is the discipline of fluid mechanics which studies this relationship. One goal of rheology is to obtain constitutive equations by which stresses may be computed. For simplicity, fluids may be classified into rheological types in reference to the simple shear flow of Fig. 6-1. Complete definitions require extension to multidimensional flow. For more information, several good references are available, including R. B. Bird, R. C. Armstrong, and O. Hassager [Dynamics of Polymeric Liquids, vol. 1: Fluid Mechanics, Wiley, New York, 1977]; H. A. Barnes, J. F. Hutton, and K. Walters [An Introduction to Rheology, Elsevier, Amsterdam, 1989], C. W. Macosko [Rheology Principles, Measurements and Applications, Wiley-VCH, New York, 1994], and F. A. Morrison [Understanding Rheology, Oxford University, Oxford, 2001]. Fluids without elasticity do not undergo any reverse deformation when shear stress is removed, and they are called purely viscous fluids. The shear stress depends only on the rate of deformation, and not on the extent of deformation (strain). Those that exhibit both viscous and elastic properties are called viscoelastic fluids. Purely viscous fluids are further classified into time-independent and timedependent fluids. For time-independent fluids, the shear stress depends on only the instantaneous shear rate. The shear stress for time-dependent fluids

A

t = τ y + µ ∞ γ

F

H

6-4

Deformation of a fluid subjected to a shear stress .

(6-4)

µ= K γ n−1

(6-5)

The factor K is the consistency index or power law coefficient, and n is the power law exponent . The exponent n is dimensionless, while K has units of kg/(m ⋅ s2 - n) . For shear-thinning fluids, n < 1 . The power law model typically provides a good fit to data over a range of one to two orders of magnitude in shear rate; behavior at very low and very high shear rates is often newtonian . Shear-thinning fluids with yield stresses are often fit to the Herschel-Bulkley model, which adds a yield stress to Eq . (6-4) . Numerous other rheological model equations for shear-thinning fluids are in common use . Dilatant, or shear-thickening, fluids show increasing viscosity with increasing shear rate . Over a limited range of shear rate, they may be fit to the power law model with n > 1 . Dilatancy is rare, observed only in certain concentration ranges in some particle suspensions [G . W . Govier and K . Aziz, The Flow of Complex Mixtures in Pipes, Krieger, Huntington, N .Y ., 1977, pp . 33–34] . Extensive discussions of dilatant suspensions, together with a listing of dilatant systems, are given by R . G . Green and R . G . Griskey [Trans . Soc . Rheol . 12(1): 13–25 (1968)]; R . G . Griskey and R . G . Green [AIChE J . 17: 725–728 (1971)]; and W . H . Bauer and E . A . Collins [“Thixotropy and Dilatancy,” in F . R . Eirich, Rheology, vol . 4, Academic, New York, 1967] .

x FIG. 6-1

t = K γ n The apparent viscosity is

V y

(6-3)

Highly concentrated suspensions of fine solid particles frequently exhibit Bingham plastic behavior . Shear-thinning fluids are those for which the slope of the rheogram decreases with increasing shear rate . These fluids have also been called pseudoplastic, but this terminology is outdated . Many polymer melts and solutions, as well as some solids suspensions, are shear-thinning . Shearthinning fluids without yield stresses are often fit to a power law model over a range of shear rates

FIG. 6-2

Shear diagrams .

c sti pla g m in ha inn ng h i B

ty

Sh ea r-t

µ=

(6-2)

Fluids for which the viscosity varies with shear rate are called nonnewtonian fluids . For nonnewtonian fluids the viscosity, defined as the ratio of shear stress to shear rate, is often called the apparent viscosity to emphasize the distinction from newtonian behavior. Purely viscous, time-independent fluids, for which the apparent viscosity may be expressed as a function of shear rate, are called generalized newtonian fluids . Nonnewtonian fluids include those for which a finite stress ty is required before continuous deformation occurs; these are called yield-stress materials. The Bingham plastic fluid is the simplest yield-stress material; its rheogram has a constant slope m∞, called the infinite shear viscosity .

Shear stress t

Deformation and Stress A fluid is a substance that undergoes continuous deformation when subjected to a shear stress, as illustrated in Fig. 6-1. A fluid is bounded by two large parallel plates, of area A, separated by a small distance H. The bottom plate is held fixed. Application of a force F to the upper plate causes it to move at velocity V. The fluid continues to deform as long as the force is applied, unlike a solid, which would undergo only a finite deformation. The force per unit area is the shear stress t = F/A . Within the fluid, a linear velocity profile u = Vy/H is established; because of the no-slip condition, the fluid bounding the lower plate has zero velocity and the fluid bounding the upper plate moves at the plate velocity V . The velocity gradient γ = du/dy is the shear rate for this flow. Shear rates are usually reported in units of reciprocal seconds. The flow in Fig. 6-1 is a simple shear flow. Viscosity The ratio of shear stress to shear rate is the viscosity m.

du dy

t an lat Di an toni New Shear rate |du/dy|

FLUID DYnAMICS Time-dependent fluids are those for which structural rearrangements occur during deformation at a rate too slow to maintain equilibrium configurations. As a result, shear stress changes with duration of shear. Thixotropic fluids, such as mayonnaise, clay suspensions used as drilling muds, and some paints and inks, starting from rest, show decreasing shear stress with time at constant shear rate. A detailed description of thixotropic behavior and a list of thixotropic systems are found in W. H. Bauer and E. A. Collins [“Thixotropy and Dilatancy,” in Eirich, Rheology, vol. 4, Academic, New York, 1967]. Rheopectic behavior is the opposite of thixotropy. Starting from rest, shear stress increases with time at a constant shear rate. Rheopectic behavior has been observed in bentonite sols, vanadium pentoxide sols, and gypsum suspensions in water [W. H. Bauer and E. A. Collins, “Thixotropy and Dilatancy,” in Eirich, Rheology, vol. 4, Academic, New York, 1967] as well as in some polyester solutions [I. Steg and D. Katz, J . Appl . Polym . Sci . 9: 3, 177 (1965)]. Viscoelastic fluids exhibit elastic recovery from deformation when stress is removed. Polymeric liquids comprise the largest group of fluids in this class. A property of viscoelastic fluids is the relaxation time, which is a measure of the time required for elastic effects to decay. Viscoelastic effects may be important with sudden changes in rates of deformation, as in flow startup and stop, rapidly oscillating flows, or flow through sudden expansions or contractions. In viscoelastic flows, normal stresses perpendicular to the direction of shear are different from those in the parallel direction. These give rise to such behaviors as the Weissenberg effect, in which fluid climbs up a rotating shaft, and die swell, where a stream of fluid issuing from a tube may expand to two or more times the tube diameter. Analysis of viscoelastic flows is very difficult. Simple constitutive equations are unable to describe all the material behavior exhibited by viscoelastic fluids even in geometrically simple flows. More-complex constitutive equations may be more accurate, but become exceedingly difficult to apply, especially for complex geometries, even with advanced numerical methods. For good discussions of viscoelastic fluid behavior, including various types of constitutive equations, see R. B. Bird, R. C. Armstrong, and O. Hassager [Dynamics of Polymeric Liquids, vol. 1: Fluid Mechanics, Wiley, New York, 1977]; S. Middleman [The Flow of High Polymers, Interscience (Wiley), New York, 1968]; or G. Astarita and G. Marrucci [Principles of Nonnewtonian Fluid Mechanics, McGraw-Hill, New York, 1974]. Polymer processing depends heavily on the flow of nonnewtonian fluids. See the texts by S. Middleman [Fundamentals of Polymer Processing, McGraw-Hill, New York, 1977] and Z. Tadmor and C. Gogos [Principles of Polymer Processing, Wiley, New York, 1979]. There are a wide variety of instruments for measurement of newtonian viscosity as well as rheological properties of nonnewtonian fluids. They are described in C. W. Macosko [Rheology Principles, Measurements and Applications, Wiley-VCH, New York, 1994]; B. D. Coleman et al. [Viscometric Flows of Nonnewtonian Fluids, Springer-Verlag, Berlin, 1966]; and J. M. Dealy and K. F. Wissbrun [Melt Rheology and Its Role in Plastics Processing, Van Nostrand Reinhold, New York, 1990]. Measurement of rheological behavior requires well-characterized flows. Such rheometric flows are thoroughly discussed by G. Astarita and G. Marrucci [Principles of Nonnewtonian Fluid Mechanics, McGraw-Hill, New York, 1974]. KInEMATICS OF FLUID FLOW Velocity Kinematics refers to the quantitative description of fluid motion or deformation. The rate of deformation depends on the distribution of velocity within the fluid. Fluid velocity v is a vector quantity, with three cartesian components υx, υy, and υz. The velocity vector is a function of spatial position and time. In a steady flow, the velocity is independent of time, while in unsteady flow v varies with time. Streamlines, Pathlines, and Streaklines These are curves in a flow field which provide insight into the flow pattern. Streamlines are tangent at every point to the local instantaneous velocity vector. A pathline is the path followed by a material element of fluid. Streaklines are curves on which are found all the material particles that passed through a particular point in space at some earlier time. For example, a streakline is revealed by releasing smoke or dye at a point in a flow field. For steady flows, the streamlines, pathlines, and streaklines coincide. In two-dimensional incompressible flows, streamlines are contours of the stream function. Many flows of practical importance, such as those in pipes and channels, are treated as one-dimensional flows . There is a single direction called the flow direction; velocity components perpendicular to this direction either are zero or are considered unimportant. In one type of one-dimensional flow, variations of quantities such as velocity, pressure, density, and temperature are considered only in the flow direction. More generally, one-dimensional flows have only one nonzero velocity component, which depends on only one coordinate direction, and this coordinate direction may or may not be the same as the flow direction.

6-5

Rate of Deformation Tensor For general three-dimensional flows, where all three velocity components may be important and may vary in all three coordinate directions, the concept of deformation previously introduced is generalized using the rate of deformation tensor Γ = (1/ 2)[ ∇v + (∇v )T ]. In cartesian components, 1  ∂v ∂v j  Γ ij =  i + 2  ∂ x j ∂ x i 

(6-6)

where the subscripts i and j refer to the three coordinate directions. Some authors define the deformation rate tensor as twice that given by Eq. (6-6). For multidimensional flows of incompressible newtonian fluids, Eq. (6-2) may be generalized to tτ = 2µΓ

(6-7)

with τij the nine components of the viscous stress tensor. For generalized newtonian fluids in multidimensional flow, m is a function of a scalar measure of the rate of deformation µ = µ(Γ ), where Γ=

1 1 Γ:Γ = ∑ ∑ Γ ij Γ ji 2 2 i j

(6-8)

The components of the rate of deformation tensor and equations for the scalar G, in cartesian, cylindrical, and spherical coordinates, are found in Table 6-1. The table also provides the viscous stress components of generalized newtonian fluids and the differential balance equations for mass and momentum (see below) in the three coordinate systems. Vorticity The relative motion between two points in a fluid can be decomposed into rigid body rotation and deformation. The rate of deformation tensor has been defined. Deformation includes uniform volumetric expansion (dilatation) and shear. Dilatation vanishes for incompressible flow. Rotation is described in cartesian coordinates by the vorticity tensor wij = (1/2)[∂υi/∂xj − ∂υj/∂xi] . A related quantity is the vector of vorticity given by one-half the curl of the velocity . In two-dimensional flow in the xy plane, the vorticity w is given by ω=

1  ∂v y ∂v x  − 2  ∂ x ∂ y 

(6-9)

Here w is the magnitude of the vorticity vector, which is directed along the z axis . An irrotational flow is one with zero vorticity . Irrotational flows have been widely studied because of their useful mathematical properties and applicability to flow regions where viscous effects may be neglected (inviscid flows) . Laminar and Turbulent Flow These terms refer to two distinct types of flow . In laminar flow, there are smooth streamlines and the fluid velocity components vary smoothly with position and time . The flow described in reference to Fig . 6-1 is laminar . In turbulent flow, streamlines are irregular, and the velocity fluctuates chaotically in time and space . For any given flow geometry, a dimensionless Reynolds number may be defined for a newtonian fluid as Re = LU r/m where L and U are the characteristic length and velocity . Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow begins . The geometry-dependent critical Reynolds number is determined experimentally . COnSERVATIOn EQUATIOnS Macroscopic and Microscopic Balances Three laws of physics are fundamental in fluid mechanics: conservation of mass, conservation of momentum, and conservation of energy . In addition, conservation of moment of momentum (angular momentum) and the entropy inequality (second law of thermodynamics) have occasional use . The momentum, moment of momentum, and energy conservation laws apply to inertial reference frames . Conservation principles may be applied to control volumes which may be of finite or differential size, resulting in either algebraic or differential conservation equations, respectively . These are often called macroscopic and microscopic balance equations . Macroscopic Equations Figure 6-3 shows an arbitrary control volume of finite size Va bounded by a surface of area Aa with an outwardly directed unit normal vector n . The volume is not necessarily fixed in space . Its boundary moves with velocity w . The fluid velocity is v . Mass Balance Applied to the control volume, the principle of conservation of mass may be written as d ρ dV + ∫ ρ( v − w ) ⋅ n dA = 0 Aa dt ∫Va This equation is also known as the continuity equation .

(6-10)

6-6

FLUID AnD PARTICLE DYnAMICS

TABLE 6-1 Differential Equations of Motion, newtonian Stress Constitutive Equation and Rate of Deformation Tensor, in Cartesian, Cylindrical, and Spherical Coordinates Continuity Equation

Dr = −ρ∇ ⋅ v Dt

Spherical

Cartesian

 ∂v 2  τ rr = µ  2 r − ∇⋅ v   ∂r 3 

∂v y ∂v z   ∂v ∂ρ ∂ρ ∂ρ ∂ρ + + vx + vy + vz = −ρ  x + ∂t ∂x ∂y ∂z  ∂ x ∂ y ∂ z 

1 ∂v r   ∂ v τ rθ = τθr = µ  r  θ  +  ∂r  r  r ∂θ 

 1 ∂v r ∂  vφ   τ rφ = τφr = µ  +r   ∂r  r    r sin θ ∂φ

Cylindrical ∂ρ ∂ρ vθ ∂ρ ∂ρ 1 ∂v θ ∂v z  1 ∂ + vr + + vz = −ρ  + (rv r ) + ∂t ∂r r ∂θ ∂z r ∂θ ∂ z   r ∂r

   1 ∂v θ v r  2 τθθ = µ  2  +  − ∇⋅ v     r ∂θ r  3

Spherical v φ ∂ρ 1 ∂ ∂ρ ∂ρ vθ ∂ρ 1 ∂ 1 ∂v φ  + vr + + = −ρ  2 (r 2 v r ) + (vθ sin θ) + ∂t ∂r r ∂θ r sin θ ∂φ r sin θ ∂θ r sin θ ∂φ   r ∂r Dv = −∇p + ∇⋅ τ + ρg Cauchy Momentum Equation ρ Dt Cartesian  ∂v ∂ p ∂τ xx ∂τ yx ∂τ zx ∂v ∂v ∂v  + + ρg x + + ρ x + v x x + v y x + v z x  = − ∂y ∂z ∂x ∂x ∂x ∂y ∂z   ∂t ∂v y ∂v y ∂v y   ∂v y ∂ p ∂τ xy ∂τ yy ∂τ zy ρ + vx + =− + vy + + vz + + ρg y ∂ y ∂x ∂x ∂y ∂y ∂ z  ∂z  ∂t  ∂v ∂ p ∂τ xz ∂τ yz ∂τ zz ∂v ∂v ∂v  + + + ρg z ρ z + v x z + v y z + v z z  = − + ∂y ∂z ∂x ∂z ∂x ∂y ∂z   ∂t

 1 ∂vθ sin θ ∂  vφ   τφθ = τθφ = µ  +  r ∂θ  sin θ    r sin θ ∂φ

  1 ∂vφ v r vθ cot θ  2  τφφ = µ  2  + + − ∇⋅ v  r  3   r sin θ ∂φ r  ∇⋅ v =

1 ∂ 2 1 ∂ 1 ∂v ( r vr ) + r sin ( vθ sin θ) + r sin θ ∂φφ θ ∂θ r 2 ∂r

Navier-Stokes Equation ρ

Dv = −∇p + µ∇ 2 v + ρg Dt

Cartesian  ∂2 v x ∂2 v x ∂2 v x   ∂v ∂p ∂v ∂v ∂v  + ρg x + m + + ρ x + v x x + v y x + v z x  = − ∂x ∂x ∂y ∂z   ∂ x 2 ∂ y 2 ∂ z 2   ∂t

Cylindrical

 ∂2 v y ∂2 v y ∂2 v y  ∂v y ∂v y ∂v y   ∂v y ∂p =− + m + + + ρg y ρ + vx + vy + vz 2  ∂y ∂ y 2 ∂ z 2  ∂x ∂y ∂z   ∂t  ∂x

∂v v ∂v v 2 ∂v  1 ∂τ θr τθθ ∂τ zr ∂p 1 ∂  ∂v (r τ rr ) + + − + + ρg r ρ  r + vr r + θ r − θ + v z r  = −  ∂t r ∂θ r ∂r r ∂r ∂z ∂r r ∂θ r ∂z 

 ∂2 v z ∂2 v z ∂2 v z   ∂v ∂p ∂v ∂v ∂v  + ρg z + m + + ρ z + v x z + v y z + v z z  = − ∂z ∂x ∂y ∂z   ∂ x 2 ∂ y 2 ∂ z 2   ∂t

∂v v ∂v v v ∂v  1 ∂p 1 ∂ 2  ∂v + ρ  θ + vr θ + θ θ + r θ + v z θ  = − ( r τrθ ) + 1r ∂τ∂θθθ + ∂τ∂zzθ + ρg θ  ∂t r ∂θ r r ∂θ r 2 ∂r ∂r ∂z 

Cylindrical

∂v v ∂v ∂v  ∂p 1 ∂ 1 ∂τθz ∂τ zz  ∂v + + + ρg z ρ  z + vr z + θ z + v z z  = − (r τ rz ) +  ∂t ∂ z r ∂r ∂z ∂r ∂z  r ∂θ r ∂θ

∂v v ∂v v 2  ∂v ∂v  ∂p ρ r + v r r + θ r − θ + v z r  = −  ∂t ∂r r ∂θ r ∂z  ∂r

Spherical vφ ∂v r vθ2 + vφ2   ∂v ∂v v ∂v ∂p 1 ∂ 2 ρ r + v r r + θ r + =− + − ( r τrr ) sin t r r r r  ∂ ∂ ∂r r 2 ∂r ∂θ θ ∂φ  1 ∂ 1 ∂τφr τθθ + τφφ (τθr sin θ) + + − + ρg r r sin θ ∂θ r sin θ ∂φ r vφ ∂vθ v r vθ vφ2 cot θ   ∂v 1 ∂p 1 ∂ 2 ∂v v ∂v ρ θ + v r θ + θ θ + =− + + − ( r τ rθ ) sin t r r r r r  r ∂θ r 2 ∂r ∂ ∂ ∂θ θ ∂φ  +

1 ∂ 1 ∂τφθ τ rθ cot θ (τθθ sin θ) + + − τφφ + ρg θ r sin θ ∂θ r sin θ ∂φ r r

v φ ∂v φ v φ v r v θ v φ ∂v φ v θ ∂v φ   ∂v φ 1 ∂p + + + + + vr ρ cot θ = −   ∂t r r r sin θ ∂φ ∂r r ∂θ r sin θ ∂φ +

1 ∂ 2 1 ∂τθφ 1 ∂τφφ τ rφ 2cot θ r τ rφ + + + + τθφ + ρg φ r 2 ∂r r ∂θ r sin θ ∂φ r r

(

)

2 2 T τ = 2µΓ − µ(∇⋅ v )d = µ[∇v + ( ∇v ) ] − µ(∇⋅ v )d 3 3

 ∂v y 2  − ∇⋅v t yy = m  2  ∂y 3  ∂v x ∂v y ∂v z + ∇⋅v = + ∂x ∂ y ∂z

∂v   ∂v t xz = t zx = m  x + z   ∂z ∂x   ∂v 2  t zz = m  2 z − ∇ ⋅ v   ∂z 3 

∂p ∂v v ∂v ∂v   ∂v ρ z + v r z + θ z + v z z  = −  ∂t ∂z ∂r r ∂θ ∂z   1 ∂  ∂v z  1 ∂ 2 v z ∂ 2 v z  + 2  + ρg z +µ + 2 r 2 ∂z   r ∂r  ∂r  r ∂θ

vφ ∂v r vθ2 + vφ2   ∂v ∂p ∂v v ∂v =− ρ r + v r r + θ r + − ∂r t r r r r  ∂ ∂ ∂θ θ ∂φ sin 

 ∂v vφ ∂vθ v r vθ vφ2 cot θ  ∂v v ∂v 1 ∂p + − ρ θ + v r θ + θ θ + =− ∂r r ∂θ r sin θ ∂φ r r  r ∂θ  ∂t  v 2 ∂v 2cos θ ∂vφ  + ρg θ + µ ∇ 2 vθ + 2 r − 2 θ 2 − 2 2 r ∂θ r sin θ r sin θ ∂φ   ∂v φ v θ ∂v φ v φ ∂v φ v φ v r v θ v φ   ∂v φ 1 ∂p ρ + vr + + + + cot θ = −   ∂t ∂r r ∂θ r sin θ ∂φ r r r sin θ ∂φ

Cylindrical  ∂v 2  τ rr = µ  2 r − ∇⋅ v   ∂r 3 

2 2  ∂ 1 ∂  1 ∂ v θ 2 ∂v r ∂ v θ  + 2 + 2  + ρg θ +µ  rvθ ) + 2 ( 2   r ∂θ r ∂θ ∂ z   ∂r r ∂r

 2v 2 ∂v 2 2 ∂v φ  + µ ∇ 2 v r − 2r − 2 θ − 2 vθ cot θ − 2 + ρg r r r ∂θ r r sin θ ∂φ  

Cartesian ∂v y   ∂v t xy = t yx = m  x +   ∂ y ∂x   ∂v ∂v y  t zy = t yz = m  z +   ∂ y ∂z 

∂v v ∂v v v ∂v  1 ∂p  ∂v ρ θ + v r θ + θ θ + r θ + v z θ  = −  ∂t ∂r r ∂θ ∂z  r r ∂θ

Spherical

Stress Constitutive Equation for Newtonian and Generalized Newtonian Fluids

2  ∂v  t xx = m  2 x − ∇ ⋅ v   ∂x 3 

1 ∂2 v 2 ∂v ∂ 2 v  ∂ 1 ∂ +µ  ( rvr ) + r 2 ∂θ2r − r 2 ∂θθ + ∂ z 2r  + ρg r  ∂r  r ∂r 

1 ∂v r   ∂ v τ rθ = τθr = µ  r  θ  +  ∂r  r  r ∂θ 

   1 ∂v θ v r  2 τ θθ = µ  2  +  − ∇⋅ v     r ∂θ r  3 1 ∂ 1 ∂vθ ∂v z ∇⋅ v = + rv r ) + ( r ∂r r ∂θ ∂ z

 ∂v ∂v  τ rz = τ zr = µ  r + z   ∂ z ∂r 

 1 ∂v z ∂v θ  τ zθ = τ θz = µ  +  r ∂θ ∂ z 

 ∂v 2  τ zz = µ  2 z − ∇⋅ v   ∂z 3 

vφ  2 ∂v r 2cos θ ∂vθ  + ρg φ + µ ∇ 2 vφ − 2 2 + 2 + r sin θ r sin θ ∂φ r 2 sin 2 θ ∂φ   ∇2 =

∂2 ∂ ∂ 1 ∂ 2 ∂ 1 1  sin θ  + 2 2 + r ∂θ r sin θ ∂φ2 r 2 ∂r  ∂r  r 2 sin θ ∂θ 

FLUID DYnAMICS

6-7

TABLE 6-1 Differential Equations of Motion, newtonian Stress Constitutive Equation and Rate of Deformation Tensor, in Cartesian, Cylindrical, and Spherical Coordinates (Continued ) 1 T Rate of deformation tensor Γ = (1/2)[∇v + ( ∆v ) ] and its magnitude Γ = Γ:Γ . 2 The rate of deformation is γ = 2 Γ .

Spherical

Cartesian Γ xx = Γ yy =

∂v x ∂x

1  ∂v ∂v y  Γ xy = Γ yx =  x + 2  ∂ y ∂ x 

1  ∂v ∂v  Γ xz = Γ zx =  x + z  2  ∂z ∂x 

∂v y

1  ∂v ∂v y  Γ zy = Γ yz =  z + 2  ∂ y ∂ z 

∂v Γ zz = z ∂z

∂y

2

 ∂v   ∂v y   ∂v  x z   +  +  ∂ x   ∂ y   ∂ z 

( 2Γ )2 = 2 

2

2

2

2

  ∂v y ∂v   ∂v ∂v y   ∂v ∂v  x + x  + z + + z +   +   ∂ x ∂ y   ∂ y ∂ z   ∂ z ∂ x 

2

Cylindrical

1 ∂ v 1 ∂v r  Γ rθ = Γ θr =  r  θ  + 2  ∂r  r  r ∂θ 

Γ rr =

∂v r ∂r

Γ θθ =

1 ∂v θ v r + r ∂θ r

Γ φφ =

1 ∂vφ v r vθ cot θ + + r r sin θ ∂φ r

∂  vφ   1  1 ∂v r Γ rφ = Γ φr =  +r   ∂r  r   2  r sin θ ∂φ

1  1 ∂vθ sin θ ∂  vφ   Γ φθ = Γ θφ =  +  2  r sin θ ∂φ r ∂θ  sin θ  

 ∂v r  2  1 ∂vθ v r  2  1 ∂vφ v r vθ cot θ  2   ∂  vθ  1 ∂v r  2 + + +  + + r   +  + r    ∂r  r  r ∂θ   ∂r   r ∂θ r   r sin θ ∂φ r

( 2 Γ )2 = 2 

2

∂v Γ rr = r ∂r Γ θθ =

1 ∂v r  1 ∂ v Γ rθ = Γ θr =  r  θ  + 2  ∂r  r  r ∂θ 

1 ∂v θ v r + r ∂θ r

1  1 ∂v z ∂v θ  Γ zθ = Γ θz =  + 2  r ∂θ ∂ z 

 sin θ ∂  vφ  ∂  vφ   1 ∂v θ   1 ∂v r +  sin θ  + r sin θ ∂φ  +  r sin θ ∂φ + r ∂r  r   ∂θ r    

1  ∂v ∂v  Γ rz = Γ zr =  r + z  2  ∂ z ∂r  Γ zz =

2

∂v z ∂z

 ∂v r  2  1 ∂v θ v r  2  ∂v z  2   ∂  v θ  1 ∂v r  2 +  +   + r   +  +   ∂r   r ∂θ r   ∂ z    ∂r  r  r ∂θ 

( 2Γ )2 = 2 

2

 1 ∂v z ∂v θ   ∂v r ∂v z  + + + +  r ∂θ ∂ z   ∂ z ∂r 

2

The equations for (2Γ)2 are taken from Deen, Analysis of Transport Phenomena, 2d ed., Oxford University Press, New York, 2012, p. 241.

Area Aa

n outwardly directed unit normal vector

Volume Va

d ρv dV + ∫ ρv ( v − w ) ⋅ n dA = ∫ ρg dV + ∫ n ⋅ σ dA Va Aa Aa dt ∫Va

w boundary velocity v fluid velocity FIG. 6-3 Arbitrary control volume for application of conservation equations.

Simplified forms of Eq. (6-10) apply to special cases frequently found in practice. For a control volume fixed in space with one inlet of area A1 through which an incompressible fluid enters the control volume at an average velocity V1, and one outlet of area A2 through which fluid leaves at an average velocity V2, as shown in Fig. 6-4, the continuity equation becomes (6-11)

V1A1 = V2A2 The average velocity across a surface is given by V = (1/A ) ∫ v dA

(6-12)

A

where v is the local velocity component perpendicular to the surface. The volumetric flow rate Q is the product of average velocity and the crosssectional area, Q = VA . The average mass velocity is G = ρV . For steady flows through fixed control volumes with multiple inlets and/or outlets,

V2 2

V1 1 FIG. 6-4

Fixed control volume with one inlet and one outlet.

conservation of mass requires that the sum of inlet mass flow rates equals the sum of outlet mass flow rates. For incompressible flows through fixed control volumes, the sum of inlet flow rates (mass or volumetric) equals the sum of exit flow rates, whether the flow is steady or unsteady. Momentum Balance Momentum is a vector quantity, and the momentum balance is a vector equation. It (and the energy balance, see below) are written in inertial reference frames. Where gravity is the only body force acting on the fluid, the linear momentum principle, applied to the arbitrary control volume of Fig. 6-3, results in the following expression. (6-13)

Here g is the gravity vector and n ⋅ σ is the force per unit area exerted by the surroundings on the fluid in the control volume. The total stress tensor σ includes both pressure and viscous stress (see below). For the special case of steady flow at a mass flow rate m through a control volume fixed in space with one inlet and one outlet (Fig. 6-4), with the inlet and outlet velocity vectors perpendicular to planar inlet and outlet surfaces, giving average velocity vectors V1 and V2, the momentum equation becomes m (β 2 V2 −β1 V1 ) = − p1 A 1 − p2 A 2 + F + Mg

(6-14)

where M is the total mass of fluid in the control volume. The factor β arises from the averaging of the velocity across the area of the inlet or outlet surface. It is the ratio of the area average of the square of velocity magnitude to the square of the area average velocity magnitude. For a uniform velocity, β = 1. For turbulent flow, β is nearly unity, while for laminar pipe flow with a parabolic velocity profile, β = 4/3. Vectors A1 and A2 have magnitude equal to the areas of the inlet and outlet surfaces, respectively, and are outwardly directed normal to the surfaces. Vector F is the force exerted on the fluid by the nonflow boundaries of the control volume. Viscous contributions to the stress vector n ⋅ σ are neglected at the inlet and outlet surfaces, leaving only pressure forces there . Equation (6-14) may be generalized to multiple inlets and/or outlets. In such cases, a distinct flow rate m i applies to each inlet or outlet i . To generalize the equation, −pA terms for each inlet and outlet, − m i βi Vi terms for each inlet, and m i βi Vi terms for each outlet are included. Balance equations for angular momentum, or moment of momentum, may also be written. They are used less frequently than the linear momentum equations. See S. Whitaker [Introduction to Fluid Mechanics, Krieger, Huntington, N.Y., 1981]; J. O. Wilkes [Fluid Mechanics for Chemical Engineers, 2d ed., Prentice-Hall, Upper Saddle River, N.J., 2006]; and N. de Nevers [Fluid Mechanics for Chemical Engineers, 3d ed., McGraw-Hill, New York, 2005]. Total Energy Balance The total energy balance derives from the first law of thermodynamics. Applied to the arbitrary control volume of Fig. 6-3, it leads to an equation for the rate of change of the sum of internal, kinetic, and gravitational potential energy. Energy input to the control volume

6-8

FLUID AnD PARTICLE DYnAMICS

comes from work and heat flux at the boundary. The balance also includes energy input by relatively uncommon volumetric sources such as inductive heating, expressed as energy input per unit volume QV . In this equation, u is the internal energy per unit mass, υ is the magnitude of the velocity vector v, Z is elevation, g is the gravitational acceleration, and q is the heat flux vector:

Microscopic Balance Equations Partial differential balance equations express the conservation principles at a point in space. The two most used equations, for mass and momentum, are presented here. Mass Balance, Continuity Equation The continuity equation, expressing conservation of mass, may be written in vector notation as

    v2 v2 ρ u + + gZ  dV + ∫ ρ u + + gZ  ( v − w ) ⋅ n dA Aa     2 2

∂ρ + ∇⋅ (ρv ) = 0 ∂t

d dt

∫

Va

(6-15)

= ∫ ( v ⋅ n ⋅ σ ) dA − ∫ (q ⋅ n ) dA + ∫ QV dV Aa

Aa

h1 + α1

V12 V2 + gz1 = h2 + α 2 2 + gz 2 − δQ − δWS 2 2

(6-16)

Here h is the enthalpy per unit mass, h = u + p/r. The shaft work per unit of mass flowing through the control volume is δWS = W S /m . Similarly, δQ is the heat input per unit of mass. The factor α is the ratio of the cross-sectional area average of the cube of the velocity to the cube of the average velocity. For a uniform velocity profile, α = 1. In turbulent flow, α is usually assumed to equal unity; in turbulent pipe flow, it is typically about 1.07. For laminar flow in a circular pipe with a parabolic velocity profile, α = 2. Mechanical Energy Balance, Bernoulli Equation A balance equation for the sum of kinetic and potential energy may be obtained from the momentum balance by forming the scalar product with the velocity vector. The resulting equation, called the mechanical energy balance, contains a term accounting for the dissipation of mechanical energy into thermal energy by viscous forces. It is also derivable from the total energy equation in a way that reveals the relationship between the dissipation and entropy generation. The macroscopic mechanical energy balance for the arbitrary control volume of Fig. 6-3 may be written, with p = thermodynamic pressure, as  v2   v2  d ρ  + gZ  dV + ∫ ρ  + gZ  ( v − w ) ⋅ n dA ∫ V A    2  a a 2 dt

(6-17)

= ∫ p∇ ⋅ v dV + ∫ ( v ⋅ n ⋅ σ ) dA − ∫ Φ dV Va

In terms of the substantial derivative, D /Dt = ∂/ ∂t + v ⋅∇, Dρ = −ρ∇ ⋅ v Dt

Va

The first integral on the right-hand side is the rate of work done on the fluid in the control volume by forces at the boundary. It includes both work done by moving solid boundaries and work done at flow entrances and exits. The work done by moving solid boundaries also includes that by surfaces such as pump impellers; this work is called shaft work; its rate is W s . A useful simplification of the total energy equation applies to a particular set of assumptions. These are a control volume with fixed solid boundaries, except for those producing shaft work, steady-state conditions, and mass flow at a rate m through a single planar entrance and a single planar exit (Fig. 6-4), to which the velocity vectors are perpendicular and QV = 0 . As with Eq. (6-14), viscous contributions to the stress vector n ⋅ σ are neglected at the entrance and exit surfaces.

Aa

Va

The last term is the rate of viscous energy dissipation to internal energy, also called the rate of viscous losses. These losses are the origin of frictional pressure drop in fluid flow. S. Whitaker [Introduction to Fluid Mechanics, Krieger, Huntington N.Y., 1981]; R. B. Bird, W. E. Stewart, and E. N. Lightfoot [Transport Phenomena, 2d ed., Wiley, New York, 2002]; and W. M. Deen [Analysis of Transport Phenomena, 2d ed., Oxford University Press, Oxford, UK, 2012] provide expressions for the dissipation function Φ for newtonian fluids in terms of the local velocity gradients. However, when one is using macroscopic balance equations, the local velocity field within the control volume is usually unknown. For such cases additional information, which may come from empirical correlations, is needed. For the same special conditions as for Eq. (6-16), except for the QV = 0 restriction, the mechanical energy equation reduces to p2 dp V2 V2 α1 1 + gZ1 + δWS = α 2 2 + gZ2 + ∫ + lv p 1 2 2 ρ

(6-18)

Here l v is the energy dissipation per unit mass. This equation has been called the engineering Bernoulli equation . For an incompressible flow, Eq. (6-18) becomes p1 V2 p V2 + α1 1 + gZ1 + δWS = 2 + α 2 2 + gZ2 + l v ρ ρ 2 2

(6-19)

The Bernoulli equation can be written for incompressible, inviscid flow along a streamline: p1 V12 p V2 + + gZ1 = 2 + 2 + gZ2 2 ρ 2 ρ

(6-20)

Unlike the momentum equation, Eq. (6-14), the Bernoulli equation does not generalize to multiple inlets or outlets by mere addition of terms.

(6-21)

(6-22)

Also called the material derivative, D /Dt is the rate of change in a lagrangian reference frame, that is, following a material particle. For incompressible flow, ∇⋅ v = 0

(6-23)

Equation (6-22) in cartesian, cylindrical, and spherical coordinates may be found in Table 6-1. Stress Tensor The stress tensor is needed to completely describe the stress state for microscopic momentum balances in multidimensional flows. The components of the stress tensor σij give the force in the j direction on a plane perpendicular to the i direction, using a sign convention defining a positive stress as one where the fluid with the greater i coordinate value exerts a force in the positive j direction on the fluid with the lesser i coordinate. Several references in fluid mechanics and continuum mechanics provide discussions, to various levels of detail, of stress in a fluid, e.g., R. Aris [Vectors, Tensors and the Basic Equations of Fluid Mechanics, Dover, New York, 1962]; W. M. Deen [Analysis of Transport Phenomena, 2d ed., Oxford University Press, Oxford, UK, 2012]; and J. C. Slattery [Advanced Transport Phenomena, Cambridge University Press, Cambridge, UK, 1999]. The stress has an isotropic contribution due to fluid pressure and a deviatoric contribution due to viscous deformation. The total stress is σ = − pδ + τ

(6-24)

where p is the pressure. The deviatoric stress for a newtonian fluid is 2 τ = 2µΓ +  κ − µ  (∇ ⋅ v ) δ  3 

(6-25)

The identity tensor components δij are zero for i ≠ j and unity for i = j . There is uncertainty about the value of the bulk viscosity κ. Traditionally, Stokes’ hypothesis, κ = 0, has been invoked. For incompressible flow, the value of bulk viscosity is immaterial as Eq. (6-25) reduces to Eq. (6-7). Similar generalizations to multidimensional flow are necessary for nonnewtonian constitutive equations. The components of the stress constitutive equation in cartesian, cylindrical, and spherical coordinates for newtonian and generalized newtonian fluids are shown in Table 6-1. Cauchy Momentum and Navier-Stokes Equations The differential equation for conservation of momentum is called the Cauchy momentum equation. ρ

Dv  ∂v  = ρ  + v ⋅∇v  = −∇p + ∇⋅ τ + ρg Dt  ∂t 

(6-26)

For an incompressible newtonian fluid with constant viscosity, substitution of Eqs. (6-7) and (6-6) into Eq. (6-26) gives the Navier-Stokes equation ρ

Dv   ∂v = ρ  + v ⋅∇v  = −∇p + µ∇ 2 v + ρg Dt   ∂t

(6-27)

The pressure and gravity terms in Eq. (6-27) may be combined by replacing the pressure p by the equivalent pressure P = p + ρgZ, where Z is elevation . The left-hand side terms of the Navier-Stokes equation are the inertial terms, while the terms including viscosity µ are the viscous terms . Limiting cases under which the Navier-Stokes equations may be simplified include creeping flows in which the inertial terms are neglected, inviscid flows in which the viscous terms are neglected, and boundary layer and lubrication flows in which certain terms are neglected based on scaling arguments. Creeping flows are described by J. Happel and H. Brenner [Low Reynolds Number Hydrodynamics, Prentice-Hall, Englewood Cliffs, N.J., 1965] and L. G. Leal [Advanced Transport Phenomena, Cambridge University Press, Cambridge, UK, 2007]; inviscid flows by H. Lamb [Hydrodynamics, 6th ed., Dover, New York, 1945] and L. M. Milne-Thompson [Theoretical Hydrodynamics, 5th ed., Macmillan, New York, 1968]; boundary layer theory by H. Schlichting and K. Gersten [Boundary Layer Theory, 8th ed rev., SpringerVerlag, Berlin, 2003] and lubrication theory by G. K. Batchelor [An Introduction to Fluid Dynamics, Cambridge University, Cambridge, UK, 1967], M. M. Denn [Process Fluid Mechanics, Prentice-Hall, Englewood Cliffs, N.J., 1979], and

FLUID DYnAMICS W. M. Deen [Analysis of Transport Phenomena, 2d ed., Oxford University Press, Oxford, UK, 2012]. Because the Navier-Stokes equations are first-order in pressure and second-order in velocity, their solution requires one pressure boundary condition and two velocity boundary conditions ( for each velocity component) to completely specify the solution for a steady flow. The no-slip condition, which requires that the fluid velocity equal the velocity of any bounding solid surface, occurs in most problems. Specification of velocity is a type of boundary condition sometimes called a Dirichlet condition . Often boundary conditions involve stresses, and thus velocity gradients, rather than the velocities themselves. Specification of velocity derivatives is a Neumann condition . For example, at the boundary between a viscous liquid and a gas, it is often assumed that the liquid shear stresses are zero. In numerical solution of the Navier-Stokes equations, Dirichlet and Neumann, or essential and natural, boundary conditions may be satisfied by different means. Fluid statics, discussed in Sec. 10 in reference to pressure measurement, is the branch of fluid mechanics in which the fluid velocity either is zero or is uniform and constant relative to an inertial reference frame. With velocity gradients equal to zero, the momentum equation reduces to a simple expression for the pressure field, ∇p = rg. Letting z be directed vertically upward, so that gz = −g where g is the gravitational acceleration (9.807 m/s2 or 32.17 ft/s2), the pressure field is given by dp = −ρg dz

(6-28)

This equation applies to any incompressible or compressible static fluid. For an incompressible liquid, pressure varies linearly with depth. The force exerted on a submerged planar surface of area A is given by F = pcA where pc is the pressure at the geometric centroid of the surface. The center of pressure, the point of application of the net force, is always lower than the centroid. For details see, for example, I. H. Shames [Mechanics of Fluids, 3d ed., McGraw-Hill, New York, 1992] where may also be found discussion of forces on curved surfaces, buoyancy, and stability of floating bodies . Examples Four examples follow, illustrating the application of the conservation equations. Example 6-1 Force Exerted on a Reducing Bend An incompressible fluid flows through a reducing elbow (Fig. 6-5) situated in a horizontal plane. The inlet velocity V1 is given, and pressures p1 and p2 are measured. By selecting the inlet and outlet surfaces 1 and 2 as shown, the continuity equation, Eq. (6-11), can be used to find the exit velocity V2 = V1A1/A2. The mass flow rate is obtained by m = ρV1 A1 . Assume that the velocity profile is nearly uniform so that b is approximately unity. The force exerted on the fluid by the bend has x and y components; these can be found from Eq. (6-14). The x component gives Fx = m (V2 x − V1 x ) + p1 A1 x + p2 A2 x

FIG. 6-6

6-9

Simplified ejector.

Example 6-2 Simplified Ejector Figure 6-6 shows a very simplified sketch of an ejector, a device that uses a high-velocity primary fluid to pump another (secondary) fluid. The continuity and momentum equations may be applied on the control volume with inlet and outlet surfaces 1 and 2, as indicated in the figure. The cross-sectional area is uniform, A1 = A2 = A . Let the mass flow rates and velocities of the primary and secondary fluids be m p , m s , V p , and Vs . Assume for simplicity that the density is uniform. Conservation of mass gives m 2 = m p + m s . The exit velocity is V2 = m 2 /(ρA ). The principal momentum exchange in the ejector occurs between the two fluids. Relative to this exchange, the force exerted by the walls of the device is small. Therefore, the force term F is neglected from the momentum equation. Written in the flow direction, assuming uniform velocity profiles, and using the extension of Eq. (6-14) for multiple inlets, it gives the pressure rise developed by the device: ( p2 − p1 ) A = (m p + m s )V2 − m p V p − m s Vs Application of the momentum equation to ejectors of other types is discussed in C. E. Lapple (Fluid and Particle Dynamics, University of Delaware, Newark, 1951) and in Sec. 10 of this handbook.

Example 6-3 Venturi Flowmeter An incompressible fluid flows through the venturi flowmeter in Fig. 6-7. An equation is needed to relate the flow rate Q to the pressure drop measured by the manometer. This problem can be solved using the mechanical energy balance. In a well-made venturi, viscous losses are negligible, the pressure drop is the result of acceleration into the throat, and the flow rate predicted neglecting losses is quite accurate. The inlet area is A and the throat area is a . Gravity may be neglected even if the venturi is not horizontal, due to the small elevation change. With control surfaces at 1 and 2 as shown in the figure, Eq. (6-19) in the absence of losses and shaft work gives p1 V12 p2 V22 + = + 2 2 ρ ρ The continuity equation gives V2 = V1A/a, and V1 = Q/A . The pressure drop measured by the manometer is p1 − p2 = (rm − r)g DZ . By substituting these relations into the energy balance and rearranging, the desired expression for the flow rate is found. Q=

while the y component gives

1 2(ρm − ρ) g ∆Z A ρ[( A /a )2 − 1]

Fy = m (V2 y − V1 y ) + p1 A1 y + p2 A2 y The velocity components are V1x = V1, V1y = 0, V2x = V2 cos q, and V2y = V2 sin q. The area vector components are A1x = −A1, A1y = 0, A2x = A2 cos q, and A2y = A2 sin q. Therefore, the force components may be calculated from Fx = m (V2 cos θ − V1 ) − p1 A1 + p2 A2 cos θ Fy = m V2 sin θ + p2 A2 sin θ The force acting on the fluid is F; the force exerted by the fluid on the bend is −F.

V2 θ

Example 6-4 Plane Poiseuille Flow Driven by a pressure gradient, an incompressible newtonian fluid with constant viscosity flows at a steady rate in the x direction between two very large stationary plates, as shown in Fig. 6-8. The flow is laminar. Cartesian coordinates are used for this rectangular geometry. The fully developed velocity profile is to be found. This is the velocity field in the region sufficiently far from the inlet and exit that the velocity is independent of x. This problem requires use of the microscopic balance equations because the velocity is to be determined as a function of position. The boundary conditions result from the no-slip condition. All three velocity components must be zero at the plate surfaces y = H/2 and y = −H/2. For fully developed flow, all velocity derivatives in the x direction vanish. Since the flow field is infinite in the z direction, all velocity derivatives in the z direction are zero. Therefore, velocity components are a function of y alone. It is also assumed that there is

1

2

V1 F ∆Z

y x FIG. 6-5 Force at a reducing bend. F is the force exerted by the bend on the fluid. The force exerted by the fluid on the bend is −F.

FIG. 6-7

Venturi flowmeter.

6-10

FLUID AnD PARTICLE DYnAMICS The integration constants C1 and C2 are evaluated from the boundary conditions υx = 0 at y = ±H/2 . The result is

y H

x FIG. 6-8

vx =

2 H 2  dP    2 y    −  1−  8µ  dx    H  

This is a parabolic velocity distribution . The average velocity V = (1/H ) ∫

Plane Poiseuille flow .

no flow in the z direction, so υz = 0. The continuity equation from Table 6-1, with υz = 0 and ∂υx/∂x = 0, reduces to dv y dy

=0

Since υy = 0 at y = ±H/2, the continuity equation integrates to υy = 0 . This is a direct result of the assumption of fully developed flow . The only nonzero velocity component is vx, and it is a function only of y . The flow is one-dimensional . The Navier-Stokes equations are greatly simplified with υy, υz, ∂υx/∂x, ∂υx/∂z, and ∂υx/∂t all being zero . The three cartesian components from Table 6-1 are written in terms of the equivalent pressure P: ∂2 v x ∂P +µ ∂x ∂y2 ∂P 0=− ∂y 0=−

0=−

∂P ∂z

The latter two equations require that P be a function only of x, and therefore ∂P/∂x = dP/dx . Inspection of the first equation then shows one term that is a function of only x and one that is a function of only y . This requires that both terms be constant . The pressure gradient −dP/dx is constant . The x-component equation becomes d 2 v x 1 dP = dy 2 µ dx Two integrations give vx =

1 dP 2 y + C1 y + C 2 2µ dx

V=

H /2 − H /2

v x dy is

H 2  dP  −  12µ  dx 

InCOMPRESSIBLE FLOW In PIPES AnD CHAnnELS Mechanical Energy Balance The mechanical energy balance, Eq . (6-19), for fully developed incompressible flow in a straight circular pipe of constant diameter D reduces to p1 p (6-29) + gZ1 = 2 + gZ2 + l v ρ ρ In terms of the equivalent pressure P = p + rgZ, P1 − P2 = rlυ

(6-30)

The pressure drop due to frictional losses lυ is proportional to pipe length L for fully developed flow and may be denoted as the (positive) quantity DP ≡ P1 − P2 . Friction Factor and Reynolds Number For a newtonian fluid in a smooth pipe, dimensional analysis relates the frictional pressure drop per unit length DP/L to the pipe diameter D, density r, viscosity m, and average velocity V through two dimensionless groups, the Fanning friction factor f and the Reynolds number Re . f≡ Re ≡

D ∆P 2ρV 2 L

(6-31)

DV ρ µ

(6-32)

For smooth pipe, the friction factor is a function of only the Reynolds number . In rough pipe, the relative roughness ε/D also affects the friction factor . Figure 6-9 plots f as a function of Re and ε/D . Values of ε for various

FIG. 6-9 Fanning friction factors . Reynolds number Re = DVr/m, where D = pipe diameter, V = velocity, r = fluid density, and m = fluid viscosity . [Based on L . F . Moody, Trans . ASME, 66: 671 (1944) .]

FLUID DYnAMICS TABLE 6-2 Values of Surface Roughness for Various Materials* Surface roughness ε, mm

Material Drawn tubing (brass, lead, glass, and the like) Commercial steel or wrought iron Asphalted cast iron Galvanized iron Cast iron Wood stave Concrete Riveted steel

0.00152 0.0457 0.122 0.152 0.259 0.183–0.914 0.305–3.05 0.914–9.14

∗From Moody, Trans . Am . Soc . Mech . Eng . 66: 671–684 (1944); Mech . Eng . 69: 1005–1006 (1947). Additional values of ε for various types or conditions of concrete wrought-iron, welded steel, riveted steel, and corrugated-metal pipes are given in Brater and King, Handbook of Hydraulics, 6th ed., McGraw-Hill, New York, 1976, pp. 6-12–6-13. To convert millimeters to feet, multiply by 3.281 × 10−3.

materials are given in Table 6-2. The Fanning friction factor should not be confused with the Darcy friction factor used by L. F. Moody [Trans . ASME, 66: 671 (1944)], which is four times greater. The Darcy-Weisbach equation is equivalent to Eq. (6-31). Using the momentum equation, the stress at the wall of the pipe may be expressed in terms of the friction factor: tw = f

ρV 2 2

(6-33)

In laminar flow, f is independent of ε/D . In turbulent flow, the friction factor for rough pipe follows the smooth tube curve for a range of Reynolds numbers (hydraulically smooth flow). For greater Reynolds numbers, f deviates from the smooth pipe curve, eventually becoming independent of Re. This region, often called complete turbulence, is frequently encountered in commercial pipe flows. Two common pipe flow problems are calculation of pressure drop given the flow rate (or velocity) and calculation of flow rate (or velocity) given the pressure drop. When the flow rate is given, the Reynolds number may be calculated directly to determine the flow regime, so that the appropriate relations between f and Re can be selected. When the flow rate is specified and the flow is turbulent, Eq. (6-38), being explicit in f, may be preferable to Eq. (6-37), which is implicit in f and pressure drop. When the pressure drop is given and the velocity and flow rate are to be determined, the Reynolds number cannot be computed directly, since the velocity is unknown. For such problems, it is useful to note that Re f = ( D 3/2 /µ) ρ∆P / (2 L), appearing in the Colebrook equation (6-37), does not include velocity and so can be computed directly, so that f may be computed without iteration. Thus Eq. (6-37) is preferable to Eq. (6-38) or Eq. (6-39) when the pressure drop is given. Velocity Profiles In laminar flow, the solution of the Navier-Stokes equation, corresponding to the Hagen-Poiseuille equation, gives the velocity v as a function of radial position r in a circular pipe of radius R in terms of the average velocity V = Q/A . The parabolic profile, with centerline velocity twice the average velocity, is shown in Fig. 6-10.

Laminar and Turbulent Flow Below a critical Reynolds number of about 2100, the flow is laminar; over the range 2100 < Re < 5000 there is a transition to turbulent flow. Reliable correlations for the friction factor in transitional flow are not available. For laminar flow, the Hagen-Poiseuille equation f=

16 Re ≤ 2100 Re

(6-34)

may be derived from the Navier-Stokes equation and is in excellent agreement with experimental data. It may be rewritten in terms of volumetric flow rate Q = V πD2/4 as Q=

π ∆PD 4 Re ≤ 2100 128µL

6-11

r2   v = 2V  1 − 2   R 

(6-40)

In turbulent flow, the velocity profile is more blunt, with a lower velocity gradient near the center and a steeper gradient near the wall. The region near the wall is described by a universal velocity profile, characterized by a viscous sublayer, a buffer zone, and a turbulent core . Viscous sublayer u+ = y+

(6-35)

y+ < 5

for

(6-41)

Buffer zone

For turbulent flow in smooth tubes, the Blasius equation gives the friction factor accurately for a wide range of Reynolds number. 0.079 f = 0.25 4000 < Re < 10 5 Re

(6-36)

The Colebrook formula [C. F. Colebrook, J . Inst . Civ . Eng . (London), 11: 133–156 (1938–39)] gives a good approximation for the f-Re-(ε/D) data for rough pipes over the entire turbulent flow range: 1 ε 1.256  = − 4 log  +  Re > 4000 f  3.7 D Re f 

(6-37)

Equation (6-37) was used to construct the curves in the turbulent flow regime in Fig. 6-9. An equation by S. W. Churchill [Chem . Eng . 84(24): 91–92 (Nov. 7, 1977)] closely approximating the Colebrook formula offers the advantage of being explicit in f:  0.27 ε  7  0.9  1 = −4 log  +    Re > 4000  Re   f  D

(6-38)

Churchill also provided a single equation that may be used for Reynolds numbers in laminar, transitional, and turbulent flow, closely fitting f = 16/Re in the laminar regime and the Colebrook formula in the turbulent regime, and giving reasonable values in the transition regime, where the friction factor is uncertain.

u+ = 5.00 ln y+ − 3.05

for

5 < y+ < 30

(6-42)

for

y+ > 30

(6-43)

Turbulent core u+ = 2.5 ln y+ + 5.5

Here, u+ = v/u∗ is the dimensionless, time-averaged axial velocity, u∗ = τw /ρ is the friction velocity, and tw = f ρV 2 /2 is the wall stress. The friction velocity is of the order of the root mean square velocity fluctuation perpendicular to the wall in the turbulent core. The dimensionless distance from the wall is y+ = yu∗r/m. At sufficient Re, the universal velocity profile is valid in the wall region for any cross-sectional channel shape. For incompressible flow in constant-diameter circular pipes, tw = D ∆P /4 L where DP is the equivalent pressure drop in length L . For rough pipes, the velocity profile in the turbulent core is given by u+ = 2.5 ln y/ε + 8.5

for

y+ > 30

(6-44)

when the dimensionless roughness ε+ = εu∗r/m is greater than about 5 to 10; for smaller ε+, the velocity profile in the turbulent core is unaffected by roughness.

1/12

  8 12 1 f = 2   +  ( A + B )3/2   Re 

r z

where 16

  1 A =  2.457 ln (7 / Re)0.9 + 0.27 ε/D   and

37,530  B =   Re 

16

(6-39)

R

(

2 v = 2V 1 – r 2 R

(

v max = 2V FIG. 6-10 Parabolic velocity profile for laminar flow in a pipe, with average velocity V .

6-12

FLUID AnD PARTICLE DYnAMICS

For velocity profiles in the transition region, see Patel and Head [ J . Fluid Mech . 38: part 1, 181–201 (1969)] where profiles over the range 1500 < Re < 10,000 are reported. Entrance and Exit Effects In the entrance region of a pipe, some distance is required for the flow to adjust from upstream conditions to the fully developed velocity profile. This distance depends on the Reynolds number and on the flow conditions upstream. For a uniform velocity profile at the pipe entrance, the computed length in laminar flow required for the centerline velocity to reach 99 percent of its fully developed value is [N. Dombrowski et al., Can . J . Chem . Engr . 71: 472–476 (1993)] Lent/D = 0.370 exp(−0.148 Re) + 0.0550 Re + 0.260

(6-45)

In turbulent flow, the entrance length is about Lent/D = 40

(6-46)

The frictional losses in the entrance region are larger than those for the same length of fully developed flow. (See the subsection Frictional Losses in Pipeline Elements later.) At the pipe exit, the velocity profile also undergoes rearrangement, but the exit length is much shorter than the entrance length. At low Re, it is about one pipe radius. At Re > 100, the exit length is negligible. Residence Time Distribution For the parabolic profile for laminar flow in a pipe, neglecting diffusion, the cumulative residence time distribution F(q) is given by F (θ) = 0 1  θavg  F (θ) = 1 −  4  θ 

for

θ
1, the flow is supercritical . Surface disturbances move at a wave velocity c = gh ; they cannot propagate upstream in supercritical flows. The specific energy Esp is nearly constant. Esp = h +

V2 2g

(6-56)

This equation is cubic in liquid depth. Below a minimum value of Esp there are no real positive roots; above the minimum value there are two positive real roots. At this minimum value of Esp the flow is critical; that is, Fr = 1, V = gh , and Esp = (3/2)h . Near critical flow conditions, wave motion and sudden depth changes called hydraulic jumps are likely. V. T. Chow [Open Channel Hydraulics, McGraw-Hill, New York, 1959] discusses the numerous surface profile shapes which may exist in nonuniform open-channel flows. For flow over a sharp-crested weir of width b and height L, from a liquid depth H, the flow rate is given approximately by 2 Q = C d b 2 g ( H − L)3/2 3

(6-57)

where Cd ≈ 0 .6 is a discharge coefficient . Flow through notched weirs is described under flowmeters in Sec . 10 of this handbook . Nonnewtonian Flow For isothermal laminar flow of time-independent nonnewtonian liquids, integration of the Cauchy momentum equation yields the fully developed velocity profile and flow rate–pressure drop relations . For the Bingham plastic fluid described by Eq . (6-3), in a pipe of diameter D and a pressure drop per unit length of DP/L, the flow rate is given by Q=

πD 3 τw 32µ ∞

 4 τ y τ 4y  + 4 1 −  3 τw 3 τw 

(6-58)

where the wall stress is tw = D ∆P /(4 L) . The velocity profile consists of a central nondeforming plug of radius rP = 2ty/(DP/L) and an annular deforming region . The velocity profile in the annular region is given by vz =

29n 2 f = 1/3 RH

Surface

For gradual changes in channel cross section and liquid depth, and for slopes less than 10°, the momentum equation for a rectangular channel of width b and liquid depth h may be written as a differential equation in the flow direction x .

(6-53)

The most often used friction correlation for open-channel flows is due to R. Manning [Trans . Inst . Civ . Engrs . Ireland 20: 161 (1891)] and is equivalent to

6-13

1  ∆P 2 2 ( R − r ) − τ y ( R − r )  rP ≤ r ≤ R µ ∞  4 L 

(6-59)

where r is the radial coordinate and R is the pipe radius . The velocity of the central, nondeforming plug is obtained by setting r = rP in Eq . (6-59) . When Q is given and Eq . (6-58) is to be solved for τw and the pressure drop, multiple positive roots for the pressure drop may be found . The root corresponding to τw < τ y is physically unrealizable, as it corresponds to rP > R and the pressure drop is insufficient to overcome the yield stress . For a power law fluid, Eq . (6-4), with constant properties K and n, the flow rate is given by ∆P  Q = π   2 KL 

1/n

 n  R (1+3 n )/n   1 + 3n 

(6-60)

and the velocity profile by ∆P  v z =   2 KL 

1/n

 n  [ R (1+n )/n − r (1+n )/n ]   1+ n 

(6-61)

Similar relations for other nonnewtonian fluids may be found in G . W . Govier and K . Aziz [The Flow of Complex Mixtures in Pipes, Krieger, Huntington, N .Y ., 1977] and in R . B . Bird, R . C . Armstrong, and O . Hassager [Dynamics of Polymeric Liquids, vol . 1: Fluid Mechanics, Wiley, New York, 1977] . For steady laminar flow of any time-independent viscous fluid, at average velocity V in a pipe of diameter D, the Rabinowitsch-Mooney equation gives the shear rate at the pipe wall . γ w =

8V  1 + 3n ′    D  4n ′ 

(6-62)

6-14

FLUID AnD PARTICLE DYnAMICS

where n′ is the slope of a plot of DDP/(4L) versus 8V/D on logarithmic coordinates, n′ =

d ln [ D ∆P /(4 L)] d ln (8V /D )

(6-63)

By plotting capillary viscometry data in this way, they can be used directly for pressure drop design calculations, or to construct the rheogram for the fluid. For pressure drop calculation, the flow rate and diameter determine the velocity, from which 8V/D is calculated and D DP/(4L) read from the plot. For a newtonian fluid, n′ = 1 and the shear rate at the wall is γ = 8V /D . For a power law fluid, n′ = n . To construct a rheogram, n′ is obtained from the slope of the experimental plot at a given value of 8V/D . The shear rate at the wall is given by Eq. (6-62), and the corresponding shear stress at the wall is tw = DDP/(4L) read from the plot. By varying the value of 8V/D, the shear stress versus shear rate plot can be constructed. The generalized approach of A. B. Metzner and J. C. Reed [AIChE J . 1: 434 (1955)] for time-independent nonnewtonian fluids uses a modified Reynolds number D n′V 2−n′ρ Re MR ≡ K ′8 n′−1

FIG. 6-11

Fanning friction factor for nonnewtonian flow . The abscissa is defined in Eq . (6-65) . [From D . W . Dodge and A . B . Metzner, Am . Inst . Chem . Eng . J ., 5: 189 (1959) .]

(6-64) where fN is the friction factor for newtonian fluid evaluated at Re = DVr/meff and where the effective viscosity is

where K ′ satisfies D ∆P 8V  = K ′   D  4L

n′

With this definition, f = 16/ReMR is automatically satisfied at the value of 8V/D where K ′ and n′ are evaluated. For newtonian fluids, K ′ = m and n′ = 1; for power law fluids, K ′ = K [(1 + 3n)/(4n)]n and n′ = n . For Bingham plastics, K ′ and n′ are variable, given as a function of tw (A. B. Metzner, Ind . Eng . Chem . 49: 1429–1432 [1957]). µ∞  K ′ = τ1w−n ′  4  − τ τ + τ τ 1 4 /3 ( / ) /3 y w y w   n′ =

 3n + 1  µ eff = K   4 n 

(6-65)

n′

1 − 4 τ y /(3 τw ) + (τ y /τw ) 4 /3 1 − (τ y /τw ) 4

(6-66)

(6-67)

For laminar flow of power law fluids in channels of noncircular cross section, see R. S. Schechter [AIChE J . 7: 445–448 (1961)]; J. A. Wheeler and E. H. Wissler [AIChE J . 11: 207–212 (1965)]; R. B. Bird, R. C. Armstrong, and O. Hassager [Dynamics of Polymeric Liquids, vol. 1: Fluid Mechanics, Wiley, New York, 1977]; and A. H. P. Skelland [Nonnewtonian Flow and Heat Transfer, Wiley, New York, 1967]. Steady, fully developed laminar flows of viscoelastic fluids in straight, constant-diameter pipes show no effects of viscoelasticity. The viscous component of the constitutive equation may be used to develop the flow rate–pressure drop relations, which apply downstream of the entrance region after viscoelastic effects have disappeared. A similar situation exists for time-dependent fluids in pipes of sufficient length. The transition to turbulent flow begins at ReMR in the range of 2000 to 2500 [A. B. Metzner and J. C. Reed, AIChE J . 1: 434 (1955)]. For Bingham plastic materials, K ′ and n′ must be evaluated for the τw condition in question in order to determine ReMR and establish whether the flow is laminar. An alternative method for Bingham plastics is by R. W. Hanks [AIChE J . 9: 306 (1963); 14: 691 (1968)]; R. W. Hanks and D. R. Pratt [Soc . Petrol . Engrs . J . 7: 342 (1967)]; and G. W. Govier and K. Aziz [The Flow of Complex Mixtures in Pipes, Krieger, Huntington, N.Y., 1977, pp. 213–215]. The transition from laminar to turbulent flow is influenced by viscoelastic properties [A. B. Metzner and M. G. Park, J . Fluid Mech . 20: 291 (1964)] with the critical value of ReMR increased to beyond 10,000 for some materials. As a rough guide, the lower limit for the Fanning friction factor in laminar flow is ~0.01 for a wide range of rheological behavior. For turbulent flow of nonnewtonian fluids, the design chart of D. W. Dodge and A. B. Metzner [AIChE J . 5: 189 (1959)], Fig. 6-11, is widely used. K. C. Wilson and A. D. Thomas [Can . J . Chem . Eng . 63: 539–546 (1985)] give friction factor equations for turbulent flow of power law fluids and Bingham plastic fluids. Power law fluids: 1−n 1 1 1+n = + 8.2 + 1.77 ln   2  f fN 1+n

(6-68)

n −1

 8V    D

n −1

(6-69)

Bingham fluids: 1 1  (1 − ξ)2  = + 1.77 ln  + ξ(10 + 0.884 ξ) f fN  1 + ξ 

(6-70)

where fN is evaluated at Re = DVr/m∞ and ξ = τ y / τw . Iteration is required to use this equation since tw = f ρV 2 /2 . Drag Reduction In turbulent flow, drag reduction can be achieved by adding soluble high-molecular-weight polymers even in extremely low concentration to newtonian liquids . The reduction in friction is generally believed to be associated with the extensional thickening viscoelastic nature of the solutions effective in the wall region . For a given polymer, there is a minimum molecular weight necessary to initiate drag reduction at a given flow rate, and a critical concentration above which drag reduction will not occur [O . K . Kim, R . C . Little, and R . Y . Ting, J . Colloid Interface Sci . 47: 530–535 (1974)] . Drag reduction is reviewed by J . W . Hoyt [ J . Basic Eng . 94: 258–285 (1972)]; R . C . Little et al . [Ind . Eng . Chem . Fundam . 14: 283–296 (1975)]; and P . S . Virk [AIChE J . 21: 625–656 (1975)] . At maximum possible drag reduction in smooth pipes, 1 50.73  = −19 log  f  Re f  or approximately,

f=

0.58 Re0.58

(6-71)

(6-72)

for 4000 < Re < 40,000 . The actual drag reduction depends on the polymer system . For further details, see P . S . Virk [ AIChE J . 21: 625–656 (1975)] . More recently, K . D . Housiadas and A . N . Beris [Int . J . Heat Fluid Flow 42: 49–67 (2013)] analyzed direct numerical simulation results to develop an expression for the drag reduction, defined as 1 − ( f /f s ) where f and fs are the Fanning friction factors for the polymer solution and the pure solvent, respectively, at the same Reynolds number . The expression depends on two parameters, a Weissenberg number and a limiting drag reduction (LDR) . The Weissenberg number is the ratio of polymer relaxation time to a wall friction time scale . The LDR characterizes the extensional characteristics of the polymer solution rheology, and it depends on the polymer, polymer molecular weight, and polymer concentration . Note that the Reynolds number is defined based on the wall shear viscosity, which can be approximated by the laminar shear viscosity evaluated under the same shear rate conditions [K . D . Housiadas and A . N . Beris, Int . J . Heat Fluid Flow 42: 49–67 (2013) and Phys . Fluids 16: 1581–1586 (2004)] . Economic Pipe Diameter, Turbulent Flow The economic optimum pipe diameter may be computed so that the last increment of investment reduces the operating cost enough to produce the required minimum return on investment . For long cross-country pipelines, either alloy pipes of appreciable length and complexity or pipelines with control valves, detailed

FLUID DYnAMICS analyses of investment, and operating costs should be made. M. Peters and K. Timmerhaus [Plant Design and Economics for Chemical Engineers, 4th ed., McGraw-Hill, New York, 1991] provide a detailed method for determining the economic optimum size. For pipelines of the lengths usually encountered in chemical plants and petroleum refineries, simplified selection charts are often adequate. In many cases there is an economic optimum velocity that is nearly independent of diameter, which may be used to estimate the economic diameter from the flow rate. For low-viscosity liquids in Schedule 40 steel pipe, economic optimum velocity is typically in the range of 1.8 to 2.4 m/s (6 to 8 ft/s). For gases with density ranging from 0.2 to 20 kg/m3 (0.012 to 1.2 lbm/ft3), the economic optimum velocity is about 40 to 9 m/s (130 to 30 ft/s). Charts and rough guidelines for economic optimum size do not apply to multiphase flows. Economic Pipe Diameter, Laminar Flow Pipelines for the transport of high-viscosity liquids are seldom designed purely on the basis of economics. More often the size is dictated by operability considerations such as available pressure drop, shear rate, or residence time distribution. M. Peters and K. Timmerhaus [Plant Design and Economics for Chemical Engineers, 4th ed., McGraw-Hill, New York, 1991] provide an economic pipe diameter chart for laminar flow. For nonnewtonian fluids, see A. H. P. Skelland [Nonnewtonian Flow and Heat Transfer, Wiley, New York, 1967]. Vacuum Flow When gas flows under high vacuum conditions or through very small openings, the continuum hypothesis is no longer appropriate if the channel dimension is not very large compared to the mean free path of the gas. When the mean free path is comparable to the channel dimension, flow is dominated by collisions of molecules with the wall, rather than by collisions between molecules. An approximate expression based on G. P. Brown et al. [ J . Appl . Phys . 17: 802–813 (1946)] for the mean free path is  2µ  λ=    p

8 RT πM w

(6-73)

The Knudsen number Kn is the ratio of the mean free path to the channel dimension. For pipe flow, Kn = λ/D . Molecular flow is characterized by Kn > 1.0; continuum viscous (laminar or turbulent) flow is characterized by Kn < 0.01. Transition or slip flow applies over the range 0.01 < Kn < 1.0. Vacuum flow is usually described with flow variables different from those used for normal pressures, often leading to confusion. Pumping speed S is the actual volumetric flow rate of gas through a flow cross section. Throughput Q is the product of pumping speed and absolute pressure. In SI, Q has units of Pa ⋅ m3/s. (6-74)

Q = Sp

The mass flow rate w is related to the throughput by using the ideal gas law. w=

Mw Q RT

(6-75)

The relation between throughput and pressure drop Dp = p1 − p2 across a flow element is written in terms of the conductance C . Resistance is the reciprocal of conductance. Conductance has dimensions of volume per time. Q = C ∆p

6-15

TABLE 6-4 Constants for Circular Annuli D2/D1

K

D2/D1

K

0 0.259 0.500

1.00 1.072 1.154

0.707 0.866 0.966

1.254 1.430 1.675

C = 0.40 A

RT Mw

For an orifice of area A, (6-81)

Conductance equations for several other geometries are given by J. L. Ryans and D. L. Roper [Process Vacuum System Design and Operation, chap. 2, McGraw-Hill, New York, 1986]. For a circular annulus of outer and inner diameters D1 and D2 and length L, the method of A. Guthrie and R. K. Wakerling [Vacuum Equipment and Techniques, McGraw-Hill, New York, 1949] may be written C = 0.42 K

( D1 − D2 )2 ( D1 + D2 ) L

RT Mw

(6-82)

where K is a dimensionless constant with values given in Table 6-4. For a short pipe of circular cross section, the conductance as calculated for an orifice from Eq. (6-81) is multiplied by a correction factor K which may be approximated as [E. H. Kennard, Kinetic Theory of Gases, McGraw-Hill, New York, 1938, pp. 306–308] 1 K= for 0 ≤ L/D ≤ 0.75 (6-83) 1 + ( L/D ) 1 + 0.8( L/D ) K= for L/D > 0.75 (6-84) 1 + 1.90( L/D ) + 0.6( L/D )2 For L/D > 100, the error in neglecting the end correction by using the fully developed pipe flow equation, Eq. (6-80), is less than 2 percent. For rectangular channels, see C. E. Normand [Ind . Eng . Chem . 40: 783–787 (1948)]. H. S. Yu and E. M. Sparrow [ J . Basic Eng . 70: 405–410 (1970)] give a chart for slot seals with or without a sheet located in or passing through the seal, giving the mass flow rate as a function of the ratio of seal plate thickness to gap opening. Slip Flow In the transition region between molecular flow and continuum viscous flow, the conductance for fully developed pipe flow is most easily obtained by the method of G. P. Brown et al. [ J . Appl . Phys . 17: 802–813 (1946)] which uses the parameter X=

8  λ   2µ   = π  D   pm D 

RT M

(6-85)

where pm is the arithmetic mean absolute pressure. A correction factor F, read from Fig. 6-12 as a function of X, is applied to the conductance for viscous flow. C=F

πD 4 pm 128 µL

(6-86)

(6-76)

The conductance of a series of flow elements is given by 1 1 1 1 = + + + C C1 C 2 C 3

(6-77)

while for elements in parallel, C = C1 + C2 + C3 + · · ·

(6-78)

For a vacuum pump of speed Sp withdrawing from a vacuum vessel through a connecting line of conductance C, the pumping speed at the vessel is S=

S pC S p +C

(6-79)

Molecular Flow Under molecular flow conditions, conductance is independent of pressure. It is proportional to T /M w , with the proportionality constant a function of geometry. For fully developed pipe flow, πD 3 C= 8L

RT Mw

(6-80)

FIG. 6-12 Correction factor for Poiseuille’s equation at low pressures. Curve A: experimental curve for glass capillaries and smooth metal tubes. [From G. P. Brown, et al., J . Appl . Phys., 17, 802 (1946).] Curve B: experimental curve for iron pipe. [From Riggle, courtesy of E . I . du Pont de Nemours & Co .]

6-16

FLUID AnD PARTICLE DYnAMICS

(a) FIG. 6-13

(b)

(c)

(d)

Contractions and enlargements: (a) sudden contraction, (b) rounded contraction, (c) sudden enlargement, and (d) uniformly diverging duct.

For slip flow through square channels, see M. W. Milligan and H. J. Wilkerson [ J . Eng . Ind . 95: 370–372 (1973)]. For slip flow through annuli, see W. J. Maegley and A. S. Berman [Phys . Fluids 15: 780–785 (1972)]. The pump-down time q for evacuating a vessel in the absence of air in-leakage is given approximately by V  p − p0  θ =  t  ln  1  S0   p2 − p0 

(6-87)

where Vt = volume of vessel plus volume of piping between vessel and pump; S0 = system speed as given by Eq. (6-79), assumed independent of pressure; p1 = initial vessel pressure; p2 = final vessel pressure; and p0 = lowest pump intake pressure attainable with the pump in question. See S. Dushman and J. M. Lafferty [Scientific Foundations of Vacuum Technique, 2d ed., Wiley, New York, 1962]. The rate at which inert materials must be removed by a pumping system after the pump-down stage depends on the in-leakage of air at the various fittings, connections, etc. Air leakage is often correlated with system volume and pressure, but this approach is uncertain because the number and size of leaks may not correlate with system volume, and leakage is sensitive to maintenance quality. J. L. Ryans and D. L. Roper [Process Vacuum System Design and Operation, chap. 2, McGraw-Hill, New York, 1986] present a thorough discussion of air leakage. FRICTIOnAL LOSSES In PIPELInE ELEMEnTS The viscous loss term in the mechanical energy balance for most cases is obtained experimentally. For many common fittings found in piping systems, such as expansions, contractions, elbows, and valves, data are available to estimate the losses. Substitution into the energy balance allows calculation of pressure drop. A common error is to assume that pressure drop and frictional losses are equivalent. Equation (6-19) shows that in addition to frictional losses, other factors such as shaft work and velocity or elevation change influence pressure drop. Losses lv for incompressible flow in sections of straight pipe of constant diameter may be calculated as previously described, using the Fanning friction factor: lv =

∆P 2 fV 2 L = D ρ

(6-88)

where DP = drop in equivalent pressure, P = p + rgZ, with p = pressure, r = fluid density, g = acceleration of gravity, and Z = elevation. Losses in the fittings of a piping network are frequently termed minor losses or miscellaneous losses . These descriptions are misleading because in process piping fitting losses may be greater than the losses in straight piping sections. Equivalent Length and Velocity Head Methods Two methods are in common use for estimating fitting loss. The equivalent length method reports the losses in a piping element as the length of straight pipe which would have the same loss. For turbulent flows, the equivalent length is usually reported as a number of diameters of pipe of the same size as the fitting connection; Le/D is given as a fixed quantity, independent of D. This approach tends to be most accurate for a single fitting size and loses accuracy with deviation from this size. For laminar flows, Le/D correlations normally have size dependence through a Reynolds number term. The other method is the velocity head method. The term V 2/2g has dimensions of length and is commonly called a velocity head but this name is also used for ρV 2 /2. In the velocity head method, the losses are reported as a number of velocity heads K . Then the engineering Bernoulli equation for an incompressible fluid can be written as ρV 2 ρV 2 ρV 2 p1 − p2 = α 2 2 − α1 1 + ρg ( Z2 − Z1 ) + K 2 2 2

(6-89)

where V is the reference velocity upon which the velocity head loss coefficient K is based. For a section of straight pipe, K = 4fL/D . Contraction and Entrance Losses For a sudden contraction at a sharp-edged entrance to a pipe or sudden reduction in cross-sectional area of a channel, as shown in Fig. 6-13a, the loss coefficient based on the downstream velocity V2 is given for turbulent flow in Crane Co. [Tech. Paper 410 1980] approximately by A K = 0.5  1 − 2  A1  

(6-90)

Example 6-5 Entrance Loss Water, r = 1000 kg/m3, flows from a large vessel through a sharp-edged entrance into a pipe at a velocity in the pipe of 2 m/s. The flow is turbulent. Estimate the pressure drop from the vessel into the pipe. With A2/A1 ~ 0, the viscous loss coefficient is K = 0.5 from Eq. (6-90). The mechanical energy balance, Eq. (6-19) with V1 = 0 and Z2 − Z1 = 0 and assuming uniform flow (a2 = 1), becomes p1 − p2 =

ρV22 ρV 2 + 0.5 2 = 2000 + 1000 = 3000 Pa 2 2

Note that the total pressure drop consists of 0.5 velocity head of frictional loss, and 1 velocity head of acceleration. The frictional contribution is a permanent loss of mechanical energy. The acceleration contribution is reversible; if the fluid were subsequently decelerated in a frictionless diffuser, a pressure rise would occur.

For a trumpet-shaped rounded entrance, with a radius of rounding greater than about 15 percent of the pipe diameter (Fig. 6-13b), the turbulent flow loss coefficient K is only about 0.1 [ J. F. Vennard and R. L. Street, Elementary Fluid Mechanics, 5th ed., Wiley, New York, 1975, pp. 420–421]. Rounding of the inlet prevents formation of the vena contracta, reducing the resistance to flow. For laminar flow the losses in sudden contraction may be estimated for area ratios A2/A1 < 0.2 by an equivalent additional pipe length Le given by Le/D = 0.3 + 0.04 Re (6-91) where D is the diameter of the smaller pipe and Re is the Reynolds number in the smaller pipe. For laminar flow in the entrance to rectangular ducts, see R. K. Shah [ J . Fluids Eng . 100: 177–179 (1978)]. For creeping flow, Re < 1, of power law fluids, the entrance loss is approximately Le/D = 0.3/n [D. V. Boger et al., J . Nonnewtonian Fluid Mech . 4: 239–248 (1978)]. For viscoelastic fluid flow in circular channels with sudden contraction, a toroidal vortex forms upstream of the contraction plane. Such flows are reviewed by D. V. Boger [Ann . Review Fluid Mech . 19: 157–182 (1987)]. For creeping flow through conical converging channels, the viscous pressure drop Dp = rlυ may be computed by integration of the differential form of the Hagen-Poiseuille equation, Eq. (6-35), provided the angle of convergence is small. The result for a power law fluid is  3n + 1   8V2  ∆p = 4 K   4 n   D2  n

n

   D  3 n   1 1 −  2      6n tan (α /2)   D1   

(6-92)

where D1 = inlet diameter D2 = exit diameter V2 = velocity at the exit a = total included angle Equation (6-92) agrees with experimental data [Z. Kemblowski and T. Kiljanski, Chem . Eng . J . (Lausanne), 9: 141–151 (1975)] for a < 11°. For newtonian liquids, Eq. (6-95) simplifies to   D2  3   32V2   1 ∆p = µ   1 −   D2   6 tan (α /2)   D1   

(6-93)

FLUID DYnAMICS For creeping flow through noncircular converging channels, the differential form of the Hagen-Poiseuille equation with equivalent diameter given by Eqs. (6-49) to (6-51) may be used, provided the convergence is gradual. Expansion and Exit Losses For ducts of any cross section, the frictional loss for a sudden enlargement (Fig. 6-13c) with turbulent flow is given by the Borda-Carnot equation: lv =

2 V12 − V22 V12  A =  1 − 1  2 2  A2 

(6-94)

where V1 = velocity in smaller duct V2 = velocity in larger duct A1 = cross-sectional area of smaller duct A2 = cross-sectional area of larger duct Equation (6-94) is valid for incompressible flow. For compressible flows, see R. P. Benedict et al. [ J . Eng . Power 98: 327–334 (1976)]. For an infinite expansion, A1/A2 = 0, Eq. (6-97) shows that the exit loss from a pipe is 1 velocity head. This exit loss is due to the dissipation of the discharged jet; there is no pressure drop at the exit. For creeping newtonian flow (Re < 1), the frictional loss due to a sudden enlargement should be obtained from the same equation for a sudden contraction, Eq. (6-91). Note, however, that D. V. Boger et al. [ J . Nonnewtonian Fluid Mech . 4: 239–248 (1978)] give an exit friction equivalent length of 0.12 diameter, increasing for power law fluids as the exponent decreases. For laminar flows at higher Reynolds numbers, the pressure drop is twice that given by Eq. (6-91). This results from the velocity profile factor α in the mechanical energy balance being 2.0 for the parabolic laminar velocity profile. If the transition from a small to a large duct of any cross-sectional shape is accomplished by a uniformly diverging duct (see Fig. 6-13d) with a straight axis, the total frictional pressure drop can be computed by integrating the differential form of Eq. (6-88), d l v /dx = 2 f V 2 /D over the length of the expansion, provided the total angle α between the diverging walls is less than 7°. For angles between 7° and 45°, the loss coefficient may be estimated as 2.6 sin (a/2) times the loss coefficient for a sudden expansion; see W. B. Hooper [Chem . Eng . Nov. 7, 1988]. A. H. Gibson [Hydraulics and Its Applications, 5th ed., Constable, London, 1952, p. 93] recommends multiplying the sudden enlargement loss by 0.13 for 5° < a < 7.5° and by 0.0110a1.22 for 7.5° < a < 35°. For angles greater than 35° to 45°, the losses are normally considered equal to those for a sudden expansion, although in some cases the losses may be greater. Expanding flow through standard pipe reducers should be treated as sudden expansions. Trumpet-shaped enlargements for turbulent flow designed for constant decrease in velocity head per unit length were found by A. H. Gibson [Hydraulics and Its Applications, 5th ed., Constable, London, 1952, p. 95] to give 20 to 60 percent less frictional loss than straight taper pipes of the same length. When viscoelastic liquids are extruded through a die at a low Reynolds number, the extrudate may expand to a diameter several times greater than the die diameter, whereas for a newtonian fluid the diameter expands only 10 percent. This phenomenon, called die swell, is most pronounced with short dies [W. W. Graessley et al., Trans . Soc . Rheol . 14: 519–544 (1970)]. For velocity distribution measurements near the die exit, see D. D. Goulden and W. C. MacSporran [ J . Nonnewtonian Fluid Mech . 1: 183–198 (1976)] and B. A. Whipple and C. T. Hill [AIChE J . 24: 664–671 (1978)]. At high flow rates, the extrudate becomes distorted, suffering melt fracture, a phenomenon reviewed by M. M. Denn [Ann . Review Fluid Mech . 22: 13–34 (1990)]. A. V. Ramamurthy [ J . Rheol . 30: 337–357 (1986)] found a dependence of apparent stick-slip behavior in melt fracture to be dependent on the material of construction of the die. Fittings and Valves For turbulent flow, the frictional loss for fittings and valves can be expressed by the equivalent length or velocity head methods. As fitting size is varied, K values are relatively more constant than Le/D values, but since fittings generally do not achieve geometric similarity between sizes, K values tend to decrease with increasing fitting size. Table 6-5 gives K values for many types of fittings and valves. Manufacturers of valves, especially control valves, express valve capacity in terms of a flow coefficient Cυ, which gives the flow rate through the valve in gallons per minute of water at 60°F under a pressure drop of 1 lbf/in2. It is related to K by Cv =

C1 d 2 K

(6-95)

where C1 is a dimensional constant equal to 29.9 and d is the diameter of the valve connections in inches.

6-17

TABLE 6-5 Additional Frictional Loss for Turbulent Flow Through Fittings and Valvesa Type of fitting or valve

Additional friction loss, equivalent no. of velocity heads, K

45° ell, standardb,c,d,e,f 45° ell, long radiusc 90° ell, standardb,c,e,f,g,h Long radiusb,c,d,e Square or miterh 180° bend, close returnb,c,e Tee, standard, along run, branch blanked off e Used as ell, entering rung,g,i Used as ell, entering branchc,g,i Branching flowi,j,k Couplingc,e Unione Gate valve,b,e,m open ¾ open ½ open ¾ open Diaphragm valve, open ¾ open ½ open ½ open Globe valvee,e,m Bevel seat, open ½ open Composition seat, open ½ open Plug disk, open ¾ open ½ open ¼ open Angle valve,b,e open Y or blowoff valve,b,m open Plug cock q = 5° q = 10° q = 20° q = 40° q = 60° Butterfly valve q = 5° q = 10° q = 20° q = 40° q = 60° Check valve,b,e,m swing Disk Ball Foot valvee Water meter,h disk Piston Rotary (star-shaped disk) Turbine wheel

0.35 0.2 0.75 0.45 1.3 1.5 0.4 1.0 1.0 1l 0.04 0.04 0.17 0.9 4.5 24.0 2.3 2.6 4.3 21.0 6.0 9.5 6.0 8.5 9.0 13.0 36.0 112.0 2.0 3.0 0.05 0.29 1.56 17.3 206.0 0.24 0.52 1.54 10.8 118.0 2.0 10.0 70.0 15.0 7.0 15.0 10.0 6.0

Lapple, Chem . Eng . 56(5): 96–104 (1949), general survey reference. “Flow of Fluids through Valves, Fittings, and Pipe,” Tech. Pap. 410, Crane Co., 1969. Freeman, Experiments upon the Flow of Water in Pipes and Pipe Fittings, American Society of Mechanical Engineers, New York, 1941. d Giesecke, J . Am . Soc . Heat . Vent . Eng . 32: 461 (1926). e Pipe Friction Manual, 3d ed., Hydraulic Institute, New York, 1961. f Ito, J . Basic Eng . 82: 131–143 (1960). g Giesecke and Badgett, Heat . Piping Air Cond . 4(6): 443–447 (1932). h Schoder and Dawson, Hydraulics, 2d ed., McGraw-Hill, New York, 1934, p. 213. i Hoopes, Isakoff, Clarke, and Drew, Chem . Eng . Prog . 44: 691–696 (1948). j Gilman, Heat . Piping Air Cond . 27(4): 141–147 (1955). k McNown, Proc . Am . Soc . Civ . Eng . 79, Separate 258, 1–22 (1953); discussion, ibid., 80, Separate 396, 19–45 (1954). For the effect of branch spacing on junction losses in dividing flow, see Hecker, Nystrom, and Qureshi, Proc . Am . Soc . Civ . Eng ., J . Hydraul . Div . 103(HY3): 265–279 (1977). l This is pressure drop (including friction loss) between run and branch, based on velocity in the mainstream before branching. Actual value depends on the flow split, ranging from 0.5 to 1.3 if mainstream enters run and from 0.7 to 1.5 if mainstream enters branch. m Lansford, Loss of Head in Flow of Fluids through Various Types of 1½-in . Valves, Univ. Eng. Exp. Sta. Bull. Ser. 340, 1943. a

b c

For laminar and turbulent flow, the “2K” method of W. B. Hooper [Chem . Eng. 88(17), 96–100 (August 1981)] yields approximate fitting losses accounting for Re and fitting size of K=

K1 1 + K ∞  1 +   d Re

(6-96)

6-18

FLUID AnD PARTICLE DYnAMICS

where d is the fitting size in inches and K1 and K∞ are shown in length and homogeneous equilibrium flow at 100. Methods to calculate losses in tee and wye junctions for dividing and combining flow are given by D. S. Miller [Internal Flow Systems, 2d ed., chap. 13, British Hydrodynamics Research Association, Cranfield, UK, 1990], including effects of Reynolds number, angle between legs, area ratio, and radius. Junctions with more than three legs are also discussed. The sources of data for the loss coefficient charts are F. W. Blaisdell and P. W. Manson [U .S . Dept . Agric . Res . Serv . Tech . Bull . 1283 (August 1963)] for combining flow and A. Gardel [Bull . Tech . Suisses Romande 85(9): 123–130 (1957); 85(10): 143–148 (1957)] together with additional unpublished data for dividing flow. D. S. Miller [Internal Flow Systems, 2d ed., chap. 13, British Hydrodynamics Research Association, Cranfield, UK, 1990] gives the most complete information on losses in bends and curved pipes . For turbulent flow in circular cross-section bends of constant area, as shown in Fig. 6-14a, a more accurate estimate of the loss coefficient K than that given in Tables 6-5 and 6-6 is K = K ∗ CRe Co Cf

K∗ ∗ K + 0.2(1 − C

Re, r / D = 1

0.0054  = 0.24 × 1.24 × 1.0 ×   0.0044  = 0.37 This value is close to the value from Table 6-6, and more accurate than the value in Table 6-5. The value fsmooth = 0.0044 is obtainable from Eq. (6-36) or Fig. 6-9. The total losses are then l v = (1.23 + 0.5 + 0.52 + 0.37)

Z= =

(6-100)

where Dc is the coil diameter. Equation (6-100) is valid for 10 < Dc/D < 250. The Dean number is defined as De =

Re ( Dc /D )1/2

(6-101)

TABLE 6-6 2‐K Method Friction Loss Parameters

f rough

(6-99)

f smooth

45°

liquid level in the vessel shown in Fig. 6-15 required to produce a discharge velocity of 2 m/s. The fluid is water at 20°C with r = 1000 kg/m3 and m = 0.001 Pa ⋅ s, and the butterfly valve is at q = 10°. The pipe is 2-in Schedule 40, with an inner diameter of 0.0525 m. The pipe roughness is 0.046 mm. Assuming the flow is turbulent and taking the velocity profile factor a = 1, the engineering Bernoulli equation, Eq. (6-19), written between surfaces 1 and 2, where the pressures are both atmospheric and the fluid velocities are zero and V = 2 m/s, respectively, and there is no shaft work, simplifies to

DV ρ 0.0525 × 2 × 1000 = = 1.05 × 10 5 0.001 µ

From Fig. 6-9 or Eq. (6-37), at ε/D = 0.046 × 10−3/0.0525 = 0.00088, the friction factor is about 0.0054. The straight pipe losses are then

0.20

500

0.15

Mitered

500 500

0.25 0.15

800 800 800

0.40 0.25 0.20

1000 800 800 800 800

1.15 0.35 0.30 0.27 0.25

Tees

1 weld 2 welds

Standard (R/D = 1) screwed Standard (R/D = 1) flanged or welded Long radius (R/D = 1.5) 1 weld 2 welds 3 welds 4 welds 5 welds

180°

Standard (R/D = 1), screwed Standard (R/D = 1) flanged or welded Long radius (R/D = 1.5)

1000 1000 1000

0.60 0.35 0.30

Used as elbows

Standard, screwed Long radius, screwed Standard, flanged or welded Stub‐in‐type branch

500 800 800 1000

0.70 0.40 0.80 1.00

Run through

Screwed Flanged or welded Stub‐in‐type branch

200 150 100

0.10 0.05 0.00

Full line size, b = 1.0 Reduced trim, b = 0.9 Reduced trim, b = 0.8

300 500 1000

0.10 0.15 0.25

Standard Angle or Y-type

1500 1000

4.00 2.00

1000

2.00

Full open Gate, ball, or plug valves* Globe

2

4 fL  V =   D  2

K∞

500

Mitered

V2 + lv 2

Contributing to lυ are losses for the entrance to the pipe, the three sections of straight pipe, the butterfly valve, and the 90° bend. Note that no exit loss is used because the discharged jet is outside the control volume. Instead, the V 2/2 term accounts for the kinetic energy of the discharging stream. The Reynolds number in the pipe is

K1

Standard (R/D = 1) screwed, flanged, or welded Long radius (R/D = 1.5)

Fitting or valve Elbows

90°

l v (sp)

3.62 × 2 2 = 0.74 m 2 × 9.807

 D Recrit = 2100  1 + 12  D  c 

Example 6-6 Losses with Fittings and Valves It is desired to calculate the

Re =

1 V2 V2 V2 + 2.62  = 3.62 g  2 2  2g

Curved Pipes and Coils For flow through curved pipe or coil, a secondary circulation perpendicular to the main flow called the Dean effect occurs. This increases the friction relative to straight pipe flow and stabilizes laminar flow, delaying the transition Reynolds number to about

where frough is the friction factor for a pipe of diameter D with the roughness of the bend, at the bend inlet Reynolds number. Similarly, fsmooth is the friction factor for smooth pipe. For Re > 106 and r/D ≥ 1, use the value of Cf for Re = 106.

gZ =

V2 V2 = 2.62 2 2

and the liquid level Z is

(6-98)

)

The correction Co (Fig. 6-14d) accounts for the extra losses due to developing flow in the outlet tangent of the pipe, of length Lo . The total loss for the bend plus outlet pipe includes the bend loss K plus the straight pipe frictional loss in the outlet pipe 4fLo/D . Note that Co = 1 for Lo/D greater than the termination of the curves on Fig. 6-14d, which indicate the distance at which fully developed flow in the outlet pipe is reached. Finally, the roughness correction is Cf =

K = K ∗ C ReCoC f

(6-97)

where K ∗, given in Fig. 6-14b, is the loss coefficient for a smooth-walled bend at a Reynolds number of 106. The Reynolds number correction factor CRe is given in Fig. 6-14c. For 0.7 < r/D < 1 or for K ∗ < 0.4, use the CRe value for r/D = 1. Otherwise, if r/D < 1, obtain CRe from C Re =

the table gives K = 0.75. The value calculated using Table 6-6 is 0.38. The method of Eq. (6-97), using Fig. 6-14, gives

Diaphragm Dam type 2

 4 × 0.0054 × (1 + 1 + 1)  V =   0.0525 2 2

= 1.23

V 2

The losses from Table 6-5 in terms of velocity heads K are K = 0.5 for the sudden contraction and K = 0.52 for the butterfly valve. For the 90° standard radius (r/D = 1),

Butterfly Check

Lift Swing Tilting disk

800

0.25

2000 1500 1000

10.0 1.50 0.50

*For use as rough guide only. Consult manufacturer’s data for greater accuracy. source: Adapted from Hooper, Chem . Eng . Aug 24, 1981, pp. 96–100.

FLUID DYNAMICS

(a)

6-19

(b)

(c)

(d)

FIG. 6-14 Loss coefficients for flow in bends and curved pipes: (a) flow geometry, (b) loss coefficient for a smooth-walled bend at Re = 106, (c) Re correction factor, (d ) outlet pipe correction factor. [From D. S. Miller, Internal Flow Systems, 2d ed., BHRA, Cranfield, U.K., 1990 .]

In laminar flow, the friction factor for curved pipe fc may be expressed in terms of the straight pipe friction factor f = 16/Re as [ J. Hart et al., Chem . Eng . Sci . 43: 775–783 (1988)]  De1.5  f c /f = 1 + 0.090   70 + De 

(6-102) fc =

V2 = 2 m/s 2

1

m

1 Z

90 horizontal bend 1m FIG. 6-15

Tank discharge example.

1m

For turbulent flow, equations by H. Ito [ J . Basic Eng . 81: 123 (1959)] and P. S. Srinivasan et al. [Chem . Eng . (London) no. 218, CE113–CE119 (May 1968)] may be used, with probable accuracy of ±15 percent. Their equations are similar to 0.079 0.0073 + Re0.25 ( Dc /D )

(6-103)

The pressure drop for flow in spirals is discussed by P. S. Srinivasan et al. [Chem . Eng . (London) no. 218, CE113–CE119 (May 1968)] and S. Ali and C. V. Seshadri [Ind . Eng . Chem . Process Des . Dev . 10: 328–332 (1971)]. For friction loss in laminar flow through semicircular ducts, see J. H. Masliyah and K. Nandakumar [AIChE J . 25: 478–487 (1979)]; for curved channels of square cross section, see K. C. Cheng et al. [ J . Fluids Eng . 98: 41–48 (1976)]. For nonnewtonian (power law) fluids in coiled tubes, R. A. Mashelkar and G. V. Devarajan [Trans . Inst . Chem . Eng . (London), 54: 108–114 (1976)] propose the correlation fc = (9.07 − 9.44n + 4.37n2)(D/Dc)0.5(De′ )−0.768 + 0.122n

(6-104)

6-20

FLUID AND PARTICLE DYNAMICS entrance effects [ J. F. Carley and W. C. Smith, Polym . Eng . Sci . 18: 408–415 (1978)]. For screen stacks, the losses of individual screens should be summed.

where De′ is a modified Dean number given by n

De′ =

D 1  6n + 2    Re MR Dc 8 n 

(6-105)

and ReMR is the Metzner-Reed Reynolds number, Eq. (6-64). This correlation was tested for the range De′ = 70 to 400, D/Dc = 0.01 to 0.135, and n = 0.35 to 1. See also D. R. Oliver and S. M. Asghar [Trans . Inst . Chem . Eng . (London), 53: 181–186 (1975)]. Screens The pressure drop for incompressible flow across a screen of fractional free area a may be computed from ∆p = K

ρV 2 2

(6-106)

where r = fluid density V = superficial velocity based on gross area of the screen K = velocity head loss 1  1 − α2  K =  2   2  C   α 

(6-107)

The discharge coefficient for the screen C with aperture Ds is given as a function of screen Reynolds number Re = Ds(V/a)r/m in Fig. 6-16 for plain square-mesh screens, a = 0.14 to 0.79. This curve fits most of the data within ±20 percent. In the laminar flow region, Re < 20, the discharge coefficient can be computed from C = 0.1 Re

(6-108)

Coefficients greater than 1.0 in Fig. 6-16 probably indicate partial pressure recovery downstream of the minimum aperture, due to rounding of the wires. P. Grootenhuis [Proc . Inst . Mech . Eng . (London), A168: 837–846 (1954)] presents data indicating that for a series of screens, the total pressure drop equals the number of screens times the pressure drop for one screen, and is not affected by the spacing between screens or their orientation with respect to one another, and presents a correlation for frictional losses across plain square-mesh screens and sintered gauzes. Armour and Cannon [AIChE J . 14: 415–420 (1968)] give a correlation based on a packed-bed model for plain, twill, and “dutch” weaves. For losses through monofilament fabrics see G. C. Pedersen [Filtr . Sep . 11: 586–589 (1975)]. For screens inclined at an angle q, use the normal velocity component V ′ V ′ = V cos q

(6-109)

[P. J. D. Carothers and W. D. Baines, J . Fluids Eng . 97: 116–117 (1975)] in place of V in Eq. (6-109). This applies for Re > 500, C = 1.26, a ≤ 0.97, and 0 < q < 45°, for square-mesh screens and diamond-mesh netting. Screens inclined at an angle to the flow direction also experience a tangential stress. For nonnewtonian fluids in creeping flow, frictional loss across a squarewoven or full-twill-woven screen can be estimated by considering the screen as a set of parallel tubes, each of diameter equal to the average minimum opening between adjacent wires, and length twice the diameter, without

FIG. 6-16

JET BEHAVIOR A free jet, upon leaving an outlet, will entrain the surrounding fluid, expand, and decelerate. Total momentum is conserved as jet momentum is transferred to the entrained fluid. For practical purposes, a jet is considered free when its cross-sectional area is less than one-fifth of the total crosssectional flow area of the region through which the jet is flowing [H. G. Elrod, Heat . Piping Air Cond . 26(3): 149–155 (1954)], and the surrounding fluid is the same as the jet fluid. A turbulent jet in this discussion is considered to be a free jet issuing with Re > 2000. Additional discussion on the relation between Reynolds number and turbulence in jets is given by H. G. Elrod [Heat . Piping Air Cond . 26(3): 149–155 (1954)]. G. N. Abramowitsch [The Theory of Turbulent Jets, MIT Press, Cambridge, Mass., 1963] and N. Rajaratnam [Turbulent Jets, Elsevier, Amsterdam, 1976] provide thorough discourses on turbulent jets. H. J. Hussein et al. [ J . Fluid Mech . 258: 31–75 (1994)] give extensive velocity data for a free jet, discussion of free jet experimentation, and comparison of data with momentum conservation equations. A turbulent-free jet is normally considered to consist of four flow regions [G. L. Tuve, Heat . Piping Air Cond . 25(1): 181–191 (1953); J. T. Davies, Turbulence Phenomena, Academic, New York, 1972, p. 93], as shown in Fig. 6-17: 1. Region of flow establishment, which is a short region of length about 6.4 nozzle diameters. The fluid in the conical core of the same length has a velocity about the same as the initial discharge velocity. The termination of this potential core occurs when the growing mixing (boundary) layer between the jet and the surroundings reaches the centerline of the jet. 2. A transition region that extends to about 8 nozzle diameters. 3. Region of established flow, which is the principal region of the jet. In this region, the velocity profile transverse to the jet is self-preserving when normalized by the decaying centerline velocity. 4. A terminal region where the residual centerline velocity reduces rapidly within a short distance. For air jets, the residual velocity will reduce to less than 0.3 m/s (1 ft/s), usually considered still air. Several references quote 100 nozzle diameters for the length of the established flow region. However, this length is dependent on the initial velocity and Reynolds number. Table 6-7 gives characteristics of rounded-inlet circular jets and roundedinlet infinitely wide slot jets (aspect ratio > 15). The information in the table is for a homogeneous, incompressible air system under isothermal conditions. The table uses the following nomenclature: B0 = slot height D0 = circular nozzle opening q = total jet flow at distance x q0 = initial jet flow rate r = radius from circular jet centerline y = transverse distance from slot jet centerline Vc = centerline velocity Vr = circular jet velocity at r Vy = velocity at y

Screen discharge coefficients, plain square-mesh screens. [Courtesy of E . I . du Pont de Nemours & Co .]

FLUID DYNAMICS

FIG. 6-17

Configuration of a turbulent free jet.

P. O. Witze [Am . Inst . Aeronaut . Astronaut . J . 12: 417–418 (1974)] gives equations for the centerline velocity decay of different types of subsonic and supersonic circular free jets. Entrainment of surrounding fluid in the region of flow establishment is lower than in the region of established flow [see B. J. Hill, J . Fluid Mech . 51: 773–779 (1972)]. Data of M. B. Donald and H. Singer [Trans . Inst . Chem . Eng . (London), 37: 255–267 (1959)] indicate that jet angle and the coefficients given in Table 6-5 depend upon the fluids; for a water system, the jet angle for a circular jet is 14° and the entrainment ratio is about 70 percent of that for an air system. Most likely these variations are due to Reynolds number effects which are not taken into account in Table 6-7. J. H. Rushton [AIChE J . 26: 1038–1041 (1980)] examined available published results for circular jets and found that the centerline velocity decay is given by Vc D = 1.41Re0.135  0   x  V0

(6-110)

TABLE 6-7 Turbulent Free-Jet Characteristics Where both jet fluid and entrained fluid are air Rounded-inlet circular jet Longitudinal distribution of velocity along jet centerline∗† Vc D =K 0 V0 x

for 7
1000

600

‡

M

0.5% R

10:1

L, G, SL

1 to 60

Piping limits

To 600

Long

L

0.2 to 2% R

10:1

L

0.15 to 60

5000

-40 to 350

Short

L

Propeller

2% R

15:1

L

2 to 12

230

0 to 300

Turbine

0.15 to 1% R

10:1

L, G

0.5 to 30

6000

-450 to 600

Short

M

Ultrasonic Doppler

1 to 30% R

50:1

L, G, SL

0.5 to 200

6000

-40 to 250

Long

L

Ultrasonic transit time

0.5 to 5% R

Down to zero flow

L, G

1 to 540

6000

-40 to 650

Long

L

Vortex

0.5 to 2% R

20:1

L, G, S

0.5 to 16

1500

-330 to 800

Short

M

Orifice and multivariable flow transmitter Venturi Flow nozzle

L, G, S

Velocity Meters Correlation Electromagnetic

M

Mass Meters Coriolis

0.1 to 0.3% R

10:1 to 80:1

L, G

0.06 to 12

5700

-400 to 800

None

L, M

Thermal ( for gases)

1% F

50:1

G

0.125 to 8

4500

32 to 572

Short

L

Thermal ( for liquids)

0.5% F

50:1

L

0.06 to 0.25

4500

40 to 165

Short

L

0.15 to 2% R

10:1

L

0.25 to 16

2000

-40 to 600

None

M to H

1 to 5% F

10:1

L, G

0.125 to 6

6000

30,000 with the upstream tap located between 1 and 2 pipe diameters from the orifice plate. [Spitzglass, Trans. Am. Soc. Mech. Eng. 44: 919 (1922).]

FIG. 10-12

MEASUREMENT OF FLOW For a centered circular orifice in a pipe, the pressure differential is customarily measured between one of the following pressure-tap pairs. Except in the case of flange taps, all measurements of distance from the orifice are made from the upstream face of the plate. 1. Corner taps. Static holes are drilled, one in the upstream and one in the downstream flange, with the openings as close as possible to the orifice plate. 2. Radius taps. Static holes are located 1 pipe diameter upstream and 0.5 pipe diameter downstream from the plate. 3. Pipe taps. Static holes are located 2½ pipe diameters upstream and 8 pipe diameters downstream from the plate. 4. Flange taps. Static holes are located 25.4 mm (1 in) upstream and 25.4 mm (1 in) downstream from the plate. 5. Vena contracta taps. The upstream static hole is 0.5 to 2 pipe diameters from the plate. The downstream tap is located at the position of minimum pressure (see Fig. 10-12). Radius taps are best from a practical standpoint; the downstream pressure tap is located at about the mean position of the vena contracta, and the upstream tap is sufficiently far upstream to be unaffected by distortion of the flow in the immediate vicinity of the orifice (in practice, the upstream tap can be as much as 2 pipe diameters from the plate without affecting the results). Vena contracta taps give the largest differential head for a given rate of flow but are inconvenient if the orifice size is changed from time to time. Corner taps offer the sometimes great advantage that the pressure taps can be built into the plate carrying the orifice. Thus the entire apparatus can be quickly inserted in a pipeline at any convenient flanged joint without having to drill holes in the pipe. Flange taps are similarly convenient since by merely replacing standard flanges with special orifice flanges, suitable pressure taps are made available. Pipe taps give the lowest differential pressure, the value obtained being close to the permanent pressure loss.  of discharge, adopted The practical working equation for flow rate (m) by the ASME Research Committee on Fluid Meters for use with either gases or liquids, is m = q1ρ1 = CYA2

2 g c ( p1 − p2 ) ρ1 1 − β4

= KYA2 2 g c ( p1 − p2 ) ρ1

(10-20)

10-15

where A2 = cross-sectional area of throat; C = coefficient of discharge, dimensionless; gc = dimensional constant; K = C/ 1 − β 4 , dimensionless; p1, p2 = pressure at upstream and downstream static pressure taps, respectively; q1 = volumetric rate of discharge measured at upstream pressure and temperature; m = weight rate of discharge; Y = expansion factor, dimensionless; β = ratio of throat diameter to pipe diameter, dimensionless; and ρ1 = density at upstream pressure and temperature. For the case of subsonic flow of a gas (rc < r < 1.0), the expansion factor Y for orifices is approximated by Y = 1 − [(1 − r)/k] (0.41 + 0.35β4)

(10-21)

where r = ratio of downstream to upstream static pressure ( p2/p1), k = ratio of specific heats (cp/cv), and β = diameter ratio. (See also Fig. 10-15.) Values of Y for supercritical flow of a gas (r < rc) through orifices are given by Benedict [ J. Basic Eng. 93: 121–137 (1971)]. For the case of liquids, expansion factor Y is unity, and Eq. (10-25) should be used, since it allows for any difference in elevation between the upstream and downstream taps. Coefficient of discharge C for a given orifice type is a function of the Reynolds number NRe (based on orifice diameter and velocity) and diameter ratio β. At Reynolds numbers greater than about 30,000, the coefficients are substantially constant. For square-edged or sharp-edged concentric circular orifices, the value will fall between 0.595 and 0.620 for vena contracta or radius taps for β up to 0.8 and for flange taps for β up to 0.5. Figure 10-12 gives the coefficient of discharge K, including the velocity-of-approach factor 1/ 1 − β 4 , as a function of β and the location of the downstream tap. Precise values of K are given in ASME, PTC, 1997, pp. 20–39, for flange taps, radius taps, vena contracta taps, and corner taps. Precise values of C are given in ASME, Report of the Research Committee on Fluid Meters, 1971, pp. 202–207, for the first three types of taps. The discharge coefficient of sharp-edged orifices was shown by Benedict, Wyler, and Brandt [ J. Eng. Power 97: 576–582 (1975)] to increase with edge roundness. Typical as-purchased orifice plates may exhibit deviations on the order of 1 to 2 percent from ASME values of the discharge coefficient. In the transition region (NRe between 50 and 30,000), the coefficients are generally higher than the above values. Although calibration is generally advisable in this region, the curves given in Fig. 10-13 for corner and vena

FIG. 10-13 Coefficient of discharge for square-edged circular orifices with corner taps. [Tuve and Sprenkle, Instruments 6: 201 (1933).]

10-16

TRANSPORT AND STORAGE OF FLUIDS

contracta taps can be used as a guide. In the laminar-flow region (NRe < 50), the coefficient C is proportional to N Re . For 1 < NRe < 100, Johansen [Proc. R. Soc. (London), A121: 231–245 (1930)] presents discharge coefficient data for sharp-edged orifices with corner taps. For NRe < 1, Miller and Nemecek [ASME Paper 58-A-106 (1958)] present correlations giving coefficients for sharp-edged orifices and short-pipe orifices (L/D from 2 to 10). For shortpipe orifices (L/D from 1 to 4), Dickerson and Rice [ J. Basic Eng. 91: 546–548 (1969)] give coefficients for the intermediate range (27 < NRe < 7000). See also the subsection Contraction and Entrance Losses. Permanent pressure loss across a concentric circular orifice with radius or vena contracta taps can be approximated for turbulent flow by ( p1 - p4)/( p1 - p2) = 1 - β2

(10-22)

where p1, p2 = upstream and downstream pressure-tap readings, respectively, p4 = fully recovered pressure (4 to 8 pipe diameters downstream of the orifice), and β = diameter ratio. See ASME, PTC, 1997, fig. 5. See Benedict, J. Fluids Eng. 99: 245–248 (1977), for a general equation for pressure loss for orifices installed in pipes or with plenum inlets. Orifices show higher loss than nozzles or ventura’s. Permanent pressure loss for laminar flow depends on the Reynolds number in addition to β. See Alvi, Sridharan, and Rao, J. Fluids Eng. 100(3): 99–307 (1978). For the case of critical flow through a square- or sharp-edged concentric circular orifice (where r ≤ rc, as discussed earlier in this subsection), use Eqs. (10-29), (10-30), and (10-31) as given for critical-flow nozzles. However, unlike with nozzles, the flow through a sharp-edged orifice continues to increase as the downstream pressure drops below that corresponding to the critical pressure ratio rc . This is due to an increase in the cross section of the vena contracta as the downstream pressure is reduced, giving a corresponding increase in the coefficient of discharge. At r = rc , C is about 0.75, while at r = 0, C has increased to about 0.84. See Benedict, J. Basic Eng. 93: 99–120 (1971). Measurements by Harris and Magnall [Trans. Inst. Chem. Eng. (London), 50: 61–68 (1972)] with a venturi (β = 0.62) and orifices with radius taps (β = 0.60 to 0.75) indicate that the discharge coefficient for nonnewtonian fluids, in the range of NRe (generalized Reynolds number) from 3500 to 100,000, is approximately the same as for newtonian fluids at the same Reynolds number. Quadrant-edge orifices have holes with rounded edges on the upstream side of the plate. The quadrant-edge radius is equal to the thickness of the plate at the orifice location. The advantages claimed for this type versus the square- or sharp-edged orifice are constant-discharge coefficients extending to lower Reynolds numbers and less possibility of significant changes in coefficient because of erosion or other damage to the inlet shape. Values of discharge coefficient C and Reynolds number limits for constant C are presented in Table 10-6, based on Ramamoorthy and Seetharamiah [ J. Basic Eng. 88: 9–13 (1966)] and Bogema and Monkmeyer ( J. Basic Eng. 82: 729–734 (1960)]. At Reynolds numbers above those listed for the upper limits, the coefficients rise abruptly. As Reynolds numbers decrease below those listed for the lower limits, the coefficients pass through a hump and then drop off. According to Bogema, Spring, and Ramamoorthy [ J. Basic Eng. 84: 415–418 (1962)], the hump can be eliminated by placing a fine-mesh screen about 3 pipe diameters upstream of the orifice. This reduces the lower NRe limit to about 500. Permanent pressure loss across quadrant-edge orifices for turbulent flow is somewhat lower than that given by Eq. (10-22). See Alvi, Sridharan, and Rao, loc. cit., for values of the discharge coefficient and permanent pressure loss in laminar flow. Slotted orifices offer significant advantages over a standard square-edged orifice with an identical open area for homogeneous gases or liquids [Morrison and Hall, Hydrocarbon Processing 79: 12, 65–72 (2000)]. The slotted orifice flowmeter only requires compact header configurations with very short upstream

pipe lengths and maintains accuracy in the range of 0.25 percent with no flow conditioner. Permanent head loss is less than or equal to that of a standard orifice that has the same β ratio. Discharge coefficients for the slotted orifice are much less sensitive to swirl or to axial velocity profiles. A slotted orifice plate can be a “drop-in” replacement for a standard orifice plate. Segmental and eccentric orifices are frequently used for gas metering when there is a possibility that entrained liquids or solids would otherwise accumulate in front of a concentric circular orifice. This can be avoided if the opening is placed on the lower side of the pipe. For liquid flow with entrained gas, the opening is placed on the upper side. The pressure taps should be located on the opposite side of the pipe from the opening. Coefficient C for a square-edged eccentric circular orifice (with opening tangent to pipe wall) varies from about 0.61 to 0.63 for β values from 0.3 to 0.5, respectively, and pipe Reynolds numbers > 10,000 for either vena contracta or flange taps (where β = diameter ratio). For square-edged segmental orifices, coefficient C falls generally between 0.63 and 0.64 for 0.3 ≤ β ≤ 0.5 and pipe Reynolds numbers > 10,000, for vena contracta or flange taps, where β = diameter ratio for an equivalent circular orifice = α (α = ratio of orifice to pipe cross-sectional areas). Values of expansion factor Y are slightly higher than for concentric circular orifices, and the location of the vena contracta is moved farther downstream as compared with concentric circular orifices. For further details, see ASME, Report of the Research Committee on Fluid Meters, 1971, pp. 210–213. For permanent pressure loss with segmental and eccentric orifices with laminar pipe flow see Lakshmana Rao and Sridharan, Proc. Am. Soc. Civ. Eng., J. Hydraul. Div. 98(HY 11): 2015–2034 (1972). Annular orifices can also be used to advantage for gas metering when there is a possibility of entrained liquids or solids and for liquid metering with entrained gas present in small concentrations. Coefficient K was found by Bell and Bergelin [Trans. Am. Soc. Mech. Eng. 79: 593–601 (1957)] to range from about 0.63 to 0.67 for annulus Reynolds numbers in the range of 100 to 20,000, respectively, for values of 2L/(D - d) less than 1 where L = thickness of orifice at outer edge, D = inside pipe diameter, and d = diameter of orifice disk. The annulus Reynolds number is defined as NRe = (D - d ) (G/µ)

where G = mass velocity ρV through orifice opening and µ = fluid viscosity. The above coefficients were determined for β values (= d/D) in the range of 0.95 to 0.996 and with pressure taps located 19 mm (¾ in) upstream of the disk and 230 mm (9 in) downstream in a 5.25-in-diameter pipe. Venturi Meters The standard Herschel-type venturi meter consists of a short length of straight tubing connected at either end to the pipeline by conical sections (see Fig. 10-14). Recommended proportions (ASME, PTC, 1997, p. 17) are entrance cone angle α1 = 21 ± 2°, exit cone angle α2 = 5 to 15°, throat length = 1 throat diameter, and upstream tap located 0.25 to 0.5 pipe diameter upstream of the entrance cone. The straight and conical sections should be joined by smooth curved surfaces for best results. Rate of discharge of either gases or liquids through a venturi meter is given by Eq. (10-20). For the flow of gases, expansion factor Y, which allows for the change in gas density as it expands adiabatically from p1 to p2, is given by k   1 − r ( k −1)/k   1 − β 4  Y = r 2/k   k − 1   1 − r   1 − β 4 r 2/k 

∗ for constant Limiting NRe coefficient† β

C‡

K‡

Lower

Upper

0.770 0.780 0.824 0.856 0.885

0.771 0.790 0.851 0.918 0.964

5000 5000 4000 3000 3000

60,000 150,000 200,000 120,000 105,000

∗Based on pipe diameter and velocity. † For a precision of about ±0.5 percent. ‡ Can be used with corner taps, flange taps, or radius taps .

(10-24)

for venturi meters and flow nozzles, where r = p2/p1 and k = specific heat ratio cp/cv . Values of Y computed from Eq. (10-24) are given in Fig. 10-15 as a function of r, k, and β.

TABLE 10-6 Discharge Coefficients for Quadrant-Edge Orifices

0.225 0.400 0.500 0.600 0.630

(10-23)

FIG. 10-14

Herschel-type venturi tube .

MEASUREMENT OF FLOW

FIG. 10-15

Values of expansion factor Y for orifices, nozzles, and venturis.

For the flow of liquids, expansion factor Y is unity. The change in potential energy in the case of an inclined or vertical venturi meter must be allowed for. Equation (10-20) is accordingly modified to give m = q1ρ = CA2

[2 g c ( p1 − p2 ) + 2 g ρ(Z1 − Z2 )]ρ 1 − β4

(10-25)

where g = local acceleration due to gravity and Z1, Z2 = vertical heights above an arbitrary datum plane corresponding to the centerline pressure-reading locations for p1 and p2, respectively. The value of the discharge coefficient C for a Herschel-type venturi meter depends on the Reynolds number and to a minor extent on the size of the venturi, increasing with diameter. A plot of C versus pipe Reynolds number is given in ASME, PTC, 1997, p. 19. A value of 0.984 can be used for pipe Reynolds numbers larger than 200,000. Permanent pressure loss for a Herschel-type venturi tube depends on the diameter ratio β and discharge cone angle α2. It ranges from 10 to 15 percent of the pressure differential p1 − p2 for small angles (5° to 7°) and from 10 to 30 percent for large angles (15°), with the larger losses occurring at low values of β (see ASME, PTC, 1997, p. 12). See Benedict, J. Fluids Eng. 99: 245–248 (1977), for a general equation for pressure loss for venturis installed in pipes or with plenum inlets. For flow measurement of steam and water mixtures with a Herschel-type venturi in 2½-in- and 3-in-diameter pipes, see Collins and Gacesa, J. Basic Eng. 93: 11–21 (1971). A variety of short-tube venturi meters are available commercially. They require less space for installation and are generally (although not always) characterized by a greater pressure loss than the corresponding Herschel-type venturi meter. Discharge coefficients vary widely for different types, and individual calibration is recommended if the manufacturer’s calibration is not available. Results of tests on the Dall flow tube are given by Miner [Trans. Am. Soc. Mech. Eng. 78: 475–479 (1956)] and Dowdell [Instrum. Control Syst. 33: 1006–1009 (1960)]; and on the Gentile flow tube (also called the Beth flow tube or Foster flow tube) by Hooper [Trans. Am. Soc. Mech. Eng. 72: 1099–1110 (1950)]. The use of a multiventuri system (in which an inner venturi discharges into the throat of an outer venturi) to increase both the differential pressure for a given flow rate and the signal-to-loss ratio is described by Klomp and Sovran [ J. Basic Eng. 94: 39–45 (1972)]. Flow Nozzles A simple form of flow nozzle is shown in Fig. 10-16. It consists essentially of a short cylinder with a flared approach section.

10-17

The approach cross section is preferably elliptical but may be conical. Recommended contours for long-radius flow nozzles are given in ASME, PTC, 1997, p. 13. In general, the length of the straight portion of the throat is about one-half the throat diameter, the upstream pressure tap is located about 1 pipe diameter from the nozzle inlet face, and the downstream pressure tap is about ½ pipe diameter from the inlet face. For subsonic flow, the pressures at points 2 and 3 will be practically identical. If a conical inlet is preferred, the inlet and throat geometry specified for a Herschel-type venturi meter can be used, omitting the expansion section. The rate of discharge through a flow nozzle for subcritical flow can be determined by the equations given for venturi meters, Eq. (10-20) for gases and Eq. (10-25) for liquids. The expansion factor Y for nozzles is the same as that for venturi meters [Eq. (10-24), Fig. 10-15]. The value of the discharge coefficient C depends primarily on the pipe Reynolds number and to a lesser extent on the diameter ratio β. Curves of recommended coefficients for long-radius flow nozzles with pressure taps located 1 pipe diameter upstream and ½ pipe diameter downstream of the inlet face of the nozzle are given in ASME, PTC, 1997, p. 15. In general, coefficients range from 0.95 at a pipe Reynolds number of 10,000 to 0.99 at 1,000,000. The performance characteristics of pipe wall-tap nozzles (Fig. 10-16) and throat-tap nozzles are reviewed by Wyler and Benedict [ J. Eng. Power 97: 569–575 (1975)]. Permanent pressure loss across a subsonic flow nozzle is approximated by p1 − p4 =

1 − β2 ( p1 − p2 ) 1 + β2

(10-26)

where p1, p2, p4 = static pressures measured at the locations shown in Fig. 10-16 and β = ratio of nozzle throat diameter to pipe diameter, dimensionless. Equation (10-26) is based on a momentum balance assuming constant fluid density (see Lapple et al., Fluid and Particle Mechanics, University of Delaware, Newark, 1951, p. 13). See Benedict, R. P., “On the Determination and Combination of Loss. Coefficients for Compressible Fluid Flows,” J. Eng. Power, ASME Trans., vol. 88, for a general equation for pressure loss for nozzles installed in pipes or with plenum inlets. Nozzles show higher loss than venturis. Permanent pressure loss for laminar flow depends on the Reynolds number in addition to β. For details, see Alvi, Sridharan, and Lakshamana Rao, J. Fluids Eng. 100: 299–307 (1978). Critical Flow Nozzle For a given set of upstream conditions, the rate of discharge of a gas from a nozzle will increase for a decrease in the absolute pressure ratio p2/p1 until the linear velocity in the throat reaches that of sound in the gas at that location. The value of p2/p1 for which the acoustic velocity is just attained is called the critical pressure ratio rc. The actual pressure in the throat will not fall below p1rc even if a much lower pressure exists downstream. The critical pressure ratio rc can be obtained from the following theoretical equation, which assumes a perfect gas and a frictionless nozzle: k − 1  4 2/k k + 1 βr = rc(1− k )/k +   2  c 2

(10-27)

This reduces, for β ≤ 0.2, to 2  rc =   k + 1 

k /(k −1)

(10-28)

where k = ratio of specific heats cp/cv and β = diameter ratio. A table of values of rc as a function of k and β is given in ASME, Report of the Research Committee on Fluid Meters, New York, 1971, p. 68. For small values of β, rc = 0.487 for k = 1.667, rc = 0.528 for k = 1.40, rc = 0.546 for k = 1.30, and rc = 0.574 for k = 1.15. Under critical flow conditions, only the upstream conditions p1, υ1, and T1 need be known to determine the flow rate, which, for β ≤ 0.2, is given p  2  m max = CA2 g c k  1     υ1   k + 1 

(k +1)/(k −1)

(10-29)

For a perfect gas, this corresponds to  M   2  (k+1)/(k−1) m max = CA2 p1 g c k     RT1   k + 1 

(10-30)

For air, Eq. (10-30) reduces to m max = C1CA2 p1 / T1

FIG. 10-16

Flow nozzle assembly.

(10-31)

where A2 = cross-sectional area of throat; C = coefficient of discharge, dimensionless; gc = dimensional constant; k = ratio of specific heats cp/cv; M = molecular weight; p1 = pressure on upstream side of nozzle; R = gas constant;

10-18

TRANSPORT AND STORAGE OF FLUIDS

T1 = absolute temperature on upstream side of nozzle; v1 = specific volume on upstream side of nozzle; C1 = dimensional constant, 0.0405 SI unit (0.533 U.S. Customary System unit); and m max = maximum-weight flow rate. Discharge coefficients for critical flow nozzles are, in general, the same as those for subsonic nozzles. See Grace and Lapple, Trans. Am. Soc. Mech. Eng. 73: 639–647 (1951); and Szaniszlo, J. Eng. Power 97: 521–526 (1975). Arnberg, Britton, and Seidl [ J. Fluids Eng. 96: 111–123 (1974)] present discharge coefficient correlations for circular-arc venturi meters at critical flow. For the calculation of the flow of natural gas through nozzles under critical-flow conditions, see Johnson, J. Basic Eng. 92: 580–589 (1970). Elbow Meters A pipe elbow can be used as a flowmeter for liquids if the differential centrifugal head generated between the inner and outer radii of the bend is measured by means of pressure taps located midway around the bend. Equation (10-25) can be used, except that the pressure difference term p1 - p2 is now taken to be the differential centrifugal pressure and β is taken as zero, if one assumes no change in cross section between the pipe and the bend. The discharge coefficient should preferably be determined by calibration, but as a guide it can be estimated within ±6 percent for circular pipe for Reynolds numbers greater than 105 from C = 0.98 Rc /2 D , where Rc = radius of curvature of the centerline and D = inside pipe diameter in consistent units. See Murdock, Foltz, and Gregory, J. Basic Eng. 86: 498–506 (1964); or ASME, Report of the Research Committee on Fluid Meters, 1971, pp. 75–77. Accuracy Square-edged orifices and venturi tubes have been so extensively studied and standardized that reproducibility within 1 to 2 percent can be expected between standard meters when new and clean. This is therefore the order of reliability to be had, if one assumes (1) accurate measurement of meter differential, (2) selection of the coefficient of discharge from recommended published literature, (3) accurate knowledge of fluid density, (4) accurate measurement of critical meter dimensions, (5) smooth upstream face of orifice, and (6) proper location of the meter with respect to other flow-disturbing elements in the system. Care must also be taken to avoid even slight corrosion or fouling during use. Presence of swirling flow or an abnormal velocity distribution upstream of the metering element can cause serious metering error unless calibration in place is employed or sufficient straight pipe is inserted between the meter and the source of disturbance. Table 10-7 gives the minimum lengths of straight pipe required to avoid appreciable error due to the presence of certain fittings and valves either upstream or downstream of an orifice or nozzle. These values were extracted from plots presented by Sprenkle [Trans. Am. Soc. Mech. Eng. 67: 345–360 (1945)]. Table 10-7 also shows the reduction

TABLE 10-7 Locations of Orifices and Nozzles Relative to Pipe Fittings Distances in pipe diameters D1 Distance, upstream fitting to orifice With straightening vanes

D2 D1

Without straightening vanes

Single 90° ell, tee, or cross used as ell

0.2 0.4 0.6 0.8

6 6 9 20

2 short-radius 90° ells in form of S

0.2 0.4 0.6 0.8

7 8 13 25

8 10 15

6 11

2 long- or shortradius 90° ells in perpendicular planes

0.2 0.4 0.6 0.8

15 18 25 40

9 10 11 13

5 6 7 9

Contraction or enlargement

0.2 0.4 0.6 0.8

8 9 10 15

Globe valve or stop check

0.2 0.4 0.6 0.8

9 10 13 21

0.2 0.4 0.6 0.8

6 6 8 14

Type of fitting upstream

Gate valve, wide open, or plug cocks

Distance, vanes to orifice

in spacing made possible by the use of straightening vanes between the fittings and the meter. Entirely adequate straightening vanes can be provided by fitting a bundle of thin-wall tubes within the pipe. The center-to-center distance between tubes should not exceed one-fourth of the pipe diameter, and the bundle length should be at least 8 times this distance. The distances specified in Table 10-7 will be conservative if applied to venturi meters. For specific information on requirements for venturi meters, see a discussion by Pardoe appended to Sprenkle [Trans. Am. Soc. Mech. Eng. 67: 345–360 (1945)]. Extensive data on the effect of installation on the coefficients of venturi meters are given elsewhere by Pardoe [Trans. Am. Soc. Mech. Eng. 65: 337–349 (1943)]. As a general rule, a concentric orifice plate is the most economical solution to flow measurement for most applications if the calculated permanent pressure loss is acceptable and the upstream and downstream piping configuration provides for a stabilized flow pattern. Unique designs such as the conditioning orifice plate offered by Emerson Rosemount Pak or a flow tube with an integral flow stabilization design such as the FlowPak flow tube assembly offered by Fluidic Techniques provide optional considerations for areas where straight lengths of upstream and downstream piping are problematic. 1. Conditioning orifice plate (see Fig. 10-17) This copyrighted design requires only 2 pipe diameters upstream and downstream from a flow disturbance and is suitable for most liquids, gases, and steam. Refer to the Emerson Rosemount web site for more details. 2. The high head recovery FlowPak (see Fig. 10-18) is a patented flow tube design with a uniquely designed flow-conditioning translineal flow plate which eliminates the requirement of straight pipe between the upstream disturbances while providing the known properties of the flow tube characteristics including constant discharge coefficient, low uncertainty, and low permanent pressure loss. Refer to the Fluidics Techniques web site for more details. In the presence of flow pulsations, the indications of head meters such as orifices, nozzles, and venturis will often be undependable for several reasons. First, the measured pressure differential will tend to be high, since the pressure differential is proportional to the square of the flow rate for a head meter, and the square root of the mean differential pressure is always greater than the mean of the square roots of the differential pressures. Second, there is a phase shift as the wave passes through the metering restriction, which can affect the differential. Third, pulsations can be set up in the manometer leads themselves. Frequency of the pulsation also plays a part. At low frequencies, the meter reading can generally faithfully follow the flow pulsations, but at high frequencies it cannot. This is due to inertia of the fluid in the manometer leads or of the manometric fluid, whereupon the meter would give a reading intermediate between the maximum and minimum flows but having no readily predictable relation to the mean flow. Pressure transducers with flush-mounted diaphragms can be used together

Distance, nearest downstream fitting from orifice

Rosemount 1595 conditioning orifice plate

2 9 12

8

4 2 4 2

Vanes have no advantage 9 10 10 13

4 2

4 5 6 6 9

Same as globe valve

2

Discharge coefficient uncertainty of ±0.5% Conditioning orifice plate is based on AGA, ASME, and ISO industry standards Can be installed between standard orifice flanges

4 2 4

FIG. 10-17

Rosemont 1595 Conditioning Orifice Plate. (Courtesy of Rosemont.)

MEASUREMENT OF FLOW TABLE 10-8a

10-19

Minimum Hodgson Numbers

Simplex double-acting compressor s

Flow

0.167 0.333 0.50

TABLE 10-8b

NH

s

NH

1.31 1.00 0.80

0.667 0.833 1.00

0.60 0.43 0.34

Minimum Hodgson Numbers

Duplex double-acting compressor

FIG. 10-18 High Head Recovery FloPak. (Courtesy of Fluidic Technology.)

with high-speed recording equipment to provide accurate records of the pressure profiles at the upstream and downstream pressure taps, which can then be analyzed and translated into a mean flow rate. The rather general practice of producing a steady differential reading by placing restrictions in the manometer leads can result in a reading which, under a fixed set of conditions, may be useful in control of an operation but which has no readily predictable relation to the actual average flow. If calibration is employed to compensate for the presence of pulsations, then complete reproduction of operating conditions, including source of pulsations and waveform, is necessary to ensure reasonable accuracy. According to Head [Trans. Am. Soc. Mech. Eng. 78: 1471–1479 (1956)], a pulsation intensity limit of G = 0.1 is recommended as a practical pulsation threshold below which the performance of all types of flowmeters will differ negligibly from steady-flow performance (an error of less than 1 percent in flow due to pulsation). The peak-to-trough flow variation G is expressed as a fraction of the average flow rate. According to the Report of the ASME Research Committee on Fluid Meters (pp. 34–35), the fractional metering error E for liquid flow through a head meter is given by (1 + E)2 = 1 + Γ 2/8

(10-32)

When the pulsation amplitude is such as to result in a greater-than-permissible metering error, consideration should be given to installation of a pulsation damper between the source of pulsations and the flowmeter. References to methods of pulsation damper design are given in the subsection Unsteady-State Behavior. Pulsations are most likely to be encountered in discharge lines from reciprocating pumps or compressors and in lines supplying steam to reciprocating machinery. For gas flow, a combination involving a surge chamber and a constriction in the line can be used to damp out the pulsations to an acceptable level. The surge chamber is generally located as close to the pulsation source as possible, with the constriction between the surge chamber and the metering element. This arrangement can be used for either a suction or a discharge line. For such an arrangement, the metering error has been found to be a function of the Hodgson number NH, which is defined as NH = Qn ∆ps/qps

(10-33)

where Q = volume of surge chamber and pipe between metering element and pulsation source; n = pulsation frequency; ∆ps = permanent pressure drop between metering element and surge chamber; q = average volume flow rate, based on gas density in the surge chamber; and ps = pressure in surge chamber.

Triplex double-acting compressor

s

NH

s

NH

0.167 0.333 0.50 0.667 0.833 1.00

1.00 0.70 0.30 0.10 0.05 0.00

0.167 0.333 0.50 0.667 0.833 1.00

0.85 0.30 0.15 0.06 0.00 0.00

Herning and Schmid [Z. Ver. Dtsch. Ing. 82: 1107–1114 (1938)] presented charts for a simplex double-acting compressor for the prediction of metering error as a function of the Hodgson number and s, the ratio of piston discharge time to total time per stroke. Table 10-8a gives the minimum Hodgson numbers required to reduce the metering error to 1 percent as given by the charts ( for specific heat ratios between 1.28 and 1.37). Schmid [Z. Ver. Dtsch. Ing. 84: 596–598 (1940)] presented similar charts for a duplex double-acting compressor and a triplex double-acting compressor for a specific heat ratio of 1.37. Table 10-8b gives the minimum Hodgson numbers corresponding to a 1 percent metering error for these cases. The value of Q ∆ps can be calculated from the appropriate Hodgson number, and appropriate values of Q and ∆ps selected so as to satisfy this minimum requirement. VELOCITY METERS Anemometers An anemometer may be any instrument for the measurement of gas velocity, e.g., a pitot tube, but usually the term refers to one of the following types. The vane anemometer is a delicate revolution counter with jeweled bearings, actuated by a small windmill, usually 75 to 100 mm (about 3 to 4 in) in diameter, constructed of flat or slightly curved radially disposed vanes. Gas velocity is determined by using a stopwatch to find the time interval required to pass a given number of meters ( feet) of gas as indicated by the counter. The velocity so obtained is inversely proportional to gas density. If the original calibration was carried out in a gas of density ρ0 and the density of the gas stream being metered is ρ1, the true gas velocity can be found as follows: From the calibration curve for the instrument, find Vt,0 corresponding to the quantity Vm ρ1 /ρ0 , where Vm = measured velocity. Then the actual velocity Vt,1 is equal to Vt , 0 ρ0 /ρ1 . In general, when working with air, the effects of atmospheric density changes can be neglected for all velocities above 1.5 m/s (about 5 ft/s). In all cases, care must be taken to hold the anemometer well away from one’s body or from any object not normally present in the stream. Vane anemometers can be used for gas velocity measurements in the range of 0.3 to 45 m/s (about 1 to 150 ft/s), although a given instrument generally has about a 20-fold velocity range. Bearing friction has to be minimized in instruments designed for accuracy at the low end of the range, while ample rotor and vane rigidity must be provided for measurements at the higher velocities. Vane anemometers are sensitive to shock and cannot be used in corrosive atmospheres. Therefore, accuracy is questionable unless a recent calibration has been done and the history of the instrument subsequent to calibration is known. For additional information, see Ower et al., chap. 8. Turbine Flowmeters They consist of a straight flow tube containing a turbine which is free to rotate on a shaft supported by one or more bearings and located on the centerline of the tube. Means are provided for magnetic detection of the rotational speed, which is proportional to the volumetric flow rate. Its use is generally restricted to clean, noncorrosive fluids. Additional information on construction, operation, range, and accuracy can be obtained from Baker, Flow Measurement Handbook, 2000, pp. 215–252; Miller, Flow Measurement Engineering Handbook, 1996; and Spitzer, 2005, pp. 303–317. The current meter is generally used for measuring velocities in open channels such as rivers and irrigation channels. There are two types, the cup meter and the propeller meter. The former is more widely used. It consists

10-20

TRANSPORT AND STORAGE OF FLUIDS

of six conical cups mounted on a vertical axis pivoted at the ends and free to rotate between the rigid arms of a U-shaped clevis to which a vaned tailpiece is attached. The wheel rotates because of the difference in drag for the two sides of the cup, and a signal proportional to the revolutions of the wheel is generated. The velocity is determined from the count over a period of time. The current meter is generally useful in the range of 0.15 to 4.5 m/s (about 0.5 to 15 ft/s) with an accuracy of ±2 percent. For additional information see Creager and Justin, Hydroelectric Handbook, 2d ed., Wiley, New York, 1950, pp. 42–46. Other important classes of velocity meters include electromagnetic flowmeters and ultrasonic flowmeters. Both are described in Sec. 8. MASS FLOWMETERS General Principles There are two main types of mass flowmeters: (1) the so-called true mass flowmeter, which responds directly to mass flow rate, and (2) the inferential mass flowmeter, which commonly measures volume flow rate and fluid density separately. A variety of types of true mass flowmeters have been developed, including the following: (a) the Magnuseffect mass flowmeter, (b) the axial-flow, transverse-momentum mass flowmeter, (c) the radial-flow, transverse-momentum mass flowmeter, (d ) the gyroscopic transverse-momentum mass flowmeter, and (e) the thermal mass flowmeter. Type b is the basis for several commercial mass flowmeters, one version of which is briefly described here. Axial-Flow Transverse-Momentum Mass Flowmeter This type is also referred to as an angular-momentum mass flowmeter. One embodiment of its principle involves the use of axial flow through a driven impeller and a turbine in series. The impeller imparts angular momentum to the fluid, which in turn causes a torque to be imparted to the turbine, which is restrained from rotating by a spring. The torque, which can be measured, is proportional to the rotational speed of the impeller and the mass flow rate. Inferential Mass Flowmeter There are several types in this category, including the following: 1. Head meters with density compensation. Head meters such as orifices, venturis, or nozzles can be used with one of a variety of densitometers [e.g., based on (a) buoyant force on a float, (b) hydraulic coupling, (c) voltage output from a piezoelectric crystal, or (d) radiation absorption]. The signal from the head meter, which is proportional to ρV2 (where ρ = fluid density and V = fluid velocity), is multiplied by ρ given by the densitometer. The square root of the product is proportional to the mass flow rate. 2. Head meters with velocity compensation.    The signal from the head meter, which is proportional to ρV2, is divided by the signal from a velocity meter to give a signal proportional to the mass flow rate. 3. Velocity meters with density compensation. The signal from the velocity meter (e.g., turbine meter, electromagnetic meter, or sonic velocity meter) is multiplied by the signal from a densitometer to give a signal proportional to the mass flow rate. Coriolis Mass Flowmeter This type, described in Sec. 8, offers simultaneous direct measurement of both mass flow rate and fluid density. The Coriolis flowmeter is insensitive to upstream and downstream flow disturbances, but its performance is adversely affected by the presence of even a few percent of a gas when measuring a liquid flow. VARIABLE-AREA METERS General Principles The underlying principle of an ideal area meter is the same as that of a head meter of the orifice type (see subsection Orifice Meters). The stream to be measured is throttled by a constriction, but instead of observing the variation with flow of the differential head across an orifice of fixed size, the constriction of an area meter is so arranged that its size is varied to accommodate the flow while the differential head is held constant. A simple example of an area meter is a gate valve of the rising-stem type provided with static-pressure taps before and after the gate and a means for measuring the stem position. In most common types of area meters, the variation of the opening is automatically brought about by the motion of a weighted piston or float supported by the fluid. Two different cylinderand piston-type area meters are described in the Report of ASME Research Committee on Fluid Meters, pp. 82–83. Rotameters The rotameter, an example of which is shown in Fig. 10-19, has become one of the most popular flowmeters in the chemical-process industries. It consists essentially of a plummet, or “float,” which is free to move up or down in a vertical, slightly tapered tube having its small end down. The fluid enters the lower end of the tube and causes the float to rise until the annular area between the float and the wall of the tube is such that the pressure drop across this constriction is just sufficient to support the float. Typically, the tapered tube is of glass and carries etched upon it a nearly linear scale on which the position of the float may be visually noted as an indication of the flow.

FIG. 10-19

Rotameter.

Interchangeable precision-bore glass tubes and metal metering tubes are available. Rotameters have proved satisfactory both for gases and for liquids at high and low pressures. A single instrument can readily cover a 10-fold range of flow, and by providing floats of different densities a 200-fold range is practicable. Rotameters are available with pneumatic, electric, and electronic transmitters for actuating remote recorders, integrators, and automatic flow controllers (see Considine, pp. 4-35 to 4-36, and Sec. 8 of this text). Rotameters require no straight runs of pipe before or after the point of installation. Pressure losses are substantially constant over the whole flow range. In experimental work, for greatest precision, a rotameter should be calibrated with the fluid to be metered. However, most modern rotameters are precision-made so that their performance closely corresponds to a master calibration plot for the type in question. Such a plot is supplied with the meter upon purchase. According to Head [Trans. Am. Soc. Mech. Eng. 76: 851–862 (1954)], the flow rate through a rotameter can be obtained from m = qρ = KD f

and

W f (ρ f − ρ) ρ ρf

D µ  K = φ  t , D f W f (ρ f − ρ) ρ    ρf  

(10-34)

(10-35)

where m = weight flow rate; q = volume flow rate; ρ = fluid density; K = flow parameter, m1/2/s ( ft1/2/s); Df = float diameter at constriction; Wf = float weight; ρf = float density; Dt = tube diameter at point of constriction; and µ = fluid viscosity. The appropriate value of K is obtained from a composite correlation of K versus the parameters shown in Eq. (10-35) corresponding to the float shape being used. The relation of Dt to the rotameter reading is also required for the tube taper and size being used. The ratio of flow rates for two different fluids A and B at the same rotameter reading is given by m A K A (ρ f − ρ A ) ρ A = m B K B (ρ f − ρ B ) ρ B

(10-36)

PUMPS AND COMPRESSORS A measure of self-compensation, with respect to weight rate of flow, for fluid density changes can be introduced through the use of a float with a density twice that of the fluid being metered, in which case an increase of 10 percent in ρ will produce a decrease of only 0.5 percent in w for the same reading. The extent of immunity to changes in fluid viscosity depends on the shape of the float. According to Baird and Cheema [Can. J. Chem. Eng. 47: 226–232 (1969)], the presence of square-wave pulsations can cause a rotameter to overread by as much as 100 percent. The higher the pulsation frequency, the less the float oscillation, although the error can still be appreciable even when the frequency is high enough that the float is virtually stationary. Use of a damping chamber between the pulsation source and the rotameter will reduce the error. Additional information on rotameter theory is presented by Fischer [Chem. Eng. 59(6): 180–184 (1952)], Coleman [Trans. Inst. Chem. Eng. 34: 339–350 (1956)], and McCabe, Smith, and Harriott (Unit Operations of Chemical Engineering, 4th ed., McGraw-Hill, New York, 1985, pp. 202–205).

10-21

TABLE 10-9 Flowmeter Classes Class I: Flowmeters with wetted moving parts Positive displacement Turbine Variable-area

Class III: Obstructionless flowmeters Coriolis mass Electromagnetic Ultrasonic

Class II: Flowmeters with no wetted moving parts Differential pressure Vortex Target Thermal Class IV: Flowmeters with sensors mounted external to the pipe Clamp-on ultrasonic Correlation

Adapted from Spitzer, op. cit., 2005.

TWO-PHASE SYSTEMS It is generally preferable to meter each of the individual components of a two-phase mixture separately prior to mixing, since it is difficult to meter such mixtures accurately. Problems arise because of fluctuations in composition with time and variations in composition over the cross section of the channel. Information on metering of such mixtures can be obtained from the following sources. Gas-Solid Mixtures Carlson, Frazier, and Engdahl [Trans. Am. Soc. Mech. Eng. 70: 65–79 (1948)] describe the use of a flow nozzle and a squareedged orifice in series for the measurement of both the gas rate and the solids rate in the flow of a finely divided solid-in-gas mixture. The nozzle differential is sensitive to the flow of both phases, whereas the orifice differential is not influenced by the solids flow. Farbar [Trans. Am. Soc. Mech. Eng. 75: 943–951 (1953)] describes how a venturi meter can be used to measure solids flow rate in a gas-solids mixture when the gas rate is held constant. Separate calibration curves (solids flow versus differential) are required for each gas rate of interest. Cheng, Tung, and Soo [ J. Eng. Power 92: 135–149 (1970)] describe the use of an electrostatic probe for measurement of solids flow in a gas-solids mixture. Goldberg and Boothroyd [Br. Chem. Eng. 14: 1705–1708 (1969)] describe several types of solids-in-gas flowmeters and give an extensive bibliography. Gas-Liquid Mixtures An empirical equation was developed by Murdock [ J. Basic Eng. 84: 419–433 (1962)] for the measurement of gas-liquid mixtures using sharp-edged orifice plates with radius, flange, or pipe taps. An equation for use with venturi meters was given by Chisholm [Br. Chem. Eng. 12: 454–457 (1967)]. A procedure for determining steam quality via pressure drop measurement with upflow through either venturi meters or sharp-edged orifice plates was given by Collins and Gacesa [ J. Basic Eng. 93: 11–21 (1971)]. Liquid-Solid Mixtures Liptak [Chem. Eng. 74(4): 151–158 (1967)] discusses a variety of techniques that can be used for the measurement of solidsin-liquid suspensions or slurries. These include metering pumps, weigh tanks, magnetic flowmeter, ultrasonic flowmeter, gyroscope flowmeter, etc. Shirato, Gotoh, Osasa, and Usami [ J. Chem. Eng. Japan 1: 164–167 ( January 1968)] present a method for determining the mass flow rate of suspended solids in a liquid stream wherein the liquid velocity is measured by an electromagnetic flowmeter and the flow of solids is calculated from the pressure drops across each of two vertical sections of pipe of different diameter through which the suspension flows in series. FLOWMETER SELECTION Web sites for process equipment and instrumentation, such as www.globalspec .com and www.thomasnet.com, are valuable tools when one is selecting a flowmeter. These search engines can scan the flowmeters manufactured by more than 800 companies for specific products that meet the user’s specifications. Table 10-4 was based in part on information from these web sites. Note that the accuracies claimed are achieved only under ideal conditions when the flowmeters are clean, properly installed, and calibrated for the application.

The purpose of this subsection is to summarize the preferred applications as well as the advantages and disadvantages of some of the common flowmeter technologies. Table 10-9 divides flowmeters into four classes. Flowmeters in class I depend on wetted moving parts that can wear, plug, or break. The potential for catastrophic failure is a disadvantage. However, in clean fluids, class I flowmeters have often proved reliable and stable when properly installed, calibrated, and maintained. Class II flowmeters have no wetted moving parts to break and are thus not subject to catastrophic failure. However, the flow surfaces such as orifice plates may wear, eventually biasing flow measurements. Other disadvantages of some flowmeters in this class include high pressure drop and susceptibility to plugging. Very dirty and abrasive fluids should be avoided. Because class III flowmeters have neither moving parts nor obstructions to flow, they are suitable for dirty and abrasive fluids provided that appropriate materials of construction are available. Class IV flowmeters have sensors mounted external to the pipe, and would thus seem to be ideal, but problems of accuracy and sensitivity have been encountered in early devices. These comparatively new technologies are under development, and these problems may be overcome in the future. Section 8 outlines the following criteria for selection of measurement devices: measurement span, performance, reliability, materials of construction, prior use and potential for releasing process materials to the environment, electrical classification, physical access, invasive or non-invasive, and life-cycle cost. Spitzer, Industrial Flow Measurement, 2005, cites four intended end uses of the flowmeter: rate indication, control, totalization, and alarm. Thus high accuracy may be important for rate indication, while control may just need good repeatability. Volumetric flow or mass flow indication is another choice. Baker, Flow Measurement Handbook, 2003, identifies the type of fluid (liquid or gas, slurry, multiphase), special fluid constraints (clean or dirty, hygienic, corrosive, abrasive, high flammability, low lubricity, fluids causing scaling). He lists the following flowmeter constraints: accuracy or measurement uncertainty, diameter range, temperature range, pressure range, viscosity range, flow range, pressure loss caused by the flowmeter, sensitivity to installation, sensitivity to pipework supports, sensitivity to pulsation, whether the flowmeter has a clear bore, availability of a clamp-on version, response time, and ambient conditions. Finally, Baker identifies these environmental considerations: ambient temperature, humidity, exposure to weather, level of electromagnetic radiation, vibration, tamperproof for domestic use, and classification of area requiring explosion proof, intrinsic safety, etc. Note that the accuracies cited in Table 10-4 can be achieved by those flowmeters only under ideal conditions of application, installation, and calibration. This subsection has given only an introduction to issues to consider in the choice of a flowmeter for a given application. See Baker, 2003; Miller, 1996; and Spitzer, 2005, for further guidance. To further refine choices, obtain application-specific data from flowmeter vendors.

PUMPS AND COMPRESSORS General References: Meherwan P. Boyce, P.E., Centrifugal Compressors: A Basic Guide, Pennwell Books, Tulsa, Okla., 2002; Royce N. Brown, Compressors: Selection and Sizing, 3d ed., Gulf Professional Publishing, Houston, Tex., 2005; James Corley, “The Vibration Analysis of Pumps: A Tutorial,” Fourth International Pump Symposium, Texas A & M University, Houston, Tex., May 1987; John W. Dufor and William E. Nelson, Centrifugal Pump Sourcebook, McGraw-Hill, New York, 1992; Engineering Data Book, 12th ed., vol. I, Secs. 12 and 13, Gas Processors Suppliers Association,

Tulsa, Okla., 2004; Paul N. Garay, P.E., Pump Application Desk Book, Fairmont Press, Lilburn, Ga., 1993; Process Pumps, IIT Fluid Technology Corporation, 1992; Igor J. Karassik et al., Pump Handbook, 3d ed., McGraw-Hill, New York, 2001; Val S. Lobanoff and Robert R. Ross, Centrifugal Pumps: Design and Application, 2d ed., Gulf Professional Publishing, Houston, Tex., 1992; A. J. Stephanoff, Centrifugal and Axial Flow Pumps: Theory, Design, and Application, 2d ed., Krieger Publishing, Melbourne, Fla., 1992.

10-22

TRANSPORT AND STORAGE OF FLUIDS

INTRODUCTION The following subsections deal with pumps and compressors. A pump or compressor is a physical contrivance that is used to deliver fluids from one location to another through conduits. The term pump is used when the fluid is a liquid, while the term compressor is used when the fluid is a gas. The basic requirements to define the application are suction and delivery pressures, pressure loss in transmission, and flow rate. Special requirements may exist in food, pharmaceutical, nuclear, and other industries that impose material selection requirements of the pump. The primary means of transfer of energy to the fluid that causes flow are gravity, displacement, centrifugal force, electromagnetic force, transfer of momentum, mechanical impulse, and a combination of these energy transfer mechanisms. Displacement and centrifugal force are the most common energy transfer mechanisms in use. Pumps and compressors are designed per technical specifications and standards developed over years of operating and maintenance experience. Table 10-10 lists some of these standards for pumps and compressors and for related equipment such as lubrication systems and gearboxes which, if not properly specified, could lead to many operational and maintenance problems with the pumps and compressors. These standards specify design, construction, maintenance, and testing details such as terminology, material selection, shop inspection and tests, drawings, clearances, construction procedures, and so on. Three major types of pumps are discussed here: (1) positive-displacement, (2) dynamic (kinetic), and (3) lift. Piston pumps are positive-displacement pumps. The most common centrifugal pumps are of dynamic type; ancient bucket-type pumps are lift pumps. Canned pumps are also becoming popular in the petrochemical industry because of the drive to minimize fugitive emissions. Figure 10-20 shows pump classification. TERMINOLOGY Displacement Discharge of a fluid from a vessel by partially or completely displacing its internal volume with a second fluid or by mechanical means is the TABLE 10-10

Standards Governing Pumps and Compressors

ASME Standards, American Society of Mechanical Engineers, New York B73.1-2001, Specification for Horizontal End Suction Centrifugal Pumps for Chemical Process B73.2-2003, Specification for Vertical In-Line Centrifugal Pumps for Chemical Process PTC 10, 1997 Test Code on Compressors and Exhausters PTC 11, 1984 Fans B19.3-1991, Safety Standard for Compressors for Process Industries API Standards, American Petroleum Institute, Washington API Standard 610, Centrifugal Pumps for Petroleum, Petrochemical, and Natural Gas Industries, Adoption of ISO 13709, October 2004 API Standard 613, Special Purpose Gear Units for Petroleum, Chemical and Gas Industry Services, February 2003 API Standard 614, Lubrication, Shaft-Sealing, and Control-Oil Systems and Auxiliaries for Petroleum, Chemical and Gas Industry Services, April 1999 API Standard 616, Gas Turbines for the Petroleum, Chemical, and Gas Industry Services, August 1998 API Standard 617, Axial and Centrifugal Compressors and Expanders— Compressors for Petroleum, Chemical, and Gas Industry Services, June 2003 API Standard 618, Reciprocating Compressors for Petroleum, Chemical, and Gas Industry Services, June 1995 API Standard 619, Rotary-Type Positive Displacement Compressors for Petroleum, Petrochemical, and Natural Gas Industries, December 2004 API Standard 670, Machinery Protection Systems, November 2003 API Standard 671, Special Purpose Couplings for Petroleum, Chemical, and Gas Industry Services, October 1998 API Standard 672, Packaged, Integrally Geared, Centrifugal Air Compressors for Petroleum, Chemical, and Gas Industry Services, March 2004 API Standard 673, Centrifugal Fans for Petroleum, Chemical, and Gas Industry Services, October 2002 API Standard 674, Positive Displacement Pumps—Reciprocating, June 1995 API Standard 675, Positive Displacement Pumps—Controlled Volume, March 2000 API Standard 677, General Purpose Gear Units for Petroleum, Chemical, and Gas Industry Services, April 2006 API Standard 680, Packaged Reciprocating Plant and Instrument Air Compressors for General Refinery Services, October 1987 API Standard 681, Liquid Ring Vacuum Pumps and Compressors for Petroleum, Chemical, and Gas Industry Services, June 2002 API Standard 682, Pumps—Shaft Sealing Systems for Centrifugal and Rotary Pumps, September 2004 API Standard 685, Sealless Centrifugal Pumps for Petroleum, Heavy Duty Chemical, and Gas Industry Services, October 2000 Hydraulic Institute, Parsippany, N.J. (www.pumps.org) ANSI/HI Pump Standards, 2005 (covers centrifugal, vertical, rotary, and reciprocating pumps) National Fire Protection Association, Quincy, Mass. (www.nfpa.org) Standards for pumps used in fire protection systems

principle upon which a great many fluid-transport devices operate. Included in this group are reciprocating-piston and diaphragm machines, rotary-vane and gear types, fluid piston compressors, acid eggs, and air lifts. The large variety of displacement-type fluid-transport devices makes it difficult to list characteristics common to each. However, for most types it is correct to state that (1) they are adaptable to high-pressure operation, (2) the flow rate through the pump is variable (auxiliary damping systems may be employed to reduce the magnitude of pressure pulsation and flow variation), (3) mechanical considerations limit maximum throughputs, and (4) the devices are capable of efficient performance at extremely low-volume throughput rates. Centrifugal Force Centrifugal force is applied by means of the centrifugal pump to a liquid. Though the physical appearance of the many types of centrifugal pumps and compressors varies greatly, the basic function of each is the same, i.e., to produce kinetic energy by the action of centrifugal force and then to convert this energy to pressure by efficiently reducing the velocity of the flowing fluid. In general, centrifugal fluid-transport devices have these characteristics: (1) discharge is relatively free of pulsation; (2) mechanical design lends itself to high throughputs, and capacity limitations are rarely a problem; (3) the devices are capable of efficient performance over a wide range of pressures and capacities even at constant-speed operation; (4) discharge pressure is a function of fluid density; and (5) these are relatively small high-speed devices and less costly. A device that combines the use of centrifugal force with mechanical impulse to produce an increase in pressure is the axial-flow compressor or pump. In this device the fluid travels roughly parallel to the shaft through a series of alternately rotating and stationary radial blades having airfoil cross sections. The fluid is accelerated in the axial direction by mechanical impulses from the rotating blades; concurrently, a positive-pressure gradient in the radial direction is established in each stage by centrifugal force. The net pressure rise per stage results from both effects. Electromagnetic Force When the fluid is an electrical conductor, as is the case with molten metals, it is possible to impress an electromagnetic field around the fluid conduit in such a way that a driving force that will cause flow to be created. Such pumps have been developed for the handling of heat-transfer liquids, especially for nuclear reactors. Transfer of Momentum Deceleration of one fluid (motivating fluid) in order to transfer its momentum to a second fluid (pumped fluid) is a principle commonly used in the handling of corrosive materials, in pumping from inaccessible depths, or for evacuation. Jets and eductors are in this category. Absence of moving parts and simplicity of construction have frequently justified the use of jets and eductors. However, they are relatively inefficient devices. When air or steam is the motivating fluid, operating costs may be several times the cost of alternative types of fluid-transport equipment. In addition, environmental considerations in today’s chemical plants often inhibit their use. Mechanical Impulse The principle of mechanical impulse when applied to fluids is usually combined with one of the other means of imparting motion. As mentioned earlier, this is the case in axial-flow compressors and pumps. The turbine or regenerative-type pump is another device that functions partially by mechanical impulse. Measurement of Performance The amount of useful work that any fluid-transport device performs is the product of (1) the mass rate of fluid flow through it and (2) the total pressure differential measured immediately before and after the device, usually expressed in the height of column of fluid equivalent under adiabatic conditions. The first of these quantities is normally referred to as capacity, and the second is known as head. Capacity This quantity is expressed in the following units. In SI units, capacity is expressed in cubic meters per hour (m3/h) for both liquids and gases. In U.S. Customary System units it is expressed in U.S. gallons per minute (gal/min) for liquids and in cubic feet per minute ( ft3/min) for gases. Since all these are volume units, the density or specific gravity must be used for conversion to mass rate of flow. When gases are being handled, capacity must be related to a pressure and a temperature, usually the conditions prevailing at the machine inlet. It is important to note that all heads and other terms in the following equations are expressed in height of column of liquid. PUMPS Total Dynamic Head The total dynamic head H of a pump is the total discharge head hd minus the total suction head hs. Total Suction Head This is the reading hgs of a gauge at the suction flange of a pump (corrected to the pump centerline), plus the barometer reading and the velocity head hvs at the point of gauge attachment: hs = hgs + atm + hvs

(10-37)

If the gauge pressure at the suction flange is less than atmospheric, requiring use of a vacuum gauge, this reading is used for hgs in Eq. (10-38) with a negative sign.

PUMPS AND COMPRESSORS

Piston Plunger Reciprocating

Double acting

Simplex Duplex

Steam

Single acting Double acting

Simplex Duplex Triplex Multiplex

Power

Simplex Multiplex

Diaphragm Positive displacement

Single rotor

Vane Piston Flexible member Screw

Multiple rotor

Gear Lobe Circumferential piston Screw

Blow cover

10-23

Fluid operated Mech. operated

Rotary

Fluid ring

Pumps

Radial flow Mixed flow

Single suction Double suction Double valves

Self-priming Non-self-priming Open impeller Single stage Semi-open impeller Multistage Closed impeller

Axial flow

Single Suction

Single stage Multistage

Peripheral

Single stage Multistage

Self-priming Non-self-priming

Regenerative

Special

Viscous drag Jet (ejector-boosted) Gas lift Hydraulic ram Electromagnetic Screw centrifugal Rotating casing (pitot)

Centrifugal

Kinetic

Open impeller Closed impeller

Open screw FIG. 10-20

Classification of pumps. (Courtesy of Hydraulic Institute.)

Before installation it is possible to estimate the total suction head as follows:

Before installation it is possible to estimate the total discharge head from the static discharge head hsd and the discharge friction head hfd as follows:

hs = hss - hfs

hd = hsd + hfd

(10-38)

where hss = static suction head and hfs = suction friction head. Static Suction Head The static suction head hss is the vertical distance measured from the free surface of the liquid source to the pump centerline plus the absolute pressure at the liquid surface. Total Discharge Head The total discharge head hd is the reading hgd of a gauge at the discharge flange of a pump (corrected to the pump centerline∗), plus the barometer reading and the velocity head hvd at the point of gauge attachment: hd = hgd + atm + hvd

(10-39)

Again, if the discharge gauge pressure is below atmospheric, the vacuumgauge reading is used for hgd in Eq. (10-39) with a negative sign. ∗On vertical pumps, the correction should be made to the eye of the suction impeller.

(10-40)

Static Discharge Head The static discharge head hsd is the vertical distance measured from the free surface of the liquid in the receiver to the pump centerline,∗ plus the absolute pressure at the liquid surface. Total static head hts is the difference between discharge and suction static heads. Velocity Since most liquids are practically incompressible, the relation between the quantity flowing past a given point at a given time and the volume flow rate is expressed as follows: Q = AVavg

(10-41)

This relationship in SI units is as follows: Vavg ( for circular conduits) = 3.54Q/d 2

(10-42)

where Vavg = average velocity of flow, m/s; Q = quantity of flow, m3/h; and d = inside diameter of conduit, cm.

10-24

TRANSPORT AND STORAGE OF FLUIDS

This same relationship in U.S. Customary System (USCS) units is Vavg ( for circular conduits) = 0.409Q/d 2

(10-43)

where Vavg = average velocity of flow, ft/s; Q = volume flow rate, gal/min; and d = inside diameter of conduit, in. Velocity Head This is the force generated by the pump and is given in ft · lbf/lbm, the vertical height that the pump can maintain. H = V 2/2gc = ft · lbf/lbm

(10-44)

where gc = the gravitational constant = 32.2 ft · lbm/lbf ⋅ s2 In the SI system the head is in meters. Viscosity (See Sec. 6 for further information.) In flowing liquids, the existence of internal friction or the internal resistance to relative motion of the fluid particles must be considered. This resistance is called viscosity. Frictional losses in pipes increase with higher viscosity. Viscosity decreases with the rising temperature of the fluid. The increase in viscosity of fluids will increase the pump power required for the same head and capacity and will reduce the efficiency of the pump. Friction Head This is the pressure required to overcome the resistance to flow in pipe and fittings. It is dealt with in detail in Sec. 6. Work Performed in Pumping To cause liquid to flow, work must be expended. A pump may raise the liquid to a higher elevation, force it into a vessel at higher pressure, provide the head to overcome pipe friction, or perform any combination of these. Regardless of the service required of a pump, all energy imparted to the liquid in performing this service must be accounted for; consistent units for all quantities must be employed in arriving at the work or power performed. When arriving at the performance of a pump, it is customary to calculate its power output, which is the product of (1) the total dynamic head and (2) the mass of liquid pumped in a given time. In SI units power is expressed in kilowatts; horsepower is the conventional unit used in the United States. In SI units, kW = HQρ/3.670 × 105

(10-45)

where kW is the pump power output, kW; H = total dynamic head, N · m/kg (column of liquid); Q = capacity, m3/h; and ρ = liquid density, kg/m3. When the total dynamic head H is expressed in pascals, then kW = HQρ/3.599 × 106

(10-46)

In USCS units, hp = HQs/3.960 × 103

(10-47)

where hp is the pump power output, hp; H = total dynamic head, lbf · ft/lbm (column of liquid); Q = capacity, U.S. gal/min; and s = liquid specific gravity. When the total dynamic head hp is expressed in pounds force per square inch, then hp = HQ/1.714 × 103

(10-48)

The power input to a pump is greater than the power output because of internal losses resulting from friction, leakage, etc. The efficiency of a pump is therefore defined as Pump efficiency = (power output)/(power input)

(10-49)

PUMP SELECTION When one is selecting pumps for any service, it is necessary to know the liquid to be handled, total dynamic head, suction and discharge heads, and, in most cases, temperature, viscosity, vapor pressure, and specific gravity. In the chemical industry, the task of pump selection is frequently further complicated by the presence of solids in the liquid and liquid corrosion characteristics requiring special materials of construction. Solids may accelerate erosion and corrosion, have a tendency to agglomerate, or require delicate handling to prevent undesirable degradation.

FIG. 10-21 Pump coverage chart based on normal ranges of operation of commercially available types. Solid lines: use left ordinate, head scale. Broken lines: use right ordinate, pressure scale. To convert gallons per minute to cubic meters per hour, multiply by 0.2271; to convert feet to meters, multiply by 0.3048; and to convert pounds-force per square inch to kilopascals, multiply by 6.895.

Range of Operation Because of the wide variety of pump types and the number of factors that determine the selection of any one type for a specific installation, the designer must first eliminate all but those types of reasonable possibility. Since range of operation is always an important consideration, Fig. 10-21 should be of assistance. The boundaries shown for each pump type are at best approximate. In most cases, following Fig. 10-21 will select the pump that is best suited for a given application. Reciprocating pumps and rotary pumps such as gear and roots rotor-type pumps are examples of positive-displacement pumps. Displacement pumps provide high heads at low capacities which are beyond the capability of centrifugal pumps. Displacement pumps achieve high pressure with low velocities and are thus suited for high-viscosity service and slurry. The centrifugal pump operates over a very wide range of flows and pressures. The axial pump is best suited for low heads but high flows. Both the centrifugal and axial-flow pumps impart energy to the fluid by the rotational speed of the impeller and the velocity it imparts to the fluid. NET POSITIVE SUCTION HEAD Net positive suction head available (NPSH)A is the difference between the total absolute suction pressure at the pump suction nozzle when the pump is running and the vapor pressure at the flowing liquid temperature. All pumps require the system to provide adequate (NPSH)A. In a positivedisplacement pump the (NPSH)A should be large enough to open the suction valve, to overcome the friction losses within the pump liquid end, and to overcome the liquid acceleration head. Suction Limitations of a Pump Whenever the pressure in a liquid drops below the vapor pressure corresponding to its temperature, the liquid will vaporize. When this happens within an operating pump, the vapor bubbles will be carried along to a point of higher pressure, where they suddenly collapse. This phenomenon is known as cavitation. Cavitation in a pump should be avoided, as it is accompanied by metal removal, vibration, reduced flow, loss in efficiency, and noise. When the absolute suction pressure is low, cavitation may occur in the pump inlet and damage may result in the pump suction and on the impeller vanes near the inlet edges. To avoid this phenomenon, it is necessary to maintain a required net positive suction head (NPSH)R, which is the equivalent total head of liquid at the pump centerline less the vapor pressure p. Each pump manufacturer publishes curves relating (NPSH)R to capacity and speed for each pump. When a pump installation is being designed, the available net positive suction head (NPSH)A must be equal to or greater than the (NPSH)R for the desired capacity. The (NPSH)A can be calculated as follows: (NPSH)A = hss - hfs - p

(10-50)

If (NPSH)A is to be checked on an existing installation, it can be determined as follows: (NPSH)A = atm + hgs - p + h vs

(10-51)

PUMPS AND COMPRESSORS Practically, the NPSH required for operation without cavitation and vibration in the pump is somewhat greater than the theoretical. The actual (NPSH)R depends on the characteristics of the liquid, total head, pump speed, capacity, and impeller design. Any suction condition which reduces (NPSH)A below that required to prevent cavitation at the desired capacity will produce an unsatisfactory installation and can lead to mechanical difficulty. The following two equations usually provide an adequate design margin between (NPSH)A and (NPSH)R: (NPSH)A = (NPSH)R + 5 ft

(10-52)

(NPSH)A = 1.35(NPSH)R

(10-53)

Use the larger value of (NPSH)A calculated with Eqs. (10-52) and (10-53). NPSH Requirements for Other Liquids NPSH values depend on the fluid being pumped. Since water is considered a standard fluid for pumping, various correction methods have been developed to evaluate NPSH when pumping other fluids. The most recent of these corrective methods has been developed by the Hydraulic Institute and is shown in Fig. 10-22. The chart shown in Fig. 10-22 is for pure liquids. Extrapolation of data beyond the ranges indicated in the graph may not produce accurate results. Figure 10-22 shows the variation of vapor pressure and NPSH reductions for various hydrocarbons and hot water as a function of temperature. Certain rules apply while using this chart. When using the chart for hot water, if the NPSH reduction is greater than one-half of the NPSH required for cold water, deduct one-half of cold water NPSH to obtain the corrected NPSH required. However, if the value read on the chart is less than one-half of cold water NPSH, deduct this chart value from the cold water NPSH to obtain the corrected NPSH. Example 10-1 NPSH Calculation Suppose a selected pump requires a minimum NPSH of 16 ft (4.9 m) when pumping cold water. What will be the NPSH limitation to pump propane at 55°F (12.8°C) with a vapor pressure of 120 psi ( 8.274 bar)? Using the chart in Fig. 10-22, NPSH reduction for propane gives 9.5 ft (2.9 m). This is greater than one-half of the cold water NPSH of 16 ft (4.9 m). The corrected NPSH is therefore 8 ft (2.4 m) or one-half of the cold water NPSH. PUMP SPECIFICATIONS Pump specifications depend on numerous factors but mostly on application. Typically, the following factors should be considered while preparing a specification: 1. Application, scope, and type 2. Service conditions

e an

p ro

P

100

o

Rho 11 l

e

0

50

100

10 8 6 5 4 3 2 1.5 1.0 0.5

Wa

ter

lco la

Me

thy

fri ge

ra

n ta Bu

5 4 3 2 1.5 1.0

e

an

nt

Is

50 40 30 20 15 10

t bu

Re

Vapor pressure, PSIA

500 400 300 200 150

150 200 250300

NPSH reductions, feet

1000

400

Temperature, F NPSH reductions for pumps handling hydrocarbon liquids and hightemperature water. This chart has been constructed from test data obtained using the liquids shown. (Hydraulic Institute Standards.)

FIG. 10-22

10-25

3. Operating conditions 4. Construction application-specific details and special considerations a. Casing and connections b. Impeller details c. Shaft d. Stuffing box details—lubrications, sealing, etc. e. Bearing frame and bearings f. Baseplate and couplings g. Materials h. Special operating conditions and miscellaneous items Table 10-11 is based on the API and ASME codes and illustrates a typical specification for centrifugal pumps. POSITIVE-DISPLACEMENT PUMPS Positive-displacement pumps and those that approach positive displacement will ideally produce whatever head is impressed upon them by the system restrictions to flow. The maximum head attainable is determined by the power available in the drive (slippage neglected) and the strength of the pump parts. A pressure relief valve on the discharge side should be set to open at a safe pressure for the casing and the internal components of the pump such as piston rods, cylinders, crankshafts, and other components which would be pressurized. In the case of a rotary pump, the total dynamic head developed is uniquely determined for any given flow by the speed at which it rotates. In general, overall efficiencies of positive-displacement pumps are higher than those of centrifugal equipment because internal losses are minimized. However, the flexibility of each piece of equipment in handling a wide range of capacities is somewhat limited. Positive-displacement pumps may be of either the reciprocating or the rotary type. In all positive-displacement pumps, a cavity or cavities are alternately filled and emptied of the pumped fluid by the action of the pump. Reciprocating Pumps There are three classes of reciprocating pumps: piston pumps, plunger pumps, and diaphragm pumps. Basically, the action of the liquid-transferring parts of these pumps is the same, with a cylindrical piston, or plunger, or bucket or a round diaphragm being caused to pass or flex back and forth in a chamber. The device is equipped with valves for the inlet and discharge of the liquid being pumped, and the operation of these valves is related in a definite manner to the motions of the piston. In all modern-design reciprocating pumps, the suction and discharge valves are operated by pressure difference. That is, when the pump is on its suction stroke and the pump cavity is increasing in volume, the pressure is lowered within the pump cavity, permitting the higher suction pressure to open the suction valve and allowing liquid to flow into the pump. At the same time, the higher discharge-line pressure holds the discharge valve closed. Likewise, on the discharge stroke, as the pump cavity is decreasing in volume, the higher pressure developed in the pump cavity holds the suction valve closed and opens the discharge valve to expel liquid from the pump into the discharge line. The overall efficiency of these pumps varies from about 50 percent for the small pumps to about 90 percent or more for the larger sizes. Reciprocating pumps may be of single-cylinder or multicylinder design. Multicylinder pumps have all cylinders in parallel for increased capacity. Piston-type pumps may be single-acting or double-acting; i.e., pumping may be accomplished from one end or both ends of the piston. Plunger pumps are always single-acting. The tabulation in Table 10-12 provides data on the flow variation of reciprocating pumps of various designs. Piston Pumps There are two ordinary types of piston pumps: simplex double-acting pumps and duplex double-acting pumps. Simplex Double-Acting Pumps These pumps may be direct-acting (i.e., direct-connected to a steam cylinder) or power-driven (through a crank and flywheel from the crosshead of a steam engine). Duplex Double-Acting Pumps These pumps differ primarily from those of the simplex type in having two cylinders whose operation is coordinated. They may be direct-acting, steam-driven, or power-driven with crank and flywheel. Plunger Pumps These differ from piston pumps in that they have one or more constant-diameter plungers reciprocating through packing glands and displacing liquid from cylinders in which there is considerable radial clearance. They are always single-acting, in the sense that only one end of the plunger is used in pumping the liquid. Plunger pumps are available with one, two, three, four, five, or even more cylinders. Simplex and duplex units are often built in a horizontal design. Those with three or more cylinders are usually of vertical design. Diaphragm Pumps These pumps perform similarly to piston and plunger pumps, but the reciprocating driving member is a flexible diaphragm fabricated of metal, rubber, or plastic. The chief advantage of this arrangement is the elimination of all packing and seals exposed to the liquid

10-26

TRANSPORT AND STORAGE OF FLUIDS

TABLE 10-11

Typical Pump Specification

Specification 1.0

Description

Specification

Scope: This specification covers horizontal, end suction, vertically split, singlestage centrifugal pumps with top centerline discharge and “back pullout” feature.

2.0

Service Conditions: Pump shall be designed to operate satisfactorily with a reasonable service life when operated either intermittently or continuously in typical process applications.

3.0

Operating Conditions:

4.8

Pump Construction: 4.1 Casing. Casing shall be vertically split with self-venting top centerline discharge, with an integral foot located directly under the casing for added support. All casings shall be of the “back pullout” design with suction and discharge nozzles cast integrally. Casings shall be provided with bosses in suction and discharge nozzles, and in bottom of casing for gauge taps and drain tap. (Threaded taps with plugs shall be provided for these features.) 4.2 Casing Connections. Connections shall be ANSI flat-faced flanges. [Cast iron (125) (250) psig rated] [Duron metal, steel, alloy steel (150) (300) psig rated] 4.3 Casing Joint Gasket. A confined-type nonasbestos gasket suitable for corrosive service shall be provided at the casing joint. 4.4 Impeller. Fully-open impeller with front edge having contoured vanes curving into the suction for minimum NPSH requirements and maximum efficiency shall be provided. A hex head shall be cast in the eye of the impeller to facilitate removal, and eliminate need for special impeller removing tool. All impellers shall have radial “pump-out” vanes on the back side to reduce stuffing box pressure and aid in eliminating collection of solids at stuffing box throat. Impellers shall be balanced within A.N.S.I. guidelines to ISO tolerances. 4.4.1 Impeller Clearance Adjustment. All pumps shall have provisions for adjustment of axial clearance between the leading edge of the impeller and casing. This adjustment shall be made by a precision microdial adjustment at the outboard bearing housing, which moves the impeller forward toward the suction wall of the casing. 4.5 Shafts. Shafts shall be suitable for hook-type sleeve. Shaft material shall be (SAE 1045 steel on Duron and 316 stainless steel pumps) or (AISI 316 stainless steel on CD-4MCu pumps and #20 stainless steel pumps). Shaft deflection shall not exceed .005 at the vertical center-line of the impeller. 4.6 Shaft Sleeve. Renewable hook-type shaft sleeve that extends through the stuffing box and gland shall be provided. Shaft sleeve shall be (316 stainless steel), (#20 stainless steel) or (XH-800 Ni-chrome-boron coated 316 stainless steel with coated surface hardness of approximately 800 Brinell). 4.7 Stuffing Box. Stuffing box shall be suitable for packing, single (inside or outside) or double-inside mechanical seal without modifications. Stuffing box shall be accurately centered by machined rabbit fits on case and frame adapter. 4.7.1 Packed Stuffing Box. The standard packed stuffing box shall consist of five rings of graphited nonasbestos packing; a stainless steel packing base ring in the bottom of the box to prevent extrusion of the packing past the throat; a Teflon seal cage, and a two-piece 316 stain-less steel packing gland to ensure even pressure on the packing. Ample space shall be provided for repacking the stuffing box. 4.7.1.1 Lubrication-Packed Stuffing Box. A tapped hole shall be provided in the stuffing box directly over the seal cage for lubrication and cooling of the packing. Lubrication liquid shall be supplied ( from an external source) (through a by-pass line from the pump discharge nozzle). 4.7.2 Stuffing Box with Mechanical Seal. Mechanical seal shall be of the (single inside) (single outside) (double inside) (cartridge) type and (balanced) (unbalanced). Stuffing box is to be (standard) (oversize) (oversize tapered).

*Omit if not applicable.

Bearing Frame and Bearings: 4.8.1 Bearing Frame. Frames shall be equipped with axial radiating fins extending the length of the frame to aid in heat dissipation. Frame shall be provided with ductile iron outboard bearing housing. Both ends of the frame shall be provided with lip-type oil seals and labyrinth-type deflectors of metallic reinforced synthetic rubber to prevent the entrance of contaminants.

Capacity             U.S. gallons per minute              Head (       ft total head) (       psig). Speed       r/min Suction Pressure (       ft head) (positive) (lift) (        psig) Liquid to be handled                                      Specific gravity               Viscosity (                 ) Temperature of liquid at inlet            °F Solids content           %            Max. size 4.0

Description Suitable space shall be provided in the standard and oversized stuffing box for supplying a (throttle bushing) (dilution control bushing) with single seals. Throttle bushings and dilution control bushings shall be made of (glass-filled Teflon) (a suitable metal material). 4.7.2.1 Lubrication—Stuffing Box with Mechanical Seals. Suitable tapped connections shall be provided to effectively lubricate, cool, flush, quench, etc., as required by the application or recommendations of the mechanical seal manufacturer.

4.8.2 Bearings. Pump bearings shall be heavy-duty, antifriction ball-type on both ends. The single row inboard bearing, nearest the impeller, shall be free to float within the frame and shall carry only radial load. The double row outboard bearing (F4-G1 and F4-I1) or duplex angular contact bearing (F4-H1), coupling end, shall be locked in place to carry radial and axial thrust loads. Bearings shall be designed for a minimum life of 20,000 hours in any normal pump operating range. 4.9

Bearing Lubrication. Ball bearings shall be oil-mist—lubricated by means of a slinger. The oil slinger shall be mounted on the shaft between the bearings to provide equal lubrication to both bearings. Bulls-eye oil-sight glasses shall be provided on both sides of the frame to provide a positive means of checking the proper oil level from either side of the pump. A tapped and plugged hole shall also be provided in both sides of the frame to mount bottle-type constant-level oilers where desired. A tapped and plugged hole shall be provided on both sides for optional straight-through oil cooling device.

5.0

Baseplate and Coupling: 5.1 Baseplate. Baseplates shall be rigid and suitable for mounting pump and motor. Baseplates shall be of channel steel construction. 5.2 Coupling. Coupling shall be flexible-spacer type. Coupling shall have at least three–and–one-half–inch spacer length for ease of rotating element removal. Both coupling hubs shall be provided with flats 180° apart to facilitate removal of impeller. Coupling shall not require lubrication.*

6.0

Mechanical Modifications Required for High Temperature: 6.1 Modifications Required, Temperature Range 250–350∞F. Pumps for operation in this range shall be provided with a water-jacketed stuffing box. 6.2 Modifications Required, Temperature Range 351–550∞F (Maximum). Pumps for operation in this range shall be provided with a water-jacketed stuffing box and a water-cooled bearing frame.

7.0

Materials: Pump materials shall be selected to suit the particular service requirements. 7.1 Cast Iron—316 SS Fitted. 15″ only; pump shall have cast iron casing and stuffing box cover. 316 SS metal impeller; shaft shall be 1045 steel with 316 SS sleeve. 7.2 All Duron Metal. All pump materials shall be Duron metal. Shaft shall be 1045 steel, with 316 SS sleeve. 316 SS metal impeller optional. 7.3 All AISI 316 Stainless Steel. All pump materials shall be AISI 316 stainless steel. Shaft should be 1045 steel, with 316 SS sleeve. 7.4 All #20 Stainless Steel. All pump materials shall be #20 SS stainless steel. Shaft shall be 316 SS, with #20 SS sleeve. 7.5 All CD-4MCu. All pump materials shall be CD-4MCu. Shaft shall be 316 SS, with #20 SS sleeve. Miscellaneous: 8.1 Nameplates. All nameplates and other data plates shall be stainless steel, suitably secured to the pump. 8.2 Hardware. All machine bolts, stud nuts, and cap screws shall be of the hex-head type. 8.3 Rotation. Pump shall have clockwise rotation viewed from its driven end. 8.4 Parts Numbering. Parts shall be completely identified with a numerical system (no alphabetical letters) to facilitate parts inventory control and stocking. Each part shall be properly identified by a separate number, and those parts that are identical shall have the same number to effect minimum spare parts inventory.

8.0

PUMPS AND COMPRESSORS TABLE 10-12 Number of cylinders Single Single Duplex Duplex Triplex Quintuplex

10-27

Flow Variation of Reciprocating Pumps Single- or double-acting

Flow variation per stroke from mean, percent

Single Double Single Double Single and double Single

+220 to -100 +60 to -100 +24.1 to -100 +6.1 to -21.5 +1.8 to -16.9 +1.8 to -5.2

being pumped. This is an important asset for equipment required to handle hazardous or toxic liquids. Low-capacity diaphragm pumps are designed for metering service and employ a plunger working in oil to actuate a metallic or plastic diaphragm. Built for pressures in excess of 6.895 MPa (1000 lbf/in2) with flow rates up to about 1.135 m3/h (5 gal/min) per cylinder, such pumps possess all the characteristics of plunger-type metering pumps with the added advantage that the pumping head can be mounted in a remote (even a submerged) location entirely separate from the drive. Figure 10-23 shows a high-capacity 22.7 m3/h (100 gal/min) pump with actuation provided by a mechanical linkage. Rotary Pumps In rotary pumps the liquid is displaced by rotation of one or more members within a stationary housing. Because internal clearances, although minute, are a necessity in all but a few special types, capacity decreases somewhat with increasing pump differential pressure. Therefore, these pumps are not truly positive-displacement pumps. However, for many other reasons they are considered as such. The selection of materials of construction for rotary pumps is critical. The materials must be corrosion-resistant, compatible when one part is running against another, and capable of some abrasion resistance. Gear Pumps When two or more impellers are used in a rotary-pump casing, the impellers will take the form of toothed-gear wheels as in Fig. 10-24, of helical gears, or of lobed cams. In each case, these impellers rotate with extremely small clearance between them and between the surfaces of the impellers and the casing. In Fig. 10-24, the two toothed impellers rotate as indicated by the arrows; the suction connection is at the bottom. The pumped liquid flows into the spaces between the impeller teeth as these cavities pass the suction opening. The liquid is then carried around the casing to the discharge opening, where it is forced out of the impeller teeth mesh. The arrows indicate this flow of liquid. Rotary pumps are available in two general classes: interior-bearing and exterior-bearing. The interior-bearing type is used for handling liquids of a lubricating nature, and the exterior-bearing type is used with nonlubricating liquids. The interior-bearing pump is lubricated by the liquid being pumped, and the exterior-bearing type is oil-lubricated. The use of spur gears in gear pumps will produce in the discharge pulsations having a frequency equivalent to the number of teeth on both gears multiplied by the speed of rotation. The amplitude of these disturbances is a

FIG. 10-24

Positive-displacement gear-type rotary pump.

function of tooth design. The pulsations can be reduced markedly by the use of rotors with helical teeth. This in turn introduces end thrust, which can be eliminated by the use of double-helical or herringbone teeth. Screw Pumps A modification of the helical gear pump is the screw pump. A screw pump delivers and increases the pressure of slightly lubricating liquids. Both gear and screw pumps are positive-displacement pumps. Figure 10-25 illustrates a two-rotor version in which the liquid is fed to either the center or the ends, depending on the direction of rotation, and progresses axially in the cavities formed by the meshing threads or teeth. In three-rotor versions, the center rotor is the driving member while the other two are driven. Figure 10-26 shows still another arrangement, in which a metal rotor of unique design rotates without clearance in an elastomeric stationary sleeve. Screw pumps, because of multiple dams that reduce slip, are well adapted for producing higher pressure rises, for example, 6.895 MPa (1000 lbf/in2), especially when handling viscous liquids such as heavy oils. The all-metal pumps are generally subject to the same limitations on handling abrasive solids as conventional gear pumps. In addition, the wide bearing spans usually demand that the liquid have considerable lubricity to prevent metal-tometal contact. Among the liquids handled by rotary pumps are mineral oils, vegetable oils, animal oils, greases, glucose, viscose, molasses, paints, varnish, shellac, lacquers, alcohols, catsup, brine, mayonnaise, sizing, soap, tanning liquors, vinegar, and ink. Some screw-type units are specially designed for the gentle handling of large solids suspended in the liquid. CENTRIFUGAL PUMPS

FIG. 10-23 Mechanically actuated diaphragm pump.

The centrifugal pump is the type most widely used in the chemical industry for transferring liquids of all types—raw materials, materials in manufacture, and finished products—as well as for general services of water supply, boiler feed, condenser circulation, condensate return, etc. These pumps are available through a vast range of sizes, in capacities from 0.5 m3/h to 2 × 104 m3/h (2 gal/min to 105 gal/min), and for discharge heads (pressures) from a few meters to approximately 48 MPa (7000 lbf/in2). The primary advantages of a centrifugal pump are simplicity, low first cost, uniform (nonpulsating) flow, small floor space, low maintenance expense, quiet operation, and adaptability for use with a motor or a turbine drive. A centrifugal pump, in its simplest form, consists of an impeller rotating within a casing. The impeller consists of a number of blades, either open or shrouded, mounted on a shaft that projects outside the casing. Its axis of rotation may be either horizontal or vertical, to suit the work to be done. Closed-type, or shrouded, impellers are generally the most efficient. Open or semi-open impellers are used for viscous liquids or for liquids containing solid materials and on many small pumps for general service. Impellers may be of the single-suction or double-suction type—single if the liquid enters from one side, double if it enters from both sides. Casings There are three general types of casings, but each consists of a chamber in which the impeller rotates, provided with inlet and exit for the liquid being pumped. The simplest form is the circular casing, consisting of an annular chamber around the impeller; no attempt is made to overcome the losses that will arise from eddies and shock when the liquid leaving the impeller at relatively high velocities enters this chamber. Such casings are seldom used.

10-28

TRANSPORT AND STORAGE OF FLUIDS

FIG. 10-25

Two-rotor screw pump. (Courtesy of Warren Quimby Pump Co.)

Volute casings take the form of a spiral increasing uniformly in crosssectional area as the outlet is approached. The volute efficiently converts the velocity energy imparted to the liquid by the impeller into pressure energy. A third type of casing is used in diffuser-type or turbine pumps. In this type, guide vanes or diffusers are interposed between the impeller discharge and the casing chamber. Losses are kept to a minimum in a well-designed pump of this type, and improved efficiency is obtained over a wider range of capacities. This construction is often used in multistage high-head pumps. Action of a Centrifugal Pump Briefly, the action of a centrifugal pump may be shown by Fig. 10-27. Power from an outside source is applied to shaft A, rotating the impeller B within the stationary casing C. The blades of the impeller in revolving produce a reduction in pressure at the entrance or eye of the impeller. This causes liquid to flow into the impeller from the suction pipe D. This liquid is forced outward along the blades at increasing tangential velocity. The velocity head it has acquired when it leaves the blade tips is changed to pressure head as the liquid passes into the volute chamber and then out the discharge E. Centrifugal Pump Characteristics Figure 10-28 shows a typical characteristic curve of a centrifugal pump. It is important to note that at any fixed speed the pump will operate along this curve and at no other points. For instance, on the curve shown, at 45.5 m3/h (200 gal/min) the pump will generate 26.5-m (87-ft) head. If the head is increased to 30.48 m (100 ft), then 27.25 m3/h (120 gal/min) will be delivered. It is not possible to reduce the capacity to 27.25 m3/h (120 gal/min) at 26.5-m (87-ft) head unless the discharge is throttled so that 30.48 m (100 ft) is actually generated within the pump. On pumps with variable-speed drivers such as steam turbines, it is possible to change the characteristic curve, as shown by Fig. 10-29. As shown in Eq. (10-44), the head depends on the velocity of the fluid, which in turn depends on the capability of the impeller to transfer energy to the fluid. This is a function of the fluid viscosity and the impeller design. It is important to remember that the head produced will be the same for any liquid of the same viscosity. The pressure rise, however, will vary in proportion to the specific gravity. For quick pump selection, manufacturers often give the most essential performance details for a whole range of pump sizes. Figure 10-30 shows typical performance data for a range of process pumps based on suction and discharge pipes and impeller diameters. The performance data consist of the pump flow rate and the head. Once a pump meets a required specification, then more-detailed performance data for the particular pump can be easily found based on the curve reference number. Figure 10-31 shows a more detailed pump performance curve that includes, in addition to pump head and flow, the brake horsepower required, NPSH required, number of vanes, and pump efficiency for a range of impeller diameters.

FIG. 10-26

If detailed manufacturer-specified performance curves are not available for a different size of the pump or operating condition, then a best estimate of the off-design performance of pumps can be obtained through similarity relationship or the affinity laws: 1. Capacity Q is proportional to impeller rotational speed N. 2. Head h varies as square of the impeller rotational speed. 3. Brake horsepower (BHP) varies as the cube of the impeller rotational speed. These equations can be expressed mathematically and appear in Table 10-13. System Curves In addition to the pump design, the operational performance of a pump depends on factors such as the downstream load characteristics, pipe friction, and valve performance. Typically, head and flow follow the following relationship: (Q2 )2 h2 = (Q1 )2 h1

(10-54)

where subscript 1 refers to the design condition and subscript 2 to the actual conditions. The above equation indicates that head will change as the square of the water flow rate. Figure 10-32 shows the schematic of a pump, moving a fluid from tank A to tank B, both of which are at the same level. The only force that the pump has to overcome in this case is the pipe friction, variation of which with fluid flow rate is also shown in the figure. On the other hand, for the use shown in Fig. 10-33, the pump in addition to pipe friction should overcome head due to the difference in elevation between tanks A and B. In this case, elevation head is constant, whereas the head required to overcome friction depends on the flow rate. Figure 10-34 shows the pump performance requirement of a valve opening and closing. Pump Selection One of the parameters that is extremely useful in selecting a pump for a particular application is specific speed Ns. Specific speed of a pump can be evaluated based on its design speed, flow, and head: NS =

NQ 1/2 H 3/4

(10-55)

where N = rpm, Q is flow rate in gpm, and H is head in ft ⋅ lbf/lbm. Specific speed is a parameter that defines the speed at which impellers of geometrically similar design have to be run to discharge 1 gal/min against a 1-ft head. In general, pumps with a low specific speed have a low capacity; and high specific speed, high capacity. Specific speeds of different types of pumps are shown in Table 10-14 for comparison.

Single-rotor screw pump with an elastomeric lining. (Courtesy of Moyno Pump Division, Robbins & Myers, Inc.)

PUMPS AND COMPRESSORS

10-29

Another parameter that helps in evaluating the pump suction limitations, such as cavitation, is the suction-specific speed, S: S=

FIG. 10-27

A simple centrifugal pump.

FIG. 10-28 Characteristic curve of a centrifugal pump operating at a constant speed

of 3450 r/min. To convert gallons per minute to cubic meters per hour, multiply by 0.2271; to convert feet to meters, multiply by 0.3048; to convert horsepower to kilowatts, multiply by 0.746; and to convert inches to centimeters, multiply by 2.54.

FIG. 10-29

Characteristic curve of a centrifugal pump at various speeds. To convert gallons per minute to cubic meters per hour, multiply by 0.2271; to convert feet to meters, multiply by 0.3048; to convert horsepower to kilowatts, multiply by 0.746; and to convert inches to centimeters, multiply by 2.54.

NQ 1/2 (NPSH)3/4

(10-56)

Typically, for single-suction pumps, suction-specific speed above 11,000 is considered excellent. Below 7000 is poor and 7000 to 9000 is of an average design. Similarly, for double-suction pumps, suction-specific speed above 14,000 is considered excellent, below 7000 is poor, and 9000 to 11,000 is average. Figure 10-35 shows the schematic of specific-speed variation for different types of pumps. The figure clearly indicates that as the specific speed increases, the ratio of the impeller outer diameter D1 to inlet or eye diameter D2 decreases, tending to become unity for pumps of axial-flow type. Typically, axial-flow pumps are of high-flow and low-head type and have a high specific speed. On the other hand, purely radial pumps are of high head and low flow rate capability and have a low specific speed. Obviously, a pump with a moderate flow and head has an average specific speed. A typical pump selection chart such as shown in Fig. 10-36 calculates the specific speed for given flow, head, and speed requirements. Based on the calculated specific speed, the optimal pump design is indicated. Process Pumps This term is usually applied to single-stage pedestalmounted units with single-suction overhung impellers and with a single packing box. These pumps are ruggedly designed for ease in dismantling and accessibility, with mechanical seals or packing arrangements, and are built specially to handle corrosive or otherwise difficult-to-handle liquids. Specifically, but not exclusively for the chemical industry, most pump manufacturers now build to national standards horizontal and vertical process pumps. ASME Standards B73.1–2001 and B73.2–2003 apply to the horizontal (Fig. 10-37) and vertical in-line (Fig. 10-38) pumps, respectively. The horizontal pumps are available for capacities up to 900 m3/h (4000 gal/min); the vertical in-line pumps, for capacities up to 320 m3/h (1400 gal/min). Both horizontal and vertical in-line pumps are available for heads up to 120 m (400 ft). The intent of each ANSI specification is that pumps from all vendors for a given nominal capacity and total dynamic head at a given rotative speed shall be dimensionally interchangeable with respect to mounting, size, and location of suction and discharge nozzles, input shaft, baseplate, and foundation bolts. The vertical in-line pumps, although relatively new additions, are finding considerable use in chemical and petrochemical plants in the United States. An inspection of the two designs will make clear the relative advantages and disadvantages of each. Chemical pumps are available in a variety of materials. Metal pumps are the most widely used. Although they may be obtained in iron, bronze, and iron with bronze fittings, an increasing number of pumps of ductile-iron, steel, and nickel alloys are being used. Pumps are also available in glass, glass-lined iron, carbon, rubber, rubber-lined metal, ceramics, and a variety of plastics, such units usually being employed for special purposes. Sealing the Centrifugal Chemical Pump Engineers who specify an appropriate mechanical sealing system on their pumps can significantly improve the energy efficiency of a manufacturing plant as it is estimated that around 10 percent of electric power is used for pumping equipment. Regulatory bodies and engineers are focused on improving the energy efficiency of pumps and pumping systems. Choosing the right mechanical seal is one of the most effective ways of doing this. The purpose of a mechanical seal is to seal the process fluid—whether it is toxic or expensive, the objective is to keep it within the system and pipework to avoid its seeping out and resulting in a cost for lost process fluid and cleanup. Seals not only prevent process fluid contamination and leakage to the external atmosphere but are an important part of conserving energy within the system. Mechanical seals on pumps are probably the most delicate components, and using seal flush plans to change the environment that the seals operate in and flourish enables them to provide reliable operation. Flush plans are formalized by the American Petroleum Institute in its Standard API-682, where they are detailed in standardized formats. Current practice demands that packing boxes be designed to accommodate both packing and mechanical seals. With either type of seal, one consideration is of paramount importance in chemical service: the liquid present at the sealing surfaces must be free of solids. Consequently, it is necessary to provide a secondary compatible liquid to flush the seal or packing whenever the process liquid is not absolutely clean. The use of packing seals requires the continuous escape of liquid past the seal to minimize and to carry away the frictional heat developed. If the effluent is toxic or corrosive, quench glands or catch pans are usually employed. Although packing can be adjusted with the pump operating, leaking mechanical seals require shutting down the pump to correct the leak. Properly applied and maintained mechanical seals usually show no visible

TRANSPORT AND STORAGE OF FLUIDS

800

3500 16

15

600

12

400

13

11

14 5 8

7

Selection and curves

6

200

10

Feet

9 100 80

1

2

4 3

60 40

20

20

200

60 80 100

40

400

600 800 1000

2000

GPM Range Pump No. 1.5 × 6 E 731 Plus 1 3 × 1.5 × 6 731 Plus 2 3×2×6 731 Plus 3 4×3×6 731 Plus 4 1.5 × 1 × 8 731 Plus 5 3 × 1.5 × 8 731 Plus 6 3 × 1.5 × 8.5 E 731 Plus 7 8 3 × 2 × 8.5 E 731 Plus

Range Pump No. 4 × 3 × 8.5 731 Plus 9 6 × 4 × 8.5 731 Plus 10 2 × 1 × 10 E 731 Plus 11 3 × 1.5 × 11 E 731 Plus 12 3 × 2 × 11 731 Plus 13 4 × 3 × 11 731 Plus 14 3 × 1.5 × 13 E 731 Plus 15 3 × 2 × 13 731 Plus 16

Curve A-8475 A-6982 A-8159 A-8551 A-8153 A-8155 A-8529 A-8506

Curve A-8969 A-8547 A-8496 A-8543 A-8456 A-7342 A-8492 A-7338

FIG. 10-30 Performance curves for a range of open impeller pumps.

Pump 1.5 × 1 × 6 E 731 Plus

Curve A-8475-1

175

6.0′′

Total head in feet

150

45

50

5.0′′

100

4.5′′

75

4.0′′

Speed 3525 RPM

55

58

61

63

Max. Inlet sphere 0.28′′ area

63

2.7σ

65 68

55 50 B

3.5′′

50

Impeller data Imp. No. of P-3708 6 no. vanes Max. dia. 6.0′′ Min. dia. 3.5′′

5.5′′

125

A

C

25

E

F

3.0 4.0

10

6.0

8.0

10.0

D

NPSI Req’d (ft)

A BHP

10-30

B

5

C F

0

0

20

40

60

E

D

100 120 80 U.S. gallons per minute

140

160

FIG. 10-31 Typical pump performance curve. The curve is shown for water at 85°F. If the specific gravity of the fluid is other than unity, BHP must be corrected.

PUMPS AND COMPRESSORS The Affinity Laws Constant impeller diameter Q1 N 1 = Q2 N 2

Capacity

Pump head capacity cur ve

Constant impeller speed Q1 D1 = Q2 D2

2

2

Head

H1 ( N1 ) = H 2 ( N 2 )2

h1 ( D1 ) = h2 ( D2 )2

Brake horsepower

BHP1 ( N 1 )3 = BHP2 ( N 2 )3

BHP1 ( P1 )3 = BHP2 ( P2 )3

Head

TABLE 10-13

10-31

Valve partially closed Valve open 2

m Syste

head

e curv

1

S1 Q1

Q2

Frictional resistance

Total static head

Capacity Typical steady-state response of a pump system with a valve fully and partially open.

FIG. 10-34

A

B

ys te m

fric tio n

Total head, feet

Flow

S

Capacity, GPM FIG. 10-32

Variation of total head versus flow rate to overcome friction.

B

A

cu rve

ad he

Total head, feet

Flow

S

te ys

m

System friction TABLE 10-14 Specific Speeds of Different Types of Pumps

Static difference Variation of total head as a function of flow rate to overcome both friction and static head.

FIG. 10-33

leakage. In general, owing to the more effective performance of mechanical seals, they have gained almost universal acceptance. Double-Suction, Single-Stage Pumps These pumps are used for general water supply and circulating service and for chemical service when liquids that are noncorrosive to iron or bronze are being handled. They are available for capacities from about 5.7 m3/h (25 gal/min) up to as high as 1.136 × 104 m3/h (50,000 gal/min) and heads up to 304 m (1000 ft). Such units are available in iron, bronze, and iron with bronze fittings. Other materials increase the cost; when they are required, a standard chemical pump is usually more economical. Close-Coupled Pumps Pumps equipped with a built-in electric motor or sometimes steam-turbine-driven (i.e., with pump impeller and driver on the same shaft) are known as close-coupled pumps (Fig. 10-39). Such units are extremely compact and are suitable for a variety of services for which standard iron and bronze materials are satisfactory. They are available in capacities up to about 450 m3/h (2000 gal/min) for heads up to about 73 m (240 ft). Two-stage units in the smaller sizes are available for heads to around 150 m (500 ft). Canned-Motor Pumps These pumps (Fig. 10-40) command considerable attention in the chemical industry. They are close-coupled units in which the cavity housing the motor rotor and the pump casing are interconnected. As a result, the motor bearings run in the process liquid, and all seals are eliminated. Because the process liquid is the bearing lubricant, abrasive solids cannot be tolerated. Standard single-stage canned-motor pumps are available for flows up to 160 m3/h (700 gal/min) and heads up to 76 m (250 ft). Two-stage units are available for heads up to 183 m (600 ft). Canned-motor pumps are being widely used for handling organic solvents, organic heattransfer liquids, and light oils as well as many clean toxic or hazardous liquids or for installations in which leakage is an economic problem. Vertical Pumps In the chemical industry, the term vertical process pump (Fig. 10-41) generally applies to a pump with a vertical shaft having a length from drive end to impeller of approximately 1 m (3.1 ft) minimum to 20 m (66 ft) or more. Vertical pumps are used as either wet-pit pumps (immersed) or dry-pit pumps (externally mounted) in conjunction with stationary or mobile tanks containing difficult-to-handle liquids. They have the following advantages: the liquid level is above the impeller, and the pump is thus self-priming; and the shaft seal is above the liquid level and is not wetted by the pumped liquid, which simplifies the sealing task. When no bottom connections are permitted on the tank (a safety consideration for highly corrosive or toxic liquid), the vertical wet-pit pump may be the only logical choice. These pumps have the following disadvantages: intermediate or line bearings are generally required when the shaft length exceeds about 3 m (10 ft) in order to avoid shaft resonance problems; these bearings must be lubricated whenever the shaft is rotating. Since all wetted parts must be corrosion-resistant, low-cost materials may not be suitable for the shaft, column, etc. Maintenance is costlier since the pumps are larger and more difficult to handle.

Pump type Below 2000 2000–5000 4000–10,000 9000–15,000

Specific speed range Process pumps and feed pumps Turbine pumps Mixed-flow pumps Axial-flow pumps

10-32

TRANSPORT AND STORAGE OF FLUIDS

20000

15000

9000 10000

8000

7000

6000

5000

4000

3000

2000

1500

1000

900

800

700

600

500

Values of specific speed, Ns

D2 D2 Radial-vane area D2 >2 D1

Francis-flow area

Mixed-flow area

Axial-flow area

D2 = 1.5 to 2 D1

D2 < 1.5 D1

D2 0.385. Calculation of pressure design thickness for straight pipe requires special consideration of factors such as theory of failure, effects of fatigue, and thermal stress. For flanges of nonstandard dimensions or for sizes beyond the scope of the approved standards, design shall be in accordance with the requirements of the ASME Boiler and Pressure Vessel Code, Sec. VIII, except that requirements for fabrication, assembly, inspection testing, and the pressure and temperature limits for materials of the Piping Code are to prevail. Countermoment flanges of flat face or otherwise providing a reaction outside the bolt circle are permitted if designed or tested in accordance with code requirements under pressure-containing components “not covered by standards and for which design formulas or procedures are not given.” Test Conditions The shell pressure test for flanged fittings shall be at a pressure no less than 1.5 times the 38°C (100°F) pressure rating rounded off to the next higher 1-bar (25 psi) increment. In accordance with listed standards, blind flanges may be used at their pressure-temperature ratings. The minimum thickness of nonstandard blind flanges shall be the same as for a bolted flat cover, in accordance with the rules of the ASME Boiler and Pressure Vessel Code, Sec. VIII. Operational blanks shall be of the same thickness as blind flanges or may be calculated by the following formula (use consistent units): t = d 3 P /16 SE + C

(10-94)

where d = inside diameter of gasket for raised- or flat (plain)-face flanges, or gasket pitch diameter for retained gasketed flanges P = internal design pressure or external design pressure S = applicable allowable stress E = quality factor C = sum of the mechanical allowances

Valves must comply with the applicable standards listed in Table 326.1 and App. E of the code and with the allowable pressure-temperature limits established thereby but not beyond the code-established service or materials limitations. Special valves must meet the same requirements as for countermoment flanges. The code contains no specific rules for the design of fittings other than as branch openings. Ratings established by recognized standards are acceptable, however. ASME Standard B16.5 for steel-flanged fittings incorporates a 1.5 shape factor and thus requires the entire fitting to be 50 percent heavier than a simple cylinder in order to provide reinforcement for openings and/or general shape. ASME B16.9 for butt-welded fittings, on the other hand, requires only that the fittings be able to withstand the calculated bursting strength of the straight pipe with which they are to be used. The thickness of pipe bends shall be determined as for straight pipe, provided the bending operation does not result in a difference between maximum and minimum diameters greater than 8 and 3 percent of the nominal outside diameter of the pipe for internal and external pressure, respectively. The maximum allowable internal pressure for multiple miter bends shall be the lesser value calculated from Eqs. (10-95) and (10-96). These equations are not applicable when θ exceeds 22.5°. Pm =

SEW (T − C ) T −C = r2 (T − C ) + 0.643 tanθ r2 (T − C )

(10-95)

Pm =

SEW (T − C ) R −r = 1 2 R1 − 0.5 r2 r2

(10-96)

where the nomenclature is the same as for straight pipe except as follows (see Fig. 10-159): S = stress value for material C = sum of mechanical allowances r2 = mean radius of pipe R1 = effective radius of miter bend, defined as the shortest distance from the pipe centerline to the intersection of the planes of adjacent miter joints θ = angle of miter cut α = angle of change in direction at miter joint = 2θ T = pipe wall thickness W = weld joint strength reduction factor E = quality factor

10-98

TRANSPORT AND STORAGE OF FLUIDS

No.

Type of joint

Type of seam

Examination

Factor, Ej

1

Furnace butt weld, continuous weld

Straight

As required by listed specification

0.60 [Note (1)]

2

Electric resistance weld

Straight or spiral

As required by listed specification

0.85 [Note (1)]

3

Electric fusion weld Straight or spiral

As required by listed specification or this Code

0.80

Additionally spot radiographed per para. 341.5.1 ASME B31.3

0.90

Additionally 100% radiographed per para. 344.5.1 and Table 341.3.2 ASME B31.3

1.00

As required by listed specification or this Code

0.85

Additionally Spot radiographed per para. 341.5.1 ASME B31.3

0.90

Additionally 100% radiographed per para. 344.5.1 and Table 341.3.2 ASME B31.3

1.00

As required by specification

0.95

Additionally 100% radiographed in accordance with para. 344.5.1 and Table 341.3.2 ASME B31.3

1.00

(a) Single butt weld

(with or without filler metal)

Straight or spiral [except as provided in 4 below]

(b) Double butt weld

(with or without filler metal)

4

Per specific specification API 5L

Straight (with one or two seams) or spiral

Submerged arc weld (SAW) Gas metal arc weld (GMAW) Combined GMAW, SAM

FIG. 10-158 Longitudinal weld joint quality factor Ej. [note (1): It is not permitted to increase the joint quality factor by additional examination for joint 1 or 2 .] (Reproduced from ASME B31.3 with permission of the publisher, the American Society of Mechanical Engineers, New York. All rights reserved.)

TABLE 10-43

Values of Coefficient Y for t < D/6 Temperature, °C (°F)

Material Ferritic steels Austenitic steels Nickel alloys UNS Nos . N06617, N08800, N08810, and N08825 Gray iron Other ductile metals

482 (900) and below

510 (950)

538 (1000)

566 (1050)

593 (1100)

621 (1150)

649 (1200)

677 (1250) and above

0 .4 0 .4 0 .4

0 .5 0 .4 0 .4

0 .7 0 .4 0 .4

0 .7 0 .4 0 .4

0 .7 0 .5 0 .4

0 .7 0 .7 0 .4

0 .7 0 .7 0 .5

0 .7 0 .7 0 .7

0 .0 0 .4

. . . 0 .4

. . . 0 .4

. . . 0 .4

. . . 0 .4

. . . 0 .4

. . . 0 .4

. . . 0 .4

PROCESS PLANT PIPING

10-99

FIG. 10-159 Nomenclature for miter bends. (Extracted from the Process Piping Code, ASME B31.3-2014, with permission of the publisher, the American Society of Mechanical Engineers, New York. All rights reserved.)

For compliance with the code, the value of R1 shall not be less than that given by Eq. (10-97): (10-97)

R1 = A/tan θ + D/2 where A has the following empirical values: t, in

A

t ≤ 0.5 0.5 < t < 0.88 t ≥ 0.88

1.0 2(T - C) [2(T - C)/3] + 1.17

Piping branch connections involve the same considerations as pressurevessel nozzles. However, outlet size in proportion to piping header size is unavoidably much greater for piping. The current Piping Code rules for calculation of branch-connection reinforcement are similar to those of the ASME Boiler and Pressure Vessel Code, Sec. VIII, Division I-2014 for a branch with axis at right angles to the header axis. If the branch connection makes an angle β with the header axis from 45 to 90°, the Piping Code requires that the area to be replaced be increased by dividing it by sin b. In such cases the half width of the reinforcing zone measured along the header axis is similarly increased, except that it may not exceed the outside diameter of the header. Some details of commonly used reinforced branch connections are given in Fig. 10-160. The rules provide that a branch connection has adequate strength for pressure if a fitting (tee, lateral, or cross) is in accordance with an approved standard and is used within the pressure-temperature limitations or if the connection is made by welding a coupling or half coupling (wall thickness not less than the branch anywhere in reinforcement zone or less than extra heavy or 3000 lb) to the run and provided the ratio of branch to run diameters is not greater than one-fourth and that the branch is not greater than 2 in nominal diameter. Dimensions of extra-heavy couplings are given in the Steel Products Manual published by the American Iron and Steel Institute. In ASME B16.11-2014, 2000-lb couplings were superseded by 3000-lb couplings. ASME B31.3 states that the reinforcement area for resistance to external pressure is to be at least one-half of that required to resist internal pressure. The code provides no guidance for analysis but requires that external and internal attachments be designed to avoid flattening of the pipe, excessive localized bending stresses, or harmful thermal gradients, with further emphasis on minimizing stress concentrations in cyclic service. The code provides design requirements for closures which are flat, ellipsoidal, spherically dished, hemispherical, conical (without transition knuckles),

Types of reinforcement for branch connections. (From Kellogg, Design of Piping Systems, Wiley, New York, 1965.)

FIG. 10-160

conical convex to pressure, toriconical concave to pressure, and toriconical convex to pressure. Openings in closures over 50 percent in diameter are designed as flanges in flat closures and as reducers in other closures. Openings of not over onehalf of the diameter are to be reinforced as branch connections. Thermal Expansion and Flexibility: Metallic Piping ASME B31.3 requires that piping systems have sufficient flexibility to prevent thermal expansion or contraction or the movement of piping supports or terminals from causing (1) failure of piping supports from overstress or fatigue; (2) leakage at joints; or (3) detrimental stresses or distortions in piping or in connected equipment (pumps, turbines, or valves, for example), resulting from excessive thrusts or movements in the piping. To ensure that a system meets these requirements, the computed displacement–stress range SE shall not exceed the allowable stress range SA [Eqs. (10-91) and (10-92)], the reaction forces Rm [Eq. (10-104)] shall not be detrimental to supports or connected equipment, and movement of the piping shall be within any prescribed limits. Displacement Strains Strains result from piping being displaced from its unrestrained position: 1. Thermal displacements. A piping system will undergo dimensional changes with any change in temperature. If it is constrained from free movement by terminals, guides, and anchors, then it will be displaced from its unrestrained position. 2. Reaction displacements. If the restraints are not considered rigid and there is a predictable movement of the restraint under load, this may be treated as a compensating displacement. 3. Externally imposed displacements. Externally caused movement of restraints will impose displacements on the piping in addition to those related to thermal effects. Such movements may result from causes such as wind sway or temperature changes in connected equipment. Total Displacement Strains Thermal displacements, reaction displacements, and externally imposed displacements all have equivalent effects on the piping system and must be considered together in determining the total displacement strains in a piping system.

10-100

TRANSPORT AND STORAGE OF FLUIDS

Expansion strains may be taken up in three ways: by bending, by torsion, or by axial compression. In the first two cases, maximum stress occurs at the extreme fibers of the cross section at the critical location. In the third case, the entire cross-sectional area over the entire length for practical purposes is equally stressed. Bending or torsional flexibility may be provided by bends, loops, or offsets; by corrugated pipe or expansion joints of the bellows type; or by other devices permitting rotational movement. These devices must be anchored or otherwise suitably connected to resist end forces from fluid pressure, frictional resistance to pipe movement, and other causes. Axial flexibility may be provided by expansion joints of the slip-joint or bellows types, suitably anchored and guided to resist end forces from fluid pressure, frictional resistance to movement, and other causes. Displacement Stresses Stresses may be considered proportional to the total displacement strain only if the strains are well distributed and not excessive at any point. The methods outlined here and in the code are applicable only to such a system. Poor distribution of strains (unbalanced systems) may result from the following: 1. Highly stressed small-size pipe runs in series with large and relatively stiff pipe runs 2. Local reduction in size or wall thickness or local use of a material having reduced yield strength ( for example, girth welds of substantially lower strength than the base metal) 3. A line configuration in a system of uniform size in which expansion or contraction must be absorbed largely in a short offset from the major portion of the run If unbalanced layouts cannot be avoided, appropriate analytical methods must be applied to ensure adequate flexibility. If the designer determines that a piping system does not have adequate inherent flexibility, additional flexibility may be provided by adding bends, loops, offsets, swivel joints, corrugated pipe, expansion joints of the bellows or slip-joint type, or other devices. Suitable anchoring must be provided. As contrasted with stress from sustained loads such as internal pressure or weight, displacement stresses may be permitted to cause limited overstrain in various portions of a piping system. When the system is operated initially at its greatest displacement condition, any yielding reduces stress. When the system is returned to its original condition, there occurs a redistribution of stresses which is referred to as self-springing. It is similar to cold springing in its effects. Stresses resulting from thermal strain tend to diminish with time. However, the algebraic difference in displacement condition and in either the original (as-installed) condition or any anticipated condition with a greater opposite effect than the extreme displacement condition remains substantially constant during any one cycle of operation. This difference is defined as the displacement-stress range, and it is a determining factor in the design of piping for flexibility. See Eqs. (10-91) and (10-92) for the allowable stress range S A and Eq. (10-99) for the computed stress range SE. Cold Spring The intentional deformation of piping during assembly to produce a desired initial displacement and stress is called cold spring. For pipe operating at a temperature higher than that at which it was installed, cold spring is accomplished by fabricating it slightly shorter than design length. Cold spring is beneficial in that it serves to balance the magnitude of stress under initial and extreme displacement conditions. When cold spring is properly applied, there is less likelihood of overstrain during initial operation; hence, it is recommended especially for piping materials of limited ductility. There is also less deviation from as-installed dimensions during initial operation, so that hangers will not be displaced as far from their original settings. Inasmuch as the service life of a system is affected more by the range of stress variation than by the magnitude of stress at a given time, no credit for cold spring is permitted in stress-range calculations. However, in calculating the thrusts and moments when actual reactions as well as their range of variations are significant, credit is given for cold spring. Values of thermal expansion coefficients to be used in determining total displacement strains for computing the stress range are determined from Table 10-44 as the algebraic difference between the value at the design maximum temperature and that at the design minimum temperature for the thermal cycle under analysis. Values for Reactions Values of thermal displacements to be used in determining total displacement strains for the computation of reactions on supports and connected equipment shall be determined as the algebraic difference between the value at design maximum (or minimum) temperature for the thermal cycle under analysis and the value at the temperature expected during installation. The as-installed and maximum or minimum moduli of elasticity Ea and Em, respectively, shall be taken as the values shown in Table 10-45. Poisson’s ratio may be taken as 0.3 at all temperatures for all metals. The allowable stress range for displacement stresses SA and permissible additive stresses shall be as specified in Eqs. (10-91) and (10-92) for systems

primarily stressed in bending and/or torsion. For pipe or piping components containing longitudinal welds, the basic allowable stress S may be used to determine SA. Nominal thicknesses and outside diameters of pipe and fittings shall be used in flexibility calculations. In the absence of more directly applicable data, the flexibility factor k and stress intensification factor i shown in Table 10-46 may be used in flexibility calculations in Eq. (10-100). For piping components or attachments (such as valves, strainers, anchor rings, and bands) not covered in the table, suitable stress intensification factors may be assumed by comparison of their significant geometry with that of the components shown. Requirements for Analysis No formal analysis of adequate flexibility is required in systems which (1) are duplicates of successfully operating installations or replacements without significant change of systems with a satisfactory service record; (2) can readily be judged adequate by comparison with previously analyzed systems; or (3) are of uniform size, have no more than two points of fixation, have no intermediate restraints, and fall within the limitations of empirical Eq. (10-98)∗ Dy ≤ K1 ( L − U )2

(10-98)

where D = outside diameter of pipe, in (mm) y = resultant of total displacement strains, in (mm), to be absorbed by the piping system L = developed length of piping between anchors, ft (m) U = anchor distance, straight line between anchors, ft (m) K1 = 208,000 SA/Ear, (mm/m)2 = 30 SA/Ear (in/ft)2 = 208.0 for SI units listed in parentheses 1. All systems not meeting these criteria shall be analyzed by simplified, approximate, or comprehensive methods of analysis appropriate for the specific case. 2. Approximate or simplified methods may be applied only if they are used in the range of configurations for which their adequacy has been demonstrated. 3. Acceptable comprehensive methods of analysis include analytical and chart methods that provide an evaluation of the forces, moments, and stresses caused by displacement strains. 4. Comprehensive analysis shall take into account stress-intensification factors for any component other than straight pipe. Credit may be taken for the extra flexibility of such a component. In calculating the flexibility of a piping system between anchor points, the system shall be treated as a whole. The significance of all parts of the line and of all restraints introduced for the purpose of reducing moments and forces on equipment or small branch lines and also the restraint introduced by support friction shall be recognized. Consider all displacements over the temperature range defined by the operating and shutdown conditions. Flexibility Stresses Bending and torsional stresses shall be computed using the as-installed modulus of elasticity Ea and then combined in accordance with Eq. (10-99) to determine the computed displacement stress range SE, which shall not exceed the allowable stress range SA [Eqs. (10-91) and (10-92)]: SE =

Sb2 + 4 St2

(10-99)

where Sa = axial stress range due to displacement strains = iaFa/Ap Ap = cross-sectional area of pipe; nominal thickness and outside diameters of pipe Fa = axial force range between any two conditions being evaluated ia = axial stress intensification factor it = torsional stress intensification factor Sb = resultant bending stress, lbf/in2 (MPa) St = Mt/2Z = torsional stress, lbf/in2 (MPa) Mt = torsional moment, in ⋅ lbf (N ⋅ mm) Z = section modulus of pipe, in3 (mm3)

∗Warning: No general proof can be offered that this equation will yield accurate or

consistently conservative results. It is not applicable to systems used under severe cyclic conditions. It should be used with caution in configurations such as unequal leg U bends (L/U > 2.5) or near-straight sawtooth runs, or for large thin-wall pipe (i ≥ 5), or when extraneous displacements (not in the direction connecting anchor points) constitute a large part of the total displacement. There is no assurance that terminal reactions will be acceptably low even if a piping system falls within the limitations of Eq. (10-98).

TABLE 10-44

Thermal Coefficients, USCS Units, for Metals

Mean coefficient of linear thermal expansion between 70°F and indicated temperature, µin/(in ⋅ °F) Material

Temp., °F

Carbon steel carbon–moly– low–chrome (through 3Cr–Mo)

-450 -425 -400 -375 -350 -325 -300 -275 -250 -225 -200 -175 -150 -125 -100 -75 -50 -25 0 25 50 70 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600 625 650 675 700 725 750 775 800 825

... ... ... ... ... 5.00 5.07 5.14 5.21 5.28 5.35 5.42 5.50 5.57 5.65 5.72 5.80 5.85 5.90 5.96 6.01 6.07 6.13 6.19 6.25 6.31 6.38 6.43 6.49 6.54 6.60 6.65 6.71 6.76 6.82 6.87 6.92 6.97 7.02 7.07 7.12 7.17 7.23 7.28 7.33 7.38 7.44 7.49 7.54 7.59 7.65 7.70

5Cr–Mo through 9Cr–Mo ... ... ... ... ... 4.70 4.77 4.84 4.91 4.98 5.05 5.12 5.20 5.26 5.32 5.38 5.45 5.51 5.56 5.62 5.67 5.73 5.79 5.85 5.92 5.98 6.04 6.08 6.12 6.15 6.19 6.23 6.27 6.30 6.34 6.38 6.42 6.46 6.50 6.54 6.58 6.62 6.66 6.70 6.73 6.77 6.80 6.84 6.88 6.92 6.96 7.00

Austenitic stainless steels 18Cr–8Ni

12Cr 17Cr 27Cr

... ... ... ... ... 8.15 8.21 8.28 8.34 8.41 8.47 8.54 8.60 8.66 8.75 8.83 8.90 8.94 8.98 9.03 9.07 9.11 9.16 9.20 9.25 9.29 9.34 9.37 9.41 9.44 9.47 9.50 9.53 9.56 9.59 9.62 9.65 9.67 9.70 9.73 9.76 9.79 9.82 9.85 9.87 9.90 9.92 9.95 9.99 10.02 10.05 10.08

... ... ... ... ... 4.30 4.36 4.41 4.47 4.53 4.59 4.64 4.70 4.78 4.85 4.93 5.00 5.05 5.10 5.14 5.19 5.24 5.29 5.34 5.40 5.45 5.50 5.54 5.58 5.62 5.66 5.70 5.74 5.77 5.81 5.85 5.89 5.92 5.96 6.00 6.05 6.09 6.13 6.17 6.20 6.23 6.26 6.29 6.33 6.36 6.39 6.42

25Cr–20Ni

UNS N04400 Monel 67Ni–30Cu

3½Ni

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 8.79 8.81 8.83 8.85 8.87 8.89 8.90 8.91 8.92 8.92 8.92 8.92 8.93 8.93 8.93 8.93 8.94 8.94 8.95 8.95 8.96 8.96 8.96 8.96 8.97 8.97

... ... ... ... ... 5.55 5.72 5.89 6.06 6.23 6.40 6.57 6.75 6.85 6.95 7.05 7.15 7.22 7.28 7.35 7.41 7.48 7.55 7.62 7.70 7.77 7.84 7.89 7.93 7.98 8.02 8.07 8.11 8.16 8.20 8.25 8.30 8.35 8.40 8.45 8.49 8.54 8.58 8.63 8.68 8.73 8.78 8.83 8.87 8.92 8.96 9.01

... ... ... ... ... 4.76 4.90 5.01 5.15 5.30 5.45 5.52 5.59 5.67 5.78 5.83 5.88 5.94 6.00 6.08 6.16 6.25 6.33 6.36 6.39 6.42 6.45 6.50 6.55 6.60 6.65 6.69 6.73 6.77 6.80 6.83 6.86 6.89 6.93 6.97 7.01 7.04 7.08 7.12 7.16 7.19 7.22 7.25 7.29 7.31 7.34 7.37

Copper and copper alloys 6.30 6.61 6.93 7.24 7.51 7.74 7.94 8.11 8.26 8.40 8.51 8.62 8.72 8.81 8.89 8.97 9.04 9.11 9.17 9.23 9.28 9.32 9.39 9.43 9.48 9.52 9.56 9.60 9.64 9.68 9.71 9.74 9.78 9.81 9.84 9.86 9.89 9.92 9.94 9.97 9.99 10.1 10.04 ... ... ... ... ... ... ... ... ...

Aluminum

Gray cast iron

Bronze

Brass

... ... ... ... ... 9.90 10.04 10.18 10.33 10.47 10.61 10.76 10.90 11.08 11.25 11.43 11.60 11.73 11.86 11.99 12.12 12.25 12.39 12.53 12.67 12.81 12.95 13.03 13.12 13.20 13.28 13.36 13.44 13.52 13.60 13.68 13.75 13.83 13.90 13.98 14.05 14.13 14.20 ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 5.75 5.80 5.84 5.89 5.93 5.97 6.02 6.06 6.10 6.15 6.19 6.24 6.28 6.33 6.38 6.42 6.47 6.52 6.56 6.61 6.65 6.70 6.74 6.79 6.83 6.87

... ... ... ... ... 8.40 8.45 8.50 8.55 8.60 8.65 8.70 8.75 8.85 8.95 9.05 9.15 9.23 9.32 9.40 9.49 9.57 9.66 9.75 9.85 9.93 10.03 10.05 10.08 10.10 10.12 10.15 10.18 10.20 10.23 10.25 10.28 10.30 10.32 10.35 10.38 10.41 10.44 10.46 10.48 10.50 10.52 10.55 10.57 10.60 10.62 10.65

... ... ... ... ... 8.20 8.24 8.29 8.33 8.37 8.41 8.46 8.50 8.61 8.73 8.84 8.95 9.03 9.11 9.18 9.26 9.34 9.42 9.51 9.59 9.68 9.76 9.82 9.88 9.94 10.00 10.06 10.11 10.17 10.23 10.29 10.35 10.41 10.47 10.53 10.58 10.64 10.69 10.75 10.81 10.86 10.92 10.98 11.04 11.10 11.16 11.22

70Cu–30Ni ... ... ... ... ... 6.65 6.76 6.86 6.97 7.08 7.19 7.29 7.40 7.50 7.60 7.70 7.80 7.87 7.94 8.02 8.09 8.16 8.24 8.31 8.39 8.46 8.54 8.58 8.63 8.67 8.71 8.76 8.81 8.85 8.90 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

UNS N08XXX series Ni–Fe–Cr ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 7.90 8.01 8.12 8.24 8.35 8.46 8.57 8.69 8.80 8.82 8.85 8.87 8.90 8.92 8.95 8.97 9.00 9.02 9.05 9.07 9.10 9.12 9.15 9.17 9.20 9.22

UNS N06XXX series Ni–Cr–Fe ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 7.13 7.20 7.25 7.30 7.35 7.40 7.44 7.48 7.52 7.56 7.60 7.63 7.67 7.70 7.72 7.75 7.77 7.80 7.82 7.85 7.88 7.90 7.92 7.95 7.98 8.00 8.02 8.05 8.08 8.10 ...

Ductile iron ... ... ... ... ... ... ... ... ... ... 4.65 4.76 4.87 4.98 5.10 5.20 5.30 5.40 5.50 5.58 5.66 5.74 5.82 5.87 5.92 5.97 6.02 6.08 6.14 6.20 6.25 6.31 6.37 6.43 6.48 6.57 6.66 6.75 6.85 6.88 6.92 6.95 6.98 7.02 7.04 7.08 7.11 7.14 7.18 7.22 7.25 7.27

10-101

10-102

TABLE 10-44 Thermal Coefficients, USCS Units, for Metals (Continued ) Mean coefficient of linear thermal expansion between 70°F and indicated temperature, µin/(in ⋅ °F) Material

Temp., °F

Carbon steel carbon–moly– low–chrome (through 3Cr–Mo)

850 875 900 925 950 975 1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400 1425 1450 1475 1500

7.75 7.79 7.84 7.87 7.91 7.94 7.97 8.01 8.05 8.08 8.12 8.14 8.16 8.17 8.19 8.21 8.24 8.26 8.28 8.30 8.32 8.34 8.36 ... ... ... ...

5Cr–Mo through 9Cr–Mo 7.03 7.07 7.10 7.13 7.16 7.19 7.22 7.25 7.27 7.30 7.32 7.34 7.37 7.39 7.41 7.43 7.45 7.47 7.49 7.51 7.52 7.54 7.55 ... ... ... ...

Austenitic stainless steels 18Cr–8Ni

12Cr 17Cr 27Cr

10.11 10.13 10.16 10.19 10.23 10.26 10.29 10.32 10.34 10.37 10.39 10.41 10.44 10.46 10.48 10.50 10.51 10.53 10.54 10.56 10.57 10.59 10.60 10.64 10.68 10.72 10.77

6.46 6.49 6.52 6.55 6.58 6.60 6.63 6.65 6.68 6.70 6.72 6.74 6.75 6.77 6.78 6.80 6.82 6.83 6.85 6.86 6.88 6.89 6.90 ... ... ... ...

25Cr–20Ni

UNS N04400 Monel 67Ni–30Cu

3½Ni

Copper and copper alloys

8.98 8.99 9.00 9.05 9.10 9.15 9.18 9.20 9.22 9.24 9.25 9.29 9.33 9.36 9.39 9.43 9.47 9.50 9.53 9.53 9.54 9.55 9.56 ... ... ... ...

9.06 9.11 9.16 9.21 9.25 9.30 9.34 9.39 9.43 9.48 9.52 9.57 9.61 9.66 9.70 9.75 9.79 9.84 9.88 9.92 9.96 10.00 10.04 ... ... ... ...

7.40 7.43 7.45 7.47 7.49 7.52 7.55 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

Aluminum

Gray cast iron

Bronze

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

6.92 6.96 7.00 7.05 7.10 7.14 7.19 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

10.67 10.70 10.72 10.74 10.76 10.78 10.80 10.83 10.85 10.88 10.90 10.93 10.95 10.98 11.00 ... ... ... ... ... ... ... ... ... ... ... ...

Brass 11.28 11.34 11.40 11.46 11.52 11.57 11.63 11.69 11.74 11.80 11.85 11.91 11.97 12.03 12.09 ... ... ... ... ... ... ... ... ... ... ... ...

70Cu–30Ni

UNS N08XXX series Ni–Fe–Cr

UNS N06XXX series Ni–Cr–Fe

Ductile iron

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

9.25 9.27 9.30 9.32 9.35 9.37 9.40 9.42 9.45 9.47 9.50 9.52 9.55 9.57 9.60 9.64 9.68 9.71 9.75 9.79 9.83 9.86 9.90 9.94 9.98 10.01 10.05

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

7.31 7.34 7.37 7.41 7.44 7.47 7.50 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

GENERAL NOTE: For Code references to this table, see para. 319.3.1, ASME B31.3. These data are for use in the absence of more applicable data . It is the designer’s responsibility to verify that materials are suitable for the intended service at the temperatures shown . Reprinted from ASME B31 .3, para 319 .1, with permission of the publisher, the American Society of Mechanical Engineers, New York, New York . All rights reserved .

TABLE 10-45 Modulus of Elasticity, USCS Units, for Metals E = modulus of elasticity, Msi (millions of psi), at temperature, °F Material Ferrous Metals Gray cast iron Carbon steels, C ≤ 0.3% Carbon steels, C ≤ 0.3% Carbon-moly steels Nickel steels, Ni 2%–9%

Cr-Mo steels, Cr ½%–2% Cr-Mo steels, Cr 2¼%–3%

Cr-Mo steels, Cr 5%–9% Chromium steels, Cr 12%, 17%, 27% Austenitic steels (TP304, 310, 316, 321, 347)

Copper and Copper Alloys (UNS Nos.) Comp. and leaded Sn-bronze (C83600, C92200) Naval brass, Si- and Al-bronze (C46400, C65500, C95200, C95400) Copper (C11000) Copper, red brass, Al-bronze (C10200, C12000, C12200, C12500, C14200, C23000, C61400) 90Cu 10Ni (C70600) Leaded Ni-bronze 80Cu-20Ni (C71000) 70Cu-30Ni (C71500) Nickel and Nickel Alloys (UNS Nos.) Monel 400 N04400 Alloys N06007, N08320 Alloys N08800, N08810, N06002 Alloys N06455, N10276 Alloys N02200, N02201, N06625 Alloy N06600 Alloy N10001 Alloy N10665 Unalloyed Titanium Grades 1, 2, 3, and 7 Aluminum and Aluminum Alloys (UNS Nos.) Grades 443, 1060, 1100, 3003, 3004, 6061, 6063 (A24430, A91060, A91100, A93003, A93004, A96061, A96063) Grades 5052, 5154, 5454, 5652 (A95052, A95154, A95454, A95652) Grades 356, 5083, 5086, 5456 (A03560, A95083, A95086, A95456)

–425

–400

–350

–325

–200

–100

70

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

... 31.9 31.7 31.7 30.1 32.1 33.1 33.4 31.8 30.8

... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ...

... 31.4 31.2 31.1 29.6 31.6 32.6 32.9 31.2 30.3

... 30.8 30.6 30.5 29.1 31.0 32.0 32.3 30.7 29.7

... 30.2 30.0 29.9 28.5 30.4 31.4 31.7 30.1 29.0

13.4 29.5 29.3 29.2 27.8 29.7 30.6 30.9 29.2 28.3

13.2 28.8 28.6 28.5 27.1 29.0 29.8 30.1 28.5 27.6

12.9 28.3 28.1 28.0 26.7 28.5 29.4 29.7 27.9 27.0

12.6 27.7 27.5 27.4 26.1 27.9 28.8 29.0 27.3 26.5

12.2 27.3 27.1 27.0 25.7 27.5 28.3 28.6 26.7 25.8

11.7 26.7 26.5 26.4 25.2 26.9 27.7 28.0 26.1 25.3

11.0 25.5 25.3 25.3 24.6 26.3 27.1 27.3 25.6 24.8

10.2 24.2 24.0 23.9 23.0 25.5 26.3 26.1 24.7 24.1

... 22.4 22.2 22.2 ... 24.8 25.6 24.7 22.2 23.5

... 20.4 20.2 20.1 ... 23.9 24.6 22.7 21.5 22.8

... 18.0 17.9 17.8 ... 23.0 23.7 20.4 19.1 22.1

... ... 15.4 15.3 ... 21.8 22.5 18.2 16.6 21.2

... ... ... ... ... 20.5 21.1 15.5 ... 20.2

... ... ... ... ... 18.9 19.4 12.7 ... 19.2

... ... ... ... ... ... ... ... ... 18.1

...

...

...

14.8

14.6

14.4

14.0

13.7

13.4

13.2

12.9

12.5

12.0

...

...

...

...

...

...

...

...

...

...

...

15.9

15.6

15.4

15.0

14.6

14.4

14.1

13.8

13.4

12.8

...

...

...

...

...

...

...

...

... ...

... ...

... ...

16.9 18.0

16.6 17.7

16.5 17.5

16.0 17.0

15.6 16.6

15.4 16.3

15.0 16.0

14.7 15.6

14.2 15.1

13.7 14.5

... ...

... ...

... ...

... ...

... ...

... ...

... ...

... ...

... ... ... ...

... ... ... ...

... ... ... ...

19.0 20.1 21.2 23.3

18.7 19.8 20.8 22.9

18.5 19.6 20.6 22.7

18.0 19.0 20.0 22.0

17.6 18.5 19.5 21.5

17.3 18.2 19.2 21.1

16.9 17.9 18.8 20.7

16.6 17.5 18.4 20.2

16.0 16.9 17.8 19.6

15.4 16.2 17.1 18.8

... ... ... ...

... ... ... ...

... ... ... ...

... ... ... ...

... ... ... ...

... ... ... ...

... ... ... ...

... ... ... ...

28.3 30.3 31.1 32.5 32.7 33.8 33.9 34.2

... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ...

27.8 29.5 30.5 31.6 32.1 33.2 33.3 33.3

27.3 29.2 29.9 31.3 31.5 32.6 32.7 33.0

26.8 28.6 29.4 30.6 30.9 31.9 32.0 32.3

26.0 27.8 28.5 29.8 30.0 31.0 31.1 31.4

25.4 27.1 27.8 29.1 29.3 30.2 30.3 30.6

25.0 26.7 27.4 28.6 28.8 29.9 29.9 30.1

24.7 26.4 27.1 28.3 28.5 29.5 29.5 29.8

24.3 26.0 26.6 27.9 28.1 29.0 29.1 29.4

24.1 25.7 26.4 27.6 27.8 28.7 28.8 29.0

23.7 25.3 25.9 27.1 27.3 28.2 28.3 28.6

23.1 24.7 25.4 26.5 26.7 27.6 27.7 27.9

22.6 24.2 24.8 25.9 26.1 27.0 27.1 27.3

22.1 23.6 24.2 25.3 25.5 26.4 26.4 26.7

21.7 23.2 23.8 24.9 25.1 25.9 26.0 26.2

21.2 22.7 23.2 24.3 24.5 25.3 25.3 25.6

... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ...

...

...

...

...

...

...

15.5

15.0

14.6

14.0

13.3

12.6

11.9

11.2

...

...

...

...

...

...

...

11.4

...

...

11.1

10.8

10.5

10.0

9.6

9.2

8.7

11.6

...

...

11.3

11.0

10.7

10.2

9.7

9.4

8.9

11.7

...

...

11.4

11.1

10.8

10.3

9.8

9.5

9.0

10-103

10-104

TRANSPORT AND STORAGE OF FLUIDS

TABLE 10-46

Flexibility Factor, k, and Stress Intensification Factor, i Stress Intensification Factor [Notes (1), (2)] Flexibility factor, k

Out-of-plane, io

In-plane, ii

Flexibility characteristic, h

Welding elbow or pipe bend [Notes (1), (3)–(6)]

1.65 h

0.75 h 2/3

0.9 h 2/3

T R1 r22

Closely spaced miter bend s < r2 (1 + tan θ) [Notes (1), (3), (4), (6)]

1.52 h 5/6

0.9 h 2/3

0.9 h 2/3

cot θ  ST  2  r22 

Single miter bend or widely spaced miter bend s ≥ r2 (1 + tan θ) [Notes (1), (3), (6)]

1.52 h 5/6

0.9 h 2/3

0.9 h 2/3

1 + cot θ  T   r  2 2

Welding tee in accordance with ASME B16.9 [Notes (1), (3), (5), (7), (8)]

1

0.9 h 2/3

3

Reinforced fabricated tee with pad or saddle [Notes (1), (3), (8), (9), (10)]

1

0.9 h 2/3

3

Unreinforced fabricated tee [Notes (1), (3), (8), (10)]

1

0.9 h 2/3

3

Extruded welding tee with rx ≥ 0.05 Db Tc < 1.5 T [Notes (1), (3), (8)]

1

0.9 h 2/3

3

Welded-in contour insert [Notes (1), (3), (7), (8)]

1

0.9 h 2/3

3

Branch welded-on fitting (integrally reinforced) [Notes (1), (3), (10), (11)]

1

Description

0.9 h 2/3

i + 14

4 o

i + 14

4 o

3.1

(T +

T r2

T) T r2 1

2.5

2 r

1.5

i + 14

T r2

i + 14

 1 + rx  T  r  r 2 2

4 o

4 o

i + 14

4 o

0.9 h 2/3

3.1

T r2

3.3

T r2

Sketch

PROCESS PLANT PIPING TABLE 10-46

10-105

Flexibility Factor, k, and Stress Intensification Factor, i (Continued )

Description

Flexibility factor, k

Stress intensification factor, i

1

1.0

1 1 1

1.2 1.3 [Note (12)] 1.6

1

2.3

5

2.5

Butt welded joint, reducer, or weld neck flange Double-welded slip-on flange Fillet or socket weld Lap joint flange (with ASME B16.9 lap joint stub) Threaded pipe joint or threaded flange Corrugated straight pipe, or corrugated or creased bend [Note (13)]

GENERAL NOTE: Stress intensification and flexibility factor data in Table 10-46 are for use in the absence of more directly applicable data (see para . 319 .3 .6) . Their validity has been demonstrated for D /T ≤ 100. NOTES:

(1) The flexibility factor, k, in the Table applies to bending in any plane; also see para . 319 .3 .6 . The flexibility factors, k, and stress intensification factors, i, shall apply over the effective arc length (shown by heavy centerlines in the illustrations) for curved and miter bends, and to the intersection point for tees . (2) A single intensification factor equal to 0 .9/h2/3 may be used for both ii and io if desired . (3) The values of k and i can be read directly from Chart A by entering with the characteristic h computed from the formulas given above . Nomenclature is as follows: Db = outside diameter of branch R1 = bend radius of welding elbow or pipe bend rx = see definition in para . 304 .3 .4(c) r2 = mean radius of matching pipe s = miter spacing at centerline T = for elbows and miter bends, the nominal wall thickness of the fitting = for tees, the nominal wall thickness of the matching pipe Tc = crotch thickness of branch connections measured at the center of the crotch where shown in the illustrations Tr = pad or saddle thickness θ = one-half angle between adjacent miter axes (4) Where flanges are attached to one or both ends, the values of k and i in the Table shall be corrected by the factors C1, which can be read directly from Chart B, entering with the computed h . (5) The designer is cautioned that cast buttwelded fittings may have considerably heavier walls than that of the pipe with which they are used . Large errors may be introduced unless the effect of these greater thicknesses is considered . (6) In large diameter thin-wall elbows and bends, pressure can significantly affect the magnitudes of k and i . To correct values from the Table, divide k by  Pj  r 1 + 6    2   Ej  T 

7/3

 R1   r  2

1/3

divide i by 2/3 5/2 R  Pj  r 1 + 3.25    2   1   E j   T   r2 

For consistency, use kPa and mm for SI metric, and psi and in . for U .S . customary notation . (7) If rx ≥ ⅛ Db and Tc ≥ 1.5T , a flexibility characteristic of 4.4T /r2 may be used . (8) Stress intensification factors for branch connections are based on tests with at least two diameters of straight run pipe on each side of the branch centerline . More closely loaded branches may require special consideration . (9) When Tr is > 1½T , use h = 4T /r2 . (10) The out-of-plane stress intensification factor (SIF) for a reducing branch connection with branch-to-run diameter ratio of 0 .5 < d /D < 1 .0 may be nonconservative . A smooth concave weld contour has been shown to reduce the SIF . Selection of the appropriate SIF is the designer’s responsibility . (11) The designer must be satisfied that this fabrication has a pressure rating equivalent to straight pipe . (12) For welds to socket welded fittings, the stress intensification factor is based on the assumption that the pipe and fitting are matched in accordance with ASME B16 .11 and a fillet weld is made between the pipe and fitting . For welds to socket welded flanges, the stress intensification factor is based on the weld geometry and has been shown to envelope the results of the pipe to socket welded fitting tests . Blending the toe of the fillet weld smoothly into the pipe wall has been shown to improve the fatigue performance of the weld . (13) Factors shown apply to bending . Flexibility factor for torsion equals 0 .9 .

The resultant bending stresses Sb to be used in Eq . (10-99) for elbows and miter bends shall be calculated in accordance with Eq . (10-100), with moments as shown in Fig . 10-161: Sb =

(ii M i )2 + (io M o )2 Ze

where Sb = resultant bending stress, lbf/in2 (MPa) ii = in-plane stress intensification factor from Table 10-46 io = out-plane stress intensification factor from Table 10-46

(10-100)

Mi = in-plane bending moment, in ⋅ lbf (N ⋅ mm) Mo = out-of-plane bending moment, in ⋅ lbf (N ⋅ mm) Z = section modulus of pipe, in3 (mm3) The resultant bending stresses Sb to be used in Eq . (10-99) for branch connections shall be calculated in accordance with Eqs . (10-101) and (10-102), with moments as shown in Fig . 10-162 . For header (legs 1 and 2): Sb =

(ii M i )2 + (io M o )2 Z

(10-101)

10-106

TRANSPORT AND STORAGE OF FLUIDS r2 = mean branch cross-sectional radius, in (mm) Ts = effective branch wall thickness, in (mm) [lesser of Th and (io ) (Tb )] Th = thickness of pipe matching run of tee or header exclusive of reinforcing elements, in (mm) Tb = thickness of pipe matching branch, in (mm) io = out-of-plane stress − intensification factor (Table 10-46) ii = in-plane stress − intensification factor (Table 10-46)

FIG. 10-161 Moments in bends. (Extracted from the Process Piping Code, B31.3-2014, with permission of the publisher, the American Society of Mechanical Engineers, New York. All rights reserved.)

Allowable stress range SA and permissible additive stresses shall be computed in accordance with Eqs. (10-91) and (10-92). Required Weld Quality Assurance Any weld at which SE exceeds 0.8SA for any portion of a piping system, and the equivalent number of cycles N exceeds 7000, shall be fully examined in accordance with the requirements for severe cyclic service (presented later in this section). Reactions: Metallic Piping Reaction forces and moments to be used in the design of restraints and supports and in evaluating the effects of piping displacements on connected equipment shall be based on the reaction range R for the extreme displacement conditions, considering the range previously defined for reactions and using Ea. The designer shall consider instantaneous maximum values of forces and moments in the original and extreme displacement conditions as well as the reaction range in making these evaluations. Maximum Reactions for Simple Systems For two-anchor systems without intermediate restraints, the maximum instantaneous values of reaction forces and moments may be estimated from Eqs. (10-104) and (10-105). 1. For extreme displacement conditions Rm. The temperature for this computation is the design maximum or design minimum temperature as previously defined for reactions, whichever produces the larger reaction:

For branch (leg 3): 2

Sb =

(ii M i ) + (io M o )

2C E Rm = R  1 −  m  3  Ea

2

Ze

(10-102)

where Sb = resultant bending stress, lbf/in2 (MPa) Ze = effective section modulus for branch, in3 (mm3) Ze = πr22Ts

(10-103)

(10-104)

where C = cold-spring factor varying from 0 for no cold spring to 1.0 for 100 percent cold spring. (The factor ⅔ is based on experience, which shows that specified cold spring cannot be fully ensured even with elaborate precautions.) Ea = modulus of elasticity at installation temperature, lbf/in2 (MPa) Em = modulus of elasticity at design maximum or design minimum temperature, lbf/in2 (MPa) R = range of reaction forces or moments (derived from flexibility analysis) corresponding to the full displacement-stress range and based on reaction force, Ea, lbf or on moment in ⋅ lbf (N or N ⋅ mm) Rm = estimated instantaneous maximum reaction force or moment at design maximum or design minimum temperature, reaction force lbf or moment in ⋅ lbf (N or N ⋅ mm) 2. For original condition Ra. The temperature for this computation is the expected temperature at which the piping is to be assembled. Ra = CR

or

C1R

whichever is greater

(10-105)

where nomenclature is as for Eq. (10-104) and

FIG. 10-162 Moments in branch connections. (Extracted from the Process Piping

Code, B31.3-2004, with permission of the publisher, the American Society of Mechanical Engineers, New York. All rights reserved.)

C1 = 1 - ShEa/SEEm = estimated self-spring or relaxation factor (use 0 if value of C1 is negative) Ra = estimated instantaneous reaction force or moment at installation temperature, lbf or in ⋅ lbf (N or N ⋅ mm) SE = computed displacement-stress range, lbf/in2 (MPa); see Eq. (10-99) Sh = see Eq. (10-91) Maximum Reactions for Complex Systems For multianchor systems and for two-anchor systems with intermediate restraints, Eqs. (10-104) and (10-105) are not applicable. Each case must be studied to estimate the location, nature, and extent of local overstrain and its effect on stress distribution and reactions. Acceptable comprehensive methods of analysis are analytical, modeltest, and chart methods, which evaluate for the entire piping system under consideration the forces, moments, and stresses caused by bending and torsion from a simultaneous consideration of terminal and intermediate restraints to thermal expansion and include all external movements transmitted under thermal change to the piping by its terminal and

PROCESS PLANT PIPING

10-107

FIG. 10-163 Flexibility classification for piping systems. (From Kellogg, Design of Piping Systems, Wiley, New York, 1965.)

intermediate attachments. Correction factors, as provided by the details of these rules, must be applied for the stress intensification of curved pipe and branch connections and may be applied for the increased flexibility of such component parts. Expansion Joints All the foregoing applies to “stiff piping systems,” i.e., systems without expansion joints (see detail 1 of Fig. 10-163). When space limitations, process requirements, or other considerations result in configurations of insufficient flexibility, the capacity for deflection within allowable stress range limits may be increased successively by the use of one or more hinged bellows expansion joints, i.e., semirigid (detail 2) and nonrigid (detail 3) systems, and expansion effects essentially eliminated by a free-movement joint (detail 4) system. Expansion joints for semirigid and nonrigid systems are restrained against longitudinal and lateral movement by the hinges with the expansion element under bending movement only and are known as rotation or hinged joints (see Fig. 10-164). Semirigid systems are limited to one plane; nonrigid systems require a minimum of three joints for two-dimensional and five joints for three-dimensional expansion movement. Joints similar to that shown in Fig. 10-164, except with two pairs of hinge pins equally spaced around a gimbal ring, achieve similar results with fewer joints. Expansion joints for free-movement systems can be designed for axial or offset movement alone, or for combined axial and offset movements (see Fig. 10-165). For offset movement alone, the end load due to pressure and weight can be transferred across the joint by tie rods or structural members (see Fig. 10-166). For axial or combined movements, anchors must be provided to absorb the unbalanced pressure load and to force bellows to deflect. Commercial bellows elements are usually light-gauge (of the order of 0.05 to 0.10 in thick) and are available in stainless and other alloy steels, copper, and other nonferrous materials. Multiply bellows, bellows with external reinforcing rings, and toroidal contour bellows are available for higher pressures. Since bellows elements are ordinarily rated for strain ranges that involve repetitive yielding, predictable performance is ensured only by adequate fabrication controls and knowledge of the potential fatigue performance of each design. The attendant cold work can affect

Hinged expansion joint. (From Kellogg, Design of Piping Systems, Wiley, New York, 1965.)

FIG. 10-164

Action of expansion bellows under various movements. (From Kellogg, Design of Piping Systems, Wiley, New York, 1965.)

FIG. 10-165

corrosion resistance and promote susceptibility to corrosion fatigue or stress corrosion; joints in a horizontal position cannot be drained and have frequently undergone pitting or cracking due to the presence of condensate during operation or off-stream. For low-pressure essentially nonhazardous service, nonmetallic bellows of fabric-reinforced rubber or special materials are sometimes used. For corrosive service PTFE bellows may be used. Because of the inherently greater susceptibility of expansion bellows to failure from unexpected corrosion, failure of guides to control joint movements, etc., it is advisable to examine critically their design choice in comparison with a stiff system. Slip-type expansion joints (Fig. 10-167) substitute packing (ring or plastic) for bellows. Their performance is sensitive to adequate design with respect to guiding to prevent binding and the adequacy of stuffing boxes and attendant packing, sealant, and lubrication. Anchors must be provided for the

FIG. 10-166 Constrained-bellows expansion joints. (From Kellogg, Design of Piping Systems, Wiley, New York, 1965.)

10-108

TRANSPORT AND STORAGE OF FLUIDS

FIG. 10-167 Slip-type expansion joint. (From Kellogg, Design of Piping Systems, Wiley, New York, 1965.)

unbalanced pressure force and for the friction forces to move the joint. The latter can be much higher than the elastic force required to deflect a bellows joint. Rotary packed joints, ball joints, and other special joints can absorb end load. Corrugated pipe and corrugated and creased bends are also used to decrease stiffness. Pipe Supports Loads transmitted by piping to attached equipment and supporting elements include weight, temperature- and pressureinduced effects, vibration, wind, earthquake, shock, and thermal expansion and contraction. The design of supports and restraints is based on concurrently acting loads (if it is assumed that wind and earthquake do not act simultaneously). Resilient and constant-effort-type supports shall be designed for maximum loading conditions including test unless temporary supports are provided. Though not specified in the code, supports for discharge piping from relief valves must be adequate to withstand the jet reaction produced by their discharge. The code states further that pipe-supporting elements shall (1) avoid excessive interference with thermal expansion and contraction of pipe which is otherwise adequately flexible; (2) be such that they do not contribute to leakage at joints or excessive sag in piping, requiring drainage; (3) be designed to prevent overstress, resonance, or disengagement due to variation of load with temperature; also, so that combined longitudinal stresses in the piping shall not exceed the code allowable limits; (4) be such that a complete release of the piping load will be prevented in the event of spring failure or misalignment, weight transfer, or added load due to test during erection; (5) be of steel or wrought iron; (6) be of alloy steel or protected from temperature when the temperature limit for carbon steel may be exceeded; (7) not be cast iron except for roller bases, rollers, anchor bases, etc., under mainly compression loading; (8) not be malleable or nodular iron except for pipe clamps, beam clamps, hanger flanges, clips, bases, and swivel rings; (9) not be wood except for supports mainly in compression when the pipe temperature is at or below ambient; and (10) have threads for screw adjustment which shall conform to ASME B1.1. A supporting element used as an anchor shall be designed to maintain an essentially fixed position. To protect terminal equipment or other (weaker) portions of the system, restraints (such as anchors and guides) shall be provided where necessary to control movement or to direct expansion into those portions of the system that are adequate to absorb them. The design, arrangement, and location of restraints shall ensure that expansion-joint movements occur in the directions for which the joint is designed. In addition to the other thermal forces and moments, the effects of friction in other supports of the system shall be considered in the design of such anchors and guides. Anchors for Expansion Joints Anchors (such as those of the corrugated, omega, disk, or slip type) shall be designed to withstand the algebraic sum of the forces at the maximum pressure and temperature at which the joint is to be used. These forces are as follows: 1. Pressure thrust, which is the product of the effective thrust area and the maximum pressure to which the joint will be subjected during normal operation. (For slip joints the effective thrust area shall be computed by using the outside diameter of the pipe. For corrugated, omega, or disk-type joints, the effective thrust area shall be that area recommended by the joint manufacturer. If this information is unobtainable, the effective area shall be computed by using the maximum inside diameter of the expansion-joint bellows.) 2. The force required to compress or extend the joint in an amount equal to the calculated expansion movement. 3. The force required to overcome the static friction of the pipe in expanding or contracting on its supports, from installed to operating position. The length of pipe considered should be that located between the anchor and the expansion joint.

Support Fixtures Hanger rods may be pipe straps, chains, bars, or threaded rods that permit free movement for thermal expansion or contraction. Sliding supports shall be designed for friction and bearing loads. Brackets shall be designed to withstand movements due to friction in addition to other loads. Spring-type supports shall be designed for weight load at the point of attachment, to prevent misalignment, buckling, or eccentric loading of springs, and provided with stops to prevent spring overtravel. Compensating-type spring hangers are recommended for high-temperature and critical-service piping to make the supporting force uniform with appreciable movement. Counterweight supports shall have stops to limit travel. Hydraulic supports shall be provided with safety devices and stops to support load in the event of loss of pressure. Vibration dampers or sway braces may be used to limit vibration amplitude. The code requires that the safe load for threaded hanger rods be based on the root area of the threads. This, however, assumes concentric loading. When hanger rods move to a non-vertical position so that the load is transferred from the rod to the supporting structure via the edge of one flat of the nut on the rod, it is necessary to consider the root area to be reduced by onethird. If a clamp is connected to a vertical line to support its weight, then it is recommended that shear lugs be welded to the pipe, or that the clamp be located below a fitting or flange, to prevent slippage. Consideration shall be given to the localized stresses induced in the piping by the integral attachment. Typical pipe supports are shown in Fig. 10-168. Much piping is supported from structures installed for other purposes. It is common practice to use beam formulas for tubular sections to determine stress, maximum deflection, and maximum slope of piping in spans between supports. When piping is supported from structures installed for that sole purpose and those structures rest on driven piles, detailed calculations are usually made to determine maximum permissible spans. Limits imposed on maximum slope to make the contents of the line drain to the lower end require calculations made on the weight per foot of the empty line. To avoid interference with other components, maximum deflection should be limited to 25.4 mm (1 in). Pipe hangers are essentially frictionless but require taller pipe-support structures which cost more than structures on which pipe is laid. Devices that reduce friction between laid pipe subject to thermal movement and its supports are used to accomplish the following: 1. Reduce loads on anchors or on equipment acting as anchors. 2. Reduce the tendency of pipe acting as a column loaded by friction at supports to buckle sideways off supports. 3. Reduce nonvertical loads imposed by piping on its supports so as to minimize the cost of support foundations. 4. Reduce longitudinal stress in pipe. Linear bearing surfaces made of fluorinated hydrocarbons or of graphite and also rollers are used for this purpose. Design Criteria: Nonmetallic Pipe In using a nonmetallic material, designers must satisfy themselves as to the adequacy of the material and its manufacture, considering such factors as strength at design temperature, impact- and thermal-shock properties, toxicity, methods of making connections, and possible deterioration in service. Rating information, based usually on ASTM standards or specifications, is generally available from the manufacturers of these materials. Particular attention should be given to provisions for the thermal expansion of nonmetallic piping materials, which may be as much as 5 to 10 times that of steel (Table 10-47). Special consideration should be given to the strength of small pipe connections to piping and equipment and to the need for extra flexibility at the junction of metallic and nonmetallic systems. Table 10-48 gives values for the modulus of elasticity for nonmetals; however, no specific stress-limiting criteria or methods of stress analysis are presented. Stress-strain behavior of most nonmetals differs considerably from that of metals and is less well defined for mathematic analysis. The piping system should be designed and laid out so that flexural stresses resulting from displacement due to expansion, contraction, and other movement are minimized. This concept requires special attention to supports, terminals, and other restraints. Displacement Strains The concepts of strain imposed by restraint of thermal expansion or contraction and by external movement described for metallic piping apply in principle to nonmetals. Nevertheless, the assumption that stresses throughout the piping system can be predicted from these strains because of fully elastic behavior of the piping materials is not generally valid for nonmetals. In thermoplastics and some thermosetting resins, displacement strains are not likely to produce immediate failure of the piping, but may result in detrimental distortion. Especially in thermoplastics, progressive deformation may occur upon repeated thermal cycling or on prolonged exposure to elevated temperature. In brittle nonmetallics (such as porcelain, glass, impregnated graphite) and some thermosetting resins, the materials show rigid behavior and develop high displacement stresses up to the point of sudden breakage due to overstrain.

PROCESS PLANT PIPING

FIG. 10-168 Typical pipe supports and attachments. (From Kellogg, Design of Piping Systems, Wiley, New York, 1965.)

10-109

10-110

TRANSPORT AND STORAGE OF FLUIDS TABLE 10-47

Thermal Expansion Coefficients, Nonmetals Mean coefficients (divide table values by 106)

Material description

in/in, °F

Range, °F

mm/mm, °C

Range, °C

Thermoplastics 3.6

...

108 99 72 72

... 7–13 ... ...

... ...

144 171

... ...

35 72 45

... ... ...

63 130 81

... ... ...

100 90 80 70 60

46–100 46–100 46–100 46–100 46–100

180 162 144 126 108

8–38 8–38 8–38 8–38 8–38

Acetal AP2012 Acrylonitrile-butadiene-styrene ABS 1208 ABS 1210 ABS 1316 ABS 2112

60 55 40 40

Cellulose acetate butyrate CAB MH08 CAB S004

80 95

Chlorinated poly(vinyl chloride) CPVC 4120 Polybutylene PB 2110 Polyether, chlorinated Polyethylene PE 1404 PE 2305 PE 2306 PE 3306 PE 3406

2

... ... 45–55 ... ...

Polyphenylene POP 2125

30

...

54

...

Polypropylene PP1110 PP1208 PP2105

48 43 40

33–67 ... ...

86 77 72

1–19 ... ...

Poly(vinyl chloride) PVC 1120 PVC 1220 PVC 2110 PVC 2112 PVC 2116 PVC 2120

30 35 50 45 40 30

23–37 34–40 ... ... 37–45 ...

54 63 90 81 72 54

-5 to +3 1–4 ... ... 3–7 ...

Poly(vinylidene fluoride) Poly(vinylidene chloride)

79 100

... ...

142 180

... ...

Polytetrafluoroethylene

55

73–140

99

46–58

73–140

67 94 111

70–212 212–300 300–408

Poly( fluorinated ethylene propylene) Poly(perfluoroalkoxy alkane) Poly(perfluoroalkoxy alkane) Poly(perfluoroalkoxy alkane)

83–104 121 169 200

23–60 23–60 21–100 100–149 149–209

Reinforced Thermosetting Resins and Reinforced Plastic Mortars Glass-epoxy, centrifugally cast Glass-polyester, centrifugally cast Glass-polyester, filament-wound Glass-polyester, hand lay-up Glass-epoxy, filament-wound

9–13 9–15 9–11 12–15 9–13

... ... ... ... ...

16–23.5 16–27 16–20 21.5–27 16–23.5

... ... ... ... ...

...

3.25

...

Other Nonmetallic Materials Borosilicate glass

1.8

GENERAL NOTES:

For Code references to this table, see para. A319.3.1, ASME B31.3-2014. Reprinted from ASME B31.3-2014 by permission of the American Society of Mechanical Engineers, New York. All rights reserved. These data are for use in the absence of more applicable data. It is the designer’s responsibility to verify that materials are suitable for the intended service at the temperatures shown. Individual compounds may vary from the values shown. Consult manufacturer for specific values for products .

Elastic Behavior The assumption that displacement strains will produce proportional stress over a sufficiently wide range to justify an elasticstress analysis often is not valid for nonmetals. In brittle nonmetallic piping, strains initially will produce relatively large elastic stresses. The total displacement strain must be kept small, however, since overstrain results in failure rather than plastic deformation. In plastic and resin nonmetallic piping, strains generally will produce stresses of the overstrained (plastic) type even at relatively low values of total displacement strain. FABRICATION, ASSEMBLY, AND ERECTION Welding, Brazing, or Soldering Code requirements dealing with fabrication are more detailed for welding than for other methods of joining, since

welding is the predominant method of construction and the method used for the most demanding applications. The code requirements for welding processes and operators are essentially the same as covered in the subsection on pressure vessels (i.e., qualification to Sec. IX of the ASME Boiler and Pressure Vessel Code) except that welding processes are not restricted, the material grouping (P number) must be in accordance with ASME B31.3 App. A-1 (A-1M Metric), and welding positions are related to pipe position. The code also permits one fabricator to accept welders or welding operators qualified by another employer without requalification when welding pipe by the same or equivalent procedure. The code may require that the welding procedure qualification include low-temperature toughness testing (see Table 10-49). Filler metal is required to conform with the requirements of Sec. IX. Backing rings (of ferrous material), when used, shall be of weldable quality

PROCESS PLANT PIPING TABLE 10-48

Modulus of Elasticity, Nonmetals

Material description

E, ksi (73 .4°F)

E, MPa (23°C)

Thermoplastics [Note (1)] Acetal

410

2,830

ABS, Type 1210

250

1,725 2,345

ABS, Type 1316

340

CAB

120

825

PVC, Type 1120 PVC, Type 1220 PVC, Type 2110 PVC, Type 2116

420 410 340 380

2,895 2,825 2,345 2,620

Chlorinated PVC

420

2,895

Chlorinated polyether

160

1,105

PE2606 PE2706 PE3608 PE3708 PE3710 PE4708 PE4710

100 100 125 125 125 130 130

690 690 860 860 860 895 895

Polypropylene

120

825

Poly(vinylidene chloride) Poly(vinylidene fluoride) Poly(tetrafluoroethylene) Poly( fluorinated ethylene propylene) Poly(perfluoroalkoxy alkane)

100 194 57 67 100

690 1,340 395 460 690

Thermosetting Resins, Axially Reinforced Epoxy-glass, centrifugally cast Epoxy-glass, filament-wound

1,200–1,900 1,100–2,000

8,275–13,100 7,585–13,790

Polyester-glass, centrifugally cast Polyester-glass, hand lay-up

1,200–1,900 800–1,000

8,275–13,100 5,515–6,895

Other Borosilicate glass

9,800

67,570

GENERAL NOTE: For Code references to this table, see para . A319 .3 .2, ASME B31 .3-2014 .

Reprinted from ASME B31 .3-2014 by permission of the American Society of Mechanical Engineers, New York . All rights reserved . These data are for use in the absence of more applicable data . It is the designer’s responsibility to verify that materials are suitable for the intended service at the temperatures shown . NOTE: (1) The modulus of elasticity data shown for thermoplastics are based on shortterm tests . The manufacturer should be consulted to obtain values for use under longterm loading .

with sulfur limited to 0.05 percent. Backing rings of nonferrous and nonmetallic materials may be used provided they are proved satisfactory by procedure qualification tests and provided their use has been approved by the designer. The code requires internal alignment within the dimensional limits specified in the welding procedure and the engineering design without specific dimensional limitations. Internal trimming is permitted for correcting internal misalignment provided such trimming does not result in a finished wall thickness before welding of less than required minimum wall thickness tm. When necessary, weld metal may be deposited on the inside or outside of the component to provide alignment or sufficient material for trimming. Table 10-51 is a summary of the code acceptance criteria (limits on imperfections) for welds. The defects referred to are illustrated in Fig. 10-169. Brazing procedures, brazers, and brazing operators must be qualified in accordance with the requirements of Part QB, Sec. IX, ASME Code. Qualification is not required for Category D fluid service not exceeding 93°C (200°F), unless specified in the engineering design. The clearance between surfaces to be joined by brazing or soldering shall be no larger than is necessary to allow complete capillary distribution of the filler metal. The only requirement for solderers is that they follow the procedure in ASTM B823–02, Standard Practice for Making Capillary Joints by Soldering of Copper and Copper Alloy Tube and Fittings. Bending and Forming Pipe may be bent to any radius for which the bend-arc surface will be free of cracks and substantially free of buckles. The use of qualified bends that are creased or corrugated is permitted. Bending may be done by any hot or cold method that produces a product meeting code and service requirements, and that does not have an adverse effect on the essential characteristics of the material. Hot bending and hot

10-111

forming must be done within a temperature range consistent with material characteristics, end use, and postoperation heat treatment. Postbend heat treatment may be required for bends in some materials; its necessity is dependent on the type of bending operation and the severity of the bend. Postbend heat treatment requirements are defined in the code. Piping components may be formed by any suitable hot or cold pressing, rolling, forging, hammering, spinning, drawing, or other method. Thickness after forming shall not be less than required by design. Special rules cover the forming and pressure design verification of flared laps. The development of fabrication facilities for bending pipe to the radius of commercial butt-welding long-radius elbows and forming flared metallic (Van Stone) laps on pipe is an important technique in reducing weldedpiping costs. These techniques save both the cost of the ell or stub end and that of the welding operation required to attach the fitting to the pipe. Preheating and Heat Treatment Preheating and postoperation heat treatment are used to avert or relieve the detrimental effects of the high temperature and severe thermal gradients inherent in the welding of metals. In addition, heat treatment may be needed to relieve residual stresses created during the bending or forming of metals. The code provisions shown in Tables 10-52 and 10-53 represent basic practices that are acceptable for most applications of welding, bending, and forming, but they are not necessarily suitable for all service conditions. The specification of more or less stringent preheating and heat-treating requirements is a function of those responsible for the engineering design. Refer to the code for rules establishing the thickness to be used in determining PWHT (post weld heat treatment) requirements for configurations other than butt welds (e.g., fabricated branch connections and socket welds). Joining Nonmetallic Pipe All joints should be made in accordance with procedures complying with the manufacturer’s recommendations and code requirements. General welding and heat fusion procedures are described in ASTM D-2657. ASTM D2855 describes general solvent-cementing procedures. Depending on size, thermoplastic piping can be joined with mechanical joints, solvent-cemented joints, hot-gas welding, or heat fusion procedures. Mechanical joints are frequently bell-and-spigot joints which employ an elastomer O-ring gasket. Joints of this type are generally not self-restrained against internal pressure thrust. Thermosetting resin pipe can be joined with mechanical joints or adhesivebonded joints. Mechanical joints are generally a variation of gasketed bell-and-spigot joints and may be either nonrestrained or self-restrained. Adhesive-bonded joints are typically bell-and-spigot or butt-and-strap. Butt-and-strap joints join piping components with multiple layers of resinsaturated glass reinforcement. Assembly and Erection Flanged-joint faces shall be aligned to the design plane to within 1 10 in/ft (0.5 percent) maximum measured across any diameter, and flange bolt holes shall be aligned to within 3.2-mm (⅛-in) maximum offset . Flanged joints involving flanges with widely differing mechanical properties shall be assembled with extra care, and tightening to a predetermined torque is recommended . The use of flat washers under bolt heads and nuts is a code requirement when assembling nonmetallic flanges . It is preferred that the bolts extend completely through their nuts; however, a lack of complete thread engagement not exceeding one thread is permitted by the code . The assembly of cast-iron bell-and-spigot piping is covered in AWWA Standard C600 . Screwed joints that are intended to be seal-welded shall be made up dry without any thread compound . When one is installing conductive nonmetallic piping and metallic pipe with nonmetallic linings, consideration should be given to the need to provide electrical continuity throughout the system and to grounding requirements . This is particularly critical in areas with potentially explosive atmospheres . EXAMINATION, INSPECTION, AND TESTING This subsection provides a general synopsis of code requirements . It should not be viewed as comprehensive . Examination and Inspection The code differentiates between examination and inspection . Examination applies to quality-control functions performed by personnel of the piping manufacturer, fabricator, or erector . Inspection applies to functions performed for the owner by the authorized inspector . The authorized inspector shall be designated by the owner and shall be the owner, an employee of the owner, an employee of an engineering or scientific organization, or an employee of a recognized insurance or inspection company acting as the owner’s agent . The inspector shall not represent or be an employee of the piping erector, the manufacturer, or the fabricator unless the owner is also the erector, the manufacturer, or the fabricator .

10-112

TRANSPORT AND STORAGE OF FLUIDS

TABLE 10-49 Requirements for Low-Temperature Toughness Tests for Metals* These toughness requirements are in addition to tests required by the material specification.

Type of material

Column A Design minimum temperature at or above min. temp. in Table A-1 of ASME B31.3-2014 or Table 10-50

1 Gray cast iron

A-1 No additional requirements

B-1 No additional requirements

2 Malleable and ductile cast iron: carbon steel per Note (1)

A-2 No additional requirements

B-2 Materials designated in Box 2 shall not be used.

Listed Materials

(a) Base metal

Unlisted Materials

Column B Design minimum temperature below min. temp. in Table A-1 of ASME B31.3-2014 or Table 10-50

(b) Weld metal and heat affected zone (HAZ) [Note (2)]

3 Other carbon steels, low and intermediate alloy steels, high alloy ferritic steels, duplex stainless steels

A-3 (a) No additional requirements

A-3 (b) Weld metal deposits shall be impact

4 Austenitic stainless steels

A-4 (a) If: (1) carbon content by analysis >0.1%; or (2) material is not in solution heat treated condition; then, impact test per para. 323.3† for design min. temp. < -29°C (-20°F) except as provided in Notes (3) and (6)

A-4 (b) Weld metal deposits shall be impact tested per para 323.3.† If design min. temp. < -29°C (-20°F) except as provided in para. 323.2.2b and in Notes (3) and (6)

B-4 Base metal and weld metal deposits shall be impact tested per para. 323.3‡. See Notes (2),(3), and (6).

5 Austenitic ductile iron, ASTM A 571

A-5 (a) No additional requirements

A-5 (b) Welding is not permitted

B-5 Base metal shall be impact tested per para 323.3.† Do not use < -196°C (-320°F). Welding is not permitted.

6 Aluminum, copper, nickel, and their alloys; unalloyed titanium

A-6 (a) No additional requirements

A-6 (b) No additional requirements unless filler metal composition is outside the range for base metal composition; then test per column B-6

B-6 Designer shall be assured by suitable tests [see Note (4)] that base metal, weld deposits, and HAZ are suitable at the design min. temp.

tested per para. 323.3.†

If design min. temp. < -29°C (-20°F), except as provided in Notes (3) and (5), and except as follows: for materials listed for Curves C and D of Table 10-50, where corresponding welding-consumables are qualified by impact testing at the design minimum temperature or lower in accordance with the applicable AWS specification, additional testing is not required.

B-3 Except as provided in Notes (3) and (5), heat treat base metal per applicable ASTM specification listed in para. 323.3.2†; then impact test base metal, weld deposits, and HAZ per para. 323.3† [see Note (2)]. When materials are used at design min. temp. below the assigned curve as permitted by Notes (2) and (3) of Table 10-50, weld deposits and HAZ shall be impact tested [see Note (2)].

7 An unlisted material shall conform to a published specification. Where composition, heat treatment, and product form are comparable to those of a listed material, requirements for the corresponding listed material shall be met. Other unlisted materials shall be qualified as required in the applicable section of column B.

NOTES:

(1) Carbon steels conforming to the following are subject to the limitations in Box B-2; plates per ASTM A 36, A 283, and A 570; pipe per ASTM A 134 when made from these plates; structural shapes in accordance with ASTM A992; and pipe per ASTM A 53 Type F and API 5L Gr. A25 butt weld. (2) Impact tests that meet the requirements of Table 323.3.1,† which are performed as part of the weld procedure qualification, will satisfy all requirements of para . 323 .2 .2,‡ and need not be repeated for production welds . (3) Impact testing is not required if the design minimum temperature is below -29°C (-20°F) but at or above -104°C (-155°F) and the Stress Ratio defined in Fig . 323 .2 .2B‡ does not exceed 0 .3 . (4) Tests may include tensile elongation, sharp-notch tensile strength (to be compared with unnotched tensile strength), and/or other tests, conducted at or below design minimum temperature . See also para . 323 .3 .4 .‡ (5) Impact tests are not required when the maximum obtainable Charpy specimen has a width along the notch of less than 2 .5 mm (0 .098 in) . Under these conditions, the design minimum temperature shall not be less than the lower of -48°C (-55°F) or the minimum temperature for the material in Table A-1 . (6) Impact tests are not required when the maximum obtainable Charpy specimen has a width along the notch of less than 2 .5 mm (0 .098 in) . *Table 10-49 and notes have been extracted (with minor modifications) from Process Piping, ASME B31 .3-2014, with permission of the publisher, the American Society of Mechanical Engineers, New York . All rights reserved . † Refer to the referenced code paragraph for impact testing methods and acceptance . ‡ Refer to the referenced code paragraph for comments regarding circumstances under which impact testing can be excluded .

The authorized inspector shall have a minimum of 10 years’ experience in the design, fabrication, or inspection of industrial pressure piping . Each 20 percent of satisfactory work toward an engineering degree accredited by the Engineers’ Council for Professional Development shall be considered equivalent to 1 year’s experience, up to 5 years total . It is the owner’s responsibility, exercised through the authorized inspector, to verify that all required examinations and testing have been completed and to inspect the piping to the extent necessary to be satisfied that it conforms to all applicable requirements of the code and the engineering design . This verification may include certifications and records pertaining to materials, components, heat treatment, examination and testing, and qualifications of operators and procedures . The authorized inspector may delegate the performance of inspection to a qualified person .

Inspection does not relieve the manufacturer, the fabricator, or the erector of responsibility for providing materials, components, and skill in accordance with requirements of the code and the engineering design, performing all required examinations, and preparing records of examinations and tests for the inspector’s use . Examination Methods The code establishes the types of examinations for evaluating various types of imperfections (see Table 10-54) . Personnel performing examinations other than visual shall be qualified in accordance with applicable portions of SNT TC-1A, Recommended Practice for Nondestructive Testing Personnel Qualification and Certification. Procedures shall be qualified as required in Para . T-150, Art . 1, Sec . V of the ASME Code . Limitations on imperfections shall be in accordance with the engineering design but shall at least meet the requirements of the code

PROCESS PLANT PIPING TABLE 10-50

10-113

Tabular Values for Minimum Temperatures Without Impact Testing for Carbon Steel Materials* Design minimum temperature

Nominal thickness [Note (6)] mm

Curve A [Note (2)]

Curve B [Note (3)]

Curve C [Note (3)]

Curve D

in

°C

°F

°C

°F

°C

°F

°C

°F

6.4 7.9 9.5

0.25 0.3125 0.375

-9.4 -9.4 -9.4

15 15 15

-28.9 -28.9 -28.9

-20 -20 -20

-48.3 -48.3 -48.3

-55 -55 -55

-48.3 -48.3 -48.3

-55 -55 -55

10.0 11.1 12.7 14.3 15.9

0.394 0.4375 0.5 0.5625 0.625

-9.4 -6.7 -1.1 2.8 6.1

15 20 30 37 43

-28.9 -28.9 -28.9 -21.7 -16.7

-20 -20 -20 -7 2

-48.3 -41.7 -37.8 -35.0 -32.2

-55 -43 -36 -31 -26

-48.3 -48.3 -48.3 -45.6 -43.9

-55 -55 -55 -50 -47

17.5 19.1 20.6 22.2 23.8

0.6875 0.75 0.8125 0.875 0.9375

8.9 11.7 14.4 16.7 18.3

48 53 58 62 65

-12.8 -9.4 -6.7 -3.9 -1.7

9 15 20 25 29

-29.4 -27.2 -25.0 -23.3 -21.7

-21 -17 -13 -10 -7

-41.7 -40.0 -38.3 -36.7 -35.6

-43 -40 -37 -34 -32

25.4 27.0 28.6 30.2 31.8

1.0 1.0625 1.125 1.1875 1.25

20.0 22.2 23.9 25.0 26.7

68 72 75 77 80

0.6 2.2 3.9 5.6 6.7

33 36 39 42 44

-19.4 -18.3 -16.7 -15.6 -14.4

-3 -1 2 4 6

-34.4 -33.3 -32.2 -30.6 -29.4

-30 -28 -26 -23 -21

33.3 34.9 36.5 38.1

1.3125 1.375 1.4375 1.5

27.8 28.9 30.0 31.1

82 84 86 88

7.8 8.9 9.4 10.6

46 48 49 51

-13.3 -12.2 -11.1 -10.0

8 10 12 14

-28.3 -27.8 -26.7 -25.6

-19 -18 -16 -14

39.7 41.3 42.9 44.5 46.0

1.5625 1.625 1.6875 1.75 1.8125

32.2 33.3 33.9 34.4 35.6

90 92 93 94 96

11.7 12.8 13.9 14.4 15.0

53 55 57 58 59

-8.9 -8.3 -7.2 -6.7 -5.6

16 17 19 20 22

-25.0 -23.9 -23.3 -22.2 -21.7

-13 -11 -10 -8 -7

47.6 49.2 50.8 51.6

1.875 1.9375 2.0 2.0325

36.1 36.7 37.2 37.8

97 98 99 100

16.1 16.7 17.2 17.8

61 62 63 64

-5.0 -4.4 -3.3 -2.8

23 24 26 27

-21.1 -20.6 -20.0 -19.4

-6 -5 -4 -3

54.0 55.6 57.2 58.7 60.3

2.125 2.1875 2.25 2.3125 2.375

38.3 38.9 38.9 39.4 40.0

101 102 102 103 104

18.3 18.9 19.4 20.0 20.6

65 66 67 68 69

-2.2 -1.7 -1.1 -0.6 0.0

28 29 30 31 32

-18.9 -18.3 -17.8 -17.2 -16.7

-2 -1 0 1 2

61.9 63.5 65.1 66.7

2.4375 2.5 2.5625 2.625

40.6 40.6 41.1 41.7

105 105 106 107

21.1 21.7 21.7 22.8

70 71 71 73

0.6 1.1 1.7 2.2

33 34 35 36

-16.1 -15.6 -15.0 -14.4

3 4 5 6

68.3 69.9 71.4 73.0 74.6 76.2

2.6875 2.75 2.8125 2.875 2.9375 3.0

41.7 42.2 42.2 42.8 42.8 43.3

107 108 108 109 109 110

22.8 23.3 23.9 24.4 25.0 25.0

73 74 75 76 77 77

2.8 3.3 3.9 4.4 4.4 5.0

37 38 39 40 40 41

-13.9 -13.3 -13.3 -12.8 -12.2 -11.7

7 8 8 9 10 11

(see Tables 10-51 and 10-54) for the specific type of examination. Repairs shall be made as applicable. Visual Examination This consists of observation of the portion of components, joints, and other piping elements that are or can be exposed to view before, during, or after manufacture, fabrication, assembly, erection, inspection, or testing. The examination includes verification of code and engineering design requirements for materials and components, dimensions, joint preparation, alignment, welding, bonding, brazing, bolting, threading and other joining methods, supports, assembly, and erection. Visual examination shall be performed in accordance with Art. 9, Sec. V of the ASME Code. Magnetic-Particle Examination This examination shall be performed in accordance with Art. 7, Sec. V of the ASME Code. Liquid-Penetrant Examination This examination shall be performed in accordance with Art. 6, Sec. V of the ASME Code. Radiographic Examination The following definitions apply to radiography required by the code or by the engineering design: 1. Random radiography applies only to girth and miter groove welds. It is radiographic examination of the complete circumference of a specified percentage of the girth butt welds in a designated lot of piping. 2. Unless otherwise specified in engineering design, 100 percent radiography applies only to girth welds, miter groove welds, and fabricated branch

connections that utilize butt-type welds to join the header and the branch. The design engineer may, however, elect to designate other types of welds as requiring 100 percent radiography. By definition, 100 percent radiography requires radiographic examination of the complete length of all such welds in a designated lot of piping. 3. Spot radiography is the practice of making a single-exposure radiograph at a point within a specified extent of welding. Required coverage for a singlespot radiograph is as follows: • For longitudinal welds, at least 150 mm (6 in) of weld length. • For girth, miter, and branch welds in piping 2 1 2 in NPS and smaller, a single elliptical exposure which encompasses the entire weld circumference, and in piping larger than 2 1 2 in NPS, at least 25 percent of the inside circumference or 150 mm (6 in), whichever is less. Radiography of components other than castings and of welds shall be in accordance with Art. 2, Sec. V of the ASME Code. Limitations on imperfections in components other than castings and welds shall be as stated in Table 10-51 for the degree of radiography involved. Ultrasonic Examination Ultrasonic examination of welds shall be in accordance with Art. 4, Sec. V of the ASME Code, except that the modifications stated in Para. 336.6.1 of the code shall be substituted for T434.2.1 and T434.3. Refer to the code for additional requirements. Type and Extent of Required Examination The intent of examinations is to provide the examiner and the inspector with reasonable

10-114

TRANSPORT AND STORAGE OF FLUIDS TABLE 10-50

Tabular Values for Minimum Temperatures Without Impact Testing for Carbon Steel Materials* (Continued )

NOTES:

(1) Any carbon steel material may be used to a minimum temperature of -29°C (-20°F) for Category D Fluid Service. (2) X Grades of API SL, and ASTM A 381 materials, may be used in accordance with Curve B if normalized or quenched and tempered. (3) The following materials may be used in accordance with Curve D if normalized: (a) ASTM A 516 Plate, all grades (b) ASTM A 671 Pipe, Grades CE55, CE60, and all grades made with A 516 plate (c) ASTM A 672 Pipe, Grades E55, E60, and all grades made with A 516 plate (4) A welding procedure for the manufacture of pipe or components shall include impact testing of welds and HAZ for any design minimum temperature below -29°C (-20°F), except as provided in Table 10-49, A-3(b) . (5) Impact testing in accordance with para . 323 .3† is required for any design minimum temperature below -48°C (-55°F), except as permitted by Note (3) in Table 10-49 .‡ (6) For blind flanges and blanks, T shall be ¼ of the flange thickness . *Table 10-50 and notes have been extracted (with minor modifications) from Process Piping, ASME B31 .3-2014, with permission of the publisher, the American Society of Mechanical Engineers, New York . All rights reserved . † Refer to the referenced code paragraph for impact testing methods and acceptance . ‡ Refer to the referenced code paragraph for comments regarding circumstances under which impact testing can be excluded .

assurance that the requirements of the code and the engineering design have been met. For P-number 3, 4, and 5 materials, examination shall be performed after any heat treatment has been completed. Examination Normally Required * Piping in normal fluid service shall be examined to the extent specified herein or to any greater extent specified in the engineering design. Acceptance criteria are as stated in the code for Normal Fluid Service unless more stringent requirements are specified. 1. Visual examination. At least the following shall be examined in accordance with code requirements: a. Sufficient materials and components, selected at random, to satisfy the examiner that they conform to specifications and are free from defects. b. At least 5 percent of fabrication. For welds, each welder’s and welding operator’s work shall be represented. c. One hundred percent of fabrication for longitudinal welds, except those in components made in accordance with a listed specification. Longitudinal welds required to have a joint efficiency of 0.9 must be spotradiographed to the extent of 300 mm (12 in) in each 30 m (100 ft) of weld for each welder or welding operator. Acceptance criteria shall comply with code radiography acceptance criteria for Normal Fluid Service.

∗Extracted (with minor editing) from Process Piping, ASME B31.3-2014, paragraph 341, with permission of the publisher, the American Society of Mechanical Engineers, New York.

d. Random examination of the assembly of threaded, bolted, and other joints to satisfy the examiner that they conform to the applicable code requirements for erection and assembly . When pneumatic testing is to be performed, all threaded, bolted, and other mechanical joints shall be examined . e. Random examination during erection of piping, including checking of alignment, supports, and cold spring . f. Examination of erected piping for evidence of defects that would require repair or replacement, and for other evident deviations from the intent of the design . 2 . Other examination a. Not less than 5 percent of circumferential butt and miter groove welds shall be examined fully by random radiography or random ultrasonic examination in accordance with code requirements established for these methods . The welds to be examined shall be selected to ensure that the work product of each welder or welding operator doing the production welding is included . They shall also be selected to maximize coverage of intersections with longitudinal joints . When a circumferential weld with intersecting longitudinal weld(s) is examined, at least the adjacent 38 mm (1½ in) of each intersecting weld shall be examined . In-process examination in accordance with code requirements may be substituted for all or part of the radiographic or ultrasonic examination on a weld-for-weld basis if specified in the engineering design or specifically authorized by the Inspector . b. Not less than 5 percent of all brazed joints shall be examined by inprocess examination in accordance with the code definition of in-process

PROCESS PLANT PIPING

10-115

TABLE 10-51 Acceptance Criteria for Welds—Visual and Radiographic Examination Criteria (A to M) for Types of Welds and for Service Conditions [Note (1)]

Examination Methods

Branch Connection [Note (2)]

A

A

A

A

A

A

Crack

•

•

A

A

A

A

A

A

C

A

N/A

A

Lack of fusion

•

•

Weld Imperfection

Radiography

Fillet [Note (4)]

A

Visual

Longitudinal Groove [Note (3)]

A

Fillet [Note (4)]

A

Longitudinal Groove [Note (3)]

A

Girth, Miter Groove & Branch Connection [Note (2)]

Girth and Miter Groove

Type of Weld

Fillet [Note (4)]

Category D Fluid Service

Type of Weld

Longitudinal Groove [Note (3)]

Severe Cyclic Conditions

Type of Weld Girth, Miter Groove & Branch Connection [Note (2)]

Normal and Category M Fluid Service

B

A

N/A

A

A

N/A

C

A

N/A

A

Incomplete penetration

•

•

E

E

N/A

D

D

N/A

N/A

N/A

N/A

N/A

Rounded Indications

…

•

G

G

N/A

F

F

N/A

N/A

N/A

N/A

N/A

Elongated indications

…

•

H

A

H

A

A

A

I

A

H

H

Undercutting

•

•

A

A

A

A

A

A

A

A

A

A

Surface porosity or exposed slag inclusion [Note (5)]

•

…

N/A

N/A

N/A

J

J

J

N/A

N/A

N/A

N/A

Surface finish

•

…

K

K

N/A

K

K

N/A

K

K

N/A

K

Concave surface, concave root, or burn-through

•

•

L

L

L

L

L

L

M

M

M

M

Weld reinforcement or internal protrusion

•

…

examination, the joints to be examined being selected to ensure that the work of each brazer making the production joints is included. 3. Certifications and records. The examiner shall be assured, by examination of certifications, records, and other evidence, that the materials and components are of the specified grades and that they have received required heat treatment, examination, and testing. The examiner shall provide the Inspector with a certification that all the quality control requirements of the code and of the engineering design have been carried out. Examination—Category D Fluid Service* Piping and piping elements for Category D fluid service as designated in the engineering design shall be visually examined in accordance with code requirements for visual examination to the extent necessary to satisfy the examiner that components, materials, and workmanship conform to the requirements of this code and the engineering design. Acceptance criteria shall be in accordance with code requirements and criteria in Table 10-51, for Category D fluid service, unless otherwise specified. Examination—Severe Cyclic Conditions* Piping to be used under severe cyclic conditions shall be examined to the extent specified herein or to any greater extent specified in the engineering design. Acceptance criteria shall be in accordance with code requirements and criteria in Table 10-51, for severe cyclic conditions, unless otherwise specified. 1. Visual examination. The requirements for Normal Fluid Service apply with the following exceptions. a. All fabrication shall be examined. b. All threaded, bolted, and other joints shall be examined. c. All piping erection shall be examined to verify dimensions and alignment. Supports, guides, and points of cold spring shall be checked to ensure that movement of the piping under all conditions of startup, operation, and shutdown will be accommodated without undue binding or unanticipated constraint. 2. Other examination. All circumferential butt and miter groove welds and all fabricated branch connection welds comparable to those recognized by the code (see Fig. 10-119) shall be examined by 100 percent radiography or 100 percent ultrasonic (if specified in engineering design) in accordance

∗Extracted (with minor editing) from Process Piping, ASME B31.3-2014, paragraph 341, with permission of the publisher, the American Society of Mechanical Engineers, New York.

with code requirements. Socket welds and branch connection welds which are not radiographed shall be examined by magnetic-particle or liquidpenetrant methods in accordance with code requirements. 3. In-process examination in accordance with the code definition, supplemented by appropriate nondestructive examination, may be substituted for the examination required in 2 above on a weld-for-weld basis if specified in the engineering design or specifically authorized by the Inspector. 4. Certification and records. The requirements established by the code for Normal Fluid Service apply. Impact Testing In specifying materials, it is critical that the lowtemperature limits of materials and impact testing requirements of the applicable code edition be clearly understood. In the recent past, code criteria governing low-temperature limits and requirements for impact testing have undergone extensive revision. The code contains extensive criteria detailing when impact testing is required and describing how it is to be performed. Because of the potentially changing requirements and the complexity of the code requirements, this text does not attempt to provide a comprehensive treatment of this subject or a comprehensive presentation of the requirements of the current code edition. Some of the general guidelines are provided here; however, the designer should consult the code to clearly understand additional requirements and special circumstances under which impact testing may be omitted. These exclusions permitted by the code may be significant in selecting materials or establishing material requirements. In general, materials conforming to ASTM specifications listed by the code may be used at temperatures down to the lowest temperature listed for that material in ASME B31.3 Table A-1, and A-1M. When welding or other operations are performed on these materials, additional low-temperature toughness tests (impact testing) may be required. Refer to Table 10-51 for a general summary of these requirements. Pressure Testing Prior to initial operation, installed piping shall be pressure-tested to ensure tightness except as permitted for Category D fluid service described later. The pressure test shall be maintained for a sufficient time to determine the presence of any leaks but not less than 10 min. If repairs or additions are made following the pressure tests, the affected piping shall be retested except that, in the case of minor repairs or additions, the owner may waive retest requirements when precautionary measures are taken to ensure sound construction.

10-116

TRANSPORT AND STORAGE OF FLUIDS

TABLE 10-51 Acceptance Criteria for Welds—Visual and Radiographic Examination (Continued ) Criterion Value Notes for Table 10-51 Criterion Symbol

Measure

Acceptable Value Limits [Note (6)]

A

Extent of imperfection

Zero (no evident imperfection)

B

Cumulative length of incomplete penetration

≤38 mm (1.5 in.) in any 150 mm (6 in.) weld length or 25% of total weld length, whichever is less

C

Cumulative length of lack of fusion and incomplete penetration

≤38 mm (1.5 in.) in any 150 mm (6 in.) weld length or 25% of total weld length, whichever is less

D

Size and distribution of rounded indications

See BPV Code, Section VIII, Division 1, Appendix 4 [Note (10)]

E

Size and distribution of rounded indications

For Tw ≤ 6 mm (¼ in.), limit is same as D [Note (10)]

F

Elongated indications

For Tw > 6 mm (¼ in.), limit is 1.5 × D [Note (10)]

G

H

Individual length

≤ Tw /3

Individual width

≤2.5 mm ( 3 32 in.) and ≤ Tw /3

Cumulative length

≤ Tw in any 12 Tw weld length [Note (10)]

Elongated indications Individual length

≤2 Tw

Individual width

≤3 mm (⅛ in .) and ≤ Tw /2

Cumulative length

≤4 Tw in any 150 mm (6 in .) weld length [Note (10)]

Depth of undercut Cumulative length of internal and external undercut

I

Depth of undercut Cumulative length of internal and external undercut

≤1 mm ( 1 32 in .) and ≤ Tw /4 ≤38 mm (1 .5 in .) in any 150 mm (6 in .) weld length or 25% of total weld length, whichever is less ≤1 .5 mm (1 16 in .) and [ ≤ Tw /4 or 1 mm ( 1 32 in .)] ≤38 mm (1 .5 in .) in any 150 mm (6 in .) weld length or 25% of total weld length, whichever is less ≤12 .5 µm (500 µin .) Ra in accordance with ASME B46 .1

J

Surface roughness

K

Depth of surface concavity, root concavity, or burn-through

Total joint thickness, incl . weld reinf ., ≥ Tw [Notes (7) and (11)]

L

Height of reinforcement or internal protrusion [Note (8)] in any plane through the weld shall be within limits of the applicable height value in the tabulation at right, except as provided in Note (9) . Weld metal shall merge smoothly into the component surfaces .

For Tw , mm (in .)

Height, mm (in .)

≤6 (¼) >6 (¼), ≤13 (½) >13 (½), ≤25 (1) >25 (1)

≤1 .5 (1 16) ≤3 (⅛) ≤4 ( 5 32 ) ≤5 ( 3 16 )

Height of reinforcement or internal protrusion [Note (8)] as described in L . Note (9) does not apply .

Limit is twice the value applicable for L above

M GENERAL NOTES:

(a) Weld imperfections are evaluated by one or more of the types of examination methods given, as specified in paras . 341 .4 .1, 341 .4 .2, 341 .4 .3, and M341 .4, or by the engineering design . (b) “N/A” indicates the Code does not establish acceptance criteria or does not require evaluation of this kind of imperfection for this type of weld . (c) Check (•) indicates examination method generally used for evaluating this kind of weld imperfection . (d) Ellipsis ( . . .) indicates examination method not generally used for evaluating this kind of weld imperfection . notes: (1) Criteria given are for required examination . More stringent criteria may be specified in the engineering design . Other methods of examination may be specified by engineering design to supplement the examination required by the code . The extent of supplementary examination and any acceptance criteria differing from those specified by the code shall be specified by engineering design . Any examination method recognized by the code may be used to resolve doubtful indications . Acceptance criteria shall be those established by the code for the required examination . (2) Longitudinal groove weld includes straight and spiral seam . Criteria are not intended to apply to welds made in accordance with component standards recognized by the code (ref . ASME .B31 .3 Table A1 and Table 326 .1); however, alternative leak test requirements dictate that all component welds be examined (see code for specific requirements) . (3) Fillet weld includes socket and seal welds, and attachment welds for slip-on flanges, branch reinforcement, and supports . (4) Branch connection weld includes pressure containing welds in branches and fabricated laps . (5) These imperfections are evaluated only for welds ≤ 5 mm ( 3 16 in) in nominal thickness . (6) Where two limiting values are separated by and the lesser of the values determines acceptance . Where two sets of values are separated by or the larger value is acceptable . Tw is the nominal wall thickness of the thinner of two components joined by a butt weld . (7) Tightly butted unfused root faces are unacceptable . (8) For groove welds, height is the lesser of the measurements made from the surfaces of the adjacent components; both reinforcement and internal protrusion are permitted in a weld . For fillet welds, height is measured from the theoretical throat defined by the code; internal protrusion does not apply . (9) For welds in aluminum alloy only, internal protrusion shall not exceed the following values: (a) for thickness ≤ 2 mm (5⁄64 in): 1 .5 mm (1 16 in) (b) for thickness > 2 mm and ≤ 6 mm (¼ in): 2 .5 mm ( 3 32 in) For external reinforcement and for greater thicknesses, see the tabulation for Symbol L . ∗Table 10-51 and notes have been extracted (with minor modifications) from Section 341 of Process Piping, ASME B31 .3–2004, with permission of the publisher, the American Society of Mechanical Engineers, New York . All rights reserved .

PROCESS PLANT PIPING

10-117

FIG. 10-169 Typical weld imperfections. (Extracted from Process Piping, ASME B31.3-2014, with permission of the publisher, the American Society of Mechanical Engineers, New York. All rights reserved.)

When pressure tests are conducted at metal temperatures near the ductileto-brittle transition temperature of the material, the possibility of brittle fracture shall be considered. The test shall be hydrostatic, using water, with the following exceptions. If there is a possibility of damage due to freezing or if the operating fluid or piping material would be adversely affected by water, any other suitable nontoxic liquid may be used. If a flammable liquid is used, its flash point shall not be less than 50°C (120°F), and consideration shall be given to the test environment. The hydrostatic-test pressure at any point in the system shall be as follows: 1. Not less than 1½ times the design pressure. 2. For a design temperature above the test temperature, the minimum test pressure shall be as calculated by the following formula: PT = 1.5PST /S where PT = test hydrostatic gauge pressure, MPa (lbf/in2) P = internal design pressure, MPa (lbf/in2) ST = allowable stress at test temperature, MPa (lbf/in2) S = allowable stress at design temperature, MPa (lbf/in2)

(10-106)

If the test pressure as so defined would produce a stress in excess of the yield strength at test temperature, the test pressure may be reduced to the maximum pressure that will not exceed the yield strength at test temperature. If the test liquid in the system is subject to thermal expansion, precautions shall be taken to avoid excessive pressure. A preliminary air test at not more than 0.17 MPa (25 lbf/in2) gauge pressure may be made prior to hydrostatic test in order to locate major leaks. If hydrostatic testing is not considered practicable by the owner, a pneumatic test in accordance with the following procedure may be substituted, using air or another nonflammable gas. If the piping is tested pneumatically, the test pressure shall be 110 percent of the design pressure. When pneumatically testing nonmetallic materials, ensure that the materials are suitable for compressed gas. Pneumatic testing involves a hazard due to the possible release of energy stored in compressed gas. Therefore, particular care must be taken to minimize the chance of brittle failure of metals and thermoplastics. The test temperature is important in this regard and must be considered when material is chosen in the original design. Any pneumatic test shall include a preliminary check at not more than 0.17 MPa (25 lbf/in2) gauge pressure. The pressure shall be increased gradually in steps providing sufficient time to allow the piping to equalize strains during

10-118

TRANSPORT AND STORAGE OF FLUIDS

TABLE 10-52 Preheat Temperatures Base metal P-No. [Note (1)] 1

Base Metal Group Carbon steel

3

Alloy steel, Cr ≤ ½%

4 5A

Alloy steel, ½% < Cr ≤ 2% Alloy steel

5B

Alloy steel

6 9A 9B 10I 15E ...

Martensitic stainless steel Nickel alloy steel Nickel alloy steel 27Cr steel 9Cr–1Mo–V CSEF steel All other materials

Greater material thickness mm in. ≤25 ≤1 >25 >1 >25 >1 ≤13 ≤½ >13 >½ All All All All All All All All All All All All ≤13 ≤½ All All All All All All All All All All ... ...

Additional limits [Note (2)] %C > 0.30 [Note (3)] %C ≤ 0.30 [Note (3)] %C > 0.30 [Note (3)] SMTS ≤ 450 MPa (65 ksi) SMTS ≤ 450 MPa (65 ksi) SMTS > 450 MPa (65 ksi) None SMTS ≤ 414 MPa (60 ksi) SMTS > 414 MPa (60 ksi) SMTS ≤ 414 MPa (60 ksi) SMTS > 414 MPa (60 ksi) %Cr > 6.0 [Note (3)] None None None None None None

Required minimum temperature °C °F 10 50 10 50 95 200 10 50 95 200 95 200 120 250 150 300 200 400 150 300 200 400 200 400 200 [Note (4)] 400 [Note (4)] 120 250 150 300 150 [Note (5)] 300 [Note (5)] 200 400 10 50

NOTES:

(1) P-Nos. and Group Nos. from BPV Code, Section IX, QW/QB-422. Reprinted from ASME Boiler and Pressure Vessel Code, Section IX by permission of the American Society of Mechanical Engineers, New York. All rights reserved. (2) SMTS = Specified Minimum Tensile Strength. (3) Composition may be based on ladle or product analysis or in accordance with specification limits. (4) Maximum interpass temperature 315°C (600°F). (5) Maintain interpass temperature between 150°C and 230°C (300°F and 450°F). Extracted from Process Piping, ASME B31.3-2014 with permission of the publisher, the American Society of Mechanical Engineers, New York. All rights reserved.

TABLE 10-53 Postweld Heat Treatment P-No. and Group No. (BPV Code Section IX, QW/QB-420)

Minimum Holding Time at Temperature for Control Thickness [Note (2)] Holding Temperature Range, °C (°F) [Note (1)]

Up to 50 mm (2 in.)

Over 50 mm (2 in.)

P-No. 1, Group Nos. 1–3

595 to 650 (1100 to 1200)

1 h/25 mm (1 hr/in.); 15 min min.

2 hr plus 15 min for each additional 25 mm (in.) over 50 mm (2 in.)

P-No. 3, Group Nos. 1 and 2 P-No. 4, Group Nos. 1 and 2 P-No. 5A, Group No. 1 P-No. 5B, Group No. 1 P-No. 6, Group Nos. 1–3 P-No. 7, Group Nos. 1 and 2 [Note (3)] P-No. 8, Group Nos. 1–4 P-No. 9A, Group No. 1 P-No. 9B, Group No. 1 P-No. 10H, Group No. 1 P-No. 10I, Group No. 1 [Note (3)] P-No. 11A P-No. 15E, Group No. 1

595 to 650 (1100 to 1200) 650 to 705 (1200 to 1300) 675 to 760 (1250 to 1400) 675 to 760 (1250 to 1400) 760 to 800 (1400 to 1475) 730 to 775 (1350 to 1425) PWHT not required unless required by WPS 595 to 650 (1100 to 1200) 595 t o 650 (1100 to 1200) PWHT not required unless required by WPS. If done, see Note (4). 730 to 815 (1350 to 1500) 550 to 585 (1025 to 1085) [Note (5)] 705 to 775 (1300 to 1425) [Notes (6) and (7)]

1 h/25 mm (1 hr/in.); 30 min min.

P-No. 62 All other materials

540 to 595 (1000 to 1100) PWHT as required by WPS

... In accordance with WPS

1 h/25 mm (1 hr/in.) up to 125 mm (5 in.) plus 15 min for each additional 25 mm (in.) over 125 mm (5 in.) See Note (8) In accordance with WPS

GENERAL NOTE: The exemptions for mandatory PWHT are defined in ASME B31.1-2016, Table 331.1.3. Reprinted from ASME B31.1-2016 by permission of the American Society of Mechanical Engineers, New York. All rights reserved. NOTES:

(1) (2) (3) (4)

The holding temperature range is further defined in para. 331.1.6(c), ASME B31.1-2016, and in Table 331.1.2. The control thickness is defined in para. 331.1.3. Cooling rate shall not be greater than 55°C (100°F) per hour in the range above 650°C (1200°F), after which the cooling rate shall be sufficiently rapid to prevent embrittlement. If PWHT is performed after welding, it shall be within the following temperature ranges for the specific alloy, followed by rapid cooling: Alloys S31803 and S32205 — 1020°C to 1100°C (1870°F to 2010°F) Alloy S32550 — 1040°C to 1120°C (1900°F to 2050°F) Alloy S32750 — 1025°C to 1125°C (1880°F to 2060°F) All others — 980°C to 1040°C (1800°F to 1900°F) (5) Cooling rate shall be >165°C (300°F)/h to 315°C (600°F)/h. (6) The minimum PWHT holding temperature may be 675°C (1250°F) for nominal material thicknesses [see para. 331.1.3(c)] ≤13 mm (½ in.). (7) The Ni + Mn content of the filler metal shall not exceed 1.2% unless specified by the designer, in which case the maximum temperature to be reached during PWHT shall be the A1 (lower transformation or lower critical temperature) of the filler metal, as determined by analysis and calculation or by test, but not exceeding 800°C (1470°F). If the 800°C (1470°F) limit was not exceeded but the A1 of the filler metal was exceeded or if the composition of the filler metal is unknown, the weld must be removed and replaced. It shall then be rewelded with compliant filler metal and subjected to a compliant PWHT. If the 800°C (1470°F) limit was exceeded, the weld and the entire area affected by the PWHT will be removed and, if reused, shall be renormalized and tempered prior to reinstallation. (8) Heat treat within 14 days after welding. Hold time shall be increased by 1.2 h for each 25 mm (1 in.) over 25 mm (1 in.) thickness. Cool to 425°C (800°F) at a rate ≤280°C (500°F).

PROCESS PLANT PIPING TABLE 10-54

Types of Examination for Evaluating Imperfections* Type of examination

Type of imperfection

Visual

Crack Incomplete penetration Lack of fusion Weld undercutting Weld reinforcement Internal porosity External porosity Internal slag inclusions External slag inclusions Concave root surface

X X X X X

Liquid-penetrant or magnetic-particle X

X X X

Ultrasonic or radiographic Random

100%

X X X

X X X

X

X

X

X

X

X

∗Extracted from the Chemical Plant and Petroleum Refinery Piping Code, ANSI B31.31980, with permission of the publisher, the American Society of Mechanical Engineers, New York. All rights reserved. For code acceptance criteria (limits on imperfections) for welds see Table 10-51.

test and to check for leaks. Once test pressure has been achieved, the pressure shall be reduced to design pressure prior to examining for leakage. At the owner’s option, a piping system used only for Category D fluid service as defined in the subsection Classification of Fluid Service may be tested at the normal operating conditions of the system during or prior to initial operation by examining for leaks at every joint not previously tested. A preliminary check shall be made at not more than 0.17 MPa (25 lbf/in2) gauge pressure when the contained fluid is a gas or a vapor. The pressure shall be increased gradually in steps providing sufficient time to allow the piping to equalize strains during testing and to check for leaks. Tests alternative to those required by these provisions may be applied under certain conditions described in the code. Piping required to have a sensitive leak test shall be tested by the gas and bubble formation testing method specified in Art. 10, App. I, Sec. V of the ASME Boiler and Pressure Vessel Code or by another method demonstrated to have equal or greater sensitivity. The sensitivity of the test shall be at least (100 Pa ⋅ mL)/s [(10-3 atm ⋅ mL)/s] under test conditions. Records shall be kept of each piping installation during the testing. COST COMPARISON OF PIPING SYSTEMS Piping may represent as much as 25 percent of the cost of a chemical-process plant. The installed cost of piping systems varies widely with the materials of construction and the complexity of the system. A study of piping costs shows that the most economical choice of material for a simple straight piping run may not be the most economical for a complex installation made up of many short runs involving numerous fittings and valves. The economics also depend heavily on the pipe size and fabrication techniques employed. Fabrication methods such as bending to standard long-radius-elbow dimensions and machine-flaring lap joints have a large effect on the cost of fabricating pipe from ductile materials suited to these techniques. Cost reductions of as high as 35 percent are quoted by some custom fabricators utilizing advanced techniques; however, the basis for pricing comparisons should be carefully reviewed. Figure 10-170 is based on data extracted from a comparison of the installed cost of piping systems of various materials published by Dow Chemical Co. The chart shows the relative cost ratios for systems of various materials based on two installations, one consisting of 152 m (500 ft) of 2-in pipe in a complex piping arrangement and the other of 305 m (1000 ft) of 2-in pipe in a straight-run piping arrangement. Figure 10-170 is based on field-fabrication construction techniques using welding stubs, the method commonly used by contractors. A considerably different ranking would result from using other construction methods such as machine-formed lap joints and bends in place of welding elbows. Piping cost experience shows that it is difficult to generalize and reflect accurate piping cost comparisons. Although the prices for many of the metallurgies shown in Fig. 10-170 are very volatile even over short periods, Fig. 10-170 may still be used as a reasonable initial estimate of the relative cost of metallic materials. The cost of nonmetallic materials and lined metallic materials versus solid alloy materials should be carefully reviewed prior to material selection. For an accurate comparison the cost for each type of material must be estimated individually on the basis of the actual fabrication and installation methods that will be used, pipe sizes, and the conditions anticipated for the proposed installation. FORCES OF PIPING ON PROCESS MACHINERY AND PIPING VIBRATION The reliability of process rotating machinery is affected by the quality of the process piping installation. Excessive external forces and moments upset casing alignment and can reduce clearance between motor and casing. Further, the bearings, seals, and coupling can be adversely affected, resulting

10-119

in repeated failures that may be correctly diagnosed as misalignment, and may have excessive piping forces as the root causes. Most turbine and compressor manufacturers have prescribed specification or will follow NEMA standards for allowable nozzle loading. For most of the pumps, API or ANSI pump standards will be followed when evaluating the pump nozzle loads. Pipe support restraints need to be placed at the proper locations to protect the machinery nozzles during operation. Prior to any machinery alignment procedure, it is imperative to check for machine pipe strain. This is accomplished by the placement of dial indicators on the shaft and then loosening the hold-down bolts. Movements of greater than 1 mil are considered indication of a pipe strain condition. This is an important practical problem area, as piping vibration can cause considerable downtime or even pipe failure. Pipe vibration is caused by 1. Internal flow (pulsation) 2. Plant machinery (such as compressors, pumps) Pulsation can be problematic and difficult to predict. Pulsations are also dependent on acoustic resonance characteristics. For reciprocating equipment, such as reciprocating compressors and pumps, in some cases, an analog (digital) study needs to be performed to identify the deficiency in the piping and pipe support systems as well as to evaluate the performance of the machine during operation. The study will also provide recommendations on how to improve the machine and piping system’s performance. When a pulsation frequency coincides with a mechanical or acoustic resonance, severe vibration can result. A common cause for pulsation is the presence of flow control valves or pressure regulators. These often operate with high pressure drops (i.e., high flow velocities), which can result in the generation of severe pulsation. Flashing and cavitation can also contribute. Modern-day piping design codes can model the vibration situation, and problems can thus be resolved in the design phases. HEAT TRACING OF PIPING SYSTEMS Heat tracing is used to maintain pipes and the material that pipes contain at temperatures above the ambient temperature. Two common uses of heat tracing are to prevent water pipes from freezing and maintain fuel oil pipes at high enough temperatures that the viscosity of the fuel oil will allow easy pumping. Heat tracing is also used to prevent the condensation of a liquid from a gas and to prevent the solidification of a liquid commodity. A heat-tracing system is often more expensive on an installed cost basis than the piping system it is protecting, and it will also have significant operating costs. A study of heat-tracing costs by a major chemical company showed installed costs of $31/ft to $142/ft and yearly operating costs of $1.40/ft to $16.66/ft. In addition to being a major cost, the heat-tracing system is an important component of the reliability of a piping system. A failure in the heattracing system will often render the piping system inoperable. For example, with a water freeze protection system, the piping system may be destroyed by the expansion of water as it freezes if the heat-tracing system fails. The vast majority of heat-traced pipes are insulated to minimize heat loss to the environment. A heat input of 2 to 10 W/ft is generally required to prevent an insulated pipe from freezing. With high wind speeds, an uninsulated pipe could require well over 100 W/ft to prevent freezing. Such a high heat input would be very expensive. Heat tracing for insulated pipes is generally only required for the period when the material in the pipe is not flowing. The heat loss of an insulated pipe is very small compared to the heat capacity of a flowing fluid. Unless the pipe is extremely long (several thousands of feet), the temperature drop of a flowing fluid will not be significant. There are three major methods of avoiding heat tracing: 1. Change the ambient temperature around the pipe to a temperature that will avoid low-temperature problems. Burying water pipes below the frost line or running them through a heated building are the two most common examples of this method. 2. Empty a pipe after it is used. Arranging the piping such that it drains itself when not in use can be an effective method of avoiding the need for heat tracing. Some infrequently used lines can be pigged or blown out with compressed air. This technique is not recommended for commonly used lines due to the high labor requirement. 3. Arrange a process such that some lines have continuous flow; this can eliminate the need for tracing these lines. This technique is generally not recommended because a failure that causes a flow stoppage can lead to blocked or broken pipes. Some combination of these techniques may be used to minimize the quantity of traced pipes. However, the majority of pipes containing fluids that must be kept above the minimum ambient temperature are generally going to require heat tracing. Types of Heat-Tracing Systems Industrial heat-tracing systems are generally fluid systems or electrical systems. In fluid systems, a pipe or tube called the tracer is attached to the pipe being traced, and a warm fluid is

10-120

TRANSPORT AND STORAGE OF FLUIDS

FIG. 10-170 Cost rankings and cost ratios for various piping materials. This figure is based on field-fabrication construction techniques using welding stubs, as this is the method

most often employed by contractors. A considerably different ranking would result from using other construction methods, such as machined-formed lap joints, for the alloy pipe. ºCost ratio = (cost of listed item)/(cost of Schedule 40 carbon-steel piping system, field-fabricated by using welding stubs). (Extracted with permission from Installed Cost of Corrosion Resistant Piping, copyright 1977, Dow Chemical Co.)

PROCESS PLANT PIPING

10-121

FIG. 10-171 Steam tracing system.

put through it. The tracer is placed under the insulation. Steam is by far the most common fluid used in the tracer, although ethylene glycol and more exotic heat-transfer fluids are used. In electrical systems, an electrical heating cable is placed against the pipe under the insulation. Fluid Tracing Systems Steam tracing is the most common type of industrial pipe tracing. In 1960, over 95 percent of industrial tracing systems were steam-traced. By 1995, improvements in electric heating technology increased the electric share to 30 to 40 percent. Fluid systems other than steam are rather uncommon and account for less than 5 percent of tracing systems. Half-inch copper tubing is commonly used for steam tracing. Threeeighths-inch tubing is also used, but the effective circuit length is then decreased from 150 ft to about 60 ft. In some corrosive environments, stainless steel tubing is used. In addition to the tracer, a steam tracing system (Fig. 10-171) consists of steam supply lines to transport steam from the existing steam lines to the traced pipe, a steam trap to remove the condensate and hold back the steam, and in most cases a condensate return system to return the condensate to the existing condensate return system. In the past, a significant percentage of condensate from steam tracing was simply dumped to drains, but increased energy costs and environmental rules have caused almost all condensate from new steam tracing systems to be returned. This has significantly increased the initial cost of steam tracing systems. Applications requiring accurate temperature control are generally limited to electric tracing. For example, chocolate lines cannot be exposed to steam temperatures, or the product will degrade; and if caustic soda is heated above 65°C (150°F), it becomes extremely corrosive to carbon-steel pipes. For some applications, either steam or electricity is simply not available, and this makes the decision. It is rarely economic to install a steam boiler just for tracing. Steam tracing is generally considered only when a boiler already exists or is going to be installed for some other primary purpose. Additional electric capacity can be provided in most situations for reasonable costs. It is considerably more expensive to supply steam from a long distance than it is to provide electricity. Unless steam is available close to the pipes being traced, the automatic choice is usually electric tracing. For most applications, particularly in processing plants, either steam tracing or electric tracing could be used, and the correct choice is dependent on the installed costs and the operating costs of the competing systems. Economics of Steam Tracing versus Electric Tracing The question of the economics of various tracing systems has been examined thoroughly. All these papers have concluded that electric tracing is generally less expensive to install and significantly less expensive to operate. Electric tracing has significant cost advantages in terms of installation because less labor

is required than for steam tracing. However, it is clear that there are some special cases where steam tracing is more economical. The two key variables in the decision to use steam tracing or electric tracing are the temperature at which the pipe must be maintained and the distance to the supply of steam and a source of electric power. Table 10-55 shows the installed costs and operating costs for 400 ft of 4-in pipe, maintained at four different temperatures, with supply lengths of 100 ft for both electricity and steam and $25/h labor. These are the major advantages of a steam tracing system: 1. High heat output. Due to its high temperature, a steam tracing system provides a large amount of heat to the pipe. There is a very high heattransfer rate between the metallic tracer and a metallic pipe. Even with damage to the insulation system, there is very little chance of a low-temperature failure with a steam tracing system. 2. High reliability. Many things can go wrong with a steam tracing system, but very few of the potential problems lead to a heat-tracing failure. Steam traps fail, but they usually fail in the open position, allowing for a continuous flow of steam to the tracer. Other problems such as steam leaks that can cause wet insulation are generally prevented from becoming heat-tracing failures by the extremely high heat output of a steam tracer. Also, a tracing tube is capable of withstanding a large amount of mechanical abuse without failure. 3. Safety. While steam burns are fairly common, there are generally fewer safety concerns than with electric tracing. 4. Common usage. Steam tracing has been around for many years, and many operators are familiar with the system. Because of this familiarity, failures due to operator error are not very common. These are the weaknesses of a steam tracing system: 1. High installed costs. The incremental piping required for the steam supply system and the condensate return system must be installed and insulated, and in the case of the supply system, additional steam traps are often required. TABLE 10-55

Steam versus Electric Tracing* TIC

TOC

Temperature maintained

Steam

Electric

Ratio S/E

Steam

50°F 150°F 250°F 400°F

22,265 22,265 22,807 26,924

7,733 13,113 17,624 14,056

2.88 1.70 1.29 1.92

1,671 4,356 5,348 6,724

Electric 334 1,892 2,114 3,942

Ratio S/E 5.00 2.30 2.53 1.71

*Specifications: 400 ft of 44-in pipe, $25/h labor, $0.07/kWh, $4.00/1000 lb steam, 100-ft supply lines. TIC = total installed cost; TOC = total operating costs.

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TRANSPORT AND STORAGE OF FLUIDS

The tracer itself is not expensive, but the labor required for installation is relatively high. Studies have shown that steam tracing systems typically cost from 50 to 150 percent more than a comparable electric tracing system. 2. Energy inefficiency. A steam tracing system’s total energy use is often more than 20 times the actual energy requirement to keep the pipe at the desired temperature. The steam tracer itself puts out significantly greater energy than required. The steam traps use energy even when they are properly operating and waste large amounts of energy when they fail in the open position, which is the common failure mode. Steam leaks waste large amounts of energy, and both the steam supply system and the condensate return system use significant amounts of energy. 3. Poor temperature control. A steam tracing system offers very little temperature control capability. The steam is at a constant temperature (50 psig steam is 300°F) usually well above that desired for the pipe. The pipe will reach an equilibrium temperature somewhere between the steam temperature and the ambient temperature. However, the section of pipe against the steam tracer will effectively be at the steam temperature. This is a serious problem for temperature-sensitive fluids such as food products. It also represents a problem with fluids such as bases and acids, which are not damaged by high temperatures but often become extremely corrosive to piping systems at higher temperatures. 4. High maintenance costs. Leaks must be repaired and steam traps must be checked and replaced if they have failed. Numerous studies have shown that, due to the energy lost through leaks and failed steam traps, an extensive maintenance program is an excellent investment. Steam maintenance costs are so high that for low-temperature maintenance applications, total steam operating costs are sometimes greater than electric operating costs, even if no value is placed on the steam. Electric Tracing An electric tracing system (see Fig. 10-172) consists of an electric heater placed against the pipe under the thermal insulation, the supply of electricity to the tracer, and any control or monitoring system that may be used (optional). The supply of electricity to the tracer usually consists of an electrical panel and electrical conduit or cable trays. Depending on the size of the tracing system and the capacity of the existing electrical system, an additional transformer may be required. Advantages of Electric Tracing 1. Lower installed and operating costs. Most studies have shown that electric tracing is less expensive to install and less expensive to operate. This is true for most applications. However, for some applications, the installed costs of steam tracing are equal to or less than those of electric tracing. 2. Reliability. In the past, electric heat tracing had a well-deserved reputation for poor reliability. However, since the introduction of self-regulating heaters in 1971, the reliability of electric heat tracing has improved dramatically. Self-regulating heaters cannot destroy themselves with their own heat output. This eliminates the most common failure mode of polymerinsulated constant-wattage heaters. Also, the technology used to manufacture mineral-insulated cables, high-temperature electric heat tracing, has improved significantly, and this has improved their reliability.

FIG. 10-172 Electrical beat tracing system.

FIG. 10-173

Self-regulating heating cable.

3. Temperature control. Even without a thermostat or any control system, an electric tracing system usually provides better temperature control than a steam tracing system. With thermostatic or electronic control, very accurate temperature control can be achieved. 4. Safety. The use of self-regulating heaters and ground leakage circuit breakers has answered the safety concerns of most engineers considering electric tracing. Self-regulating heaters eliminate the problems from hightemperature failures, and ground leakage circuit breakers minimize the danger of an electrical fault to ground, causing injury or death. 5. Monitoring capability. One question often asked about any heat-tracing system is, “How do I know it is working?” Electric tracing now has available almost any level of monitoring desired. The temperature at any point can be monitored with both high and low alarm capability. This capability has allowed many users to switch to electric tracing with a high degree of confidence. 6. Energy efficiency. Electric heat tracing can accurately provide the energy required for each application without the large additional energy use of a steam system. Unlike steam tracing systems, other parts of the system do not use significant amounts of energy. Disadvantages of Electric Tracing 1. Poor reputation. In the past, electric tracing has been less than reliable. Due to past failures, some operating personnel are unwilling to take a chance on any electric tracing. 2. Design requirements. A slightly higher level of design expertise is required for electric tracing than for steam tracing. 3. Lower power output. Since electric tracing does not provide a large multiple of the required energy, it is less forgiving to problems such as damaged insulation or below design ambient temperatures. Most designers include a 10 to 20 percent safety factor in the heat loss calculation to cover these potential problems. Also, a somewhat higher than required design temperature is often specified to provide an additional safety margin. For example, many water systems are designed to maintain 50°F to prevent freezing. Types of Electric Tracing Self-regulating electric tracing (see Fig. 10-173) is by far the most popular type of electric tracing. The heating element in

PROCESS PLANT PIPING TABLE 10-56

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Effect of Supply Lengths

Ratio of steam TIC to electric TIC maintained at 150°F Electric supply length

FIG. 10-174 Self-regulation.

a self-regulating heater is a conductive polymer between the bus wires. This conductive polymer increases its resistance as its temperature increases. The increase in resistance with temperature causes the heater to lower its heat output at any point where its temperature increases (Fig. 10-174). This self-regulating effect eliminates the most common failure mode of constantwattage electric heaters, which is destruction of the heater by its own heat output. Because self-regulating heaters are parallel heaters, they may be cut to length at any point without changing their power output per unit of length. This makes them much easier to deal with in the field. They may be terminated, teed, or spliced in the field with hazardous-area-approved components. MI Cables Mineral insulated cables (Fig. 10-175) are the electric heat tracers of choice for high-temperature applications. High-temperature applications are generally considered to maintain temperatures above 250°F or exposure temperatures above 420°F where self-regulating heaters cannot be used. MI cable consists of one or two heating wires, magnesium oxide insulation (whence it gets its name) and an outer metal sheath. Today the metal sheath is generally Inconel. This eliminates both the corrosion problems with copper sheaths and the stress cracking problems with stainless steel. MI cables can maintain temperatures up to 1200°F and withstand exposure up to 1500°F. The major disadvantage of MI cable is that it must be factory-fabricated to length. It is very difficult to terminate or splice the heater in the field. This means pipe measurements are necessary before the heaters are ordered. Also, any damage to an MI cable generally requires a complete new heater. It’s not as easy to splice in a good section as with selfregulating heaters. Polymer-Insulated Constant-Wattage Electric Heaters These are slightly cheaper than self-regulating heaters, but they are generally being replaced with self-regulating heaters due to inferior reliability. These heaters tend to destroy themselves with their own heat output when they are overlapped at valves or flanges. Since overlapping self-regulating heaters is the standard installation technique, it is difficult to prevent this technique from being used on the similar-looking constant-wattage heaters.

FIG. 10-175 Mineral insulated cable (MI cable).

Steam supply length, ft

40 ft

100 ft

300 ft

40 100 300

1.1 1.9 4.9

1.0 1.7 4.2

0.7 1.1 2.9

SECT (Skin-Effect Current Tracing) This is a special type of electric tracing employing a tracing pipe, usually welded to the pipe being traced, that is used for extremely long lines. With SECT circuits, up to 10 mi can be powered from one power point. All SECT systems are specially designed by heat-tracing vendors. Impedance Tracing This uses the pipe being traced to carry the current and generate the heat. Less than 1 percent of electric heat-tracing systems use this method. Low voltages and special electrical isolation techniques are used. Impedance heating is useful when extremely high heat densities are required, such as when a pipe containing aluminum metal must be melted from room temperature on a regular basis. Most impedance systems are specially designed by heat-tracing vendors. Choosing the Best Tracing System Some applications require either steam tracing or electric tracing regardless of the relative economics. For example, a large line that is regularly allowed to cool and needs to be quickly heated would require steam tracing because of its much higher heat output capability. In most heat-up applications, steam tracing is used with heattransfer cement, and the heat output is increased by a factor of up to 10. This is much more heat than would be practical to provide with electric tracing. For example, a ½-in copper tube containing 50 psig steam with heat-transfer cement would provide over 1100 Btu/(h∙ft) to a pipe at 50°F. This is over 300 W/ft or more than 15 times the output of a high-powered electric tracer. Table 10-55 shows that electric tracing has a large advantage in terms of cost at low temperatures and smaller but still significant advantages at higher temperatures. Steam tracing does relatively better at higher temperatures because steam tracing supplies significantly more power than is necessary to maintain a pipe at low temperatures. Table 10-55 indicates that there is very little difference between the steam tracing system at 50°F and the system at 250°F. However, the electric system more than doubles in cost between these two temperatures because more heaters, higher-powered heaters, and higher-temperature heaters are required. The effect of supply lengths on a 150°F system can be seen from Table 10-56. Steam supply pipe is much more expensive to run than electrical conduit. With each system having relatively short supply lines (40 ft each) the electric system has only a small cost advantage (10 percent, or a ratio of 1.1). This ratio is 2.1 at 50°F and 0.8 at 250°F. However, as the supply lengths increase, electric tracing has a large cost advantage.

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TRANSPORT AND STORAGE OF FLUIDS

STORAGE AND PROCESS VESSELS STORAGE OF LIQUIDS Atmospheric Tanks The term atmospheric tank as used here applies to any tank that is designed to operate at pressures from atmospheric through 3.45 kPag (0.5 psig). It may be either open to the atmosphere or enclosed. Atmospheric tanks may be either shop-fabricated or field-erected. The most common application is storage of fuel for transportation and power generation. See Pressure Tanks and Pressure Vessels later in this subsection. Shop-Fabricated Storage Tanks A shop-fabricated storage tank is a storage tank constructed at a tank manufacturer’s plant and transported to a facility for installation. In general, tanks 190 m3 (50,000 gal) and under can be shop-fabricated and shipped in one piece to an installation site. Shopfabricated storage tanks may be either underground storage tanks (USTs) or aboveground storage tanks (ASTs). USTs versus ASTs For decades, USTs were the standard means of storing petroleum and chemicals in quantities of 190 m3 (50,000 gal) or less. However, during the 1990s, many industrial and commercial facilities shifted to ASTs for hazardous product storage. Reasons include the ability to visually monitor the storage tank as well as to avoid perceived risks and myriad regulations surrounding underground storage tanks. Nonetheless, AST installations are also subject to certain regulations and codes, particularly fire codes. The choice of USTs or ASTs is driven by numerous factors. Local authorities having jurisdiction may allow only USTs. Limited real estate may also preclude the use of ASTs. In addition, ASTs are subject to minimum distance separations from one another and from buildings, property lines, and public ways. ASTs are visually monitorable, yet may be aesthetically undesirable. Other considerations are adequate protection from spills, vandalism, and vehicular damage. Additionally, central design elements regarding product transfer and system functionality must be taken into account. USTs are subject to myriad EPA regulations and fire codes. Further, a commonly cited drawback is the potential for unseen leaks and subsequent environmental damage and cleanup. However, advances in technology have addressed these concerns. Corrosion protection and leak detection are now standard in all UST systems. Sophisticated tank and pipe secondary containment systems have been developed to meet the EPA’s secondary containment mandate for underground storage of nonpetroleum chemicals. In-tank monitoring devices for tracking inventory, tank integrity testing equipment, statistical inventory reconciliation analysis, leak-free dry-disconnect pipe and hose joints for loading/unloading, and in-tank fill shutoff valves are just a few of the many pieces of equipment which have surfaced as marketplace solutions. Properly designed and installed in accordance with industry standards, regulations, and codes, both UST and AST systems are reliable and safe. Because of space limitations and the prevalence of ASTs at plant sites, only ASTs will be discussed further. Aboveground Storage Tanks Aboveground storage tanks are classified as either field-erected or shop-fabricated. The latter are typically 190 m3 (50,000 gal) or less and may be shipped over the highway, while larger tanks are more economically erected in the field. Whereas field-erected tanks likely constitute the majority of total AST storage capacity, shop-fabricated ASTs constitute the majority of the total number of ASTs in existence today. Most of these shop-fabricated ASTs store hazardous liquids at atmospheric pressure and have 45-m3 (12,000-gal) capacity or smaller. Shop-fabricated ASTs can be designed and fabricated as pressure vessels, but are more typically vented to atmosphere. They are oriented for either horizontal or vertical installation and are made in either cylindrical or rectangular form. Tanks are often secondarily contained and may also include insulation for fire safety or temperature control. Compartmented ASTs are also available. Over 90 percent of the atmospheric tank applications store some sort of hydrocarbon. Within that, a majority are used to store motor fuels. Fire Codes Many chemicals are hazardous and may be subject to fire codes. All hydrocarbon tanks are classified as hazardous. Notably, with the increase in the use of ASTs at private fleet fueling facilities in the 1990s, fire codes were rapidly modified to address safety concerns. In the United States, two principal organizations publish fire codes for underground storage tanks, with each state adopting all or part of the respective codes. The National Fire Protection Association (NFPA) has developed several principal codes pertaining to the storage of flammable and combustible liquids: NFPA 30, Flammable and Combustible Liquids Code (2015) NFPA 30A, Code for Motor Fuel Dispensing Facilities and Repair Garages (2015) NFPA 31, Standard for the Installation of Oil Burning Equipment (2016)

The International Code Council (ICC) was formed by the consolidation of three formerly separate fire code organizations: International Conference of Building Officials (ICBO), which had published the Uniform Fire Code under its fire service arm, the International Fire Code Institute (IFCI); Building Officials and Code Administrators (BOCA), which had published the National Fire Prevention Code; and Southern Building Congress Code International (SBCCI), which had published the Standard Fire Prevention Code. When the three groups merged in 2000, in part to develop a common fire code, the individual codes became obsolete; however, they are noted above since references to them may periodically surface. The consolidated code is IFC-2015, International Fire Code. The Canadian Commission on Building and Fire Codes (CCBFC) developed a recommended model code to permit adoption by various regional authorities. The National Research Council of Canada publishes the model code document National Fire Code of Canada (2010). Standards Third-party standards for AST fabrication have evolved over the past two decades, as have recommended practice guidelines for the installation and operations of AST systems. Standards developed by Underwriters Laboratories (UL) have been the most predominant of guidelines—in fact, ASTs are often categorized according to the UL standard that they meet, such as “a UL 142 tank.” Underwriters Laboratories Inc. standards for steel ASTs storing hazardous liquids include the following: UL 142, Steel Aboveground Tanks for Flammable and Combustible Liquids, 9th ed., covers aboveground, steel atmospheric tanks for storage of noncorrosive, stable, and hazardous liquids that have a specific gravity not exceeding that of water. UL 142 applies to single-wall and double-wall horizontal carbon-steel and stainless steel tanks up to 190 m3 (50,000 gal), with a maximum diameter of 3.66 m (12 ft) and a maximum length-to-diameter ratio of 8 to 1. A formula from Roark’s Formulas for Stress and Strain has been incorporated within UL 58 to calculate minimum steel wall thicknesses. UL 142 also applies to vertical tanks up to 10.7 m (35 ft) in height. UL 142 has been the primary AST standard since its development in 1922. Tanks covered by these standards can be fabricated in cylindrical or rectangular configurations. The standard covers secondary contained tanks, either of dual-wall construction or a tank in a steel or concrete dike or bund. It also provides listings for special AST construction, such as those used under generators for backup power. These tanks are fabricated, inspected, and tested for leakage before shipment from the factory as completely assembled vessels. UL 142 provides details for steel type, wall thickness, compartments and bulkheads, manways, and other fittings and appurtenances. Issues relating to leakage, venting, and the ability of the tank to withstand the development of internal pressures encountered during operation and production leak testing are also addressed. These requirements do not apply to large field-erected storage tanks covered by the Standard for Welded Steel Tanks for Oil Storage, API 650, or the Specification for Field-Welded Tanks for Storage of Production Liquids, API 12D; or the Specification for Shop-Welded Tanks for Storage of Production Liquids, API 12F. UL 2085, Protected Aboveground Tanks for Flammable and Combustible Liquids, covers shop-fabricated, aboveground atmospheric protected tanks intended for storage of stable, hazardous liquids that have a specific gravity not greater than that of water and that are compatible with the material and construction of the tank. The tank construction is intended to limit the heat transferred to the primary tank when the AST is exposed to a 2-h hydrocarbon pool fire of 1093°C (2000°F). The tank must be insulated to withstand the test without leakage and with an average maximum temperature rise on the primary tank not exceeding 127°C (260°F). Temperatures on the inside surface of the primary tank cannot exceed 204°C (400°F). UL 2085 also provides criteria for resistance against vehicle impact, ballistic impact, and fire hose impact. These tanks are also provided with integral secondary containment intended to prevent any leakage from the primary tank. UL 2080, Fire Resistant Tanks for Flammable and Combustible Liquids, is similar to UL 2085 tanks, except with an average maximum temperature rise on the primary tank limited to 427°C (800°F) during a 2-h pool fire. Temperatures on the inside surface of the primary tank cannot exceed 538°C (1000°F). UL 2244, Standard for Aboveground Flammable Liquid Tank Systems, covers factory-fabricated, pre-engineered aboveground atmospheric tank systems intended for dispensing hazardous liquids, such as gasoline or diesel fuel, into motor vehicles, generators, or aircraft.

STORAGE AND PROCESS VESSELS UL 80, Steel Tanks for Oil-Burner Fuel, covers the design and construction of welded, atmospheric steel tanks with a maximum capacity of 0.23 to 2.5 m3 (60 to 660 gal) intended for unenclosed installation inside of buildings or for outside aboveground applications as permitted by the Standard for Installation of Oil-Burning Equipment, NFPA 31, primarily for the storage and supply of fuel oil for oil burners. UL 2245, Below-Grade Vaults for Flammable Liquid Storage Tanks, covers below-grade vaults intended for the storage of hazardous liquids in an aboveground atmospheric tank. Below-grade vaults, constructed of a minimum of 150 mm (6 in) of reinforced concrete or other equivalent noncombustible material, are designed to contain one aboveground tank, which can be a compartment tank. Adjacent vaults may share a common wall. The lid of the vault may be at grade or below. Vaults provide a safe means to install hazardous tanks so that the system is accessible to the operator without unduly exposing the public. Southwest Research Institute (SwRI) standards for steel ASTs storing hazardous liquids include the following: SwRI 93-01, Testing Requirements for Protected Aboveground Flammable Liquid/Fuel Storage Tanks, includes tests to evaluate the performance of ASTs under fire, hose stream, ballistics, heavy vehicular impact, and different environments. This standard requires pool-fire resistance similar to that of UL 2085. SwRI 97-04, Standard for Fire Resistant Tanks, includes tests to evaluate the performance of ASTs under fire and hose stream. This standard is similar to UL 2080 in that the construction is exposed to a 2-h hydrocarbon pool fire of 1093°C (2000°F). However, SwRI 97-04 is concerned only with the integrity of the tank after the 2-h test and is not concerned with the temperature inside the tank from heat transfer. As a result, UL 142 tanks have been tested to the SwRI standard and passed. Secondary containment with insulation is not necessarily an integral component of the system. Underwriters Laboratories of Canada (ULC) publishes a number of standards for aboveground tanks and accessories. All the following pertain to the aboveground storage of hazardous liquids such as gasoline, fuel oil, or similar products with a relative density not greater than 1.0: ULC S601, Shop Fabricated Steel Aboveground Horizontal Tanks for Flammable and Combustible Liquids, covers single- and double-wall cylindrical horizontal steel atmospheric tanks. These requirements do not cover tanks of capacities greater than 200 m3 (52,800 gal). ULC S630, Shop Fabricated Steel Aboveground Vertical Tanks for Flammable and Combustible Liquids, covers single- and double-wall cylindrical vertical steel atmospheric tanks. ULC S643, Shop Fabricated Steel Utility Tanks for Flammable and Combustible Liquids, covers single- and double-wall cylindrical horizontal steel atmospheric tanks. ULC S653-94, Aboveground Steel Contained Tank Assemblies for Flammable and Combustible Liquids, covers steel contained tank assemblies. ULC S655, Aboveground Protected Tank Assemblies for Flammable and Combustible Liquids, covers shop-fabricated primary tanks that provided with secondary containment and protective encasement and are intended for stationary installation and use in accordance with 1. National Fire Code of Canada, Part 4 2. CAN/CSA-B139, Installation Code for Oil Burning Equipment 3. The Environmental Code of Practice for Aboveground Storage Tank Systems Containing Petroleum Products 4. The requirements of the authority having jurisdiction ULC/ORD C142.20, Secondary Containment for Aboveground Flammable and Combustible Liquid Storage Tanks, covers secondary containments for aboveground primary tanks. ULC S602, Aboveground Steel Tanks for the Storage of Combustible Liquids Intended to Be Used as Heating and/or Generator Fuels, covers the design and construction of tanks of the atmospheric-type, intended for installation inside or outside buildings. This standard covers single-wall tanks and tanks with secondary containment, having a maximum capacity of 2.5 m3 (660 gal). The Petroleum Equipment Institute (PEI) has developed a recommended practice for AST system installation: PEI-RP200, RP 200, Recommended Practices for Installation of Aboveground Storage Systems for Motor Vehicle Fueling. The American Petroleum Institute (API) has developed a series of standards and specifications involving ASTs: API 12F, Shop Welded Tanks for Storage of Production Liquids RP 12R1, Setting, Maintenance, Inspection, Operation, and Repair of Tanks in Production Service RP 575, Inspection of Atmospheric and Low Pressure Storage Tanks RP 579, Fitness-For-Service API 650, Welded Tanks for Oil Storage, now applies to welded aluminum alloy storage tanks as well as welded steel tanks. API 652, Lining of Aboveground Storage Tank Bottoms

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API 653, Tank Inspection, Repair, Alteration, and Reconstruction API 2350, Overfill Protection for Storage Tanks in Petroleum Facilities (overfill is the primary cause of AST releases) The American Water Works Association (AWWA) has many standards dealing with water handling and storage. A list of its publications is given in the AWWA Handbook (annually). AWWA D100, Standard for Steel Tanks— Standpipes, Reservoirs, and Elevated Tanks for Water Storage, contains rules for design and fabrication. Although AWWA tanks are intended for water, they could be used for the storage of other liquids. The Steel Tank Institute (STI) publishes construction standards and recommended installation practices pertaining to ASTs fabricated to STI technologies. STI’s recommended installation practices are notable for their applicability to similar respective technologies: SP001-06, Standard for Inspection of In-Service Shop Fabricated Aboveground Tanks for Storage of Combustible and Flammable Liquids R912-00, Installation Instructions for Shop Fabricated Aboveground Storage Tanks for Flammable, Combustible Liquids F921, Standard for Aboveground Tanks with Integral Secondary Containment Standard for Fire Resistant Tanks (Flameshield) Standard for Fireguard Thermally Insulated Aboveground Storage Tanks F911, Standard for Diked Aboveground Storage Tanks The National Association of Corrosion Engineers (NACE International) has developed the following to protect the soil side of bottoms of on-grade carbon-steel storage tanks: NACE RP0193-2001, Standard Recommended Practice—External Cathodic Protection of On-Grade Metallic Storage Tank Bottoms. Environmental Regulations A key U.S. Environmental Protection Agency (U.S. EPA) requirement for certain aboveground storage facilities is the development and submittal of Spill Prevention Control and Countermeasure (SPCC) Plans within 40 CFR 112, the Oil Pollution Prevention regulation, which in turn is part of the Clean Water Act (CWA). SPCC Plans and Facility Response Plans pertain to facilities which may discharge oil into groundwater or storm runoff, which in turn may flow into navigable waters. Enacted in 1973, these requirements were principally used by owners of large, field-fabricated aboveground tanks predominant at that time, although the regulation applied to all bulk containers larger than 2.5 m3 (660 gal) and included the requirement for a Professional Engineer to certify the spill plan. In July 2002, the U.S. EPA issued a final rule amending 40 CFR 112 which included differentiation of shop-fabricated from field-fabricated ASTs. The rule also includes new subparts outlining the requirements for various classes of oil, revises the applicability of the regulation, amends the requirements for completing SPCC Plans, and makes other modifications. The revised rule also states that all bulk storage container installations must provide a secondary means of containment for the entire capacity of the largest single container, with sufficient freeboard to contain precipitation, and that such containment must be sufficiently impervious to contain discharged oil. The U.S. EPA encourages the use of industry standards to comply with the rules. Many owners of shop-fabricated tanks have opted for double-wall tanks built to STI or UL standards as a means to comply with this requirement. State and Local Jurisdictions Due to the manner in which aboveground storage tank legislation was promulgated in 1972 for protection of surface waters from oil pollution, state environmental agencies did not receive similar jurisdiction as they did within the underground storage tank rules. Nonetheless, many state environmental agencies, state fire marshals, or Weights and Measures departments—including Minnesota, Florida, Wisconsin, Virginia, Oklahoma, Missouri, Maryland, Delaware, and Michigan—are presently regulating aboveground storage tanks through other means. Other regulations exist for hazardous chemicals and should be consulted for specific requirements. Aboveground Storage Tank Types and Options Most hydrocarbon storage applications use carbon steel as the most economical and available material that provides suitable strength and compatibility for the specific storage application. For vertical tanks installed on grade, corrosion protection can be given to exterior tank bottoms in contact with soil. The interior of the tank can incorporate special coatings and linings (e.g., polymer, glass, or other metals). Some chemical storage applications require the storage tank be made from a stainless steel or nickel alloy. Fiberglass-reinforced plastic (FRP), polyethylene, or polypropylene may be used for nonflammable storage in smaller sizes. Suppliers can be contacted to verify the appropriate material to be used. As stated earlier, shop-fabricated ASTs are often categorized according to the standards to which the tanks are fabricated, e.g., a UL 142 or UL 2085 tank. That said, however, there are defined categories such as diked tanks, protected tanks, fire-resistant tanks, and insulated tanks. It is critical that the tank be specified for the given application, code requirements, and/or owner/operator preferences—and that the tank contractor and/or manufacturer be made aware of this.

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TRANSPORT AND STORAGE OF FLUIDS

Cylindrical or rectangular tanks storing flammable and combustible liquids (UL 142 ASTs) will normally comply with UL 142. The Seventh Edition published in 1993 was particularly notable, as it incorporated secondary containment designs (diking or steel secondary containment tanks) and rectangular tank designs. The latest edition is the Ninth Edition (2006). Rectangular tanks became a desirable option for small tanks, typically less than 7.6 m3 (2000 gal), as operators liked the accessibility of the flat top to perform operations and maintenance, without the need for special ladders or catwalks. Post-tensioned concrete is frequently used for tanks to about 57,000 m3 (15 × 106 gal), usually containing water. Their design is treated in detail by Creasy (Pre-stressed Concrete Cylindrical Tanks, Wiley, New York, 1961). For the most economical design of large open tanks at ground levels, he recommends limiting vertical height to 6 m (20 ft). Seepage can be a problem if unlined concrete is used with some liquids (e.g., gasoline). Elevated tanks can supply a large flow when required, but pump capacities need be only for average flow. Thus, they may save on pump and piping investment. They also provide flow after pump failure, an important consideration for fire systems. Open tanks may be used to store materials that will not be harmed by water, weather, or atmospheric pollution. Otherwise, a roof, either fixed or floating, is required. Fixed roofs are usually either domed or coned. Large tanks have coned roofs with intermediate supports. Since negligible pressure is involved, snow and wind are the principal design loads. Local building codes often give required values. Fixed-roof atmospheric tanks require vents to prevent pressure changes which would otherwise result from temperature changes and withdrawal or addition of liquid. API Standard 2000, Venting Atmospheric and Low Pressure Storage Tanks, gives practical rules for conservative vent design. The principles of this standard can be applied to fluids other than petroleum products. Excessive losses of volatile liquids, particularly those with flash points below 38°C (100°F), may result from the use of open vents on fixedroof tanks. Sometimes vents are connected to a manifold and lead to a vent tank, or the vapor may be removed by a vapor recovery unit (VRU). An effective way of preventing vent loss is to use one of the many types of variable-volume tanks. These are built under API Standard 650. They may have floating roofs of the double-deck or the single-deck type. There are lifter-roof types in which the roof either has a skirt moving up and down in an annular liquid seal or is connected to the tank shell by a flexible membrane. A fabric expansion chamber housed in a compartment on top of the tank roof also permits variation in volume. Floating roofs must have a seal between the roof and the tank shell. If not protected by a fixed roof, they must have drains for the removal of water, and the tank shell must have a “wind girder” to avoid distortion. An industry has developed to retrofit existing tanks with floating roofs. Many details on the various types of tank roofs are given in manufacturers’ literature. Figure 10-176 shows roof types. These roofs cause less condensation buildup and are highly recommended. Fire-Rated or Insulated ASTs: Protected and Fire-Resistant These ASTs have received much attention within the fire regulatory community, particularly for motor fuel storage and dispensing applications and generator base tanks. National model codes have been revised to allow this type of storage aboveground. An insulated tank can be a protected tank, built to third-party standards UL 2085 and/or SwRI 93-01, or a fire-resistant tank built to UL 2080 or SwRI 97-04. Protected tanks were developed in line with NFPA requirements and terminology, while fire-resistant ASTs were developed in line with Uniform Fire Code (now International Fire Code) requirements and terminology. Both protected tanks and fire-resistant tanks must pass a 1093°C (2000°F), 2-h fire test.

FIG. 10-176 Some types of atmospheric storage tanks.

The insulation properties of many fire-rated ASTs marketed today are typically provided by concrete; i.e., the primary steel tank is surrounded by concrete. Due to the weight of concrete, this design is normally limited to small tanks. Another popular AST technology meeting all applicable code requirements for insulated tanks and fabricated to UL 2085 is a tank that utilizes a lightweight monolithic thermal insulation in between two walls of steel to minimize heat transfer from the outer tank to the inner tank and to make tank handling easier. A secondary containment AST to prevent contamination of our environment has become a necessity for all hazardous liquid storage, regardless of its chemical nature, in order to minimize liability and protect neighboring property. A number of different regulations exist, but the regulations with the greatest impact are fire codes and the U.S. EPA SPCC rules for oil storage. In 1991, the Spill Prevention Control and Countermeasure (SPCC) rule proposed a revision to require secondary containment that was impermeable for at least 72 h following a release. The 2003 promulgated EPA SPCC rule no longer mandates a 72-h containment requirement, instead opting to require means to contain releases until they can be detected and removed. Nonetheless, the need for impermeable containment continues to position steel as a material of choice for shop-fabricated tanks. However, release prevention barriers made from plastic or concrete can also meet U.S. EPA requirements when periodically inspected for integrity. Diked ASTs Fire codes dictate that hazardous liquid tanks have spill control in the form of dike, remote impounding, or small secondary containment tanks. The dike must contain the content of the largest tank to prevent hazardous liquids from endangering the public and property. Traditional bulk storage systems include multiple tanks within a concrete or earthen dike wall. From a shop-fabricated tank manufacturer’s perspective, a diked AST generally refers to a steel tank within a factory-fabricated steel box, or dike. An example of a diked AST is the STI F911 standard, providing an opentopped steel rectangular dike and floor as support and secondary containment of a UL 142 steel tank. The dike will contain 110 percent of the tank capacity; as rainwater may already have collected in the dike, the additional 10 percent acts as freeboard should a catastrophic failure dump a full tank’s contents into a dike. Many fabricators offer steel dikes with shields to prevent rainwater from collecting. A double-wall AST of steel fulfills the same function as a diked AST with a rain shield. Double-wall designs consist of a steel wrap over a horizontal or vertical steel storage tank. The steel wrap provides an intimate, secondary containment over the primary tank. One such design is the Steel Tank Institute’s F921 standard, based upon UL 142–listed construction for the primary tank, outer containment, associated tank supports, or skids. Venting of ASTs is critical, since they are exposed to greater ambient temperature fluctuations than are USTs. Properly designed and sized venting, both normal (atmospheric) and emergency, is required. Normal vents permit the flow of air or inert gas into and out of the tank. The vent line must be large enough to accommodate the maximum filling or withdrawal rates without exceeding the allowable stress for the tank. Fire codes’ recommended installation procedures also detail specifics on pressure/vacuum venting devices and vent line flame arresters. For example, codes mandate different ventilation requirements for Class I-A liquids versus Class I-B or I-C liquids. Tank vent piping is generally not connected to a manifold unless required for special purposes, such as pollution control or vapor recovery. As always, local codes must be followed. Emergency venting prevents an explosion during a fire or another emergency. All third-party laboratory standards except UL 80 include emergency relief provisions, since these tanks are designed for atmospheric pressure conditions.

STORAGE AND PROCESS VESSELS Separation distances are also important. Aboveground storage tanks must be separated from buildings, property lines, fuel dispensers, and delivery trucks in accordance with the level of safety the tank design provides, depending on whether they are constructed of traditional steel or are vault/fire-resistant. For most chemical storage tanks, codes such as NFPA 30 and IFC give specific separation distances. For motor vehicle fueling applications, the codes are more stringent on separation requirements due to a greater exposure of the public to the hazards. Hence codes such as NFPA 30A establish variable separation distances depending on whether the facility is private or public. Separation distance requirements may dictate whether a tank buyer purchases a traditional steel UL 142 tank, a fire-resistant tank, or a tank in a vault. For example, NFPA 30, NFPA 30A, and the IFC codes allow UL 2085 tanks to be installed closer to buildings and property lines, thereby reducing the real estate necessary to meet fire codes. Under NFPA 30A, dispensers may be installed directly over vaults or upon fire-resistant tanks at fleet-type installations, whereas a 7.6- to 15.2-m (25- to 50-ft) separation distance is required at retail-type service station installations. The IFC only allows gasoline and diesel to be dispensed from ASTs, designed with a 2-h fire rating. Non-2-h fire-rated UL 142 tanks dispensing diesel can be installed if permitted by local codes. Maintenance and Operations Water in any storage system can cause myriad problems from product quality to corrosion caused by trace contaminants and microbial action. Subsequently, any operations and maintenance program must include a proactive program of monitoring for and removal of water. Other operations and maintenance procedures include periodic integrity testing and corrosion control for vertical tank bottoms. Additional guidance is available from organizations such as API, Petroleum Equipment Institute (PEI), ASTM International, National Oilheat Research Alliance (NORA), and STI. Also see the STI document Keeping Water Out of Your Storage System (http://www.steeltank.com/ library/pubs/waterinfueltanks.pdf ). Integrity testing and visual inspection requirements are discussed in the SPCC requirements, Subpart B, Para. 112.8c(6). Chemical tanks storing toluene and benzene are subject to the rule in addition to traditional fuels. But a good inspection program is recommended regardless of applicable regulations. Both visual inspection and another testing technique are required. Comparison records must be kept, and frequent inspections must be made of the outside of the tank and system components for signs of deterioration, discharge, or accumulation of oil inside diked areas. For inspection of large field-erected tanks, API 653, Tank Inspection, Repair, Alteration, and Reconstruction, is referenced by the U.S. EPA. A certified inspector must inspect tanks. U.S. EPA references the Steel Tank Institute Standard SP001-06, Standard for Inspection of In-Service Shop Fabricated Aboveground Tanks for Storage of Combustible and Flammable Liquids, as an industry standard that may assist an owner or operator with the integrity testing and inspection of shop-fabricated tanks. The STI SP001-06 standard includes inspection techniques for all types of shopfabricated tanks—horizontal cylindrical, vertical, and rectangular. SP001-06 also addresses tanks that rest directly on the ground or on release prevention barriers, tanks that are elevated on supports, and tanks that are either single- or double-wall using a risk-based approach. Pressurized Tanks Vertical cylindrical tanks constructed with domed or coned roofs, which operate at pressures above several hundred pascals (a few pounds per square foot) but which are still relatively close to atmospheric pressure, can be built according to API Standard 650. The pressure force acting against the roof is transmitted to the shell, which may have sufficient weight to resist it. If not, the uplift will act on the tank bottom. The strength of the bottom, however, is limited, and if it is not sufficient, an anchor ring or a heavy foundation must be used. In the larger sizes, uplift forces limit this style of tank to very low pressures. As the size or the pressure goes up, curvature on all surfaces becomes necessary. Tanks in this category, up to and including a pressure of 103.4 kPag (15 psig), can be built according to API Standard 620. Shapes used are spheres, ellipsoids, toroidal structures, and circular cylinders with torispherical, ellipsoidal, or hemispherical heads. The ASME Boiler and Pressure Vessel Code, Sec. VIII-1 (2015), although not required below 15 psig (103.4 kPag), is also useful for designing such tanks. Tanks that could be subjected to vacuum should be provided with vacuumbreaking valves or be designed for vacuum (external pressure). The BPVC contains design procedures. Calculation of Tank Volume A tank may be a single geometric element, such as a cylinder, a sphere, or an ellipsoid. It may also have a compound form, such as a cylinder with hemispherical ends or a combination of a toroid and a sphere. To determine the volume, each geometric element usually must be calculated separately. Calculations for a full tank are usually simple, but calculations for partially filled tanks may be complicated.

10-127

Calculation of partially filled horizontal tanks. H = depth of liquid; R = radius; D = diameter; L = length; α = half of the included angle; and cos α = 1 − H/R = 1 − 2H/D.

FIG. 10-177

To calculate the volume of a partially filled horizontal cylinder, refer to Fig. 10-177. Calculate the angle α in degrees. Any units of length can be used, but they must be the same for H, R, and L. The liquid volume α − sin α cos α  V = LR 2   57.30 

(10-107)

This formula may be used for any depth of liquid between zero and the full tank, provided the algebraic signs are observed. If H is greater than R, then sin α cos α will be negative and thus will add numerically to α/57.30. Table 10-57 gives liquid volume, for a partially filled horizontal cylinder, as a fraction of the total volume, for the dimensionless ratio H/D or H/2R. The volumes of heads must be calculated separately and added to the volume of the cylindrical portion of the tank. The four types of heads most frequently used are the standard dished head,∗ torispherical or ASME head, ellipsoidal head, and hemispherical head. Dimensions and volumes for all four types are given in Lukens Spun Heads, Lukens Inc., Coatesville, Pennsylvania. Approximate volumes can also be calculated by the formulas in Table 10-58. Consistent units must be used in these formulas. A partially filled horizontal tank requires the determination of the partial volume of the heads. The Lukens catalog gives approximate volumes for partially filled (axis horizontal) standard ASME and ellipsoidal heads. A formula for partially filled heads (excluding conical), by Doolittle [Ind. Eng. Chem. 21: 322–323 (1928)], is V = 0.215H 2(3R − H )

(10-108)

where in consistent units V = volume, R = radius, and H = depth of liquid. Doolittle made some simplifying assumptions that affect the volume given ∗ The standard dished head does not comply with the ASME BPVC. TABLE 10-57 Volume of Partially Filled Horizontal Cylinders H/D

Fraction of volume

H/D

Fraction of volume

H/D

Fraction of volume

H/D

Fraction of volume

0.01 .02 .03 .04 .05 .06 .07 .08 .09 .10 .11 .12 .13 .14 .15 .16 .17 .18 .19 .20 .21 .22 .23 .24 .25

0.00169 .00477 .00874 .01342 .01869 .02450 .03077 .03748 .04458 .05204 .05985 .06797 .07639 .08509 .09406 .10327 .11273 .12240 .13229 .14238 .15266 .16312 .17375 .18455 .19550

0.26 .27 .28 .29 .30 .31 .32 .33 .34 .35 .36 .37 .38 .39 .40 .41 .42 .43 .44 .45 .46 .47 .48 .49 .50

0.20660 .21784 .22921 .24070 .25231 .26348 .27587 .28779 .29981 .31192 .32410 .33636 .34869 .36108 .37353 .38603 .39858 .41116 .42379 .43644 .44912 .46182 .47454 .48727 .50000

0.51 .52 .53 .54 .55 .56 .57 .58 .59 .60 .61 .62 .63 .64 .65 .66 .67 .68 .69 .70 .71 .72 .73 .74 .75

0.51273 .52546 .53818 .55088 .56356 .57621 .58884 .60142 .61397 .62647 .63892 .65131 .66364 .67590 .68808 .70019 .71221 .72413 .73652 .74769 .75930 .77079 .78216 .79340 .80450

0.76 .77 .78 .79 .80 .81 .82 .83 .84 .85 .86 .87 .88 .89 .90 .91 .92 .93 .94 .95 .96 .97 .98 .99 1.00

0.81545 .82625 .83688 .84734 .85762 .86771 .87760 .88727 .89673 .90594 .91491 .92361 .93203 .94015 .94796 .95542 .96252 .96923 .97550 .98131 .98658 .99126 .99523 .99831 1.00000

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TRANSPORT AND STORAGE OF FLUIDS TABLE 10-58

Volumes of Heads*

Knuckle radius rk

Type of head Standard dished Torispherical or ASME Torispherical or ASME Ellipsoidal Ellipsoidal Hemispherical Conical

h

Approx. 3t

L Approx. Di

0.06L

0.0809Di

Di

3t

3 2 i

Approx. 0.513hD πDi2h/6 πDi3/24 πDi3/12 πh(Di2 + Did + d 2)/12

Di Di/4 Di/2

Volume Approx. 0.050Di3 + 1.65tD2i

Di/2

% Error ±10 ±0.1   ±8  0 0 0 0

Remarks h varies with t rk must be the larger of 0.06L and 3t Standard proportions Truncated cone h = height d = diameter at small end

*Use consistent units.

by the equation, but the equation is satisfactory for determining the volume as a fraction of the entire head. This fraction, calculated by Doolittle’s formula, is given in Table 10-59 as a function of H/Di (H is the depth of liquid, and Di is the inside diameter). Table 10-59 can be used for standard dished, torispherical, ellipsoidal, and hemispherical heads with an error of less than 2 percent of the volume of the entire head. The error is zero when H/Di = 0, 0.5, and 1.0. Table 10-59 cannot be used for conical heads. When a tank volume cannot be calculated or when greater precision is required, calibration may be necessary. This is done by draining (or filling) the tank and measuring the volume of liquid. The measurement may be made by weighing, by a calibrated fluid meter or by repeatedly filling small measuring tanks which have been calibrated by weight. Container Materials and Safety Storage tanks are made of almost any structural material. Steel and reinforced concrete are most widely used. Plastics and glass-reinforced plastics are used for tanks up to about 230 m3 (60,000 gal). Resistance to corrosion, light weight, and lower cost are their advantages. Plastic and glass coatings are also applied to steel tanks. Aluminum and other nonferrous metals are used when their special properties are required. When expensive metals such as tantalum are required, they may be applied as tank linings or as clad metals. Some grades of steel listed by API and AWWA Standards are of lower quality than is customarily used for pressure vessels. The stresses allowed by these standards are also higher than those allowed by the ASME Pressure Vessel Code. Small tanks containing nontoxic substances are not particularly hazardous and can tolerate a reduced factor of safety. Tanks containing highly toxic substances and very large tanks containing any substance can be hazardous. The designer must consider the magnitude of the hazard. The possibility of brittle behavior of ferrous metal should be taken into account in specifying materials (see subsection Safety in Design). Volume 1 of National Fire Codes (NFPA, Quincy, Massachusetts) contains recommendations (NFPA 30) for venting, drainage, and dike construction of tanks for flammable liquids.

TABLE 10-59 Volume of Partially Filled Heads on Horizontal Tanks* H/Di 0.02 .04 .06 .08 .10 .12 .14 .16 .18 .20 .22 .24 .26

Fraction of volume 0.0012 .0047 .0104 .0182 .0280 .0397 .0533 .0686 .0855 .1040 .1239 .1451 .1676

H/Di

Fraction of volume

0.28 .30 .32 .34 .36 .38 .40 .42 .44 .46 .48 .50

0.1913 .216 .242 .268 .295 .323 .352 .381 .410 .440 .470 .500

*Based on Eq. (10-108).

H/Di

Fraction of volume

0.52 .54 .56 .58 .60 .62 .64 .66 .68 .70 .72 .74 .76

0.530 .560 .590 .619 .648 .677 .705 .732 .758 .784 .8087 .8324 .8549

H/Di

Fraction of volume

0.78 .80 .82 .84 .86 .88 .90 .92 .94 .96 .98 1.00

0.8761 .8960 .9145 .9314 .9467 .9603 .9720 .9818 .9896 .9953 .9988 1.0000

Container Insulation Tanks containing materials above atmospheric temperature may require insulation to reduce the loss of heat. Almost any of the commonly used insulating materials can be employed. Calcium silicate, glass fiber, mineral wool, cellular glass, and plastic foams are among those used. Tanks exposed to weather must have jackets or protective coatings, usually asphalt, to keep water out of the insulation. Tanks with contents at lower than atmospheric temperature may require insulation to minimize heat absorption. The insulation must have a vapor barrier on the outside to prevent condensation of moisture from reducing its effectiveness. The insulation techniques presently used for refrigerated systems can be applied (see subsection Low-Temperature and Cryogenic Storage). Tank Supports Large vertical atmospheric steel tanks may be built on a base of about 150 cm (6 in) of sand, gravel, or crushed stone if the subsoil has adequate bearing capacity. It can be level or slightly coned, depending on the shape of the tank bottom. The porous base provides drainage in case of leaks. A few feet beyond the tank perimeter the surface should drop about 1 m (3 ft) to ensure proper drainage of the subsoil. API Standard 650, App. B, and API Standard 620, App. C, give recommendations for tank foundations. The bearing pressure of the tank and contents must not exceed the bearing capacity of the soil. Local building codes usually specify allowable soil loading. These are some approximate bearing capacities:

Soft clay (can be crumbled between fingers) Dry fine sand Dry fine sand with clay Coarse sand Dry hard clay (requires a pick to dig it) Gravel Rock

kPa

psf

100 200 300 300 350 400 1000–4000

2,000 4,000 6,000 6,000 7,000 8,000 20,000–80,000

For high, heavy tanks, a foundation ring may be needed. Prestressed concrete tanks are sufficiently heavy to require foundation rings. Foundations must extend below the frost line. Some tanks that are not flat-bottomed may also be supported by soil if it is suitably graded and drained. When soil does not have adequate bearing strength, it may be excavated and backfilled with a suitable soil, or piles capped with a concrete mat may be required. Spheres, spheroids, and toroids use steel or concrete saddles or are supported by columns. Some may rest directly on soil. Horizontal cylindrical tanks should have two rather than multiple saddles to avoid indeterminate load distribution. Small horizontal tanks are sometimes supported by legs. Most tanks must be designed to resist the reactions of the saddles or legs, and they may require reinforcing. Neglect of this can cause collapse. Tanks without stiffeners usually need to make contact with the saddles on at least 2.1 rad (120°) of their circumference. An elevated steel tank may have either a circle of steel columns or a large central steel standpipe. Concrete tanks usually have concrete columns. Tanks are often supported by buildings. Pond and Underground Storage Low-cost liquid materials, if they will not be damaged by rain or atmospheric pollution, may be stored in ponds. A pond may be excavated or formed by damming a ravine. To prevent

STORAGE AND PROCESS VESSELS M

Cavern pressure relief

11

Instrumentation Communication

12

M 10

10-129

Receipt Vapor

Delivery

13

Water 14

3

Water table

Overburden Weathered bedrock Unweathered bedrock

Storage horizon 7

8

15

17

6

16

1

Vapor

2

Liquid

5

19

18

9 4

Legend 1. Storage gallery 2. Storage gallery section view 3. Pump wellhead 4. Pump sump 5. Submersible pump 6. Pump discharge tubing 7. Pump casing 8. Access/instrument shaft 9. Main sump 10. Fill line(s)

11. Cavern vent 12. Instrument casings 13. (Optional) water pump(s) 14. Dual shaft head 15. (Optional) access tunnel 16. (Optional) dual concrete plug 17. (Optional) water curtain gallery with injection boreholes 18. (Optional) water bed 19. Fill can

FIG. 10-178 Mined cavern.

loss by seepage, the soil which will be submerged may require treatment to make it sufficiently impervious. This can also be accomplished by lining the pond with concrete, polymeric membrane, or another barrier. Detection and mitigation of seepage is especially necessary if the pond contains material that could contaminate present or future water supplies. Underground Cavern Storage Large volumes of liquids and gases are often stored below ground in artificial caverns as an economical alternative to aboveground tanks and other modes of storage. The stored fluids must tolerate water, brine, and other contaminants that are usually present to some degree in the cavern. The liquids that are most commonly stored are natural gas liquids (NGLs), LPG, crude oil, and refined petroleum products. Gases commonly stored are natural gas and hydrogen. If fluids are suitable for cavern storage, this method may be less expensive, safer, and more secure than other storage modes. There are two types of caverns used for storing liquids. Hard rock (mined) caverns are constructed by mining rock formations such as shale,

granite, limestone, and many other types of rock. Solution-mined caverns are constructed by dissolution processes, i.e., solution mining or leaching a mineral deposit, most often salt (sodium chloride). The salt deposit may take the form of a massive salt dome or thinner layers of bedded salt that are stratified between layers of rock. Hard rock and solution-mined caverns have been constructed in the United States and many other parts of the world. Mined Caverns Caverns mined in hard rock are generally situated 100 to 150 m (325 to 500 ft) below ground level. These caverns are constructed by excavating rock with conventional drill-and-blast mining methods. The excavated cavern consists of a grouping of interconnecting tunnels or storage “galleries.” Mined caverns have been constructed for volumes ranging from as little as 3200 to 800,000 m3 [20,000 to 5 million API barrels∗ (bbl)]. Figure 10-178 illustrates a typical mined cavern for liquid storage. ∗One API barrel = 42 U.S. gal = 5.6146 ft3 = 0.159 m3.

10-130

TRANSPORT AND STORAGE OF FLUIDS

Leaching process 4

5

6

2 1 8 3

7

3

Overburden Salt rock Legend Salt cavern – direct solution mining

Salt cavern – indirect solution mining

1. Water source 2. Water injection pumps 3. Wellhead 4. Tank or pond 5. Brine pump station 6. Brine disposal 7. Blanket tank 8. Blanket pump

Rubble pile FIG. 10-179 Cavern leaching process.

Hard rock caverns are designed so that the internal storage pressure at all times is less than the hydrostatic head of the water contained in the surrounding rock matrix. Thus, the depth of a cavern determines its maximum allowable operating pressure. Groundwater that continuously seeps into hard rock caverns in permeable formations is periodically pumped out of the cavern. The maximum operating pressure of the cavern is established after a thorough geological and hydrogeological evaluation is made of the rock formation and the completed cavern is pressure-tested. Salt Caverns Salt caverns are constructed in both domal salt, more commonly referred to as “salt domes,” and bedded salt, which consists of a body of salt sandwiched between layers of rock. The greatest total volume of underground liquid storage in the United States is stored in salt dome caverns. A salt dome is a large body, mostly consisting of sodium chloride, which over geologic time moved upward thousands of feet from extensive halite deposits deep below the earth’s crust. There are numerous salt domes in the United States and other parts of the world [see Harben, P. W., and R. L. Bates, “Industrial Minerals Geology and World Deposits,” Metal Bulletin Plc, UK, pp. 229–234 (1990)]. An individual salt dome may exceed 1 mi in diameter and contain many storage caverns. The depth to the top of a salt dome may range from a few hundred to several thousand feet, although depths to about 460 m (1500 ft) are commercially viable for cavern development. The extent of many salt domes allows for caverns of many different sizes and depths to be developed. The extensive nature of salt domes has allowed the development of caverns as large as 5.7 × 106 m3 (36 million bbl) (U.S. DOE Bryan Mound Strategic Petroleum Reserve) and larger; however, cavern volumes of 159,000 to 1.59 × 106 m3 (1 to 10 million bbl) are more common for liquid storage. The benefits of salt are its high compressive strength of 13.8 to 27.6 MPa (2000 to 4000 psi), its impermeability to hydrocarbon liquids and gases, and its non–chemically reactive (inert) nature. Due to the impervious nature of salt, the maximum allowed storage pressure gradient in this type of cavern is greater than that of a mined cavern. A typical storage pressure gradient for liquids is about 18 kPa/m of depth (0.80 psi/ft) to the bottom of the well casing. Actual maximum and minimum allowable operating pressure gradients are determined from geologic evaluations and rock mechanics studies. Typical depths to the top of a salt cavern may range from 500 to 4000 ft (about 150 to 1200 m). Therefore, the maximum storage pressure (2760 to 32,060 kPag, or 400 to 3200 psig) usually exceeds the vapor pressure of all commonly stored hydrocarbon liquids. Higher-vapor-pressure products such as ethylene or ethane cannot be stored in relatively shallow caverns.

Salt caverns are developed by solution mining, a process (leaching) in which water is injected to dissolve the salt. Approximately 7 to 10 units of freshwater are required to leach 1 unit of cavern volume. Figure 10-179 illustrates the leaching process for two caverns. Modern salt dome caverns are shaped as relatively tall, slender cylinders. The leaching process produces nearly saturated brine from the cavern. Brine may be disposed into nearby disposal wells or offshore disposal fields, or it may be supplied to nearby plants as a feedstock for manufacturing of caustic (NaOH) and chlorine (Cl2). The final portion of the produced brine is retained and stored in artificial surface ponds or tanks to be used to displace the stored liquid from the cavern. Salt caverns are usually developed using a single well, although some employ two or more wells. The well consists of a series of concentric casings that protect the water table and layers of rock and sediments (overburden) that lie above the salt dome. The innermost well casing is referred to as the last cemented or well “production” casing and is cemented in place, sealing the cavern and protecting the surrounding geology. Once the last cemented casing is in place, a bore hole is drilled from the bottom of the well, through the salt to the design cavern depth. For single-well leaching, two concentric tubing strings are then suspended in the well. A liquid, such as diesel or propane, or a gas, such as nitrogen, is then injected through the outer annular space and into the top of the cavern to act as a “blanket” to prevent undesired leaching of the top of the cavern. Water is then injected into one of the suspended tubing strings, and brine is withdrawn from the other. During the leaching process, the water is injected initially for 30 to 60 days into the innermost tubing and into the inner annulus for the remaining time. The tubing strings are periodically raised upward to control the cavern shape. A typical salt dome cavern may require 9 to 30 months of leaching time, whereas smaller, bedded salt caverns may be developed in a shorter time frame. Brine-Compensated Storage As the stored product is pumped into the cavern, brine is displaced into an aboveground brine storage reservoir. To withdraw the product from the cavern, brine is pumped back into the cavern, displacing the stored liquid. This method of product transfer is termed brine-compensated, and caverns that operate in this fashion remain liquid-filled at all times. Figure 10-180 illustrates brine-compensated storage operations. Uncompensated Storage Hard rock caverns and a few bedded salt caverns do not use brine for product displacement. This type of storage operation is referred to as pump out or uncompensated storage operations. When the cavern is partially empty of liquid, the void space is filled with the vapor that is in equilibrium with the stored liquid. When liquid is introduced into the

STORAGE AND PROCESS VESSELS

10-131

Brine-compensated salt cavern 4

6 5 1 8

7

3

2 Overburden Salt rock

Hydrocarbon liquids Legend

Brine

Rubble pile

1. Product injection pump 2. Wellhead 3. Pipeline delivery pump 4. Solids separator 5. Brine reservoir (brine pond or other) 6. Execss brine disposal (injection well or other) 7. Dilution water supply 8. Brine injection (displacement) pump

FIG. 10-180 Brine-compensated storage.

cavern, it compresses and condenses this saturated vapor phase. In some cases, vapor may be vented to the surface where it may be refrigerated, liquefied, and recycled to the cavern. Submersible pumps or vertical line shaft pumps are used for withdrawing the stored liquid. Vertical line shaft pumps are suited for depths of no more than several hundred feet. Figure 10-178 illustrates an example of uncompensated storage operations. Underground chambers are also constructed in frozen earth (see subsection Low-Temperature and Cryogenic Storage). Underground tunnel or tank storage is often the most practical way of storing hazardous or radioactive materials, such as proposed at Yucca Mountain, Nevada. A cover of 30 m (100 ft) of rock or dense earth can exert a pressure of about 690 kPa (100 lbf/in2). The storage of natural gas in depleted aquifers and petroleum reservoirs is another mode of underground storage. This type of storage requires that a number of wells be drilled into the underground storage zone at different locations and depths determined from geologic analysis. STORAGE OF GASES Gas Holders Gas is sometimes stored in expandable gas holders of either the liquid-seal or dry-seal type. The liquid-seal holder is a familiar sight. It has a cylindrical container, closed at the top, and varies its volume by moving it up and down in an annular water-filled seal tank. The seal tank may be staged in several lifts (as many as five). Seal tanks have been built in sizes up to 280,000 m3 (9.9 × 106 ft3). The dry-seal holder has a rigid top attached to the sidewalls by a flexible fabric diaphragm which permits it to move up and down. It does not involve the weight and foundation costs of

the liquid-seal holder. Additional information on gas holders can be found in Gas Engineers Handbook, Industrial Press, New York, 1966. Solution of Gases in Liquids Certain gases will dissolve readily in liquids. In some cases in which the quantities are not large, this may be a practical storage procedure. Examples of gases that can be handled in this way are ammonia in water, acetylene in acetone, and hydrogen chloride in water. Whether this method is used depends mainly on whether the end use requires the anhydrous or the liquid state. Pressure may be either atmospheric or elevated. The solution of acetylene in acetone is also a safety feature because of the instability of acetylene. Storage in Pressure Vessels, Bottles, and Pipelines The distinction between pressure vessels, bottles, and pipes is arbitrary. They can all be used for storing gases under pressure. A storage pressure vessel is usually a permanent installation. Storing a gas under pressure not only reduces its volume but also in many cases liquefies it at ambient temperature. Some gases in this category are carbon dioxide, several petroleum gases, chlorine, ammonia, sulfur dioxide, and some types of Freon or Suva. Pressure tanks are frequently installed underground. Liquefied petroleum gas (LPG) is the subject of API Standard 2510, The Design and Construction of Liquefied Petroleum Gas Installations at Marine and Pipeline Terminals, Natural Gas Processing Plants, Refineries, and Tank Farms. This standard in turn refers to: 1. National Fire Protection Association (NFPA) Standard 58, Standard for the Storage and Handling of Liquefied Petroleum Gases 2. NFPA Standard 59, Standard for the Storage and Handling of Liquefied Petroleum Gases at Utility Gas Plants 3. NFPA Standard 59A, Standard for the Production, Storage, and Handling of Liquefied Natural Gas (LNG)

TRANSPORT AND STORAGE OF FLUIDS

The API Standard gives considerable information on the construction and safety features of such installations. It also recommends minimum distances from property lines. The user may wish to obtain added safety by increasing these distances. The term bottle is usually applied to a pressure vessel that is small enough to be conveniently portable. Bottles range from about 57 L (2 ft3) down to CO2 capsules of about 16.4 mL (1 in3). Bottles are convenient for small quantities of many gases, including air, hydrogen, nitrogen, oxygen, argon, acetylene, Freon, and petroleum gas. Some are one-time-use disposable containers. Pipelines A pipeline is not ordinarily a storage device. Sections of pipe have been connected in series and in parallel, buried underground, and used for storage. This avoids the necessity of providing foundations, and the earth protects the pipe from extremes of temperature. The economics of such an installation would be doubtful if it were designed to the same stresses as a pressure vessel. Storage is also obtained by increasing the pressure in operating pipelines and thus having a similar impact as a tank. Low-Temperature and Cryogenic Storage This type is used for gases that liquefy under pressure at atmospheric temperature. In cryogenic storage the gas is at, or near to, atmospheric pressure and remains liquid because of low temperature. A system may also operate with a combination of pressure and reduced temperature. The term cryogenic usually refers to temperatures below -101°C (-150°F). Some gases, however, liquefy between -101°C and ambient temperatures. The principle is the same, but cryogenic temperatures create different problems with insulation and construction materials. The liquefied gas must be maintained at or below its boiling point. Refrigeration can be used, but the usual practice is to cool by evaporation. The quantity of liquid evaporated is minimized by insulation. The vapor may be vented to the atmosphere (this may be prohibited due to emissions limitations), it may be compressed and reliquefied, or it may be consumed as fuel. At very low temperatures with liquid air and similar substances, the tank may have double walls with the interspace evacuated. The well-known Dewar flask is an example. Large tanks and even pipelines are now built this way. An alternative is to use double walls without vacuum but with an insulating material in the interspace. Perlite and plastic foams are two insulating materials employed in this way. Sometimes both insulation and vacuum are used. Materials Materials for liquefied-gas containers must be suitable for the temperatures, and they must not become embrittled. Some carbon steels can be used down to -59°C (-75°F), and low-alloy steels to -101°C (-150°F) and sometimes -129°C (-200°F). Below these temperatures austenitic stainless steel (AISI 300 series) and aluminum are the principal materials. (See discussion of brittle fracture on p. 10-139.) Low temperatures involve problems of differential thermal expansion. With the outer wall at ambient temperature and the inner wall at the liquid boiling point, relative movement must be accommodated. Proprietary systems accomplish this. The Gaz Transport of France reduces dimensional change by using a thin inner liner of Invar. Another patented French system accommodates this change by means of the flexibility of thin metal which is creased. The creases run in two directions, and the form of the crossings of the creases is a feature of the system. Low-temperature tanks may be installed in-ground to take advantage of the insulating value of the earth. Frozen-earth storage is also used. The frozen earth forms the tank. Some installations using this technique have been unsuccessful because of excessive heat absorption. Cavern Storage Gases are also stored below ground in salt caverns. The most common type of gas stored in caverns is natural gas, although hydrogen and air have also been stored. Hydrogen storage requires special consideration in selecting metallurgy for the wellhead and the wellbore casings. Air is stored for the purpose of providing compressed air energy for peak shaving power plants. Two such plants are in operation, one in the United States (McIntosh, Alabama), the other in Huntorf, Germany. A discussion of the Alabama plant is presented in History of First U.S. Compressed Air Energy Storage (CAES) Plant, vol. 1, Early CAES Development, Electric Power Research Institute (EPRI), Palo Alto, Calif., 1992. Since salt caverns contain brine and other contaminants, the type of gas to be stored should not be sensitive to the presence of contaminants. If the gas is determined suitable for cavern storage, then cavern storage may not offer only economic benefits and enhanced safety and security; salt caverns also offer relatively high rates of deliverability compared to reservoir and aquifer storage fields. Solution-mined gas storage caverns in salt formations operate as uncompensated storage—no fluid is injected into the well to displace the compressed gas. Surface gas handling facilities for storage caverns typically include custody transfer measurement for receipt and delivery, gas compressors, and gas dehydration equipment. When compressors are required for cavern injection and/or withdrawal, banks of positive-displacement-type compressors are commonly used, since this compressor type is well suited for

handling the highly variable compression ratios and flow rates associated with cavern injection and withdrawal operations. Cavern withdrawal operations typically involve single- or dual-stage pressure reduction stations and full or partial gas dehydration. Large pressure throttling requirements often require heating the gas upon withdrawal and immediately before throttling, and injection of methanol or other liquid desiccant may be necessary to help control hydrate formation. An in-depth discussion of natural gas storage in underground caverns may be found in Gas Engineering and Operating Practices, Supply, Book S-1, Part 1, Underground Storage of Natural Gas, and Part 2, Chap. 2, “Leached Caverns,” American Gas Association, Arlington, Va., 1990. Additional References API Recommended Practice 1114, Design of Solution-Mined Underground Storage Facilities, January 2013. API 1115, Operation of Solution-Mined Underground Storage Facilities, Washington, September 1994. Stanley J. LeFond, Handbook of World Salt Resources, Monographs in Geoscience, Department of Geology, Columbia University, New York, 1969. SME Mining Engineering Handbook, 2d ed., vol. 2, The Society for Mining, Metallurgy, and Exploration, Littleton, Colorado, 1992. COST OF STORAGE FACILITIES Contractors’ bids offer the most reliable information on cost. Order-ofmagnitude costs, however, may be required for preliminary studies. One way of estimating them is to obtain cost information from similar facilities and scale it to the proposed installation. Costs of steel storage tanks and vessels have been found to vary approximately as the 0.6 to 0.7 power of their weight [see Happel, Chemical Process Economics, Wiley, 1958, p. 267; also Williams, Chem. Eng. 54(12): 124 (1947)]. All estimates based on the costs of existing equipment must be corrected for changes in the price index from the date when the equipment was built. Considerable uncertainty is involved in adjusting data more than a few years old. Based on a survey in 1994 for storage tanks, the prices for field-erected tanks are for multiple-tank installations erected by the contractor on foundations provided by the owner. Some cost information on tanks is given in various references cited in Sec. 9. Cost data vary considerably from one reference to another. (See Figs. 10-181 to 10-183.) Prestressed (post-tensioned) concrete tanks cost about 20 percent more than steel tanks of the same capacity. Once installed, however, concrete tanks require very little maintenance. A true comparison with steel would therefore require evaluating the maintenance cost of both types.

Purchase cost, thousands of US dollars (2016)

10-132

180 160 316 Stainless steel

140 120

304 Stainless steel 100 80 60 Carbon steel 40 20 0 0

5

10 15 20 25 Volume, thousands of US gallons

30

FIG. 10-181 Cost of shop-fabricated tanks in mid-1980 with ¼-in walls. Multiplying factors on carbon-steel costs for other materials are: carbon steel, 1.0; rubber-lined carbon steel, 1.5; aluminum, 1.6; glass-lined carbon steel, 4.5; and fiber-reinforced plastic, 0.75 to 1.5. Multiplying factors on type 316 stainless-steel costs for other materials are: 316 stainless steel, 1.0; Monel, 2.0; Inconel, 2.0; nickel, 2.0; titanium, 3.2; and Hastelloy C, 3.8. Multiplying factors for wall thicknesses different from ¼ in are:

Thickness, in ½ ¾ 1

Carbon Steel

304 Stainless Steel

316 Stainless Steel

1.4 2.1 2.7

1.8 2.5 3.3

1.8 2.6 3.5

To convert gallons to cubic meters, multiply by 3.785 × 10-3.

Cost, thousands of US dollars (2016)

STORAGE AND PROCESS VESSELS

10-133

1200 1000 304 Stainless steel

800 600 400

Carbon steel

200 0 0

100

200

300

400

500

600

700

800

900

1000

1100

Volume, thousands of US gallons FIG. 10-182 Cost (±30 percent) of field-erected, domed, flat-bottom API 650 tanks, October 2016, includes concrete foundation and typical nozzles, ladders, and platforms. 1 gal = 0.003785 m3.

BULK TRANSPORT OF FLUIDS

Cost, millions of US dollars (2016)

Transportation is often an important part of product cost. Bulk transportation may provide significant savings. When there is a choice between two or more forms of transportation, the competition may result in rate reduction. Transportation is subject to considerable regulation, which will be discussed in some detail under specific headings. Pipelines For quantities of fluid that an economic investigation indicates are sufficiently large and continuous to justify the investment, pipelines are one of the lowest-cost means of transportation. They have been built up to 1.22 m (48 in) or more in diameter and about 3200 km (2000 mi) in length for oil, gas, and other products. Water is usually not transported more than 160 to 320 km (100 to 200 mi), but the conduits may be much greater than 1.22 m (48 in) in diameter. Open canals are also used for water transportation. Petroleum pipelines before 1969 were built to ASA (now ASME) Standard B31.4 for liquids and Standard B31.8 for gas. These standards were seldom mandatory because few states adopted them. The U.S. Department of Transportation (DOT), which now has responsibility for pipeline regulation, issued Title 49, Part 192—Transportation of Natural Gas and Other Gas by Pipeline: Minimum Safety Standards, and Part 195—Transportation of Liquids by Pipeline. These contain considerable material from B31.4 and B31.8. They allow generally higher stresses than the ASME Boiler and Pressure Vessel Code would allow for steels of comparable strength. The enforcement of their regulations is presently left to the states and is therefore somewhat uncertain. Pipeline pumping stations usually range from 16 to 160 km (10 to 100 mi) apart, with maximum pressures up to 6900 kPa (1000 lbf/in2) and velocities up to 3 m/s (10 ft/s) for liquid. Gas pipelines have higher velocities and may have greater spacing of stations. Tanks Tank cars (single and multiple tanks), tank trucks, portable tanks, drums, barrels, carboys, and cans are used to transport fluids. Interstate

transportation is regulated by the DOT. There are other regulating agencies— state, local, and private. Railroads make rules determining what they will accept, some states require compliance with DOT specifications on intrastate movements, and tunnel authorities as well as fire chiefs apply restrictions. Water shipments involve regulations of the U.S. Coast Guard. The American Bureau of Shipping sets rules for design and construction which are recognized by insurance underwriters. The most pertinent DOT regulations (Code of Federal Regulations, Title 18, Parts 171–179 and 397) were published by R. M. Graziano (then agent and attorney for carriers and freight forwarders) in his tariff titled Hazardous Materials Regulations of the Department of Transportation (1978). New tariffs identified by number are issued at intervals, and interim revisions are sent out. Agents change at intervals. Graziano’s tariff lists many regulated (dangerous) commodities (Part 172, DOT regulations) for transportation. This includes those that are poisonous, flammable, oxidizing, corrosive, explosive, radioactive, and compressed gases. Part 178 covers specifications for all types of containers from carboys to large portable tanks and tank trucks. Part 179 deals with tank-car construction. Thickness, in

Carbon steel

304 Stainless steel

316 Stainless steel

½ ¾ 1

1.4 2.1 2.7

1.8 2.5 3.3

1.8 2.6 3.5

To convert gallons to cubic meters, multiply by 3.786 × 10-3.

The Association of American Railroads (AAR) publication Specifications for Tank Cars covers many requirements beyond the DOT regulations.

6 5 4 Carbon steel 3 2 1 0 0

2500

5000 7500 10,000 Volume, thousands of US gallons

12,500

15,000

FIG. 10-183 Cost (±30 percent) of field-erected, floating roof tanks, October 2016, includes concrete foundation and typical nozzles, ladders, and platforms. 1 gal = 0.003785 m3.

10-134

TRANSPORT AND STORAGE OF FLUIDS

Some additional details are given later. Because of frequent changes, it is always necessary to check the latest rules. The shipper, not the carrier, has the ultimate responsibility for shipping in the correct container. Tank Cars These range in size from about 7.6 to 182 m3 (2000 to 48,000 gal), and a car may be single-unit or multiunit. The DOT now limits them to 130 m3 (34,500 gal) and 120,000 kg (263,000 lb) gross weight. Large cars usually result in lower investment per cubic meter and take lower shipping rates. Cars may be insulated to reduce heating or cooling of the contents. Certain liquefied gases may be carried in insulated cars; temperatures are maintained by evaporation (see subsection Low-Temperature and Cryogenic Storage). Cars may be heated by steam coils or by electricity. Some products are loaded hot, solidify in transport, and are melted for removal. Some low-temperature cargoes must be unloaded within a given time (usually 30 days) to prevent pressure buildup. Tank cars are classified as pressure or general-purpose. Pressure cars have relief-valve settings of 517 kPa (75 lbf/in2) and above. Those designated as general-purpose cars are, nevertheless, pressure vessels and may have relief valves or rupture disks. The DOT specification code number indicates the type of car. For instance, 105A500W indicates a pressure car with a test pressure of 3447 kPa (500 lbf/in2) and a relief-valve setting of 2585 kPa (375 lbf/in2). In most cases, loading and unloading valves, safety valves, and vent valves must be in a dome or an enclosure. Companies shipping dangerous materials sometimes build tank cars with metal thicker than required by the specifications in order to reduce the possibility of leakage during a wreck or fire. The punching of couplers or rail ends into heads of tanks is a hazard. Older tank cars have a center sill or beam running the entire length of the car. Most modern cars have no continuous sill, only short stub sills at each end. Cars with full sills have tanks anchored longitudinally at the center of the sill. The anchor is designed to be weaker than either the tank shell or the doubler plate between anchor and shell. Cars with stub sills have similar safeguards. Anchors and other parts are designed to meet AAR requirements. The impact forces on car couplers put high stresses on sills, anchors, and doublers. This may start fatigue cracks in the shell, particularly at the corners of welded doubler plates. With brittle steel in cold weather, such cracks sometimes cause complete rupture of the tank. Large end radii on the doublers and tougher steels will reduce this hazard. Inspection of older cars can reveal cracks prior to failure. A difference between tank cars and most pressure vessels is that tank cars are designed in terms of the theoretical ultimate or bursting strength of the tank. The test pressure is usually 40 percent of the bursting pressure (sometimes less). The safety valves are set at 75 percent of the test pressure. Thus, the maximum operating pressure is usually 30 percent of the bursting pressure. This gives a nominal factor of safety of 3.3, compared with 3.5 for Division 1 of the ASME Boiler and Pressure Vessel Code. The DOT rules require that pressure cars have relief valves designed to limit pressure to 82.5 percent (with certain exceptions) of test pressure (110 percent of maximum operating pressure) when exposed to fire. Appendix A of AAR Specifications deals with the flow capacity of relief devices. The formulas apply to cars in the upright position with the device discharging vapor. They may not protect the car adequately when it is overturned and the device is discharging liquid. Appendix B of AAR Specifications deals with the certification of facilities. Fabrication, repairing, testing, and specialty work on tank cars must be done in certified facilities. The AAR certifies shops to build cars of certain materials, to do test work on cars, or to make certain repairs and alterations. Tank Trucks These trucks may have single, compartmented, or multiple tanks. Many of their requirements are similar to those for tank cars, except that thinner shells are permitted in most cases. Trucks for nonhazardous materials are subject to few regulations other than the normal highway laws governing all motor vehicles. But trucks carrying hazardous materials must comply with DOT regulations, Parts 173, 177, 178, and 397. Maximum weight, axle loading, and length are governed by state highway regulations. Many states have limits in the vicinity of 31,750 kg (70,000 lb) total weight, 14,500 kg (32,000 lb) for tandem axles, and 18.3 m (60 ft) or less overall length. Some allow tandem trailers. Truck cargo tanks ( for dangerous materials) are built under Part 173 and Subpart J of Part 178, DOT regulations. This includes Specifications MC-306, MC-307, MC-312, and MC-331. MC-331 is required for compressed gas. Subpart J requires tanks for pressures above 345 kPa (50 lbf/in2) in one case and 103 kPa (15 lbf/in2) in another to be built according to the ASME Boiler and Pressure Vessel Code. A particular issue of the code is specified. Because of the demands of highway service, the DOT specifications have a number of requirements in addition to the ASME Code. These include design for impact forces and rollover protection for fittings. Portable tanks, drums, or bottles are shipped by rail, ship, air, or truck. Portable tanks containing hazardous materials must conform to DOT regulations, Parts 173 and 178, Subpart H.

Some tanks are designed to be shipped by trailer and transferred to railcars or ships (see following discussion). Marine Transportation Seagoing tankers are for high tonnage. The traditional tanker uses the ship structure as a tank. It is subdivided into a number of tanks by means of transverse bulkheads and a centerline bulkhead. More than one product can be carried. An elaborate piping system connects the tanks to a pumping plant which can discharge or transfer the cargo. Harbor and docking facilities appear to be the only limit to tanker size. The largest crude oil tanker size to date is about 560,000 deadweight tons. In the United States, tankers are built to specifications of the American Bureau of Shipping and the U.S. Coast Guard. Low-temperature liquefied gases are shipped in special ships with insulation between the hull and an inner tank. The largest LNG carrier’s capacity is about 145,000 m3. Poisonous materials are shipped in separate tanks built into the ship. This prevents tank leakage from contaminating harbors. Separate tanks are also used to transport pressurized gases. Barges are used on inland waterways. Popular sizes are up to 16 m (52½ ft) wide by 76 m (250 ft) long, with 2.6-m (8½-ft) to 4.3-m (14-ft) draft. Cargo requirements and waterway limitations determine the design. Use of barges of uniform size facilitates rafting them together. Portable tanks may be stowed in the holds of conventional cargo ships or special container ships, or they may be fastened on deck. Container ships have guides in the hold and on deck which hold boxlike containers or tanks. The tank is latched to a trailer chassis and hauled to shipside. A movable gantry, sometimes permanently installed on the ship, hoists the tank from the trailer and lowers it into the guides on the ship. This system achieves large savings in labor, but its application is sometimes limited by lack of agreement between ship operators and unions. Portable tanks for regulated commodities in marine transportation must be designed and built under Coast Guard regulations (see discussion under Pressure Vessels). Materials of Construction for Bulk Transport Because of the more severe service, construction materials for transportation usually are more restricted than for storage. Most large pipelines are constructed of steel conforming to API Specification 5L or 5LX. Most tanks (cars, etc.) are built of pressure-vessel steels or AAR specification steels, with a few made of aluminum or stainless steel. Carbon-steel tanks may be lined with rubber, plastic, nickel, glass, or other materials. In many cases this is practical and cheaper than using a stainless-steel tank. Other materials for tank construction may be proposed and used if approved by the appropriate authorities (AAR and DOT). PRESSURE VESSELS This discussion of pressure vessels is intended as an overview of the codes most frequently used for the design and construction of pressure vessels. Chemical engineers who design or specify pressure vessels should determine the federal and local laws relevant to the problem and then refer to the most recent issue of the pertinent code or standard before proceeding. Laws, codes, and standards are frequently changed. A pressure vessel is a closed container of limited length (in contrast to the indefinite length of piping). Its smallest dimension is considerably larger than the connecting piping, and it is subject to pressures above 7 or 14 kPa (1 or 2 lbf/in2). It is distinguished from a boiler, which in most cases is used to generate steam for use external to itself. Code Administration The American Society of Mechanical Engineers has written the ASME Boiler and Pressure Vessel Code (BPVC), which contains rules for the design, fabrication, and inspection of boilers and pressure vessels. The ASME Code is an American National Standard. Most states in the United States and all Canadian provinces have passed legislation which makes the ASME Code or certain parts of it their legal requirement. Only a few jurisdictions have adopted the code for all vessels. The others apply it to certain types of vessels or to boilers. States employ inspectors (usually under a chief boiler inspector) to enforce code provisions. The authorities also depend a great deal on insurance company inspectors to see that boilers and pressure vessels are maintained in a safe condition. The ASME Code is written by a large committee and many subcommittees, composed of engineers appointed by the ASME. The Code Committee meets regularly to review the code and consider requests for its revision, interpretation, or extension. Interpretation and extension are accomplished through “code cases.” The decisions are published in Mechanical Engineering. Code cases are also mailed to those who subscribe to the service. A typical code case might be the approval of the use of a metal which is not presently on the list of approved code materials. Inquiries relative to code cases should be addressed to the secretary of the ASME Boiler and Pressure Vessel Committee, American Society of Mechanical Engineers, New York. A new edition of the code is issued every 3 years. Between editions, alterations are handled by issuing semiannual addenda, which may be purchased by subscription. The ASME considers any issue of the code to be adequate

STORAGE AND PROCESS VESSELS and safe, but some government authorities specify certain issues of the code as their legal requirement. Inspection Authority The National Board of Boiler and Pressure Vessel Inspectors is composed of the chief inspectors of states and municipalities in the United States and Canadian provinces who have made any part of the Boiler and Pressure Vessel Code a legal requirement. This board promotes uniform enforcement of boiler and pressure-vessel rules. One of the board’s important activities is to provide examinations for, and commissioning of, inspectors. Inspectors so qualified and employed by an insurance company, state, municipality, or Canadian province may inspect a pressure vessel and permit it to be stamped ASME—NB (National Board). An inspector employed by a vessel user may authorize the use of only the ASME stamp. The ASME Code Committee authorizes fabricators to use the various ASME stamps. The stamps, however, may be applied to a vessel only with the approval of the inspector. The ASME Boiler and Pressure Vessel Code consists of eleven sections as follows: I. Power Boilers II. Materials a. Ferrous b. Nonferrous c. Welding rods, electrodes, and filler metals d. Properties III. Rules for Construction of Nuclear Power Plant Components IV. Heating Boilers V. Nondestructive Examination VI. Rules for Care and Operation of Heating Boilers VII. Guidelines for the Care of Power Boilers VIII. Pressure Vessels IX. Welding and Brazing Qualifications X. Fiber-Reinforced Plastic Pressure Vessels XI. Rules for In-service Inspection of Nuclear Power Plant Components Pressure vessels (as distinguished from boilers) are involved with Secs. II, III, V, VIII, IX, X, and XI. Section VIII, Division 1, is the Pressure Vessel Code as it existed in the past (and will continue). Division 1 was brought out as a means of permitting higher design stresses while ensuring at least as great a degree of safety as in Division 1. These two divisions plus Secs. III and X will be discussed briefly here. They refer to Secs. II and IX. ASME Code Section VIII, Division 1 Most pressure vessels used in the process industry in the United States are designed and constructed in accordance with Sec. VIII, Division 1 (see Fig. 10-184). This division is divided into three subsections followed by appendices. Introduction The Introduction contains the scope of the division and defines the responsibilities of the user, the manufacturer, and the inspector. The scope defines pressure vessels as containers for the containment of pressure. It specifically excludes vessels having an internal pressure not exceeding 103 kPa (15 lbf/in2) and further states that the rules are applicable for pressures not exceeding 20,670 kPa (3000 lbf/in2). For higher pressures it is usually necessary to deviate from the rules in this division. The scope covers many other less basic exclusions, and inasmuch as the scope is occasionally revised, except for the most obvious cases, it is prudent to review the current issue before specifying or designing pressure vessels to this division. Any vessel that meets all the requirements of this division may be stamped with the code U symbol even though exempted from such stamping. Subsection A This subsection contains the general requirements applicable to all materials and methods of construction. Design temperature and pressure are defined here, and the loadings to be considered in design are specified. For stress failure and yielding, this section of the code uses the maximum-stress theory of failure as its criterion. This subsection refers to the tables elsewhere in the division in which the maximum allowable tensile stress values are tabulated. The basis for the establishment of these allowable stresses is defined in detail in App. P; however, as the safety factors used were very important in establishing the various rules of this division, note that the safety factors for internal-pressure loads are 3.5 on ultimate strength and 1.6 or 1.5 on yield strength, depending on the material. For external-pressure loads on cylindrical shells, the safety factors are 3 for both elastic buckling and plastic collapse. For other shapes subject to external pressure and for longitudinal shell compression, the safety factors are 3.5 for both elastic buckling and plastic collapse. Longitudinal compressive stress in cylindrical elements is limited in this subsection by the lower of either stress failure or buckling failure. Internal-pressure design rules and formulas are given for cylindrical and spherical shells and for ellipsoidal, torispherical (often called ASME heads), hemispherical, and conical heads. The formulas given assume membrane-stress failure, although the rules for heads include consideration for buckling failure in the transition area from cylinder to head (knuckle area).

10-135

Longitudinal joints in cylinders are more highly stressed than circumferential joints, and the code takes this fact into account. When forming heads, there is usually some thinning from the original plate thickness in the knuckle area, and it is prudent to specify the minimum allowable thickness at this point. Unstayed flat heads and covers can be designed by very specific rules and formulas given in this subsection. The stresses caused by pressure on these members are bending stresses, and the formulas include an allowance for additional edge moments induced when the head, cover, or blind flange is attached by bolts. Rules are provided for quick-opening closures because of the risk of incomplete attachment or opening while the vessel is pressurized. Rules for braced and stayed surfaces are also provided. External-pressure failure of shells can result from overstress at one extreme or from elastic instability at the other or at some intermediate loading. The code provides the solution for most shells by using a number of charts. One chart is used for cylinders where the shell diameter-tothickness ratio and the length-to-diameter ratio are the variables. The rest of the charts depict curves relating the geometry of cylinders and spheres to allowable stress by curves which are determined from the modulus of elasticity, tangent modulus, and yield strength at temperatures for various materials or classes of materials. The text of this subsection explains how the allowable stress is determined from the charts for cylinders, spheres, and hemispherical, ellipsoidal, torispherical, and conical heads. Frequently cost savings for cylindrical shells can result from reducing the effective length-to-diameter ratio and thereby reducing shell thickness. This can be accomplished by adding circumferential stiffeners to the shell. Rules are included for designing and locating the stiffeners. Openings are always required in pressure-vessel shells and heads. Stress intensification is created by the existence of a hole in an otherwise symmetric section. The code compensates for this by an area-replacement method. It takes a cross section through the opening, and it measures the area of the metal of the required shell that is removed and replaces it in the cross section by additional material (shell wall, nozzle wall, reinforcing plate, or weld) within certain distances of the opening centerline. These rules and formulas for calculation are included in Subsection A. When a cylindrical shell is drilled for the insertion of multiple tubes, the shell is significantly weakened and the code provides rules for tube-hole patterns and the reduction in strength that must be accommodated. Fabrication tolerances are covered in this subsection. The tolerances permitted for shells for external pressure are much closer than those for internal pressure because the stability of the structure is dependent on the symmetry. Other paragraphs cover repair of defects during fabrication, material identification, heat treatment, and impact testing. Inspection and testing requirements are covered in detail. Most vessels are required to be hydrostatically tested (generally with water) at 1.3 times the maximum allowable working pressure. Some enameled (glass-lined) vessels are permitted to be hydrostatically tested at lower pressures. Pneumatic tests are permitted and are carried to at least 1.25 times the maximum allowable working pressure, and there is provision for proof testing when the strength of the vessel or any of its parts cannot be computed with satisfactory assurance of accuracy. Pneumatic or proof tests are rarely conducted because release of the stored energy of compression of the test gas can cause an explosion upon failure of the vessel under test. Pressure-relief device requirements are defined in Subsection A. Set point and maximum pressure during relief are defined according to the service, the cause of overpressure, and the number of relief devices. Safety, safety relief, relief valves, rupture disk, rupture pin, and rules on tolerances for the relieving point are given. Testing, certification, and installation rules for relieving devices are extensive. Every chemical engineer responsible for the design or operation of process units should become very familiar with these rules. The pressurerelief device paragraphs are the only parts of Sec. VIII, Division 1, that are concerned with the installation and ongoing operation of the facility; all other rules apply only to the design and manufacture of the vessel. Subsection B This subsection contains rules pertaining to the methods of fabrication of pressure vessels. Part UW is applicable to welded vessels. Service restrictions are defined. Lethal service is for lethal substances, defined as poisonous gases or liquids of such a nature that a very small amount of the gas or the vapor of the liquid mixed or unmixed with air is dangerous to life when inhaled. It is stated that it is the user’s responsibility to advise the designer or manufacturer if the service is lethal. All vessels in lethal service shall have all butt-welded joints fully radiographed, and when practical, joints shall be butt-welded. All vessels fabricated of carbon steel or low-alloy steel shall be postweld-heat-treated. Low-temperature service is defined as being below -29°C (-20°F), and impact testing of many materials is required. The code is restrictive in the type of welding permitted.

10-136

TRANSPORT AND STORAGE OF FLUIDS

FIG. 10-184 Quick reference guide to ASME Boiler and Pressure Vessel Code Section VIII, Division 1 (2014 edition). (Reprinted with permission of publisher, HSB Global Standards, Hartford, Conn.)

STORAGE AND PROCESS VESSELS

ORGANIZATION

GENERAL NOTES

Introduction

Scope, General, Referenced Standards, Units

Subsection A

Part UG-General requirements for all construction and all materials

Subsection B Part UW Part UF Part UB

Requirements for methods of fabrication Welding Forging Brazing

Subsection C Part UCS Part UNF Part UHA Part UCI Part UCL Part UCD Part UHT

Requirements for classes of materials Carbon and low alloy steels Nonferrous materials High alloy steels Cast iron Clad plate and corrosion resistant liners Cast ductile iron Ferritic steels with tensile properties enhanced by heat treatment Layered Construction Low Temperature Materials Rules for shell and tube heat exhangers Requirements for pressure vessels constructed of Impregnated Graphite

Governing Code Editions and Cases for Pressure Vessels and Parts ................................. Appendix 43 Code Jurisdiction for Piping .................................................. U-1 Design Pressure ............ UG-21; UG-98; App. 3; UCI-3; UCD-3 Design Temperature ............... UG-20; UCL-24; UCD-3; App. C Dimpled or Embossed Assemblies ................... App. 17; UW-19 Inspector’s Responsibility ........................................ U-2; UG-90 Loadings ......................................................... UG-22; App. G, H Low Temperature Service ........... UG-20(f); UW-2; UCS-66-68; .................................................. UNF-65; UHA-51; Part ULT Manufacturer’s Responsibility ................................. U-2; UG-90 User’s Responsibility ............................................ Appendix NN Material, General .............................................. UG-4, 10, 11, 15 a. Bolts and Studs ..........................................................UG-12 b. Castings .......................................................................UG-7 c. Forgings .......................................................................UG-6 d. Nuts and Washers ..................................................... UG-13 e. Pipes and Tubes .......................................................... UG-8 f. Plates ........................................................................... UG-5 g. Rod and Bar .............................................................. UG-14 h. Standard Parts ..................................................... UG-11, 44 i. Welding ....................................................................... UG-9 Material Identification, Marking, and Certification .................................... UG-77, 93, 94

Part ULW Part ULT Part UHX Part UIG

Mandatory Appendices 1-44 Nonmandatory Appendices A, C, D-H, DD, EE, FF, GG, HH, JJ, KK, LL, MM, NN, K-M, P, R-T, W, Y Endnotes

PARA

REQUIREMENTS/REMARKS

PT

MT

UT

RT

UG-24

General requirements for castings

X

X

X

X

UG-93

General requirements for the inspection of all materials

X

X

UW-11

Radiographic and ultrasonic examination required for pressure vessels and vessel parts (also see UW-51, UW-52, UW-53) [*UW-11 (e)(2)]

X*

X*

X

X

Surface examination for offset head-to-shell butt joint

X

UW-42

Surface weld metal buildup

X

X

UW-50

Welds on pneumatically tested vessels

X

X

UF-31

Vessels fabricated from SA-372 forging material to be liquid quenched and tampered

X

X

UF-32

Finished welds after postweld heat treatment

X

X

UF-37

Repair welds in forgings

X

X

UF-55

Vessels constructed of SA-372 Class VIII material

UCS-56

Surface examination following weld repairs

UCS-57

Examination in addition to UW-11 for butt welded joints on carbon and low alloy steel pressure vessels and vessel parts

UCS-68

Exemption from impact testing when RT is performed

X

X

UNF-56

Surface examination following weld repair in nonferrous materials

X

X

UNF-57

Examination in addition to UW-11 for pressure vessels and vessel parts constructed of nonferrous materials

UNF-58

All groove and fillet wels in vessels constructed of certain nonferrious materials

UHA-33

Exceptions for radiographic examinations of high alloy steel vessels

UW-13

X

X

X

X

X

X

UCI-78

Repair of defects in cast iron pressure vessels and vessel parts

X

UCL-35

Vessels or parts of vessels constructed of clad plate and those having applied corrosion resistant linings

X

X

Examination

Reference

Examination

Reference

Appendix 8 (UG-103)

UT

UW-53

MT

Appendix 6 (UG-103)

RT

UW-51

X

MT

UT

RT

X

X

X

UCL-36

Chromium stainless steel cladding or lining

X

UCD-78

Repair of defects in cast ductile iron pressure vessels and vessel parts

X

UHT-57

Pressure vessels or vessel parts constructed of ferritic steels having tensile properties enhanced by heat treatment

X

X

UHT-83

Metal removal accomplished by methods involving melting on pressure vessels and vessel parts constructed of ferritic steels haivng tensile properies enhanced by heat treatment

X

X

UHT-85

Removal of temporary welds on pressure vessels and vessel parts constructed of ferritic steels having tensile properties enhanced by heat treatment

X

X

ULW-51

Inner shells and inner heads of layered pressure vessels

ULW-52

Welded joints in the layers of layered pressure vessels

X

X

ULW-53

Step welded girth joints in the layers of layered pressure vessels

X

X

ULW-54

Butt welded joints in layered pressure vessels

ULW-55

Flat head and tube sheet welded joints in layered pressure vessels

ULW-56

Nozzle and communicating chamber welded joints in layered pressure vessels

ULW-57

Random spot examinations and repairs of welds in layered pressure vessels

ULT-57

Welds in pressure vessels and vessel parts constructed of materials having increased design stress values due to low temperature applications

X

X

PT

(Continued )

PT

Austenitic chromium-nickel alloy steel but and fillet welds

X

X

Qualifications of Personnel Performing Section VIII, Division 1 Nondestructive Examinations

FIG. 10-184

REQUIREMENTS/REMARKS

UHA-34

X

X

Material Tolerances ........................................................... UG-16 Nameplates, Stamping and Reports ..........................UG-115-120; .......................... UHT-115; ULW-115; ULT-115; App. W & 18 Nondestructive Examination a. Liquid Penetrant ........................................................ App. 8 b. Magnetic Particle ...................................................... App. 6 c. Radiography ....................................................... UW-51, 52 d. Ultrasonic .................................................. UW-53, App. 12 Porosity Charts ....................................................................App. 4 Pressure Tests ...................................... UG-99, 100, 101; UW-50 ........................................ UCI-99; UCD-99; ULT-99; App. 44 Quality Control System ........................................... U-2; App. 10 Quick Actuating Closures .......................... U-1; UG-35; App. FF Service Restrictions ......... UW-2; UB-3; UCI-2; UCL-3; UCD-2 Stress, Maximum Allowable ..UG-23; App. P; UCS-23; UNF-23; ............ UHA-23; UCI-23; UCL-23; UCD-23; UHT-23; ULT-23 Units ................................................................. U-4; App. 33, GG User’s Responsibility....................... UG-125; U-2; App. KK, NN Welding Preheat ................................................................ App. R Welding Qualifications ........................................ UW-26 thru 29; ......................................... UNF-95; UHA-52; UHT-82; ULT-82

PARA

X X

10-137

X

X X

X X X

X

X

X X

X

X

X

X

10-138

TRANSPORT AND STORAGE OF FLUIDS

Unfired steam boilers with design pressures exceeding 345 kPa (50 lbf/in2) have restrictive rules on welded-joint design, and all butt joints require full radiography. Pressure vessels subject to direct firing have special requirements relative to welded-joint design and postweld heat treatment. This subsection includes rules governing welded-joint designs and the degree of radiography, with efficiencies for welded joints specified as functions of the quality of joint. These efficiencies are used in the formulas in Subsection A for determining vessel thicknesses. Details are provided for head-to-shell welds, tube sheet-to-shell welds, and nozzle-to-shell welds. Acceptable forms of welded stay-bolts and plug and slot welds for staying plates are given here. Rules for the welded fabrication of pressure vessels cover welding processes, manufacturer’s record keeping on welding procedures, welder qualification, cleaning, fit-up alignment tolerances, and repair of weld defects. Procedures for postweld heat treatment are detailed. Checking the procedures and welders and radiographic and ultrasonic examination of welded joints are covered. Requirements for vessels fabricated by forging in Part UF include unique design requirements with particular concern for stress risers, fabrication, heat treatment, repair of defects, and inspection. Vessels fabricated by brazing are covered in Part UB. Brazed vessels cannot be used in lethal service, for unfired steam boilers, or for direct firing. Permitted brazing processes and testing of brazed joints for strength are covered. Fabrication and inspection rules are also included. Subsection C This subsection contains requirements pertaining to classes of materials. Carbon steels and low-alloy steels are governed by Part UCS, nonferrous materials by Part UNF, high-alloy steels by Part UHA, and steels with tensile properties enhanced by heat treatment by Part UHT. Each of these parts includes tables of maximum allowable stress values for all code materials for a range of metal temperatures. These stress values include appropriate safety factors. Rules governing the application, fabrication, and heat treatment of the vessels are included in each part. Part UHT also contains more stringent details for nozzle welding that are required for some of these high-strength materials. Part UCI has rules for cast-iron construction, Part UCL has rules for welded vessels of clad plate as lined vessels, and Part UCD has rules for ductile-iron pressure vessels. A relatively recent addition to the code is Part ULW, which contains requirements for vessels fabricated by layered construction. This type of construction is most frequently used for high pressures, usually in excess of 13,800 kPa (2000 lbf/in2). There are several methods of layering in common use: (1) thick layers shrunk together; (2) thin layers, each wrapped over the other and the longitudinal seam welded by using the prior layer as backup; and (3) thin layers spirally wrapped. The code rules are written for either thick or thin layers. Rules and details are provided for all the usual welded joints and nozzle reinforcement. Supports for layered vessels require special consideration, in that only the outer layer could contribute to the support. For lethal service, only the inner shell and inner heads need comply with the requirements in Subsection B. Inasmuch as radiography would not be practical for inspection of many of the welds, extensive use is made of magnetic-particle and ultrasonic inspection. When radiography is required, the code warns the inspector that indications sufficient for rejection in single-wall vessels may be acceptable. Vent holes are specified through each layer down to the inner shell to prevent buildup of pressure between layers in the event of leakage at the inner shell. Mandatory Appendices These include a section on supplementary design formulas for shells not covered in Subsection A. Formulas are given for thick shells, heads, and dished covers. Another appendix gives very specific rules, formulas, and charts for the design of bolted-flange connections. The nature of these rules is such that they are readily computer-programmable, and most flanges now are computer-designed. One appendix includes only the charts used for calculating shells for external pressure discussed previously. Jacketed vessels are covered in a separate appendix in which very specific rules are given, particularly for the attachment of the jacket to the inner shell. Other appendices cover inspection and quality control. Nonmandatory Appendices These cover a number of subjects, primarily suggested good practices and other aids in understanding the code and in designing with the code. Several current nonmandatory appendixes will probably become mandatory. Figure 10-184 illustrates a pressure vessel with the applicable code paragraphs noted for the various elements. Additional important paragraphs are referenced at the bottom of the figure. ASME BPVC Section VIII, Division 2 Paragraph AG-100e of Division 2 states: In relation to the rules of Division 1 of Section VIII, these rules of Division 2 are more restrictive in the choice of materials which may be used but permit higher design stress intensity values to be employed in

the range of temperatures over which the design stress intensity value is controlled by the ultimate strength or the yield strength; more precise design procedures are required and some common design details are prohibited; permissible fabrication procedures are specifically delineated and more complete testing and inspection are required. Most Division 2 vessels fabricated to date have been large or intended for high pressure and, therefore, expensive when the material and labor savings resulting from smaller safety factors have been greater than the additional engineering, administrative, and inspection costs. The organization of Division 2 differs from that of Division 1. Part AG This part gives the scope of the division, establishes its jurisdiction, and sets forth the responsibilities of the user and the manufacturer. Of particular importance is the fact that no upper limitation in pressure is specified and that a user’s design specification is required. The user or the user’s agent shall provide requirements for intended operating conditions in such detail as to constitute an adequate basis for selecting materials and designing, fabricating, and inspecting the vessel. The user’s design specification shall include the method of supporting the vessel and any requirement for a fatigue analysis. If a fatigue analysis is required, the user must provide information in sufficient detail that an analysis for cyclic operation can be made. Part AM This part lists permitted individual construction materials, applicable specifications, special requirements, design stress intensity values, and other property information. Of particular importance are the ultrasonic test and toughness requirements. Among the properties for which data are included are thermal conductivity and diffusivity, coefficient of thermal expansion, modulus of elasticity, and yield strength. The design stress intensity values include a safety factor of 3 on ultimate strength at temperature or 1.5 on yield strength at temperature. Part AD This part contains requirements for the design of vessels. The rules of Division 2 are based on the maximum-shear theory of failure for stress failure and yielding. Higher stresses are permitted when wind or earthquake loads are considered. Any rules for determining the need for fatigue analysis are given here. Rules for the design of shells of revolution under internal pressure differ from the Division 1 rules, particularly the rules for formed heads when plastic deformation in the knuckle area is the failure criterion. Shells of revolution for external pressure are determined on the same criterion, including safety factors, as in Division 1. Reinforcement for openings uses the same area-replacement method as Division 1; however, in many cases the reinforcement metal must be closer to the opening centerline. The rest of the rules in Part AD for flat heads, bolted and studded connections, quick-actuating closures, and layered vessels essentially duplicate Division 1. The rules for support skirts are more definitive in Division 2. Part AF This part contains requirements governing the fabrication of vessels and vessel parts. Part AR This part contains rules for pressure-relieving devices. Part AI This part contains requirements controlling inspection of the vessel. Part AT This part contains testing requirements and procedures. Part AS This part covers requirements for stamping and certifying the vessel and vessel parts. Appendices Appendix 1 defines the basis used for defining stress intensity values. Appendix 2 contains external-pressure charts, and App. 3 has the rules for bolted-flange connections; these two are exact duplicates of the equivalent appendices in Division 1. Appendix 4 gives definitions and rules for stress analysis for shells, flat and formed heads, and tube sheets, layered vessels, and nozzles including discontinuity stresses. Of particular importance are Table 4-120.1, Classification of Stresses for Some Typical Cases, and Fig. 4-130.1, Stress Categories and Limits of Stress Intensity. These are very useful in that they clarify a number of paragraphs and simplify stress analysis. Appendix 5 contains rules and data for stress analysis for cyclic operation. Except in short-cycle batch processes, pressure vessels are usually subject to few cycles in their projected lifetime, and the endurance-limit data used in the machinery industries are not applicable. Curves are given for a broad spectrum of materials, covering a range from 10 to 1 million cycles with allowable stress values as high as 650,000 lbf/in2. This low-cycle fatigue has been developed from strain-fatigue work in which stress values are obtained by multiplying the strains by the modulus of elasticity. Stresses of this magnitude cannot occur, but strains do. The curves given have a factor of safety of 2 on stress or 20 on cycles. Appendix 6 contains the requirements of experimental stress analysis, Appendix 8 has acceptance standards for radiographic examination, Appendix 9 covers nondestructive examination, Appendix 10 gives rules for capacity conversions for safety valves, and App. 18 details quality control system requirements. The remaining appendices are nonmandatory but useful to engineers working with the code.

STORAGE AND PROCESS VESSELS General Considerations Most pressure vessels for the chemicalprocess industry will continue to be designed and built to the rules of BPVC, Section VIII, Division 1. While the rules of Section VIII, Division 2, will frequently provide thinner elements, the cost of the engineering analysis, stress analysis and higher-quality construction, material control, and inspection required by these rules frequently exceeds the savings from the use of thinner walls. Additional ASME Code Considerations ASME BPVC Section III: Nuclear Power Plant Components This section of the code includes vessels, storage tanks, and concrete containment vessels as well as other nonvessel items. ASME BPVC Section X: Fiberglass–Reinforced-Plastic Pressure Vessels This section is limited to four types of vessels: bag-molded and centrifugally cast, each limited to 1000 kPa (150 lbf/in2); filament-wound with cut filaments limited to 10,000 kPa (1500 lbf/in2); and filament-wound with uncut filaments limited to 21,000 kPa (3000 lbf/in2). Operating temperatures are limited to the range from +66°C (150°F) to -54°C (-65°F). Low modulus of elasticity and other property differences between metal and plastic required that many of the procedures in Section X be different from those in the sections governing metal vessels. The requirement that at least one vessel of a particular design and fabrication shall be tested to destruction has prevented this section from being widely used. The results from the combined fatigue and burst test must give the design pressure a safety factor of 6 to the burst pressure. Safety in Design Designing a pressure vessel in accordance with the code, under most circumstances, will provide adequate safety. In the code’s own words, however, the rules “cover minimum construction requirements for the design, fabrication, inspection, and certification of pressure vessels.” The significant word is minimum. The ultimate responsibility for safety rests with the user and the designer. They must decide whether anything beyond code requirements is necessary. The code cannot foresee and provide for all the unusual conditions to which a pressure vessel might be exposed. If it tried to do so, the majority of pressure vessels would be unnecessarily restricted. Some of the conditions that a vessel might encounter are unusually low temperatures, unusual thermal stresses, stress ratcheting caused by thermal cycling, vibration of tall vessels excited by von Karman vortices caused by wind, very high pressures, runaway chemical reactions, repeated local overheating, explosions, exposure to fire, exposure to materials that rapidly attack the metal, containment of extremely toxic materials, and very large sizes of vessels. Large vessels, although they may contain nonhazardous materials, by their very size, could create a serious hazard if they burst. The failure of the Boston molasses tank in 1919 killed 12 people. For pressure vessels which are outside code jurisdiction, there are sometimes special hazards in very high-strength materials and plastics. There may be many others which the designers should recognize if they encounter them. Metal fatigue, when it is present, is a serious hazard. BPVC Section VIII, Division 1, mentions rapidly fluctuating pressures. Division 2 and Section III do require a fatigue analysis. In extreme cases, vessel contents may affect the fatigue strength (endurance limit) of the material. This is corrosion fatigue. Although most ASME Code materials are not particularly sensitive to corrosion fatigue, even they may suffer an endurance limit loss of 50 percent in some environments. High-strength heat-treated steels, on the other hand, are very sensitive to corrosion fatigue. It is not unusual to find some of these which lose 75 percent of their endurance in corrosive environments. In fact, in corrosion fatigue many steels do not have an endurance limit. The curve of stress versus cycles to failure (S/N curve) continues to slope downward regardless of the number of cycles. Brittle fracture is probably the most insidious type of pressure-vessel failure. Without brittle fracture, a pressure vessel could be pressurized approximately to its ultimate strength before failure. With brittle behavior some vessels have failed well below their design pressures (which are about 25 percent of the theoretical bursting pressures). To reduce the possibility of brittle behavior, Division 2 and Section III require impact tests. The subject of brittle fracture has been understood only since about 1950, and knowledge of some of its aspects is still inadequate. A notched or cracked plate of pressure-vessel steel, stressed at 66°C (150°F), would elongate and absorb considerable energy before breaking. It would have a ductile or plastic fracture. As the temperature is lowered, a point is reached at which the plate would fail in a brittle manner with a flat fracture surface and almost no elongation. The transition from ductile to brittle fracture actually takes place over a temperature range, but a point in this range is selected as the transition temperature. One of the ways of determining this temperature is the Charpy impact test (see ASTM Specification E-23). After the transition temperature has been determined by laboratory impact tests, it must be correlated with service experience on full-size plates. The literature on brittle fracture contains information on the relation of impact tests to service experience on some carbon steels.

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A more precise but more elaborate method of dealing with the ductilebrittle transition is the fracture-analysis diagram. This uses a transition known as the nil-ductility temperature (NDT), which is determined by the drop-weight test (ASTM Standard E208) or the drop-weight tear test (ASTM Standard E436). The application of this diagram is explained in two papers by Pellini and Puzak [Trans. Am. Soc. Mech. Eng. 429 (October 1964); Welding Res. Counc. Bull. 88, 1963]. BPVC Section VIII, Division 1, is lax with respect to brittle fracture. It allows the use of many steels down to -29°C (-20°F) without a check on toughness. Occasional brittle failures show that some vessels are operating below the nil-ductility temperature, i.e., the lower limit of ductility. Division 2 has solved this problem by requiring impact tests in certain cases. Tougher grades of steel, such as the SA516 steels (in preference to SA515 steel), are available for a small price premium. Stress relief, steel made to fine-grain practice, and normalizing all reduce the hazard of brittle fracture. Nondestructive testing of both the plate and the finished vessel is important to safety. In the analysis of fracture hazards, it is important to know the size of the flaws that may be present in the completed vessel. The four most widely used methods of examination are radiographic, magnetic-particle, liquid-penetrant, and ultrasonic. Radiographic examination is either by x-rays or by gamma radiation. The former has greater penetrating power, but the latter is more portable. Few x-ray machines can penetrate beyond 300-mm (12-in) thickness. Ultrasonic techniques use vibrations with a frequency between 0.5 and 20 MHz transmitted to the metal by a transducer. The instrument sends out a series of pulses. These show on a cathode-ray screen as they are sent out and again when they return after being reflected from the opposite side of the member. If there is a crack or an inclusion along the way, it will reflect part of the beam. The initial pulse and its reflection from the back of the member are separated on the screen by a distance which represents the thickness. The reflection from a flaw will fall between these signals and indicate its magnitude and position. Ultrasonic examination can be used for almost any thickness of material from a fraction of an inch to several feet. Its use is dependent on the shape of the body because irregular surfaces may give confusing reflections. Ultrasonic transducers can transmit pulses normal to the surface or at an angle. Transducers transmitting pulses that are oblique to the surface can solve a number of special inspection problems. Magnetic-particle examination is used only on magnetic materials. Magnetic flux is passed through the part in a path parallel to the surface. Fine magnetic particles, when dusted over the surface, will concentrate near the edges of a crack. The sensitivity of magnetic-particle examination is proportional to the sine of the angle between the direction of the magnetic flux and the direction of the crack. To be sure of picking up all cracks, it is necessary to probe the area in two directions. Liquid-penetrant examination involves wetting the surface with a fluid that penetrates open cracks. After the excess liquid has been wiped off, the surface is coated with a material which will reveal any liquid that has penetrated the cracks. In some systems a colored dye will seep out of cracks and stain whitewash. Another system uses a penetrant that becomes fluorescent under ultraviolet light. Each of these four popular methods has its advantages. Frequently, best results are obtained by using more than one method. Magnetic particles or liquid penetrants are effective on surface cracks. Radiography and ultrasonic examination are necessary for subsurface flaws. No known method of nondestructive testing can guarantee the absence of flaws. There are other less widely used methods of examination. Among these are eddy current, electrical resistance, acoustics, and thermal testing. Nondestructive Testing Handbook [Robert C. McMaster (ed.), Ronald, New York, 1959] gives information on many testing techniques. The eddy-current technique involves an alternating-current coil along and close to the surface being examined. The electrical impedance of the coil is affected by flaws in the structure or changes in composition. Commercially, the principal use of eddy-current testing is for the examination of tubing. It could, however, be used for testing other things. The electrical resistance method involves passing an electric current through the structure and exploring the surface with voltage probes. Flaws, cracks, or inclusions will cause a disturbance in the voltage gradient on the surface. Railroads have used this method for many years to locate transverse cracks in rails. The hydrostatic test is, in one sense, a method of examination of a vessel. It can reveal gross flaws, inadequate design, and flange leaks. Many believe that a hydrostatic test guarantees the safety of a vessel. This is not necessarily so. A vessel that has passed a hydrostatic test is probably safer than one that has not been tested. It can, however, still fail in service, even on the next application of pressure. Care in material selection, examination, and fabrication does more to guarantee vessel integrity than the hydrostatic test. The ASME Codes recommend that hydrostatic tests be run at a temperature that is usually above the nil-ductility temperature of the material.

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This is, in effect, a pressure-temperature treatment of the vessel. When tested in the relatively ductile condition above the nil-ductility temperature, the material will yield at the tips of cracks and flaws and at points of high residual weld stress. This procedure will actually reduce the residual stresses and cause a redistribution at crack tips. The vessel will then be in a safer condition for subsequent operation. This procedure is sometimes referred to as notch nullification. It is possible to design a hydrostatic test in such a way that it probably will be a proof test of the vessel. This usually requires, among other things, that the test be run at a temperature as low as and preferably lower than the minimum operating temperature of the vessel. Proof tests of this type are run on vessels built of ultrahigh-strength steel to operate at cryogenic temperatures. Other Regulations and Standards Pressure vessels may come under many types of regulation, depending on where they are and what they contain. Although many states have adopted the ASME Boiler and Pressure Vessel Code, either in total or in part, any state or municipality may enact its own requirements. The federal government regulates some pressure vessels through the Department of Transportation, which includes the Coast Guard. If pressure vessels are shipped into foreign countries, they may face additional regulations. Pressure vessels carried aboard United States–registered ships must conform to rules of the U.S. Coast Guard. Subchapter F of Title 46, Code of Federal Regulations, covers marine engineering. Of this, Parts 50 through 61 and 98 include pressure vessels. Many of the rules are similar to those in the ASME Code, but there are differences. The American Bureau of Shipping (ABS) has rules that insurance underwriters require for the design and construction of pressure vessels which are a permanent part of a ship. Pressure cargo tanks may be permanently attached and come under these rules. Such tanks supported at several points are independent of the ship’s structure and are distinguished from integral cargo tanks such as those in a tanker. ABS has pressure-vessel rules in two of its publications. Most of them are in Rules for Building and Classing Steel Vessels. Standards of Tubular Exchanger Manufacturers Association (TEMA) These standards give recommendations for the construction of tubular heat exchangers. Although TEMA is not a regulatory body and there is no legal requirement for the use of its standards, they are widely accepted as a good basis for design. By specifying TEMA standards, one can obtain adequate equipment without having to write detailed specifications for each piece. TEMA gives formulas for the thickness of tube sheets. Such formulas are not in ASME Codes. (See further discussion of TEMA in Sec. 11.) Vessels with Unusual Construction High pressures create design problems. ASME BPVC Section VIII, Division 1, applies to vessels rated for pressures up to 20,670 kPa (3000 lbf/in2). Division 2 is unlimited. At high pressures, special designs not necessarily in accordance with the code are sometimes used. At such pressures, a vessel designed for ordinary low-carbon-steel plate, particularly in large diameters, would become too thick for practical fabrication by ordinary methods. The alternatives are to make the vessel of high-strength plate, use a solid forging, or use multilayer construction. High-strength steels with tensile strengths over 1380 MPa (200,000 lbf/in2) are limited largely to applications for which weight is very important. Welding procedures are carefully controlled, and preheat is used. These materials are brittle at almost any temperature, and vessels must be designed to prevent brittle fracture. Flat spots and variations in curvature are avoided. Openings and changes in shape require appropriate design. The maximum permissible size of flaws is determined by fracture mechanics, and the method of examination must ensure as much as possible that larger flaws are not present. All methods of nondestructive testing may be used. Such vessels require the most sophisticated techniques in design, fabrication, and operation. Solid forgings are frequently used in construction for pressure vessels above 20,670 kPa (3000 lbf/in2) and even lower. Almost any shell thickness can be obtained, but most of them range between 50 and 300 mm (2 and 12 in). The ASME Code lists forging materials with tensile strengths from 414 to 930 MPa ( from 60,000 to 135,000 lbf/in2). Brittle fracture is a possibility, and the hazard increases with thickness. Furthermore, some forging alloys have nil-ductility temperatures as high as 121°C (250°F). A forged vessel should have an NDT at least 17°C (30°F) below the design temperature. In operation, it should be slowly and uniformly heated at least to the NDT before it is subjected to pressure. During construction, nondestructive testing should be used to detect dangerous cracks or flaws. Section VIII of the ASME Code, particularly Division 2, gives design and testing techniques. As the size of a forged vessel increases, the sizes of ingot and handling equipment become larger. The cost may increase faster than the weight. The problems of getting sound material and avoiding brittle fracture also

become more difficult. Some of these problems are avoided by use of multilayer construction. In this type of vessel, the heads and flanges are made of forgings, and the cylindrical portion is built up by a series of layers of thin material. The thickness of these layers may be between 3 and 50 mm (⅛ and 2 in), depending on the type of construction . There is an inner lining which may be different from the outer layers . Although there are multilayer vessels as small as 380-mm (15-in) inside diameter and 2400 mm (8 ft) long, their principal advantage applies to the larger sizes . When properly made, a multilayer vessel is probably safer than a vessel with a solid wall . The layers of thin material are tougher and less susceptible to brittle fracture, have lower probability of defects, and have the statistical advantage of a number of small elements instead of a single large one . The heads, flanges, and welds, of course, have the same hazards as other thick members . Proper attention is necessary to avoid cracks in these members . There are several assembly techniques . One technique frequently used is to form successive layers in half cylinders and butt-weld them over the previous layers . In doing this, the welds are staggered so that they do not fall together . This type of construction usually uses plates from 6 to 12 mm (¼ to ½ in) thick . Another method is to weld each layer separately to form a cylinder and then shrink it over the previous layers . Layers up to about 50-mm (2-in) thickness are assembled in this way . A third method of fabrication is to wind the layers as a continuous sheet . This technique is used in Japan . The Wickel construction, fabricated in Germany, uses helical winding of interlocking metal strip . Each method has its advantages and disadvantages, and the choice will depend on circumstances . Because of the possibility of voids between layers, it is preferable not to use multilayer vessels in applications where they will be subjected to fatigue . Inward thermal gradients (inside temperature lower than outside temperature) are also undesirable . Articles on these vessels have been written by Fratcher [Pet. Refiner 34(11): 137 (1954)] and by Strelzoff, Pan, and Miller [Chem. Eng. 75(21): 143–150 (1968)] . Vessels for high-temperature service may be beyond the temperature limits of the stress tables in the ASME Codes . BPVC Section VIII, Division 1, makes provision for construction of pressure vessels up to 650°C (1200°F) for carbon and low-alloy steel and up to 815°C (1500°F) for stainless steels (300 series) . If a vessel is required for temperatures above these values and above 103 kPa (15 lbf/in2), it would be necessary, in a code state, to get permission from the state authorities to build it as a special project . Above 815°C (1500°F), even the 300 series stainless steels are weak, and creep rates increase rapidly . If the metal that resists the pressure operates at these temperatures, the vessel pressure and size will be limited . The vessel must also be expendable because its life will be short . Long exposure to high temperature may cause the metal to deteriorate and become brittle . Sometimes, however, economics favor this type of operation . One way to circumvent the problem of low metal strength is to use a metal inner liner surrounded by insulating material, which in turn is confined by a pressure vessel . The liner, in some cases, may have perforations that will allow pressure to pass through the insulation and act on the outer shell, which is kept cool to obtain normal strength . The liner has no pressure differential acting on it and, therefore, does not need much strength . Ceramic linings are also useful for high-temperature work . Lined vessels are used for many applications . Any type of lining can be used in an ASME Code vessel, provided it is compatible with the metal of the vessel and the contents . Glass, rubber, plastics, rare metals, and ceramics are a few types . The lining may be installed separately, or if a metal is used, it may be in the form of clad plate . The cladding on plate can sometimes be considered as a stress-carrying part of the vessel . A ceramic lining when used with high temperature acts as an insulator so that the steel outer shell is at a moderate temperature while the temperature at the inside of the lining may be very high . Ceramic linings may be of unstressed brick, or prestressed brick, or cast in place . Cast ceramic linings or unstressed brick may develop cracks and is used when the contents of the vessel will not damage the outer shell . They are usually designed so that the high temperature at the inside will expand them sufficiently to make them tight in the outer (and cooler) shell . This, however, is not usually sufficient to prevent some penetration by the product . Prestressed-brick linings can be used to protect the outer shell . In this case, the bricks are installed with a special thermosetting-resin mortar . After lining, the vessel is subjected to internal pressure and heat . This expands the steel vessel shell, and the mortar expands to take up the space . The pressure and temperature must be at least as high as the maximum that will be encountered in service . After the mortar has set, reduction of pressure and temperature will allow the vessel to contract, putting the brick in compression . The upper temperature limit for this construction is about 190°C (375°F) . The installation of such linings is highly specialized work done by a few companies . Great care is usually exercised in operation to protect the

STORAGE AND PROCESS VESSELS vessel from exposure to asymmetrical temperature gradients. Side nozzles and other unsymmetrical designs are avoided insofar as possible. Concrete pressure vessels may be used in applications that require large sizes. Such vessels, if made of steel, would be too large and heavy to ship. Through the use of post-tensioned (prestressed) concrete, the vessel is fabricated on site. In this construction, the reinforcing steel is placed in tubes or plastic covers, which are cast into the concrete. Tension is applied to the steel after the concrete has acquired most of its strength. Concrete nuclear reactor vessels, of the order of magnitude of 15-m (50-ft) inside diameter and length, have inner linings of steel which confine the pressure. After fabrication of the liner, the tubes for the cables or wires are put in place and the concrete is poured. High-strength reinforcing steel is used. Because there are thousands of reinforcing tendons in the concrete vessel, there is a statistical factor of safety. The failure of 1 or even 10 tendons would have little effect on the overall structure. Plastic pressure vessels have the advantages of chemical resistance and light weight. Above 103 kPa (15 lbf/in2), with certain exceptions, they must be designed according to ASME BPVC Section X (see Storage of Gases) and are confined to the three types of approved code construction. Below 103 kPa (15 lbf/in2), any construction may be used. Even in this pressure range, however, the code should be used for guidance. Solid plastics, because of low strength and creep, can be used only for the lowest pressures and sizes. A stress of a few hundred pounds-force per square inch is the maximum for most plastics. To obtain higher strength, the filled plastics or filamentwound vessels, specified by the code, must be used. Solid-plastic parts, however, are often employed inside a steel shell, particularly for heat exchangers. Graphite and ceramic vessels are used fully armored; that is, they are enclosed within metal pressure vessels. These materials are also used for boxlike vessels with backing plates on the sides. The plates are drawn together by tie bolts, thus putting the material in compression so that it can withstand low pressure. ASME Code Developments ASME BPVC Section VIII (2015) has been reorganized into three classes. Class 1 is for low-pressure vessels employing spot radiography. Class 2 is for vessels requiring full radiography. Class 3 is for vessels experiencing fatigue. Material stress levels similar to those of competing vessel codes from Europe and Asia are included. Vessel Codes Other than ASME Different design and construction rules are used in other countries. Chemical engineers concerned with pressure vessels outside the United States must become familiar with local pressure-vessel laws and regulations. Boilers and Pressure Vessels, an international survey of design and approval requirements published by the British Standards Institution, Maylands Avenue, Hemel Hempstead, Hertfordshire, England, in 1975, gives pertinent information for 76 political jurisdictions. The British Code (British Standards) and the German Code (A. D. Merkblätter) in addition to the ASME Code are most commonly permitted, although Netherlands, Sweden, and France also have codes. The major difference between the codes lies in factors of safety and in whether ultimate strength is considered. BPVC, Section VIII, Division 1, vessels are generally heavier than vessels built to the other codes; however, the differences in allowable stress for a given material are less in the higher-temperature (creep) range. Engineers and metallurgists have developed alloys to comply economically with individual codes. In Germany, where design stress is determined from yield strength and creep-rupture strength and no allowance is made for ultimate strength, steels that have a very high yield strength/ultimate strength ratio are used. Other differences between codes include different bases for the design of reinforcement for openings and the design of flanges and heads. Some codes include rules for the design of heat-exchanger tube sheets, while others (ASME Code) do not. The Dutch Code (Grondslagen) includes very specific rules for calculation of wind loads, while the ASME Code leaves this entirely to the designer. There are also significant differences in construction and inspection rules. Unless engineers make a detailed study of the individual codes and keep current, they will be well advised to make use of responsible experts for any of the codes. Vessel Design and Construction The ASME Code lists a number of loads that must be considered in designing a pressure vessel. Among them are impact, weight of the vessel under operating and test conditions, superimposed loads from other equipment and piping, wind and earthquake loads, temperature-gradient stresses, and localized loadings from internal and external supports. In general, the code gives no values for these loads or methods for determining them, and no formulas are given for determining the stresses from these loads. Engineers must be knowledgeable in mechanics and strength of materials to solve these problems. Some of the problems are treated by Brownell and Young, Process Equipment Design, Wiley, New York, 1959. ASME papers treat others, and a number of books published by the ASME are collections of papers on pressure-vessel design: Pressure Vessels and Piping Design: Collected Papers, 1927–1959; Pressure

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Vessels and Piping Design and Analysis, four volumes; and International Conference: Pressure Vessel Technology, published annually. Throughout the year the Welding Research Council publishes bulletins which are final reports from projects sponsored by the council, important papers presented before engineering societies, and other reports of current interest which are not published in Welding Research. A large number of the published bulletins are pertinent for vessel designers. Care of Pressure Vessels Protection against excessive pressure is largely taken care of by code requirements for relief devices. Exposure to fire is also covered by the code. The code, however, does not provide for the possibility of local overheating and weakening of a vessel in a fire. Insulation reduces the required relieving capacity and also reduces the possibility of local overheating. A pressure-reducing valve in a line leading to a pressure vessel is not adequate protection against overpressure. Its failure will subject the vessel to full line pressure. Vessels that have an operating cycle which involves the solidification and remelting of solids can develop excessive pressures. A solid plug of material may seal off one end of the vessel. If heat is applied at that end to cause melting, the expansion of the liquid can build up a high pressure and possibly result in yielding or rupture. Solidification in connecting piping can create similar problems. Some vessels may be exposed to a runaway chemical reaction or even an explosion. This requires relief valves, rupture disks, or, in extreme cases, a frangible roof design or barricade (the vessel is expendable). A vessel with a large rupture disk needs anchors designed for the jet thrust when the disk blows. Vacuum must be considered. It is nearly always possible that the contents of a vessel might contract or condense sufficiently to subject it to an internal vacuum. If the vessel cannot withstand the vacuum, it must have vacuumbreaking valves. Improper operation of a process may result in the vessel’s exceeding design temperature. Proper control is the only solution to this problem. Maintenance procedures can also cause excessive temperatures. Sometimes the contents of a vessel may be burned out with torches. If the flame impinges on the vessel shell, overheating and damage may occur. Excessively low temperature may involve the hazard of brittle fracture. A vessel that is out of use in cold weather could be at a subzero temperature and well below its nil-ductility temperature. In startup, the vessel should be warmed slowly and uniformly until it is above the NDT. A safe value is 38°C (100°F) for plate if the NDT is unknown. The vessel should not be pressurized until this temperature is exceeded. Even after the NDT has been passed, excessively rapid heating or cooling can cause high thermal stresses. Corrosion is probably the greatest threat to vessel life. Partially filled vessels frequently have severe pitting at the liquid-vapor interface. Vessels usually do not have a corrosion allowance on the outside. Lack of protection against the weather or against the drip of corrosive chemicals can reduce vessel life. Insulation may contain damaging substances. Chlorides in insulating materials can cause cracking of stainless steels. Water used for hydrotesting should be free of chlorides. Pressure vessels should be inspected periodically. No rule can be given for the frequency of these inspections. Frequency depends on operating conditions. If the early inspections of a vessel indicate a low corrosion rate, intervals between inspections may be lengthened. Some vessels are inspected at 5-year intervals; others, as frequently as once a year. Measurement of corrosion is an important inspection item. One of the most convenient ways of measuring thickness (and corrosion) is to use an ultrasonic gauge. The location of the corrosion and whether it is uniform or localized in deep pits should be observed and reported. Cracks, any type of distortion, and leaks should be observed. Cracks are particularly dangerous because they can lead to sudden failure. Insulation is usually left in place during inspection of insulated vessels. If, however, severe external corrosion is suspected, the insulation should be removed. All forms of nondestructive testing are useful for examinations. There are many ways in which a pressure vessel can suffer mechanical damage. The shells can be dented or even punctured; they can be dropped or have hoisting cables improperly attached; bolts can be broken; flanges are bent by excessive bolt tightening; gasket contact faces can be scratched and dented; rotating paddles can drag against the shell and cause wear; and a flange can be bolted up with a gasket half in the groove and half out. Most of these forms of damage can be prevented by taking care and using common sense. If damage is repaired by straightening, as with a dented shell, it may be necessary to stress-relieve the repaired area. Some steels are susceptible to embrittlement by aging after severe straining. A safer procedure is to cut out the damaged area and replace it. The National Board Inspection Code, published by the National Board of Boiler and Pressure Vessel Inspectors, Columbus, Ohio, is helpful. Any repair, however, is acceptable if it is made in accordance with the rules of the Pressure Vessel Code. Care in reassembling the vessel is particularly important. Gaskets should be properly located, particularly if they are in grooves. Bolts should be

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Cost, US dollars/gallon (2016)

80 70 60 50 40 30 20 10 0 0.25

0.50

0.75

1.00

1.25

1.50

1.75

Vessel wall thickness, inches Carbon-steel pressure-vessel cost as a function of wall thickness . 1 gal = 0 .003875 m3; 1 in = 0 .0254 m . (Courtesy of E. S. Fox, Ltd.)

FIG. 10-185

Cost, US dollars/lbm (2016)

8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00 0.25

0.50

0.75

1.00

1.25

1.50

1.75

Vessel wall thickness, inches FIG. 10-186 Carbon-steel pressure-vessel cost as a function of wall thickness . 1 gal = 0 .003875 m3; 1 in = 0 .0254 m; 1 lb = 0 .4536 kg . (Courtesy of E. S. Fox, Ltd.)

tightened in proper sequence. In some critical cases and with large bolts, it is necessary to control bolt tightening by torque wrenches, micrometers, patented bolt-tightening devices, or heating bolts. After assembly, vessels are sometimes given a hydrostatic test. Pressure-Vessel Cost and Weight Figure 10-185 can be used for estimating carbon-steel vessel cost when a weight estimate is not available and Fig. 10-186 with a weight estimate. Weight and cost include skirts and other supports. The cost is based on several 2016 pressure vessels. Costs are for vessels not of unusual design. Complicated vessels could cost considerably more. Guthrie [Chem. Eng. 76(6): 114–142 (1969)] also gives pressure-vessel cost data. When vessels have complicated construction (large, heavy bolted connections, support skirts, etc.), it is preferable to estimate their weight and apply a unit cost in dollars per pound. Pressure-vessel weights are obtained by calculating the cylindrical shell and heads separately and then adding the weights of nozzles and attachments. Steel has a density of 7817 kg/m3 (488 lb/ft3). Metal in heads can be approximated by calculating the area of the blank (disk) used for forming the head. The required diameter of the blank can be calculated by multiplying the head outside diameter by the approximate factors given in Table 10-60. These factors make no allowance for the straight flange which is a cylindrical extension that is formed on the head. The blank diameter obtained from these factors must be increased by twice the length of straight flange, which is usually 1½ to 2 in but can be up to several inches in length. Manufacturers’ catalogs give weights of heads. Forming a head thins it in certain areas. To obtain the required minimum thickness of a head, it is necessary to use a plate that is initially thicker. Table 10-61 gives allowances for additional thickness. Nozzles and flanges may add considerably to the weight of a vessel. Their weights can be obtained from manufacturers’ catalogs (Taylor Forge Division of Gulf & Western Industries, Inc., Tube Turns Inc., Ladish Co., Lenape Forge, and others). Other parts such as skirts, legs, support brackets, and other details must be calculated.

TABLE 10-60 Factors for Estimating Diameters of Blanks for Formed Heads Ratio d/t

Blank diameter factor

ASME head

Over 50 30-50 20–30

1.09 1.11 1.15

Ellipsoidal head

Over 20 10–20

1.24 1.30

Hemispherical head

Over 30 18–30 10–18

1.60 1.65 1.70

d = head diameter t = nominal minimum head thickness

TABLE 10-61

Extra Thickness Allowances for Formed Heads* Extra thickness, in ASME and ellipsoidal

Minimum head thickness, in Up to 0.99 1 to 1 .99 2 to 2 .99 ∗Lukens, Inc .

Head OD up to 150 in incl. 1

16

⅛ ¼

Head OD over 150 in ⅛ ⅛ ¼

Hemispherical 3

16

⅜ ⅝

Section 11

Heat-Transfer Equipment

Richard L. Shilling, P.E., B.E.M.E. Senior Engineering Consultant, Heat Transfer Research, Inc.; American Society of Mechanical Engineers (Section Editor, Cryogenic Heat Exchangers, Shell-and-Tube Heat Exchangers, Hairpin/Double-Pipe Heat Exchangers, Air-Cooled Heat Exchangers, Heating and Cooling of Tanks, Fouling and Scaling, Heat Exchangers for Solids, Thermal Insulation, Thermal Design of Evaporators, Evaporators) Patrick M. Bernhagen, P.E., B.S. Director of Sales—Fired Heater, Amec Foster Wheeler North America Corp.; API Subcommittee on Heat Transfer Equipment API 530, 536, 560, and 561 (Compact and Nontubular Heat Exchangers) William E. Murphy, Ph.D., P.E. Professor of Mechanical Engineering, University of Kentucky; American Society of Heating, Refrigerating, and Air-Conditioning Engineers; American Society of Mechanical Engineers; International Institute of Refrigeration (Air Conditioning) Predrag S. Hrnjak, Ph.D. Will Stoecker Res. Professor of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign; Principal Investigator—U of I Air Conditioning and Refrigeration Center; Assistant Professor, University of Belgrade; International Institute of Chemical Engineers; American Society of Heat, Refrigerating, and Air Conditioning Engineers (Refrigeration) David Johnson, P.E., M.Ch.E. Retired (Thermal Design of Heat Exchangers, Condensers, Reboilers)

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT Introduction to Thermal Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Approach to Heat Exchanger Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overall Heat-Transfer Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mean Temperature Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Countercurrent or Cocurrent Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reversed, Mixed, or Cross-Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Design for Single-Phase Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Double-Pipe Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Baffled Shell-and-Tube Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Design of Condensers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single-Component Condensers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multicomponent Condensers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Design of Reboilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kettle Reboilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical Thermosiphon Reboilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Forced-Recirculation Reboilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Design of Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Forced-Circulation Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Long-Tube Vertical Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short-Tube Vertical Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Miscellaneous Evaporator Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heat Transfer from Various Metal Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-4 11-4 11-4 11-4 11-4 11-5 11-5 11-5 11-5 11-10 11-10 11-12 11-12 11-12 11-12 11-12 11-12 11-13 11-13 11-14 11-14 11-15

Effect of Fluid Properties on Heat Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Noncondensibles on Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cryogenic Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Batch Operations: Heating and Cooling of Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of External Heat Loss or Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Internal Coil or Jacket Plus External Heat Exchanger . . . . . . . . . . . . . . . . . . . . . . Equivalent-Area Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonagitated Batches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Storage Tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Design of Tank Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maintenance of Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heating and Cooling of Tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tank Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Teflon Immersion Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bayonet Heaters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . External Coils and Tracers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jacketed Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Extended or Finned Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finned-Surface Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-16 11-17 11-17 11-17 11-17 11-17 11-18 11-18 11-18 11-18 11-18 11-18 11-19 11-19 11-19 11-20 11-20 11-20 11-20 11-20 11-20 11-21 11-21

The prior and substantial contributions of Frank L. Rubin (Section Editor, Sixth Edition) and Dr. Kenneth J. Bell (Thermal Design of Heat Exchangers, Condensers, Reboilers), Dr. Thomas M. Flynn (Cryogenic Processes), and F. C. Standiford (Thermal Design of Evaporators, Evaporators), who were authors for the Seventh Edition, are gratefully acknowledged. 11-1

11-2

HEAT-TRANSFER EQUIPMENT

High Fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Low Fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fouling and Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control of Fouling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fouling Transients and Operating Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Removal of Fouling Deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fouling Resistances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical Heat-Transfer Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Design for Solids Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conductive Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contactive (Direct) Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convective Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiative Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scraped-Surface Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-21 11-21 11-22 11-22 11-22 11-22 11-22 11-22 11-22 11-24 11-27 11-28 11-28 11-30

TEMA-STYLE SHELL-AND-TUBE HEAT EXCHANGERS Types and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TEMA Numbering and Type Designation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Functional Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selection of Flow Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Construction Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tube Bundle Vibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Principal Types of Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fixed-Tube-Sheet Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . U-Tube Heat Exchanger. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Packed Lantern-Ring Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Outside Packed Floating-Head Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Internal Floating-Head Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pull-Through Floating-Head Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Falling-Film Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tube-Side Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tube-Side Header . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Special High-Pressure Closures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tube-Side Passes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rolled Tube Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Welded Tube Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Double-Tube-Sheet Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shell-Side Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shell Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shell-Side Arrangements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Baffles and Tube Bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Segmental Baffles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rod Baffles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tie Rods and Spacers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Impingement Baffle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vapor Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tube-Bundle Bypassing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Helical Baffles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Longitudinal Flow Baffles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Corrosion in Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Materials of Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bimetallic Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clad Tubesheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonmetallic Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shell-and-Tube Exchanger Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-31 11-31 11-31 11-31 11-31 11-31 11-31 11-33 11-33 11-33 11-33 11-36 11-36 11-37 11-37 11-37 11-37 11-38 11-38 11-38 11-38 11-38 11-38 11-38 11-38 11-38 11-38 11-40 11-40 11-40 11-41 11-41 11-41 11-41 11-41 11-41 11-41 11-41 11-41 11-42 11-42 11-42 11-42 11-42

HAIRPIN/DOUBLE-PIPE HEAT EXCHANGERS Principles of Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finned Double Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multitube Hairpins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-44 11-44 11-44 11-45

AIR-COOLED HEAT EXCHANGERS Introduction to Air-Cooled Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Forced and Induced Draft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tube Bundle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finned-Tube Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fan Drivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fan Ring and Plenum Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Air Flow Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Air Recirculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trim Coolers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Humidification Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaporative Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Steam Condensers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Air-Cooled Overhead Condensers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Air-Cooled Heat Exchanger Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-45 11-45 11-46 11-46 11-47 11-47 11-47 11-47 11-48 11-48 11-48 11-48 11-48 11-48 11-49 11-49 11-49

COMPACT AND NONTUBULAR HEAT EXCHANGERS Compact Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plate-and-Frame Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gasketed-Plate Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Welded- and Brazed-Plate Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Combination Welded-Plate Exchangers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spiral-Plate Heat Exchanger (SHE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Brazed-Plate-Fin Heat Exchangers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design and Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plate-Fin Tubular Exchanger (PFE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Printed-Circuit Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spiral-Tube Exchanger (STE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graphite Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cascade Coolers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bayonet-Tube Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Atmospheric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonmetallic Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-49 11-50 11-50 11-50 11-50 11-51 11-52 11-52 11-52 11-52 11-53 11-53 11-53 11-53 11-53 11-53 11-53 11-53 11-53 11-54 11-54 11-54 11-54 11-54 11-54 11-54 11-54 11-54 11-55 11-55

HEAT EXCHANGERS FOR SOLIDS Equipment for Solidification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Agitated-Pan Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vibratory Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Belt Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rotating-Drum Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rotating-Shelf Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equipment for Fusion of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Horizontal-Tank Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical Agitated-Kettle Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mill Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heat-Transfer Equipment for Sheeted Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cylinder Heat-Transfer Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heat-Transfer Equipment for Divided Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluidized-Bed Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Moving-Bed Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Agitated-Pan Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kneading Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shelf Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rotating-Shell Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conveyor-Belt Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spiral-Conveyor Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Double-Cone Blending Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vibratory-Conveyor Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elevator Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pneumatic Conveying Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vacuum-Shelf Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-55 11-55 11-55 11-55 11-55 11-56 11-57 11-57 11-57 11-57 11-58 11-58 11-58 11-59 11-59 11-59 11-59 11-59 11-59 11-59 11-60 11-60 11-61 11-62 11-63 11-63 11-63

THERMAL INSULATION Insulation Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Conductivity (K Factor) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finishes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . System Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cryogenic High Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Low Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Moderate and High Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Economic Thickness of Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Recommended Thickness of Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Installation Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Method of Securing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Double Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tanks, Vessels, and Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Method of Securing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-64 11-64 11-64 11-64 11-65 11-65 11-65 11-65 11-65 11-66 11-68 11-68 11-69 11-69 11-69 11-69 11-69 11-69

AIR CONDITIONING Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comfort Air Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-69 11-69

HEAT-TRANSFER EQUIPMENT Industrial Air Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ventilation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Air Conditioning Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Central Cooling and Heating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unitary Refrigerant-Based Air Conditioning Systems . . . . . . . . . . . . . . . . . . . . . . . . . Load Calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-69 11-69 11-69 11-69 11-70 11-70

REFRIGERATION Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Refrigeration Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanical Refrigeration (Vapor Compression Systems) . . . . . . . . . . . . . . . . . . . . . Vapor Compression Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multistage Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cascade System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Positive-Displacement Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Centrifugal Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Condensers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . System, Equipment, and Refrigerant Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Refrigeration Systems Applied in the Industry . . . . . . . . . . . . . . . . . . . . . . . . . Absorption Refrigeration Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Steam-Jet (Ejector) Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multistage Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Capacity Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Refrigerants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Secondary Refrigerants (Antifreezes or Brines) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Organic Compounds (Inhibited Glycols). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Safety in Refrigeration Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-70 11-70 11-71 11-72 11-72 11-73 11-74 11-74 11-74 11-74 11-76 11-77 11-78 11-79 11-81 11-81 11-81 11-84 11-86 11-86 11-86 11-87 11-87 11-88

EVAPORATORS Primary Design Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heat Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vapor-Liquid Separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selection Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Product Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaporator Types and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Forced-Circulation Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Swirl Flow Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short-Tube Vertical Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Long-Tube Vertical Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Horizontal-Tube Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Miscellaneous Forms of Heating Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaporators without Heating Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Utilization of Temperature Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vapor-Liquid Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaporator Arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single-Effect Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermocompression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiple-Effect Evaporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seawater Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaporator Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single-Effect Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermocompression Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flash Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiple-Effect Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaporator Accessories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Condensers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Salt Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaporator Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-3

11-89 11-89 11-89 11-89 11-89 11-89 11-89 11-89 11-90 11-91 11-92 11-92 11-92 11-92 11-93 11-94 11-94 11-94 11-94 11-95 11-96 11-96 11-96 11-96 11-96 11-97 11-97 11-97 11-97 11-98 11-98

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT INTRODUCTION TO THERMAL DESIGN Designers commonly use computer software to design heat exchangers. The best sources of such software are Heat Transfer Research, Inc. (HTRI), and Heat Transfer and Fluid Flow Services (HTFFS), a division of ASPENTECH. These companies develop proprietary correlations based on their research and provide software that utilizes these correlations. However, it is important that engineers understand the fundamental principles underlying the framework of the software. Therefore, design methods for several important classes of process heat-transfer equipment are presented in later subsections of this section. Mechanical descriptions and specifications of equipment are given in this subsection and should be read in conjunction with the use of this subsequent design material. However, it is impossible to present here a comprehensive treatment of heat exchanger selection, design, and application. The best general references in this field are Hewitt, Shires, and Bott, Process Heat Transfer, CRC Press, Boca Raton, FL, 1994; and Schlünder (ed.), Heat Exchanger Design Handbook, Begell House, New York, 2002. Approach to Heat Exchanger Design The proper use of basic heattransfer knowledge in the design of practical heat-transfer equipment is an art. Designers must be constantly aware of the differences between the idealized conditions for and under which the basic knowledge was obtained and the real conditions of the mechanical expression of their design and its environment. The result must satisfy process and operational requirements (such as availability, flexibility, and maintainability) and do so economically. An important part of any design process is to consider and offset the consequences of error in the basic knowledge, in its subsequent incorporation into a design method, in the translation of design into equipment, or in the operation of the equipment and the process. Heat exchanger design is not a highly accurate art under the best of conditions. The design of a process heat exchanger usually proceeds through the following steps: 1. Process conditions (stream compositions, flow rates, temperatures, pressures) must be specified. 2. Required physical properties over the temperature and pressure ranges of interest must be obtained. 3. The type of heat exchanger to be employed is chosen. 4. A preliminary estimate of the size of the exchanger is made, using a heat-transfer coefficient appropriate to the fluids, process, and equipment. 5. A first design is chosen, complete in all details necessary to carry out the design calculations. 6. The design chosen in step 5 is evaluated, or rated, as to its ability to meet the process specifications with respect to both heat transfer and pressure drop. 7. On the basis of the result of step 6, a new configuration is chosen if necessary and step 6 is repeated. If the first design was inadequate to meet the required heat load, it is usually necessary to increase the size of the exchanger while still remaining within specified or feasible limits of pressure drop, tube length, shell diameter, etc. This will sometimes mean going to multiple-exchanger configurations. If the first design more than meets heat load requirements or does not use all the allowable pressure drop, a less expensive exchanger can usually be designed to fulfill process requirements. 8. The final design should meet process requirements (within reasonable expectations of error) at lowest cost. The lowest cost should include operation and maintenance costs and credit for ability to meet long-term process changes, as well as installed (capital) cost. Exchangers should not be selected entirely on a lowest-first-cost basis, which frequently results in future penalties. Overall Heat-Transfer Coefficient The basic design equation for a heat exchanger is dA = dQ/U ∆T

the two streams is ∆T. The overall heat-transfer coefficient is related to the individual film heat-transfer coefficients and fouling and wall resistances by Eq. (11-2). Basing Uo on the outside surface area Ao results in Uo =

1 1/ho + Rdo + xAo /kw Awm + (1/ht + Rdt ) Ao /At

Equation (11-1) can be formally integrated to give the outside area required to transfer the total heat load QT: Ao = ∫

QT

0

dQ U o ∆T

(11-3)

To integrate Eq. (11-3), Uo and ∆T must be known as functions of Q. For some problems, Uo varies strongly and nonlinearly throughout the exchanger. In these cases, it is necessary to evaluate Uo and ∆T at several intermediate values and numerically or graphically integrate. For many practical cases, it is possible to calculate a constant mean overall coefficient Uom from Eq. (11-2) and define a corresponding mean value of ∆Tm, such that Ao = QT/Uom ∆Tm

(11-4)

Care must be taken that Uo does not vary too strongly, that the proper equations and conditions are chosen for calculating the individual coefficients, and that the mean temperature difference is the correct one for the specified exchanger configuration. Mean Temperature Difference The temperature difference between the two fluids in the heat exchanger will, in general, vary from point to point. The mean temperature difference (∆Tm or MTD) can be calculated from the terminal temperatures of the two streams if the following assumptions are valid: 1. All elements of a given fluid stream have the same thermal history in passing through the exchanger.∗ 2. The exchanger operates at steady state. 3. The specific heat is constant for each stream (or if either stream undergoes an isothermal phase transition). 4. The overall heat-transfer coefficient is constant. 5. Heat losses are negligible. Countercurrent or Cocurrent Flow If the flow of the streams is either completely countercurrent or completely cocurrent or if one or both streams are isothermal (condensing or vaporizing a pure component with negligible pressure change), then the correct MTD is the logarithmic-mean temperature difference (LMTD), defined as LMTD = ∆Tlm =

(t1′ − t 2′′) − (t 2′ − t1′′)  t ′ − t ′′ ln  1 2   t 2′ − t1′′

(11-5a)

for countercurrent flow (Fig. 11-1a) and LMTD = ∆Tlm =

(t1′ − t1′′) − (t 2′ − t 2′′ )  t ′ − t ′′ ln  1 1   t 2′ − t 2′′

(11-5b)

for cocurrent flow (Fig. 11-1b). If U is not constant but a linear function of ∆T, then the correct value of Uom ∆Tm to use in Eq. (11-4) is [Colburn, Ind. Eng. Chem. 25: 873 (1933)]

(11-1)

where dA is the element of surface area required to transfer an amount of heat dQ at a point in the exchanger where the overall heat-transfer coefficient is U and where the overall bulk temperature difference between

(11-2)

U om ∆Tm =

U o′′(t1′ − t 2′′ ) − U o′ (t 2′ − t1′′)  U ′′(t ′ − t ′′ )  ln  o 1 2   U o′ (t 2′ − t1′′ ) 

(11-6a)

∗This assumption is vital but is usually omitted or less satisfactorily stated as “each stream is well mixed at each point.” In a heat exchanger with substantial bypassing of the heat-transfer surface, e.g., a typical baffled shell-and-tube exchanger, this condition is not satisfied. However, the error is offset to some degree if the same MTD formulation used in reducing experimental heat-transfer data to obtain the basic correlation is used in applying the correlation to design a heat exchanger. The compensation is not in general exact, and insight and judgment are required in the use of the MTD formulations. Particularly, in the design of an exchanger with a very close temperature approach, bypassing may result in an exchanger that is inefficient and even thermodynamically incapable of meeting specified outlet temperatures. 11-4

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT

11-5

(a) FIG. 11-2 Diagram of a 1-2 exchanger (one well-baffled shell pass and two tube passes with an equal number of tubes in each pass).

THERMAL DESIGN FOR SINGLE-PHASE HEAT TRANSFER

(b) FIG. 11-1 Temperature profiles in heat exchangers. (a) Countercurrent. (b) Cocurrent.

for countercurrent flow, where U ″o is the overall coefficient evaluated when the stream temperatures are t1′ and t ″2 and Uo′ is evaluated at t2′ and t ″1. The corresponding equation for cocurrent flow is U om ∆Tm =

U o′′(t1′ − t1′′) − U o′ (t 2′ − t 2′′ )  U ′′(t ′ − t ′′)  ln  o 1 1   U o′ (t 2′ − t 2′′ ) 

(11-6b)

where Uo′ is evaluated at t2′ and t ″2 and U ″o is evaluated at t1′ and t ″1. To use these equations, it is necessary to calculate two values of Uo. The use of Eq. (11-6) will frequently give satisfactory results even if Uo is not strictly linear with temperature difference. Reversed, Mixed, or Cross-Flow If the flow pattern in the exchanger is not completely countercurrent or cocurrent, it is necessary to apply a correction factor FT by which the LMTD is multiplied to obtain the appropriate MTD. These corrections have been mathematically derived for flow patterns of interest, still by making assumptions 1 to 5 [see Bowman, Mueller, and Nagle, Trans. Am. Soc. Mech. Eng. 62: 283 (1940) or Hewitt, Shires, and Bott, Process Heat Transfer, CRC Press, Boca Raton, FL, 1994]. For a common flow pattern, the 1-2 exchanger (Fig. 11-2), the correction factor FT is given in Fig. 11-4a, which is also valid for finding FT for a 1-2 exchanger in which the shell-side flow direction is reversed from that shown in Fig. 11-2. Figure 11-4a is also applicable with negligible error to exchangers with one shell pass and any number of tube passes. Values of FT less than 0.8 (0.75 at the very lowest) are generally unacceptable because the exchanger configuration chosen is inefficient; the chart is difficult to read accurately; and even a small violation of the first assumption underlying the MTD will invalidate the mathematical derivation and lead to a thermodynamically inoperable exchanger. Correction factor charts are also available for exchangers with more than one shell pass provided by a longitudinal shell-side baffle. However, these exchangers are seldom used in practice because of mechanical complications in their construction. Also thermal and physical leakages across the longitudinal baffle further reduce the mean temperature difference and are not properly incorporated into the correction factor charts. Such charts are useful, however, when it is necessary to construct a multiple-shell exchanger train such as that shown in Fig. 11-3 and are included here for two, three, four, and six separate, identical shells and two or more tube passes per shell in Fig. 11-4b, c, d, and e. If only one tube pass per shell is required, the piping can and should be arranged to provide pure countercurrent flow, in which case the LMTD is used with no correction. Cross-flow exchangers of various kinds are also important and require correction to be applied to the LMTD calculated by assuming countercurrent flow. Several cases are given in Fig. 11-4f, g, h, i, and j. Many other MTD correction factor charts have been prepared for various configurations. The FT charts are often employed to make approximate corrections for configurations even in cases for which they are not completely valid.

Double-Pipe Heat Exchangers The design of double-pipe heat exchangers is straightforward. It is generally conservative to neglect natural convection and entrance effects in turbulent flow. In laminar flow, natural convection effects can increase the theoretical Graetz prediction by a factor of 3 or 4 for fully developed flows. Pressure drop is calculated by using the correlations given in Sec. 6. If the inner tube is longitudinally finned on the outside surface, the equivalent diameter is used as the characteristic length in both the Reynolds number and the heat-transfer correlations. The fin efficiency must also be known to calculate an effective outside area to use in Eq. (11-2). Fittings contribute strongly to the pressure drop on the annulus side. General methods for predicting this are not reliable, and manufacturer’s data should be used when available. Double-pipe exchangers are often piped in complex series-parallel arrangements on both sides. The MTD to be used has been derived for some of these arrangements and is reported in Kern (Process Heat Transfer, McGraw-Hill, New York, 1950). More complex cases may require trial-anderror balancing of the heat loads and rate equations for subsections or even for individual exchangers in the bank. Baffled Shell-and-Tube Exchangers The method given here is based on the research summarized in Final Report, Cooperative Research Program on Shell and Tube Heat Exchangers, Univ. Del. Eng. Exp. Sta. Bull. 5 (June 1963). The method assumes that the shell-side heat-transfer and pressure-drop characteristics are equal to those of the ideal tube bank corresponding to the cross-flow sections of the exchanger, modified for the distortion of flow pattern introduced by the baffles and the presence of leakage and bypass flow through the various clearances required by mechanical construction. It is assumed that process conditions and physical properties are known and the following are known or specified: tube outside diameter Do , tube geometric arrangement (unit cell), shell inside diameter Ds, shell outer tube limit Dotl, baffle cut lc , baffle spacing ls , and number of sealing strips Nss. The effective tube length between tube sheets L may be either specified or calculated after the heat-transfer coefficient has been determined. If additional specific information (e.g., tube-baffle clearance) is available, the exact values (instead of estimates) of certain parameters may be used in the calculation with some improvement in accuracy. To complete the rating, it is necessary to know also the tube material and wall thickness or inside diameter.

FIG. 11-3 Diagram of a 2-4 exchanger (two separate identical well-baffled shells and

four or more tube passes).

11-6

HEAT-TRANSFER EQUIPMENT

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

LMTD correction factors for heat exchangers. In all charts, R = (T1 − T2)/(t2 − t1) and S = (t2 − t1)/(T1 − t1). (a) One shell pass, two or more tube passes. (b) Two shell passes, four or more tube passes. (c) Three shell passes, six or more tube passes. (d) Four shell passes, eight or more tube passes. (e) Six shell passes, twelve or more tube passes. ( f ) Cross-flow, one shell pass, one or more parallel rows of tubes. (g) Cross-flow, two passes, two rows of tubes; for more than two passes, use FT = 1.0. (h) Cross-flow, one shell pass, one tube pass, both fluids unmixed. (i) Cross-flow (drip type), two horizontal passes with U-bend connections (trombone type). (j) Cross-flow (drip type), helical coils with two turns. FIG. 11-4

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT

(i) FIG. 11-4

11-7

(j)

(Continued)

This rating method, though apparently generally the best in the open literature, is not extremely accurate. An exhaustive study by Palen and Taborek [Chem. Eng. Prog. Symp. Ser. 92, 65: 53 (1969)] showed that this method predicted shell-side coefficients from about 50 percent low to 100 percent high, while the pressure drop range was from about 50 percent low to 200 percent high. The mean error for heat transfer was about 15 percent low (safe) for all Reynolds numbers, while the mean error for pressure drop was from about 5 percent low (unsafe) at Reynolds numbers above 1000 to about 100 percent high at Reynolds numbers below 10. Calculation of Shell-Side Geometric Parameters 1. Total number of tubes in exchanger Nt. If this is not known by direct count, estimate by using Eq. (11-74) or (11-75). 2. Tube pitch parallel to flow pp and normal to flow pn. These quantities are needed only for estimating other parameters. If a detailed drawing of the exchanger is available, it is better to obtain these other parameters by direct count or calculation. The pitches are described by Fig. 11-5 and read therefrom for common tube layouts.

3. Number of tube rows crossed in one cross-flow section Nc. Count from the exchanger drawing or estimate from Nc =

Ds [1 − 2(l c /Ds )] pp

4. Fraction of total tubes in cross-flow Fc   D − 2lc D − 2lc  1 − 1 Ds − 2 l c  Fc =  π + 2 s sin  cos − 1 s  − 2cos Dotl  π Dotl Dotl    

(11-8)

where Fc is plotted in Fig. 11-6. This figure is strictly applicable only to splitring, floating-head construction but may be used for other situations with minor error. 5. Number of effective cross-flow rows in each window Ncw N cw =

FIG. 11-5 Values of tube pitch for common tube layouts. To convert inches to meters, multiply by 0.0254. Note that Do, p′, pp, and pn have units of inches.

(11-7)

0.8 l c pp

(11-9)

FIG. 11-6 Estimation of fraction of tubes in cross-flow Fc [Eq. (11-8)]. To convert

inches to meters, multiply by 0.0254. Note that lc and Ds have units of inches.

11-8

HEAT-TRANSFER EQUIPMENT

6. Cross-flow area at or near centerline for one cross-flow section Sm a. For rotated and in-line square layouts:   D − Do S m = l s  Ds − Dotl + otl ( p ′ − Do )  p n  

m2 (ft 2 )

10 . Area for flow through window Sw . This area is obtained as the difference between the gross window area Swg and the window area occupied by tubes Swt: = Swg − Swt

(11-10a) Swg =

b. For triangular layouts: D − Do   S m = l s  Ds − Dotl + otl ( p ′ − Do )  p ′  

m2 (ft 2 )

(11-10b)

( Ds − Dotl )l s Sm

(11-11)

m2 ( ft2)

(11-12)

where b = (6.223)(10−4) (SI) or (1.701)(10−4) (USCS). These values are based on the Tubular Exchanger Manufacturers Association (TEMA) Class R construction which specifies ⅓2-in diametral clearance between tube and baffle . Values should be modified if extra tight or loose construction is specified or if clogging by dirt is anticipated . 9 . Shell-to-baffle leakage area for one baffle Ssb. If diametral shell-baffle clearance δsb is known, then Ssb can be calculated from  D δ  2l   S sb = s sb  π − cos − 1  1 − c   2  Ds   

m 2 (ft 2 )

(11-13)

where the value of the term cos−1 (1 − 2lc/Ds) is in radians and is between 0 and π/2 . Shell-to-baffle leakage area Ssb is plotted in Fig . 11-7, based on TEMA Class R standards . Since pipe shells are generally limited to diameters below 24 in, the larger sizes are shown by using the rolled-shell specification . Allowance should be made for especially tight or loose construction .

FIG. 11-7 Estimation of shell-to-baffle leakage area [Eq . (11-13)] . To convert inches to meters, multiply by 0 .0254; to convert square inches to square meters, multiply by (6 .45)(10−4) . Note that lc and Ds have units of inches .

m 2 (ft 2 ) (11-15)

Swg is plotted in Fig . 11-8; Swt can be calculated from m2 ( ft2)

(11-16)

11 . Equivalent diameter of window Dw [required only if laminar flow, defined as (NRe)s ≤ 100, exists] Dw =

8. Tube-to-baffle leakage area for one baffle Stb. Estimate from Stb = bDoNT (1 + Fc)

2  l   1 − 1 − 2 c   Ds    

Swt = (NT/8)(1 − Fc)πDo2

7. Fraction of cross-flow area available for bypass flow Fbp Fbp =

Ds2  − 1  l   l  cos  1 − 2 c  −  1 − 2 c  4  Ds   Ds   

(11-14)

4 Sw ( π/2) N T (1 − Fc ) Do + Ds θb

m (ft)

(11-17)

where θb is the baffle-cut angle given by  2l  θb = 2cos − 1  1 − c  Ds  

rad

(11-18)

12 . Number of baffles Nb Nb =

L − 2 le +1 ls

(11-19)

where le is the entrance/exit baffle spacing, often different from the central baffle spacing . The effective tube length L must be known to calculate Nb, which is needed to calculate the shell-side pressure drop . In designing an exchanger, the shell-side coefficient may be calculated and the required exchanger length for heat transfer obtained before Nb is calculated .

FIG. 11-8 Estimation of window cross-flow area [Eq . (11-15)] . To convert inches to meters, multiply by 0 .0254 . Note that lc and Ds have units of inches .

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT

11-9

FIG. 11-9 Correlation of j factor for ideal tube bank . To convert inches to meters, multiply by 0 .0254 . Note that p′ and Do have units of inches .

Shell-Side Heat-Transfer Coefficient Calculation 1 . Calculate the shell-side Reynolds number (NRe)s (NRe)s = DoW/µbSm

(11-20)

where W = mass flow rate and µb = viscosity at bulk temperature . The arithmetic mean bulk shell-side fluid temperature is usually adequate to evaluate all bulk properties of the shell-side fluid . For large temperature ranges or for viscosity that is very sensitive to temperature change, special care must be taken, such as using Eq . (11-6) . 2 . Find jk from the ideal-tube bank curve for a given tube layout at the calculated value of (NRe)s, using Fig . 11-9, which is adapted from ideal-tube bank data obtained at Delaware by Bergelin et al . [Trans. Am. Soc. Mech. Eng. 74: 953 (1952)] and the Grimison correlation [Trans. Am. Soc. Mech. Eng. 59: 583 (1937)] . 3 . Calculate the shell-side heat-transfer coefficient for an ideal tube bank hk. hk = jk c

W k S m  cµ 

2/3

 µb   µ 

FIG. 11-11

Correction factor for baffle leakage effects .

0 .14

(11-21)

w

where c is the specific heat, k is the thermal conductivity, and µw is the viscosity evaluated at the mean surface temperature . 4 . Find the correction factor for baffle configuration effects Jc from Fig . 11-10 . 5 . Find the correction factor for baffle leakage effects Jl from Fig . 11-11 . 6 . Find the correction factor for bundle-bypassing effects Jb from Fig . 11-12 . 7 . Find the correction factor for adverse temperature-gradient buildup at low Reynolds number Jr: a. If (NRe)s < 100, find J ∗r from Fig . 11-13, given Nb and Nc + Ncw . b. If (NRe)s ≤ 20, Jr = J ∗r . c. If 20 < (NRe)s < 100, find Jr from Fig . 11-14, given J ∗r and (NRe)s. 8 . Calculate the shell-side heat-transfer coefficient for the exchanger hs from hs = hk Jc Jl Jb Jr

FIG. 11-12

Correction factor for bypass flow .

(11-22)

Shell-Side Pressure Drop Calculation 1 . Find f k from the ideal-tube bank friction factor curve for the given tube layout at the calculated value of (NRe)s, using Fig . 11-15a for triangular and rotated square arrays and Fig . 11-15b for in-line square arrays . These curves are adapted from Bergelin et al . and Grimison .

FIG. 11-13 FIG. 11-10 Correction factor for baffle configuration effects .

numbers .

Basic correction factor for adverse temperature gradient at low Reynolds

11-10

HEAT-TRANSFER EQUIPMENT

FIG. 11-14 Correction factor for adverse temperature gradient at intermediate Reynolds numbers .

2 . Calculate the pressure drop for an ideal cross-flow section. ∆Pbk = b

f kW 2 N c  µ w  ρS m2  µ b 

0 .14

(11-23)

where b = (2 .0)(10−3) (SI) or (9 .9) (10−5) (USCS) . 3 . Calculate the pressure drop for an ideal window section. If (NRe)s ≥ 100, ∆Pwk = b

W 2 (2 + 0 .6 N w ) S m Sw ρ

(11-24a)

where b = (5)(10−4) (SI) or (2 .49)(10−5) (USCS) .

FIG. 11-16

Correction factor for baffle leakage effect on pressure drop .

If (NRe)s < 100, ∆Pwk = b1

W2 l  µ bW  N cw + s2  + b2  S m Sw ρ S m Sw ρ  p ′ − Do Dw 

(11-24b)

where b1 = (1 .681)(10−5) (SI) or (1 .08)(10−4) (USCS), and b2 = (9 .99)(10−4) (SI) or (4 .97)(10−5) (USCS) . 4 . Find the correction factor for the effect of baffle leakage on pressure drop Rl from Fig . 11-16 . Curves shown are not to be extrapolated beyond the points shown . 5 . Find the correction factor for bundle bypass Rb from Fig . 11-17 . 6 . Calculate the pressure drop across the shell side (excluding nozzles) . Units for pressure drop are lbf/ft2 .  N  ∆Ps = [( N b − 1)( ∆Pbk ) Rb + N b ∆Pwk ] Rl + 2 ∆Pbk Rb  1 + cw  Nc  

(a)

(11-25)

The values of hs and ∆Ps calculated by this procedure are for clean exchangers and are intended to be as accurate as possible, not conservative . A fouled exchanger will generally give lower heat-transfer rates, as reflected by the dirt resistances incorporated into Eq . (11-2), and higher pressure drops . Some estimate of fouling effects on pressure drop may be made by using the methods just given and assuming that the fouling deposit blocks the leakage and possibly the bypass areas . The fouling may also decrease the clearance between tubes and significantly increase the pressure drop in cross-flow . THERMAL DESIGN OF CONDENSERS

(b) FIG. 11-15

Correction of friction factors for ideal tube banks . (a) Triangular and rotated square arrays . (b) In-line square arrays .

Single-Component Condensers Mean Temperature Difference In condensing a single component at its saturation temperature, the entire resistance to heat transfer on the condensing side is generally assumed to be in the layer of condensate . A mean condensing coefficient is calculated from the appropriate correlation and combined with the other resistances in Eq . (11-2) . The overall coefficient is then used with the LMTD (no FT correction is necessary for isothermal condensation) to give the required area, even though the condensing coefficient and hence U are not constant throughout the condenser . If the vapor is superheated at the inlet, the vapor may first be desuperheated by sensible heat transfer from the vapor . This occurs if the surface temperature is above the saturation temperature, and a single-phase heat-transfer correlation is used . If the surface is below the saturation temperature, condensation will occur directly from the superheated vapor,

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT

FIG. 11-17 Correction factor on pressure drop for bypass flow .

and the effective coefficient is determined from the appropriate condensation correlation, using the saturation temperature in the LMTD . To determine whether condensation will occur directly from the superheated vapor, calculate the surface temperature by assuming single-phase heat transfer . Tsurface = Tvapor −

U (Tvapor − Tcoolant ) h

(11-26)

where h is the sensible heat-transfer coefficient for the vapor, U is calculated by using h, and both are on the same area basis . If Tsurface > Tsaturation, no condensation occurs at that point and the heat flux is actually higher than if Tsurface ≤ Tsaturation and condensation did occur . It is generally conservative to design a pure-component desuperheater-condenser as if the entire heat load were transferred by condensation, using the saturation temperature in the LMTD . The design of an integral condensate subcooling section is more difficult, especially if close temperature approach is required . The condensate layer on the surface is subcooled on average by one-third to one-half of the temperature drop across the film, and this is often sufficient if the condensate is not reheated by raining through the vapor . If the condensing-subcooling process is carried out inside tubes or in the shell of a vertical condenser, the single-phase subcooling section can be treated separately, giving an area that is added onto that needed for condensation . If the subcooling is achieved on the shell side of a horizontal condenser by flooding some of the bottom tubes with a weir or level controller, then the rate and heat-balance equations must be solved for each section to obtain the area required . Pressure drop on the condensing side reduces the final condensing temperature and the MTD and should always be checked . In designs requiring close approach between inlet coolant and exit condensate (subcooled or not), underestimation of pressure drop on the condensing side can lead to an exchanger that cannot meet specified terminal temperatures . Since pressure drop calculations in two-phase flows such as condensation are relatively inaccurate, designers must consider carefully the consequences of a larger than calculated pressure drop . Horizontal In-Shell Condensers The mean condensing coefficient for the outside of a bank of horizontal tubes is calculated from Eq . (5-87) for a single tube, corrected for the number of tubes in a vertical row . For undisturbed laminar flow over all the tubes, Eq . (5-88) is, for realistic condenser sizes, overly conservative because of rippling, splashing, and turbulent flow

11-11

(Process Heat Transfer, McGraw-Hill, New York, 1950) . Kern proposed an exponent of −1/6 on the basis of experience, while Freon-11 data of Short and Brown (General Discussion on Heat Transfer, Institute of Mechanical Engineers, London, 1951) indicate independence of the number of tube rows . It seems reasonable to use no correction for inviscid liquids and Kern’s correction for viscous condensates . For a cylindrical tube bundle, where N varies, it is customary to take N equal to two-thirds of the maximum or centerline value . Baffles in a horizontal in-shell condenser are oriented with the cuts vertical to facilitate drainage and eliminate the possibility of flooding in the upward cross-flow sections . Pressure drop on the vapor side can be estimated by the data and method of Diehl and Unruh [Pet. Refiner 36(10): 147 (1957); 37(10): 124 (1958)] . High vapor velocities across the tubes enhance the condensing coefficient . There is no correlation in the open literature to permit designers to take advantage of this . Since the vapor flow rate varies along the length, an incremental calculation procedure would be required in any case . In general, the pressure drops required to gain significant benefit are above those allowed in most process applications . Vertical In-Shell Condensers Condensers are often designed so that condensation occurs on the outside of vertical tubes . Equation (5-79) is valid as long as the condensate film is laminar . When it becomes turbulent, Eq . (5-86) or Colburn’s equation [Trans. Am. Inst. Chem. Eng. 30: 187 (1933–1934)] may be used . Some judgment is required in the use of these correlations because of the construction features of the condenser . The tubes must be supported by baffles, usually with maximum cut (45 percent of the shell diameter) and maximum spacing to minimize pressure drop . The flow of the condensate is interrupted by the baffles, which may draw off or redistribute the liquid and which will also cause some splashing of free-falling drops onto the tubes . For subcooling, a liquid inventory may be maintained in the bottom end of the shell by means of a weir or a liquid-level-controller . The subcooling heat-transfer coefficient is given by the correlations for natural convection on a vertical surface [Eq . (5-42)], with the pool assumed to be well mixed (isothermal) at the subcooled condensate exit temperature . Pressure drop may be estimated by the shell-side procedure . Horizontal In-Tube Condensers Condensation of a vapor inside horizontal tubes occurs in kettle and horizontal thermosiphon reboilers and in air-cooled condensers . In-tube condensation also offers certain advantages for condensation of multicomponent mixtures, discussed in the subsection Multicomponent Condensers . The various in-tube correlations are closely connected to the two-phase flow pattern in the tube [Chem. Eng. Prog. Symp. Ser. 66(102): 150 (1970)] . At low flow rates, when gravity dominates the flow pattern, Eq . (5-87) may be used . At high flow rates, the flow and heat transfer are governed by vapor shear on the condensate film, and Eq . (5-86) is valid . A simple and generally conservative procedure is to calculate the coefficient for a given case by both correlations and use the larger one . Pressure drop during condensation inside horizontal tubes can be computed by using the correlations for two-phase flow given in Sec . 6 and neglecting the pressure recovery due to deceleration of the flow . Vertical In-Tube Condensation Vertical tube condensers are generally designed so that vapor and liquid flow cocurrently downward; if pressure drop is not a limiting consideration, this configuration can result in higher heat-transfer coefficients than for shell-side condensation and has particular advantages for multicomponent condensation . If gravity controls, the mean heat-transfer coefficient for condensation is given by Eq . (5-79) . If vapor shear controls, Eq . (5-86) is applicable . It is generally conservative to calculate the coefficients by both methods and choose the higher value . The pressure drop can be calculated by using the LockhartMartinelli method [Chem. Eng. Prog. 45: 39 (1945)] for friction loss, neglecting momentum and hydrostatic effects . Vertical in-tube condensers are often designed for reflux or knock-back application in reactors or distillation columns . In this case, vapor flow is upward, countercurrent to the liquid flow on the tube wall; the vapor shear acts to thicken and retard the drainage of the condensate film, reducing the coefficient . Neither the fluid dynamics nor the heat transfer is well understood in this case, but Soliman, Schuster, and Berenson [ J. Heat Transfer 90: 267–276 (1968)] discuss the problem and suggest a computational method . The Diehl-Koppany correlation [Chem. Eng. Prog. Symp. Ser. 92, 65 (1969)] may be used to estimate the maximum allowable vapor velocity at the tube inlet . If the vapor velocity is great enough, the liquid film will be carried upward; this design has been employed in a few cases in which only part of the stream is to be condensed . This velocity cannot be accurately computed, and a very conservative (high) outlet velocity must be used if unstable flow and flooding are to be avoided; 3 times the vapor velocity given by the DiehlKoppany correlation for incipient flooding has been suggested as the design value for completely stable operation .

11-12

HEAT-TRANSFER EQUIPMENT

Multicomponent Condensers Thermodynamic and Mass-Transfer Considerations Multicomponent vapor mixture includes several different cases: all the components may be liquids at the lowest temperature reached in the condensing side, or there may be components that dissolve substantially in the condensate even though their boiling points are below the exit temperature, or one or more components may be both noncondensible and nearly insoluble . Multicomponent condensation always involves sensible-heat changes in the vapor and liquid along with the latent-heat load . Compositions of both phases in general change through the condenser, and concentration gradients exist in both phases . Temperature and concentration profiles and transport rates at a point in the condenser usually cannot be calculated, but the binary cases have been treated: condensation of one component in the presence of a completely insoluble gas [Colburn and Hougen, Ind. Eng. Chem. 26: 1178–1182 (1934); and Colburn and Edison, Ind. Eng. Chem. 33: 457–458 (1941)] and condensation of a binary vapor [Colburn and Drew, Trans. Am. Inst. Chem. Eng. 33: 196–215 (1937)] . It is necessary to know or calculate diffusion coefficients for the system, and a reasonable approximate method to avoid this difficulty and the reiterative calculations is desirable . To integrate the point conditions over the total condensation requires the temperature, composition enthalpy, and flow-rate profiles as functions of the heat removed . These are calculated from component thermodynamic data if the vapor and liquid are assumed to be in equilibrium at the local vapor temperature . This assumption is not exactly true, since the condensate and the liquid-vapor interface (where equilibrium does exist) are intermediate in temperature between the coolant and the vapor . In calculating the condensing curve, it is generally assumed that the vapor and liquid flow collinearly and in intimate contact so that composition equilibrium is maintained between the total streams at all points . If, however, the condensate drops out of the vapor (as can happen in horizontal shellside condensation) and flows to the exit without further interaction, the remaining vapor becomes excessively enriched in light components with a decrease in condensing temperature and in the temperature difference between vapor and coolant . The result may be not only a small reduction in the amount of heat transferred in the condenser but also an inability to condense totally the light ends even at reduced throughput or with the addition of more surface . To prevent the liquid from segregating, in-tube condensation is preferred in critical cases . Thermal Design If the controlling resistance for heat and mass transfer in the vapor is sensible-heat removal from the cooling vapor, the following design equation is obtained: A=∫

QT

o

1 + U ′Z H /hsυ dQ U ′(Tυ − Tc )

(11-27)

U ′ is the overall heat-transfer coefficient between the vapor-liquid interface and the coolant, including condensate film, dirt and wall resistances, and coolant . The condensate film coefficient is calculated from the appropriate equation or correlation for pure vapor condensation for the geometry and flow regime involved, using mean liquid properties . The ratio of the sensible heat removed from the vapor-gas stream to the total heat transferred is ZH; this quantity is obtained from thermodynamic calculations and may vary substantially from one end of the condenser to the other, especially when removing vapor from a noncondensible gas . The sensible-heat-transfer coefficient for the vapor-gas stream hsu is calculated by using the appropriate correlation or design method for the geometry involved, neglecting the presence of the liquid . As the vapor condenses, this coefficient decreases and must be calculated at several points in the process . And Tυ and Tc are temperatures of the vapor and the coolant, respectively . This procedure is similar in principle to that of Ward [Petro/Chem. Eng. 32(11): 42–48 (1960)] . It may be nonconservative for condensing steam and other high-latent-heat substances, in which case it may be necessary to increase the calculated area by 25 to 50 percent . Pressure drop on the condensing side may be estimated by judicious application of the methods suggested for pure-component condensation, taking into account the generally nonlinear decrease of vapor-gas flow rate with heat removal . THERMAL DESIGN OF REBOILERS For a single-component reboiler design, attention is focused upon the mechanism of heat and momentum transfer at the hot surface . In multicomponent systems, the light components are preferentially vaporized at the surface, and the process becomes limited by their rate of diffusion . The net effect is to decrease the effective temperature difference between the hot surface and the bulk of the boiling liquid . If one attempts to vaporize too high a fraction of the feed liquid to the reboiler, then the temperature difference between surface and liquid is reduced to the point that nucleation and

vapor generation on the surface are suppressed and heat transfer to the liquid proceeds at the lower rate associated with single-phase natural convection . The only safe procedure in design for wide boiling-range mixtures is to vaporize such a limited fraction of the feed that the boiling point of the remaining liquid mixture is still at least 5 .5°C (10°F) below the surface temperature . Positive flow of the unvaporized liquid through and out of the reboiler should be provided . Kettle Reboilers It has been generally assumed that kettle reboilers operate in the pool boiling mode, but with a lower peak heat flux because of vapor binding and blanketing of the upper tubes in the bundle . There is some evidence that vapor generation in the bundle causes a high circulation rate through the bundle . The result is that, at the lower heat fluxes, the kettle reboiler actually gives higher heat-transfer coefficients than a single tube . Present understanding of the recirculation phenomenon is insufficient to take advantage of this in design . Available nucleate pool boiling correlations are only very approximate, failing to account for differences in the nucleation characteristics of different surfaces . Equation (5-97b) may be used for single components or narrow boiling-range mixtures at low fluxes . For hydrocarbons not listed, approximation may be made assuming n-Pentane . Experimental heat-transfer coefficients for pool boiling of a given liquid on a given surface should be used if available . The bundle peak heat flux is a function of tube bundle geometry, especially of tube-packing density . But in the absence of better information, Eq . (5-99) may be used for this purpose . A general method for analyzing kettle reboiler performance is given by Fair and Klip, Chem. Eng. Prog. 79(3): 86 (1983) . It is effectively limited to computer application . Kettle reboilers are generally assumed to require negligible pressure drop . It is important to provide good longitudinal liquid flow paths within the shell so that the liquid is uniformly distributed along the entire length of the tubes and excessive local vaporization and vapor binding are avoided . This method may also be used for the thermal design of horizontal thermosiphon reboilers. The recirculation rate and pressure profile of the thermosiphon loop can be calculated by the methods of Fair [Pet. Refiner 39(2): 105–123 (1960)] . Vertical Thermosiphon Reboilers Vertical thermosiphon reboilers operate by natural circulation of the liquid from the still through the downcomer to the reboiler and of the two-phase mixture from the reboiler through the return piping . The flow is induced by the hydrostatic pressure imbalance between the liquid in the downcomer and the two-phase mixture in the reboiler tubes . Thermosiphons do not require any pump for recirculation and are generally regarded as less likely to foul in service because of the relatively high two-phase velocities obtained in the tubes . Heavy components are not likely to accumulate in the thermosiphon, but they are more difficult to design satisfactorily than kettle reboilers, especially in vacuum operation . Several shortcut methods have been suggested for thermosiphon design, but they must generally be used with caution . The method due to Fair (1960), based upon two-phase flow correlations, is the most complete in the open literature but requires a computer for practical use . Fair also suggests a shortcut method that is satisfactory for preliminary design and can be reasonably done by hand . Forced-Recirculation Reboilers In forced-recirculation reboilers, a pump is used to ensure circulation of the liquid past the heat-transfer surface . Forced-recirculation reboilers may be designed so that boiling occurs inside vertical tubes, inside horizontal tubes, or on the shell side . For forced boiling inside vertical tubes, Fair’s method may be employed, by making only the minor modification that the recirculation rate is fixed and does not need to be balanced against the pressure available in the downcomer . Excess pressure required to circulate the two-phase fluid through the tubes and back into the column is supplied by the pump, which must develop a positive pressure increase in the liquid . Fair’s method may also be modified to design forced-recirculation reboilers with horizontal tubes . In this case the hydrostatic head pressure effect through the tubes is zero but must be considered in the two-phase return lines to the column . The same procedure may be applied in principle to design of forcedrecirculation reboilers with shell-side vapor generation . Little is known about two-phase flow on the shell side, but a reasonable estimate of the friction pressure drop can be made from the data of Diehl and Unruh [Pet. Refiner 36(10): 147 (1957); 37(10): 124 (1958)] . No void-fraction data are available to permit accurate estimation of the hydrostatic or acceleration terms . These may be roughly estimated by assuming homogeneous flow . THERMAL DESIGN OF EVAPORATORS Heat duties of evaporator heating surfaces are usually determined by conventional heat and material balance calculations . Heating surface areas are normally, but not always, taken as those in contact with the material being

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT evaporated . It is the heat transfer DT that presents the greatest difficulty in deriving or applying heat-transfer coefficients . The total DT between heat source and heat sink is never all available for heat transfer . Since energy usually is carried to and from an evaporator body or effect by condensible vapors, loss in pressure represents a loss in DT. Such losses include pressure drop through entrainment separators, friction in vapor piping, and acceleration losses into and out of the piping . The latter loss has often been overlooked, even though it can be many times greater than the friction loss . Similarly, friction and acceleration losses past the heating surface, such as in a falling film evaporator, cause a loss of DT that may or may not have been included in the heat transfer DT when reporting experimental results . Boilingpoint rise, the difference between the boiling point of the solution and the condensing point of the solvent at the same pressure, is another loss . Experimental data are almost always corrected for boiling-point rise, but plant data are suspect when based on temperature measurements because vapor at the point of measurement may still contain some superheat, which represents but a very small fraction of the heat given up when the vapor condenses but may represent a substantial fraction of the actual net DT available for heat transfer . A loss of DT that must be considered in forcedcirculation evaporators is that due to temperature rise through the heater, a consequence of the heat being absorbed there as sensible heat . A further loss may occur when the heater effluent flashes as it enters the vapor-liquid separator . Some of the liquid may not reach the surface and flash to equilibrium with the vapor pressure in the separator, instead of recirculating to the heater, raising the average temperature at which heat is absorbed and further reducing the net DT. Whether these DT losses are allowed for in the heat-transfer coefficients reported depends on the method of measurement . Simply basing the liquid temperature on the measured vapor head pressure may ignore both—or only the latter if temperature rise through the heater is estimated separately from known heat input and circulation rate . In general, when one is calculating the overall heat-transfer coefficients from individual-film coefficients, all these losses must be allowed for, while when using reported overall coefficients, care must be exercised to determine which losses may already have been included in the heat transfer DT. Forced-Circulation Evaporators In evaporators of this type in which hydrostatic head prevents boiling at the heating surface, heat-transfer coefficients can be predicted for forced-convection sensible heating using Eqs . (5-54) and (5-57) . The liquid film coefficient is improved if boiling is not completely suppressed . When only the film next to the wall is above the boiling point, Boarts, Badger, and Meisenberg [Ind. Eng. Chem. 29: 912 (1937)] found that results could be correlated by Eq . (5-50) by using a constant of 0 .0278 instead of 0 .023 . In such cases, the course of the liquid temperature can still be calculated from known circulation rate and heat input . When the bulk of the liquid is boiling in part of the tube length, the film coefficient is even higher . However, the liquid temperature starts dropping as soon as full boiling develops, and it is difficult to estimate the course of the temperature curve . It is certainly safe to estimate heat transfer on the basis that no bulk boiling occurs . Fragen and Badger [Ind. Eng. Chem. 28: 534 (1936)] obtained an empirical correlation of overall heat-transfer coefficients in this type of evaporator, based on the DT at the heater inlet: In USCS units U = 2020D0 .57(Vs)3 .6/L/µ0 .25 DT 0 .1

11-13

FIG. 11-18 Acceleration losses in boiling flow . °C = (°F − 32)/1 .8 .

where b = (2 .6)(107) (SI) and b = 1 .0 (USCS) and using r2 from Fig . 11-18 . The frictional pressure drop is derived from Fig . 11-19, which shows the ratio of two-phase pressure drop to the entering liquid flowing alone . Pressure drop due to hydrostatic head can be calculated from liquid holdup R1 . For nonfoaming dilute aqueous solutions, R1 can be estimated from R1 = 1/[1 + 2 .5(V/L)(r1/rυ)1/2] . Liquid holdup, which represents the ratio of liquid-only velocity to actual liquid velocity, also appears to be the principal determinant of the convective coefficient in the boiling zone (Dengler, Sc .D . thesis, MIT, 1952) . In other words, the convective coefficient is that calculated from Eq . (5-57) by using the liquid-only velocity divided by R1 in the Reynolds number . Nucleate boiling augments convective heat transfer, primarily when DT values are high and the convective coefficient is low [Chen, Ind. Eng. Chem. Process Des. Dev. 5: 322 (1966)] . Film coefficients for the boiling of liquids other than water have been investigated . Coulson and McNelly [Trans. Inst. Chem. Eng. 34: 247 (1956)] derived the following relation, which also correlated the data of Badger and coworkers [Chem. Metall. Eng. 46: 640 (1939); Chem. Eng. 61(2): 183 (1954); and Trans. Am. Inst. Chem. Eng. 33: 392 (1937); 35: 17 (1939); 36: 759 (1940)] on water: ρ  N Nu = (1 .3 + bD )( N Pr )0 .l 9 ( N Re )0 .l 23 ( N Re )0 .g 34  l   ρg 

0 .25

 µg   µ  l

(11-28)

where D = mean tube diameter, Vs = inlet velocity, L = tube length, and µ = liquid viscosity . This equation is based primarily on experiments with copper tubes of 0 .022 m (0 .866 in) outside diameter, 0 .00165 m (0 .065 in or 16 gauge) wall thickness, and 2 .44 m (8 ft) long, but it includes some work with 0 .0127 m (½ in) tubes 2 .44 m (8 ft) long and 0 .0254 m (1 in) tubes 3 .66 m (12 ft) long . Long-Tube Vertical Evaporators In the rising-film version of this type of evaporator, there is usually a nonboiling zone in the bottom section and a boiling zone in the top section . The length of the nonboiling zone depends on heat-transfer characteristics in the two zones and on pressure drop during twophase flow in the boiling zone . The work of Martinelli and coworkers [Lockhart and Martinelli, Chem. Eng. Prog. 45: 39–48 (January 1949); and Martinelli and Nelson, Trans. Am. Soc. Mech. Eng. 70: 695–702 (August 1948)] permits a prediction of pressure drop, and a number of correlations are available for estimating film coefficients of heat transfer in the two zones . In estimating pressure drop, integrated curves similar to those presented by Martinelli and Nelson are the easiest to use . The curves for pure water are shown in Figs . 11-18 and 11-19, based on the assumption that the flow of both vapor and liquid would be turbulent if each were flowing alone in the tube . Similar curves can be prepared if one or both flows are laminar or if the properties of the liquid differ appreciably from the properties of pure water . The acceleration pressure drop DPa is calculated from the equation DPa = br2G2/32 .2

(11-29)

FIG. 11-19

Friction pressure drop in boiling flow . °C = (°F − 32)/1 .8 .

(11-30)

11-14

HEAT-TRANSFER EQUIPMENT

where b = 128 (SI) or 39 (USCS), NNu = Nusselt number based on liquid thermal conductivity, D = tube diameter, and the remaining terms are dimensionless groupings of the liquid Prandtl number, liquid Reynolds number, vapor Reynolds number, and ratios of densities and viscosities . The Reynolds numbers are calculated on the basis of each fluid flowing by itself in the tube . Additional corrections must be applied when the fraction of vapor is so high that the remaining liquid does not wet the tube wall or when the velocity of the mixture at the tube exits approaches sonic velocity . McAdams, Woods, and Bryan (Trans. Am. Soc. Mech. Eng., 1940), Dengler and Addoms (Dengler, Sc .D . thesis, MIT, 1952), and Stroebe, Baker, and Badger [Ind. Eng. Chem. 31: 200 (1939)] encountered dry-wall conditions and reduced coefficients when the weight fraction of vapor exceeded about 80 percent . Schweppe and Foust [Chem. Eng. Prog. 49: Symp . Ser . 5, 77 (1953)] and Harvey and Foust [Chem. Eng. Prog. 49: Symp . Ser . 5, 91 (1953)] found that “sonic choking” occurred at surprisingly low flow rates . The simplified method of calculation outlined includes no allowance for the effect of surface tension. Stroebe, Baker, and Badger found that by adding a small amount of surface-active agent the boiling-film coefficient varied inversely as the square of the surface tension . Coulson and Mehta [Trans. Inst. Chem. Eng. 31: 208 (1953)] found the exponent to be −1 .4 . The higher coefficients at low surface tension are offset to some extent by a higher pressure drop, probably because the more intimate mixture existing at low surface tension causes the liquid fraction to be accelerated to a velocity closer to that of the vapor . The pressure drop due to acceleration DPa derived from Fig . 11-18 allows for some slippage . In the limiting case, such as might be approached at low surface tension, the acceleration pressure drop in which “fog” flow is assumed (no slippage) can be determined from the equation ∆Pa′ =

y (V g − Vl )G 2 gc

(11-31)

where y = fraction vapor by weight Vg , Vl = specific volume gas, liquid G = mass velocity While the foregoing methods are valuable for detailed evaporator design or for evaluating the effect of changes in conditions on performance, they are cumbersome to use when making preliminary designs or cost estimates . Figure 11-20 gives the general range of overall long-tube vertical (LTV) evaporator heat-transfer coefficients usually encountered in commercial practice . The higher coefficients are encountered when evaporating dilute solutions and the lower range when evaporating viscous liquids . The dashed curve represents the approximate lower limit, for liquids with viscosities of about 0 .1 Pa · s (100 cP) . The LTV evaporator does not work well at low temperature differences, as indicated by the results shown in Fig . 11-21 for seawater in 0 .051-m (2-in), 0 .0028-m (12-gauge) brass tubes 7 .32 m (24 ft) long (W . L . Badger Associates, Inc ., U .S . Department of the Interior, Office of Saline Water, Rep . 26, December 1959, OTS Publ . PB 161290) . The feed was at its boiling point at the vapor head pressure, and feed rates varied from 0 .025 to 0 .050 kg/(s · tube) [200 to 400 lb/(h · tube)] at the higher temperature to 0 .038 to 0 .125 kg/(s · tube) [300 to 1000 lb/(h · tube)] at the lowest temperature .

FIG. 11-21 Heat-transfer coefficients in LTV seawater evaporators . °C = (°F − 32)/1 .8;

to convert British thermal units per hour per square foot per degree Fahrenheit to joules per square meter per second per kelvin, multiply by 5 .6783 .

Falling-film evaporators find their widest use at low temperature differences—also at low temperatures . Under most operating conditions encountered, heat transfer is almost all by pure convection, with a negligible contribution from nucleate boiling . Film coefficients on the condensing side may be estimated from Dukler’s correlation [Chem. Eng. Prog. 55: 62 (1950)] . The same Dukler correlation presents curves covering falling-film heat transfer to nonboiling liquids that are equally applicable to the falling-film evaporator [Sinek and Young, Chem. Eng. Prog. 58: 12, 74 (1962)] . Kunz and Yerazunis [ J. Heat Transfer 8: 413 (1969)] have since extended the range of physical properties covered, as shown in Fig . 11-22 . The boiling point in the tubes of such an evaporator is higher than that in the vapor head because of both frictional pressure drop and the head needed to accelerate the vapor to the tube-exit velocity . These factors, which can easily be predicted, make the overall apparent coefficients somewhat lower than those for nonboiling conditions . Figure 11-21 shows overall apparent heat-transfer coefficients determined in a falling-film seawater evaporator using the same tubes and flow rates as for the rising-film tests (W . L . Badger Associates, Inc ., U .S . Department of the Interior, Office of Saline Water, Rep . 26, December 1959, OTS Publ . PB 161290) . Short-Tube Vertical Evaporators Coefficients can be estimated by the same detailed method described for recirculating LTV evaporators . Performance is primarily a function of temperature level, temperature difference, and viscosity . While liquid level can also have an important influence, this is usually encountered only at levels lower than considered safe in commercial operation . Overall heat-transfer coefficients are shown in Fig . 11-23 for a basket-type evaporator (one with an annular downtake) when boiling water with 0 .051-m (2-in) outside-diameter 0 .0028-m wall (12-gauge), 1 .22-m- (4-ft-) long steel tubes [Badger and Shepard, Chem. Metall. Eng. 23: 281 (1920)] . Liquid level was maintained at the top tube sheet . Foust, Baker, and Badger [Ind. Eng. Chem. 31: 206 (1939)] measured recirculating velocities and heat-transfer coefficients in the same evaporator except with 0 .064-m (2 .5-in) 0 .0034-m-wall (10-gauge), 1 .22-m- (4-ft-) long tubes and temperature differences from 7°C to 26°C (12°F to 46°F) . In the normal range of liquid levels, their results can be expressed as Uc =

FIG. 11-20 General range of long-tube vertical (LTV) evaporator coefficients .

°C = (°F − 32)/1 .8; to convert British thermal units per hour squared per foot per degree Fahrenheit to joules per square meter per second per kelvin, multiply by 5 .6783 .

b( ∆Tc )0 .22 N pr0 .4 (V g − Vl )0 .37

(11-32)

where b = 153 (SI) or 375 (USCS) and the subscript c refers to true liquid temperature, which under these conditions was about 0 .56°C (1°F) above the vapor head temperature . This work was done with water . No detailed tests have been reported for the performance of propeller calandrias . Not enough is known regarding the performance of the propellers themselves under the cavitating conditions usually encountered to permit prediction of circulation rates . In many cases, it appears that the propeller does no good in accelerating heat transfer over the transfer for natural circulation (Fig . 11-23) . Miscellaneous Evaporator Types Horizontal-tube evaporators operating with partially or fully submerged heating surfaces behave in much the same way as short-tube verticals, and heat-transfer coefficients are of the same order of magnitude . Some test results for water were published by Badger [Trans. Am. Inst. Chem. Eng. 13: 139 (1921)] . When operating unsubmerged, their heat-transfer performance is roughly comparable to that of the falling-film vertical tube evaporator . Condensing coefficients inside the

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT

11-15

5 4

h/(K3ρ2g/µ2 ) 1/3

2

1000 400 200

NPr

6 4

1.0

NPr

100 60 40 20 10

3

2 0.6 1 0.4

Nus se 0.2 10

20

lt

50

100

200

500

1000 NRe = 4Γ/µ

2000

5000

10,000

20,000

50,000 100,000

FIG. 11-22 Kunz and Yerazunis correlation for falling-film heat transfer.

tubes can be derived from Nusselt’s theory which, based on a constant-heat flux rather than a constant film DT, gives h = 1 .59(4 Γ /µ)−1/3 ( k 3ρ2 g /µ 2 )1/3

(11-33a)

For the boiling side, a correlation based on seawater tests gives h = 0 .0147(4 Γ /µ)1/3 ( D )−1/3 ( k 3ρ2 g /µ 2 )1/3

(11-33b)

where G is based on feed rate per unit length of the top tube in each vertical row of tubes and D is in meters . Heat-transfer coefficients in clean coiled-tube evaporators for seawater are shown in Fig . 11-24 [Hillier, Proc. Inst. Mech. Eng. (London), 1B(7): 295 (1953)] . The tubes were of copper . Heat-transfer coefficients in agitated-film evaporators depend primarily on liquid viscosity . This type is usually justifiable only for very viscous materials . Figure 11-25 shows general ranges of overall coefficients [Hauschild, Chem. Ing. Tech. 25: 573 (1953); Lindsey, Chem. Eng. 60(4): 227 (1953); and Leniger and Veldstra, Chem. Ing. Tech. 31: 493 (1959)] . When used with nonviscous fluids, a wiped-film evaporator having fluted external surfaces can exhibit very high coefficients (Lustenader et al ., Trans. Am. Soc. Mech. Eng. Paper 59-SA-30, 1959), although at a probably unwarranted first cost . Heat Transfer from Various Metal Surfaces In an early work, Pridgeon and Badger [Ind. Eng. Chem. 16: 474 (1924)] published test results on copper and iron tubes in a horizontal-tube evaporator that indicated an extreme effect of surface cleanliness on heat-transfer coefficients . However, the high

FIG. 11-23 Heat-transfer coefficients for water in short-tube evaporators. °C =

(°F − 32)/1.8; to convert British thermal units per hour per square foot per degree Fahrenheit to joules per square meter per second per kelvin, multiply by 5.6783.

degree of cleanliness needed for high coefficients was difficult to achieve, and the tube layout and liquid level were changed during the course of the tests so as to make direct comparison of results difficult . Other workers have found little or no effect of conditions of surface or tube material on boilingfilm coefficients in the range of commercial operating conditions [Averin, Izv. Akad. Nauk SSSR Otd. Tekh. Nauk, no . 3, p . 116, 1954; and Coulson and McNelly, Trans. Inst. Chem. Eng. 34: 247 (1956)] . Work in connection with desalination of seawater has shown that specially modified surfaces can have a profound effect on heat-transfer coefficients in evaporators . Figure 11-26 (Alexander and Hoffman, Oak Ridge National Laboratory TM-2203) compares overall coefficients for some of these surfaces when boiling freshwater in 0 .051-m (2-in) tubes 2 .44 m (8 ft) long at atmospheric pressure in both upflow and downflow . The area basis used was the nominal outside area . Tube 20 was a smooth 0 .0016-m (0 .062-in) wall aluminum brass tube that had accumulated about 6 years of fouling in seawater service and exhibited a fouling resistance of about (2 .6)(10−5) (m2 ⋅ s ⋅ K)/J [0 .00015 ( ft2 ⋅ h ⋅ °F)/Btu] . Tube 23 was a clean aluminum tube with 20 spiral corrugations of 0.0032-m (⅛-in) radius on a 0.254-m (10-in) pitch indented into the tube. Tube 48 was a clean copper tube that had 50 longitudinal flutes pressed into the wall (General Electric double-flute profile, Diedrich, U.S. Patent 3,244,601, Apr. 5, 1966). Tubes 47 and 39 had a specially patterned porous sintered-metal deposit on the boiling side to promote nucleate boiling (Minton, U.S. Patent 3,384,154, May 21, 1968). Both of these tubes also had steam-side coatings to promote dropwise condensation—parylene for tube 47 and gold plating for tube 39. Of these special surfaces, only the double-fluted tube has seen extended services. Most of the gain in heat-transfer coefficient is due to the condensing side; the flutes tend to collect the condensate and leave the lands bare [Carnavos, Proc. First Int. Symp. Water Desalination 2: 205 (1965)].

FIG. 11-24 Heat-transfer coefficients for seawater in coil-tube evaporators. °C = (°F − 32)/1.8; to convert British thermal units per hour per square foot per degree Fahrenheit to joules per square meter per second per kelvin, multiply by 5.6783.

11-16

HEAT-TRANSFER EQUIPMENT

FIG.

11-25 Overall heat-transfer coefficients in agitated-film evaporators . °C = (°F − 32)/1 .8; to convert British thermal units per hour per square foot per degree Fahrenheit to joules per square meter per second per kelvin, multiply by 5 .6783; to convert centipoises to pascal-seconds, multiply by 10−3 .

The condensing-film coefficient (based on the actual outside area, which is 28 percent greater than the nominal area) may be approximated from the equation  k 3ρ2 g  h=b  m 2 

1/3

 µλ    L

1/3

 q  A 

−0 .833

(11-34a)

where b = 2100 (SI) or 1180 (USCS) . The boiling-side coefficient (based on actual inside area) for salt water in downflow may be approximated from the equation h = 0 .035(k3ρ2g/µ2)1/3(4Γ/µ)⅓

(11-34b)

The boiling-film coefficient is about 30 percent lower for pure water than it is for salt water or seawater . There is as yet no accepted explanation for the superior performance in salt water . This phenomenon is also seen in evaporation from smooth tubes . Effect of Fluid Properties on Heat Transfer Most of the heat-transfer data reported in the preceding paragraphs were obtained with water or with dilute solutions having properties close to those of water . Heat transfer with other materials will depend on the type of evaporator used . For forcedcirculation evaporators, methods have been presented to calculate the effect

FIG. 11-26 Heat-transfer coefficients for enhanced surfaces . °C = (°F − 32)/1 .8; to convert British thermal units per hour per square foot per degree Fahrenheit to joules per square meter per second per kelvin, multiply by 5 .6783 . (By permission from Oak Ridge National Laboratory TM-2203.)

FIG. 11-27 Kerr’s tests with full-sized sugar evaporators . °C = (°F − 32)/1 .8; to convert

British thermal units per hour per square foot per degree Fahrenheit to joules per square meter per second per kelvin, multiply by 5 .6783 .

of changes in fluid properties . For natural-circulation evaporators, viscosity is the most important variable as far as aqueous solutions are concerned . Badger (Heat Transfer and Evaporation, Chemical Catalog, New York, 1926, pp . 133–134) found that, as a rough rule, overall heat-transfer coefficients varied in inverse proportion to viscosity if the boiling film was the main resistance to heat transfer . When handling molasses solutions in a forced-circulation evaporator in which boiling was allowed to occur in the tubes, Coates and Badger [Trans. Am. Inst. Chem. Eng. 32: 49 (1936)] found that from 0 .005 to 0 .03 Pa · s (5 to 30 cP) the overall heat-transfer coefficient could be represented by U = b/µf1 .24, where b = 2 .55 (SI) or 7043 (USCS) . Fragen and Badger [Ind. Eng. Chem. 28: 534 (1936)] correlated overall coefficients on sugar and sulfite liquor in the same evaporator for viscosities to 0 .242 Pa · s (242 cP) and found a relationship that included the viscosity raised only to the 0 .25 power . Little work has been published on the effect of viscosity on heat transfer in the long-tube vertical evaporator . Cessna, Leintz, and Badger [Trans. Am. Inst. Chem. Eng. 36: 759 (1940)] found that the overall coefficient in the nonboiling zone varied inversely as the 0 .7 power of viscosity (with sugar solutions) . Coulson and Mehta [Trans. Inst. Chem. Eng. 31: 208 (1953)] found the exponent to be −0 .44, and Stroebe, Baker, and Badger arrived at an exponent of −0 .3 for the effect of viscosity on the film coefficient in the boiling zone . Kerr (Louisiana Agr. Exp. Sta. Bull. 149) obtained plant data shown in Fig . 11-27 on various types of full-sized evaporators for cane sugar . These are invariably forward-feed evaporators concentrating to about 50° Brix, corresponding to a viscosity on the order of 0 .005 Pa ⋅ s (5 cP) in the last effect . In Fig . 11-27 curve A is for short-tube verticals with central downtake, B is for standard horizontal-tube evaporators, C is for Lillie evaporators (which were horizontal-tube machines with no liquor level but having recirculating liquor showered over the tubes), and D is for long-tube vertical evaporators . These curves show apparent coefficients, but sugar solutions have boilingpoint rises low enough to not affect the results noticeably . Kerr also obtained the data shown in Fig . 11-28 on a laboratory short-tube vertical evaporator with 0 .44- by 0 .61-m (1¾- by 24-in) tubes . This work was done with sugar juices boiling at 57°C (135°F) and an 11°C (20°F) temperature difference .

FIG. 11-28 Effect of viscosity on heat transfer in short-tube vertical evaporator . To convert centipoises to pascal-seconds, multiply by 10−3; to convert British thermal units per hour per square foot per degree Fahrenheit to joules per square meter per second per kelvin, multiply by 5 .6783 .

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT Effect of Noncondensibles on Heat Transfer Most of the heat transfer in evaporators occurs not from pure steam but from vapor evolved in a preceding effect . This vapor usually contains inert gases—from air leakage if the preceding effect was under vacuum, from air entrained or dissolved in the feed, or from gases liberated by decomposition reactions . To prevent these inerts from seriously impeding heat transfer, the gases must be channeled past the heating surface and vented from the system while the gas concentration is still quite low . The influence of inert gases on heat transfer is due partially to the effect on ∆T of lowering the partial pressure and hence condensing temperature of the steam . The primary effect, however, results from the formation at the heating surface of an insulating blanket of gas through which the steam must diffuse before it can condense . The latter effect can be treated as an added resistance or fouling factor equal to 6 .5 × 10−5 times the local mole percent inert gas (in J−1 ⋅ s ⋅ m2 ⋅ K) [Standiford, Chem. Eng. Prog . 75: 59–62 (July 1979)] . The effect on ∆T is readily calculated from Dalton’s law . Inert-gas concentrations may vary by a factor of 100 or more between vapor inlet and vent outlet, so these relationships should be integrated through the tube bundle . CRYOGENIC HEAT EXCHANGERS Most cryogenic fluids behave similar to room-temperature fluids as far as thermal/hydraulic design is concerned . For tubular exchangers, the Colburn equation and the ordinary Dittus-Boelter correlation, with slight modification, work well for single-phase cryogenic fluids as long as the critical point for the fluid is not closely approached . For critical-point calculations, a number of publications may be found in the literature to direct the designer along the best path forward for the fluid under consideration . For example, the use of an unmodified Dittus-Boelter correlation appears to give satisfactory results under swirl flow conditions for flows near the critical point . Beyond the normal good design practice of the experienced thermal designer, a primary factor influencing the type of heat exchanger used in cryogenic applications is the ability of the exchanger geometry to handle large temperature changes and potential cyclic operation . Two popular geometries for these applications are coiled tube exchangers and bayonet exchangers . The coiled tube heat exchanger is well suited for designs where heat transfer between more than two fluid streams is needed . It is also capable of handling high pressures while accommodating the thermal expansion/ contraction issues of low-temperature operation . The bayonet heat exchanger is also highly suited for extremes of high pressures and differential expansion . For large duties, it is simple to design a double tube sheet shell and tube heat exchanger with each tube consisting of the scabbard/bayonet tube combination of the bayonet exchanger . Segmental baffles or extended surface may be used on the outside of the scabbard tube bundle for the shell-side fluid . For cryogenic vaporization, a wire wrapped on the outside of each bayonet tube with the cold fluid entering in the bayonet tubes and exiting while vaporizing along the annulus between the bayonet tube and the scabbard pipe produces as efficient a vaporization performance as is possible in a tubular exchanger . A third compact-type exchanger sometimes used for single-phase applications is the plate-fin heat exchanger . Again, however, the issue is to take care that the construction can handle the high differential expansion/contraction forces that the process may inflict upon the exchanger . In most cryogenic processes, there is at least one service where heat is transferred between a cryogen and a fluid which can easily freeze on the tube wall . If cyclic operation is not desired (where the service is shut down at regular intervals or flow is transferred to a second exchanger while thawing occurs in the first), the best approach is to determine the thickness of frozen fluid needed to produce a skin temperature (at the solid-to-liquid interface) equal to the freezing point temperature of the fluid where further freezing will cease . The heat exchanger is then designed to accommodate this amount of solid buildup without flow blockage or unacceptable deterioration of heat transfer . For this reason, in these applications, the cryogenic fluid is almost always located inside the tubes while the heating stream with freezing potential is placed on the outside where a larger tube pitch can be used to create the space needed for the amount of solid buildup that will occur at thermodynamic equilibrium . When properly designed, these heat exchangers will operate free of problems at steady-state conditions for as long as necessary . BATCH OPERATIONS: HEATING AND COOLING OF VESSELS Nomenclature (Use consistent units .) A = heat-transfer surface; C, c = specific heats of hot and cold fluids, respectively; L0 = flow rate of liquid added to tank; M = mass of fluid in tank; T, t = temperature of hot and cold fluids, respectively; T1, t1 = temperatures at beginning of heating or cooling period or at inlet; T2, t2 = temperature at end of period or at outlet; T0, t0 = temperature of liquid added to tank; U = coefficient of heat transfer; and W, w = flow rate through external exchanger of hot and cold fluids, respectively .

11-17

Applications One typical application in heat transfer with batch operations is the heating of a reactor mix, maintaining temperature during a reaction period, and then cooling the products after the reaction is complete . This subsection is concerned with the heating and cooling of such systems in either unknown or specified periods . The technique for deriving expressions relating time for heating or cooling agitated batches to coil or jacket area, heat-transfer coefficients, and the heat capacity of the vessel contents was developed by Bowman, Mueller, and Nagle [Trans. Am. Soc. Mech. Eng. 62: 283–294 (1940)] and extended by Fisher [Ind. Eng. Chem. 36: 939–942 (1944)] and Chaddock and Sanders [Trans. Am. Inst. Chem. Eng. 40: 203–210 (1944)] to external heat exchangers . Kern (Process Heat Transfer, McGraw-Hill, New York, 1950, chap . 18) collected and published the results of these investigators . The assumptions made were that (1) U is constant for the process and over the entire surface, (2) liquid flow rates are constant, (3) specific heats are constant for the process, (4) the heating or cooling medium has a constant inlet temperature, (5) agitation produces a uniform batch fluid temperature, (6) no partial phase changes occur, and (7) heat losses are negligible . The developed equations are as follows . If any of the assumptions do not apply to a system being designed, new equations should be developed or appropriate corrections made . Heat exchangers are counterflow except for the 1-2 exchangers, which are one-shell-pass, two-tube-pass, parallel-flow counterflow . Coil-in-Tank or Jacketed Vessel: Isothermal Heating Medium ln(T1 − t1)/(T1 − t2) = UAθ/Mc

(11-35)

Cooling-in-Tank or Jacketed Vessel: Isothermal Cooling Medium ln (T1 − t1)/(T2 − t1) = UAθ/MC

(11-35a)

Coil-in-Tank or Jacketed Vessel: Nonisothermal Heating Medium ln

T1 − t1 WC  K 1 − 1  = θ T1 − t 2 Mc  K 1 

(11-35b)

where K1 = eUA/WC . Coil-in-Tank: Nonisothermal Cooling Medium ln

T1 − t1 wc  K 2 − 1  = θ T2 − t1 MC  K 2 

(11-35c)

where K2 = eUA/wc . External Heat Exchanger: Isothermal Heating Medium ln

T1 − t1 wc  K 2 − 1  θ = T1 − t 2 MC  K 2 

(11-35d)

External Exchanger: Isothermal Cooling Medium ln

T1 − t1 WC  K 1 − 1  θ = T2 − t1 MC  K 1 

(11-35e)

External Exchanger: Nonisothermal Heating Medium ln

T1 − t1  K 3 − 1   wWC  θ =  T2 − t1  M   K 3wc − WC 

(11-35f )

where K3 = eUA(1/WC − 1/wc) . External Exchanger: Nonisothermal Cooling Medium ln

T1 − t1  K 4 − 1   Wwc  θ =  T2 − t1  M   K 4wc − WC 

(11-35g)

where K4 = eUA(1/WC − 1/wc) . External Exchanger with Liquid Continuously Added to Tank: Isothermal Heating Medium   t1 − t 0 − ln    t2 − t0 − 

 w  K2 − 1 (T1 − t1 )  L0  K 2    w  K2 − 1 (T1 − t 2 )  L0  K 2    w  K − 1   M + L0 θ =   2  + 1  ln M  L0  K 2  

(11-35h)

11-18

HEAT-TRANSFER EQUIPMENT

If the addition of liquid to the tank causes an average endothermic or exothermic heat of solution ±qs J/kg (Btu/lb) of makeup, it may be included by adding ±qs/c0 to both the numerator and the denominator of the left side . The subscript 0 refers to the makeup . External Exchanger with Liquid Continuously Added to Tank: Isothermal Cooling Medium   W  K1 − 1   T0 − T1 −   (T1 − t1 )   W  K − 1   M + L θ L K  0 1 1 0 = 1− ln  ln   L0  K 1    M W  K1 − 1  T t T T ( ) − − −  0 2 2 1  L0  K 1   

(11-35i)

The heat-of-solution effects can be included by adding ±qs/C0 to both the numerator and the denominator of the left side . External Exchanger with Liquid Continuously Added to Tank: Nonisothermal Heating Medium wWC ( K 5 − 1)(T1 − t1 )    t 0 − t1 + L ( K WC − wc )   wWC ( K − 1)  M + L0 θ 0 5 5 = (11-35j) ln  + 1  ln M  t − t + wWC ( K 5 − 1)(T1 − t 2 )   L0 ( K 5WC − wc )   0 2  L0 ( K 5WC − wc )  where K5 = e(UA/wc)(1 − wc/WC) . The heat-of-solution effects can be included by adding ±qs/c0 to both the numerator and the denominator of the left side . External Exchanger with Liquid Continuously Added to Tank: Nonisothermal Cooling Medium Wwc ( K 6 − 1)(T1 − t1 )    T0 − T1 + L ( K wc − WC )   Wwc ( K − 1)  M + L0 θ 6 0 6 = ln  + 1  ln Wwc K − T − t ( 1)( ) L K wc WC M − ( ) 6 2 1 T − T +   0 6   0 2 L0 ( K 6wc − WC )  (11-35k) where K6 = e(UA/WC)(1 − WC/wc) . The heat-of-solution effects can be included by adding ±qs/C0 to both the numerator and the denominator of the left side . Heating and Cooling Agitated Batches: 1-2 Parallel Flow-Counterflow UA 1 = wc R2 +1 R=

 2 − S ( R + 1 − R + 1)    ln  2 − S ( R + 1 − R 2 + 1) 

T1 − T2 wc = t ′ − t WC

2 − S ( R + 1 − R 2 + 1) 2 − S ( R + 1 + R 2 + 1) S=

2

and

=e

S=

(11-35l)

t′ − t T1 − t

(UA /wc ) R 2 + 1

= K7

2( K 7 − 1) K 7 ( R + 1 + R 2 + 1) − ( R + 1 − R 2 + 1)

(11-35m)

External 1-2 Exchanger: Heating ln [(T1 − t1)/(T1 − t2)] = (Sw/M)θ

(11-35n)

External 1-2 Exchanger: Cooling ln [(T1 − t1)/(T2 − t1)] = S(wc/MC)θ

(11-35o)

The cases of multipass exchangers with liquid continuously added to the tank are covered by Kern, as cited earlier . An alternative method for all multipass-exchanger gases, including those presented as well as cases with two or more shells in series, is as follows: 1 . Determine UA for using the applicable equations for counterflow heat exchangers . 2 . Use the initial batch temperature T1 or t1 . 3 . Calculate the outlet temperature from the exchanger of each fluid . (This will require trial-and-error methods .) 4 . Note the FT correction factor for the corrected mean temperature difference . (See Fig . 11-4 .) 5 . Repeat steps 2, 3, and 4 by using the final batch temperature T2 and t2 . 6 . Use the average of the two values for F, then increase the required multipass UA as follows: UA(multipass) = UA(counterflow)/FT

In general, values of FT below 0 .8 are uneconomical and should be avoided . The value of FT can be raised by increasing the flow rate of either or both of the flow streams . Increasing flow rates to give values well above 0 .8 is a matter of economic justification . If FT varies widely from one end of the range to the other, FT should be determined for one or more intermediate points . The average should then be determined for each step which has been established and the average of these taken for use in step 6 . Effect of External Heat Loss or Gain If heat loss or gain through the vessel walls cannot be neglected, equations that include this heat transfer can be developed by using energy balances similar to those used for the derivations of equations given previously . Basically, these equations must be modified by adding a heat-loss or heat-gain term . A simpler procedure, which is probably acceptable for most practical cases, is to adjust the ratio of UA or θ either up or down in accordance with the required modification in total heat load over time θ . Another procedure, which is more accurate for the external-heat exchanger cases, is to use an equivalent value for MC ( for a vessel being heated) derived from the following energy balance: Q = (Mc)e(t2 − t1) = Mc(t2 − t1) + U ′A′ (MTD ′)θ

(11-35p)

where Q is the total heat transferred over time θ, U ′A′ is the heat-transfer coefficient for heat loss times the area for heat loss, and MTD′ is the mean temperature difference for the heat loss . A similar energy balance would apply to a vessel being cooled . Internal Coil or Jacket Plus External Heat Exchanger This case can be most simply handled by treating it as two separate problems: M is divided into two separate masses M1 and M − M1, and the appropriate equations given earlier are applied to each part of the system . Time θ, of course, must be the same for both parts . Equivalent-Area Concept The preceding equations for batch operations, particularly Eq . (11-35), can be applied for the calculation of heat loss from tanks which are allowed to cool over an extended time . However, different surfaces of a tank, such as the top (which would not be in contact with the tank contents) and the bottom, may have coefficients of heat transfer different from those of the vertical-tank walls . The simplest way to resolve this difficulty is to use an equivalent area Ae in the appropriate equations, where Ae = AbUb/Us + AtUt/Us + As

(11-35q)

and the subscripts b, s, and t refer to the bottom, sides, and top, respectively . Usually U is taken as Us . Table 11-1 lists typical values for Us and expressions for Ae for various tank configurations . Nonagitated Batches Cases in which vessel contents are vertically stratified, rather than uniform in temperature, have been treated by Kern (Process Heat Transfer, McGraw-Hill, New York, 1950, chap . 18) . These are of little practical importance except for tall, slender vessels heated or cooled with external exchangers . The result is that a smaller exchanger is required than for an equivalent agitated batch system that is uniform . Storage Tanks The equations for batch operations with agitation may be applied to storage tanks even though the tanks are not agitated . This approach gives conservative results . The important cases (non-steady-state) are as follows: 1 . Tanks cool; contents remain liquid. This case is relatively simple and can be easily handled by the equations given earlier . 2 . Tanks cool, contents partially freeze, and solids drop to bottom or rise to top. This case requires a two-step calculation . The first step is handled as in case 1 . The second step is calculated by assuming an isothermal system at the freezing point . It is possible, given time and a sufficiently low ambient temperature, for tank contents to freeze solid . 3 . Tanks cool and partially freeze; solids form a layer of self-insulation. This complex case, which has been known to occur with heavy hydrocarbons and mixtures of hydrocarbons, has been discussed by Stuhlbarg [Pet. Refiner 38: 143 (Apr . 1, 1959)] . The contents in the center of such tanks have been known to remain warm and liquid even after several years of cooling . It is very important that a melt-out riser be installed whenever tank contents are expected to freeze on prolonged shutdown . The purpose is to provide a molten chimney through the crust for relief of thermal expansion or cavitation if fluids are to be pumped out or recirculated through an external exchanger . An external heat tracer, properly located, will serve the same purpose but may require greater remelt time before pumping can be started . THERMAL DESIGN OF TANK COILS The thermal design of tank coils involves the determination of the area of heat-transfer surface required to maintain the contents of the tank at a constant temperature or to raise or lower the temperature of the contents by a specified magnitude over a fixed time .

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT

11-19

TABLE 11-1 Typical Values for Use with Eqs. (11-36) to (11-44)* Fluid

Us

As

Oil Water at 150°F Oil Water Oil Water Oil Water Oil Water Oil Water Oil Water Oil Water

3 .7 5 .1 0 .45 0 .43 1 .5 1 .8 0 .36 0 .37 3 .7 5 .1 0 .36 0 .37 1 .5 1 .8 0 .36 0 .37

0 .22 At + Ab + As 0 .16 At + Ab + As 0 .7 At + Ab + As 0 .67 At + Ab + As 0 .53 At + Ab + As 0 .35 At + Ab + As 0 .8 At + Ab + As 0 .73 At + Ab + As 0 .22 At + As + 0 .43 Dt 0 .16 At + As + 0 .31 Dt 0 .7 At + As + 3 .9 Dt 0 .16 At + As + 3 .7 Dt 0 .53 At + As + 1 .1 Dt 0 .35 At + As + 0 .9 Dt 0 .8 At + As + 4 .4 Dt 0 .73 At + As + 4 .5 Dt

Application Tanks on legs, outdoors, not insulated Tanks on legs, outdoors, insulated 1 in . Tanks on legs, indoors, not insulated Tanks on legs, indoors, insulated 1 in . Flat-bottom tanks,† outdoors, not insulated Flat-bottom tanks,† outdoors, insulated 1 in . Flat-bottom tanks, indoors, not insulated Flat-bottom tanks, indoors, insulated 1 in .

∗Based on typical coefficients. † The ratio (t − tg)(t − t′) assumed at 0.85 for outdoor tanks. °C = (°F − 32)/1.8; to convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783.

Nomenclature A = area; Ab = area of tank bottom; Ac = area of coil; Ae = equivalent area; As = area of sides; At = area of top; A1 = equivalent area receiving heat from external coils; A2 = equivalent area not covered with external coils; c = heat capacity of liquid phase of tank contents; Dt = diameter of tank; F = design (safety) factor; h = film coefficient; ha = coefficient of ambient air; hc = coefficient of coil; hh = coefficient of heating medium; hi = coefficient of liquid phase of tank contents or tube-side coefficient referred to outside of coil; hz = coefficient of insulation; k = thermal conductivity; kg = thermal conductivity of ground below tank; M = mass of tank contents when full; t = temperature; ta = temperature of ambient air; td = temperature of dead-air space; tf = temperature of contents at end of heating; tg = temperature of ground below tank; th = temperature of heating medium; t0 = temperature of contents at beginning of heating; U = overall coefficient; Ub = coefficient at tank bottom; Uc = coefficient of coil; Ud = coefficient of dead air to the tank contents; Ui = coefficient through insulation; Us = coefficient at sides; Ut = coefficient at top; and U2 = coefficient at area A2 . Typical coil coefficients are listed in Table 11-2 . More exact values can be calculated by using the methods for natural convection or forced convection given elsewhere in this section . Maintenance of Temperature Tanks are often maintained at temperature with internal coils if the following equations are assumed to be applicable:

and

q = UsAe(T − t′)

(11-36)

Ac = q/Uc(MTD)

(11-36a)

TABLE 11-2

These make no allowance for unexpected shutdowns . One method of allowing for shutdown is to add a safety factor to Eq . (11-36a) . In the case of a tank maintained at temperature with internal coils, the coils are usually designed to cover only a portion of the tank . The temperature td of the dead-air space between the coils and the tank is obtained from Ud A1(td − t) = U2 A2(t − t ′)

(11-37)

q = Ud A1(td − t) + A1Ui(td − t ′)

(11-38)

The heat load is

The coil area is Ac =

qF U c (t h − t d )m

(11-39)

where F is a safety factor . Heating Heating with Internal Coil from Initial Temperature for Specified Time Q = Mc(tf − to)

(11-40)

 Q 1   t f + to Ac =  + U s Ae  − t ′    (F )   − + 2 U [ t ( t t )/2] θ  f o  h   c h

(11-41)

Overall Heat-Transfer Coefficients for Coils Immersed in Liquids U Expressed as Btu/(h ⋅ ft2 ⋅ °F)

Substance inside coil Steam Steam Steam Cold water Cold water Cold water Brine Cold water Water Water Steam Milk Cold water 60°F water Steam and hydrogen at 1500 lb./sq. in. Steam 110–146 lb./ sq. in. gage Steam Cold water

Substance outside coil Water Sugar and molasses solutions Boiling aqueous solution Dilute organic dye intermediate Warm water Hot water Amino acids 25% oleum at 60°C. Aqueous solution 8% NaOH Fatty acid Water Hot water 50% aqueous sugar solution 60°F. water

Coil material

Agitation

Lead Copper

Agitated None

Lead

Turboagitator at 95 r.p.m.

Wrought iron

Air bubbled into water surrounding coil 0.40 r.p.m. paddle stirrer 30 r.p.m. Agitated 500 r.p.m. sleeve propeller 22 r.p.m. None Agitation None Mild

Lead Wrought iron Lead Copper (pancake) Copper Lead Steel

U 70 50–240 600 300 150–300 90–360 100 20 250 155 96–100 300 105–180 50–60 100–165

Vegetable oil

Steel

None

23–29

Vegetable oil Vegetable oil

Steel Steel

Various Various

39–72 29–72

notes: Chilton, Drew, and Jebens [Ind. Eng. Chem. 36: 510 (1944)] give film coefficients for heating and cooling agitated fluids using a coil in a jacketed vessel. Because of the many factors affecting heat transfer, such as viscosity, temperature difference, and coil size, the values in this table should be used primarily for preliminary design estimates and checking calculated coefficients. °C = (°F − 32)/1.8; to convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783.

11-20

HEAT-TRANSFER EQUIPMENT

where θh is the length of heating period . This equation may also be used when the tank contents have cooled from tf to to and must be reheated to tf . If the contents cool during a time θc, the temperature at the end of this cooling period is obtained from  t − t ′  U s Ae θc ln  f = Mc  to − t ′ 

(11-42)

Heating with External Coil from Initial Temperature Specified Time The temperature of the dead-air space is obtained from Ud A1[td − 0 .5(tf − to)] = U2 A2[0 .5(tf − to) − t′] + Q/θh

(11-43)

The heat load is q = Ui A1(td − t ′) + U2 A2[0 .5(tf − to) − t′] + Q/θh

(11-44)

The coil area is obtained from Eq . (11-39) . The safety factor used in the calculations is a matter of judgment based on confidence in the design . A value of 1 .10 is normally not considered excessive . Typical design parameters are shown in Tables 11-1 and 11-2 . HEATING AND COOLING OF TANKS Tank Coils Pipe tank coils are made in a wide variety of configurations, depending upon the application and shape of the vessel . Helical and spiral coils are most commonly shop-fabricated, while the hairpin pattern is generally field-fabricated . The helical coils are used principally in process tanks and pressure vessels when large areas for rapid heating or cooling are required . In general, heating coils are placed low in the tank, and cooling coils are placed high or distributed uniformly throughout the vertical height . Stocks that tend to solidify on cooling require uniform coverage of the bottom or agitation . A maximum spacing of 0 .6 m (2 ft) between turns of 50 .8-mm (2-in) and larger pipe and a close approach to the tank wall are recommended . For smaller pipe or for low-temperature heating media, closer spacing should be used . In the case of the common hairpin coils in vertical cylindrical tanks, this means adding an encircling ring within 152 mm (6 in) of the tank wall (see Fig . 11-29a for this and other typical coil layouts) . The coils should be set directly on the bottom or raised not more than 50 .8 to 152 mm (2 to 6 in), depending upon the difficulty of remelting the solids, in order to permit free movement of product within the vessel . The coil inlet should be above the liquid level (or an internal melt-out riser installed) to provide a molten path for liquid expansion or venting of vapors . Coils may be sloped to facilitate drainage . When it is impossible to do so and remain close enough to the bottom to get proper remelting, the coils should be blown out after use in cold weather to avoid damage by freezing . Most coils are firmly clamped (but not welded) to supports . Supports should allow expansion but be rigid enough to prevent uncontrolled motion (see Fig . 11-29b) . Nuts and bolts should be securely fastened . Reinforcement of the inlet and outlet connections through the tank wall is recommended, since bending stresses due to thermal expansion are usually high at such points . In general, 50 .8- and 63 .4-mm (2- and 2½-in) coils are the most economical for shop fabrication and 38 .1- and 50 .8-mm (1½- and 2-in) for field fabrication . The tube-side heat-transfer coefficient, high-pressure, or layout problems may lead to the use of smaller-size pipe . The wall thickness selected varies with the service and material . Carbonsteel coils are often made from schedule 80 or heavier pipe to allow for corrosion . When stainless-steel or other high-alloy coils are not subject to corrosion or excessive pressure, they may be of schedule 5 or 10 pipe to keep costs at a minimum, although high-quality welding is required for these thin walls to ensure trouble-free service .

(a)

(b)

Methods for calculating heat loss from tanks and the sizing of tank coils have been published by Stuhlbarg [Pet. Refiner 38: 143 (April 1959)] . Fin-tube coils are used for fluids that have poor heat-transfer characteristics to provide greater surface for the same configuration at reduced cost or when temperature-driven fouling is to be minimized . Fin tubing is not generally used when bottom coverage is important . Fin-tube tank heaters are compact, prefabricated bundles which can be brought into tanks through manholes . These are normally installed vertically with longitudinal fins to produce good convection currents . To keep the heaters low in the tank, they can be installed horizontally with helical fins or with perforated longitudinal fins to prevent entrapment . Fin tubing is often used for heat-sensitive material because of the lower surface temperature for the same heating medium, resulting in a lesser tendency to foul . Plate or panel coils made from two metal sheets with one or both embossed to form passages for a heating or cooling medium can be used in lieu of pipe coils . Panel coils are relatively lightweight, easy to install, and easily removed for cleaning . They are available in a range of standard sizes and in both flat and curved patterns . Process tanks have been built by using panel coils for the sides or bottom . A serpentine construction is generally utilized when liquid flows through the unit . Header-type construction is used with steam or other condensing media . Standard glass coils with 0 .18 to 11 .1 m2 (2 to 120 ft2) of heat-transfer surface are available . Also available are plate-type units made of impervious graphite. Teflon Immersion Coils Immersion coils made of Teflon fluorocarbon resin are available with 2 .5-mm- (0 .10-in-) ID tubes to increase overall heattransfer efficiency . The flexible bundles are available with 100, 160, 280, 500, and 650 tubes with standard lengths varying in 0 .6-m (2-ft) increments between 1 .2 and 4 .8 m (4 and 16 ft) . These coils are most commonly used in metal-finishing baths and are adaptable to service in reaction vessels, crystallizers, and tanks where corrosive fluids are used . Bayonet Heaters A bayonet-tube element consists of an outer tube and an inner tube . These elements are inserted into tanks and process vessels for heating and cooling purposes . Often the outer tube is of expensive alloy or nonmetallic (e .g ., glass, impervious graphite), while the inner tube is of carbon steel . In glass construction, elements with 50 .8- or 76 .2-mm (2- or 3-in) glass pipe [with lengths to 2 .7 m (9 ft)] are in contact with the external fluid, with an inner tube of metal . External Coils and Tracers Tanks, vessels, and pipelines can be equipped for heating or cooling purposes with external coils . These are generally 9 .8 to 19 mm (⅜ to ¾ in) so as to provide good distribution over the surface and are often of soft copper or aluminum, which can be bent by hand to the contour of the tank or line . When it is necessary to avoid “hot spots,” the tracer is so mounted that it does not touch the tank . External coils spaced away from the tank wall exhibit a coefficient of around 5 .7 W/(m2 ⋅ °C) [1 Btu/(h ⋅ ft2 of coil surface ⋅ °F)] . Direct contact with the tank wall produces higher coefficients, but these are difficult to predict since they are strongly dependent upon the degree of contact . The use of heat-transfer cements does improve performance . These puttylike materials of high thermal conductivity are troweled or caulked into the space between the coil and the tank or pipe surface . Costs of the cements (in 1960) varied from 37 to 63 cents per pound, with requirements running from about 0 .27 lb/ft of ⅜-in outside-diameter tubing to 1 .48 lb/ft of 1-in pipe . Panel coils require ½ to 1 lb/ft2 . A rule of thumb for preliminary estimating is that the per-foot installed cost of tracer with cement is about double that of the tracer alone . Jacketed Vessels Jacketing is often used for vessels needing frequent cleaning and for glass-lined vessels that are difficult to equip with internal coils . The jacket eliminates the need for the coil yet gives a better overall coefficient than external coils do . However, only a limited heat-transfer area is available . The conventional jacket is of simple construction and is frequently used . It is most effective with a condensing vapor . A liquid heat-transfer fluid does not maintain uniform flow characteristics in such a jacket . Nozzles, which set up a swirling motion in the jacket, are effective in improving

(c)

(d)

FIG. 11-29a Typical coil designs for good bottom coverage . (a) Elevated inlet on spiral coil . (b) Spiral with recircling ring . (c) Hairpin with encircling ring . (d) Ring header type .

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT

11-21

FIG. 11-30b Efficiencies for annular fins of constant thickness . FIG. 11-29b Right and wrong ways to support coils . [Chem. Eng., 172 (May 16, 1960) .]

heat transfer . Wall thicknesses are often high unless reinforcement rings are installed . Spiral baffles, which are sometimes installed for liquid services to improve heat transfer and prevent channeling, can be designed to serve as reinforcements . A spiral-wound channel welded to the vessel wall is an alternative to the spiral baffle which is more predictable in performance, since crossbaffle leakage is eliminated, and is reportedly lower in cost [Feichtinger, Chem. Eng. 67: 197 (Sept . 5, 1960)] . The half-pipe jacket is used when high jacket pressures are required . The flow pattern of a liquid heat-transfer fluid can be controlled and designed for effective heat transfer . The dimple jacket offers structural advantages and is the most economical for high jacket pressures . The low volumetric capacity produces a fast response to temperature changes . EXTENDED OR FINNED SURFACES Finned-Surface Application Extended or finned surfaces are often used when one film coefficient is substantially lower than the other, the goal being to make hoAoe ≈ hiAi . A few typical fin configurations are shown in Fig . 11-30a. Longitudinal fins are used in double-pipe exchangers . Transverse fins are used in cross-flow and shell-and-tube configurations .

High transverse fins are used mainly with low-pressure gases; low fins are used for boiling and condensation of nonaqueous streams as well as for sensible-heat transfer . Finned surfaces have proved to be a successful means of controlling temperature-driven fouling such as coking and scaling . Fin spacing should be great enough to avoid entrapment of particulate matter in the fluid stream (5-mm minimum spacing) . The area added by the fin is not as efficient for heat transfer as bare tube surface owing to resistance to conduction through the fin . The effective heat-transfer area is Aoe = Auf + Af Ω

The fin efficiency is found from mathematically derived relations, in which the film heat-transfer coefficient is assumed to be constant over the entire fin and temperature gradients across the thickness of the fin have been neglected (see Kraus, Extended Surfaces, Spartan Books, Baltimore, Md ., 1963) . The efficiency curves for some common fin configurations are given in Fig . 11-30a and b. High Fins To calculate heat-transfer coefficients for cross-flow to a transversely finned surface, it is best to use a correlation based on experimental data for that surface . Such data are not often available, and a more general correlation must be used, making allowance for the possible error . Probably the best general correlation for bundles of finned tubes is given by Schmidt [Kaltetechnik 15: 98–102, 370–378 (1963)]: hDr/k = K(Dr ρV ′max/µ)0 .625Rf −0 .375 N Pr1/3

FIG. 11-30a

Efficiencies for several longitudinal fin configurations .

(11-45)

(11-46)

where K = 0 .45 for staggered tube arrays and 0 .30 for in-line tube arrays; Dr is the root or base diameter of the tube; V m′ ax is the maximum velocity through the tube bank, i .e ., the velocity through the minimum flow area between adjacent tubes; and Rf is the ratio of the total outside surface area of the tube (including fins) to the surface of a tube having the same root diameter but without fins . Pressure drop is particularly sensitive to geometric parameters, and available correlations should be extrapolated to geometries different from those on which the correlation is based only with great caution and conservatism . The best correlation is that of Robinson and Briggs [Chem. Eng. Prog. 62: Symp . Ser . 64, 177–184 (1966)] . Low Fins Low-finned tubing is generally used in shell-and-tube configurations . For sensible-heat transfer, only minor modifications are needed to permit the shell-side method given earlier to be used for both heat transfer and pressure [see Briggs, Katz, and Young, Chem. Eng. Prog. 59(11): 49–59 (1963)] . For condensing on low-finned tubes in horizontal bundles, the Nusselt correlation is generally satisfactory for low-surfacetension [σ < (3)(10−6) N/m (30 dyn/cm)] condensates; fins of finned surfaces should not be closely spaced for high-surface-tension condensates (notably water), which do not drain easily . The modified Palen-Small method can be employed for reboiler design using finned tubes, but the maximum flux is calculated from Ao, the total outside heat-transfer area including fins . The resulting value of qmax refers to Ao .

11-22

HEAT-TRANSFER EQUIPMENT

FOULING AND SCALING Fouling refers to any change in the solid boundary separating two heattransfer fluids, whether by dirt accumulation or other means, which results in a decrease in the rate of heat transfer occurring across that boundary . Fouling may be classified by mechanism into six basic categories: 1 . Corrosion fouling.  The heat-transfer surface reacts chemically with elements of the fluid stream, producing a less conductive corrosion layer on all or part of the surface . 2 . Biofouling.    Organisms present in the fluid stream are attracted to the warm heat-transfer surface where they attach, grow, and reproduce . The two subgroups are microbiofoulants such as slime and algae and macrobiofoulants such as snails and barnacles . 3 . Particulate fouling.    Particles held in suspension in the flow stream will deposit out on the heat-transfer surface in areas of sufficiently lower velocity . 4 . Chemical reaction fouling (e .g ., coking) .  Chemical reaction of the fluid takes place on the heat-transfer surface, producing an adhering solid product of reaction . 5 . Precipitation fouling (e .g ., scaling) .  A fluid containing some dissolved material becomes supersaturated with respect to this material at the temperatures seen at the heat-transfer surface . This results in a crystallization of the material which “plates out” on the warmer surface . 6 . Freezing fouling.  Overcooling of a fluid below the fluid’s freezing point at the heat-transfer surface causes solidification and coating of the heattransfer surface . Control of Fouling Once the combination of mechanisms contributing to a particular fouling problem is recognized, methods to substantially reduce the fouling rate may be implemented . For the case of corrosion fouling, the common solution is to choose a less corrosive material of construction, balancing material cost with equipment life . In cases of biofouling, the use of copper alloys and/or chemical treatment of the fluid stream to control organism growth and reproduction is the most common solution . In the case of particulate fouling, one of the more common types, ensuring a sufficient flow velocity and minimizing areas of lower velocities and stagnant flows to help keep particles in suspension are the most common means of dealing with the problem . For water, the recommended tube-side minimum velocity is about 0 .9 to 1 .0 m/s . This may not always be possible for moderate to high-viscosity fluids where the resulting pressure drop can be prohibitive . Special care should be taken in the application of any velocity requirement to the shell side of segmental-baffled bundles due to the many different flow streams and velocities present during operation, the unavoidable existence of high-fouling areas of flow stagnation, and the danger of flow-induced tube vibration . In general, shell-side particulate fouling will be greatest for segmentally baffled bundles in the regions of low velocity, and the TEMA fouling factors (which are based upon the use of this bundle type) should be used . However, since the 1940s, there have been a host of successful, low-fouling exchangers developed, some tubular and others not, which have in common the elimination of the cross-flow plate baffle and provide practically no regions of flow stagnation at the heat-transfer surface . Some examples are the plate and frame exchanger, the spiral-plate exchanger, and the twisted tube exchanger, all of which have dispensed with baffles altogether and use the heat-transfer surface itself for bundle support . The general rule for these designs is to provide between 25 and 30 percent excess surface to compensate for potential fouling, although this can vary in special applications . For the remaining classifications—polymerization, precipitation, and freezing—fouling is the direct result of temperature extremes at the heattransfer surface and is reduced by reducing the temperature difference between the heat-transfer surface and the bulk-fluid stream . Conventional wisdom says to increase velocity, thus increasing the local heat-transfer coefficient to bring the heat-transfer surface temperature closer to the bulkfluid temperature . However, due to a practical limit on the amount of heattransfer coefficient increase available by increasing velocity, this approach, although better than nothing, is often not satisfactory by itself . A more effective means of reducing the temperature difference is by using, in concert with adequate velocities, some form of extended surface . As discussed by Shilling (Proceedings of the 10th International Heat Transfer Conference, Brighton, U .K ., 4: 423, 1994), this will tend to reduce the temperature extremes between the fluid and heat-transfer surface and not only reduce the rate of fouling but also make the heat exchanger generally less sensitive to the effects of any fouling that does occur . In cases where unfinned tubing in a triangular tube layout would not be acceptable because fouling buildup and eventual mechanical cleaning are inevitable, an extended surface should be used only when the exchanger construction allows access for cleaning . Fouling Transients and Operating Periods Three common behaviors are noted in the development of a fouling film over time . One is asymptotic fouling in which the speed of fouling resistance increase decreases over time as it approaches some asymptotic value beyond which

no further fouling can occur . This is commonly found in temperature-driven fouling . A second behavior is linear fouling in which the increase in fouling resistance follows a straight line over the time of operation . This could be experienced in a case of severe particulate fouling where the accumulation of dirt during the time of operation did not appreciably increase velocities to mitigate the problem . The third behavior, falling rate fouling, is neither linear nor asymptotic but instead lies somewhere between these two extremes . The rate of fouling decreases with time but does not appear to approach an asymptotic maximum during the time of operation . This is the most common type of fouling in the process industry and is usually the result of a combination of different fouling mechanisms occurring together . The optimum operating period between cleanings depends upon the rate and type of fouling, the heat exchanger used (i .e ., baffle type, use of extended surface, and velocity and pressure drop design constraints), and the ease with which the heat exchanger may be removed from service for cleaning . As noted above, care must be taken in the use of fouling factors for exchanger design, especially if the exchanger configuration has been selected specifically to minimize fouling accumulation . An oversurfaced heat exchanger which will not foul enough to operate properly can be almost as much of a problem as an undersized exchanger . This is especially true in steam-heated exchangers where the ratio of design MTD to minimum achievable MTD is less than Uclean divided by Ufouled . Removal of Fouling Deposits Chemical removal of fouling can be achieved in some cases by weak acid, special solvents, and so on . Other deposits adhere weakly and can be washed off by periodic operation at very high velocities or by flushing with a high-velocity steam or water jet or using a sand-water slurry . These methods may be applied to both the shell side and tube side without pulling the bundle . Many fouling deposits, however, must be removed by positive mechanical action such as rodding, turbining, or scraping the surface . These techniques may be applied inside of tubes without pulling the bundle but can be applied on the shell side only after bundle removal . Even then there is limited access because of the tube pitch, and rotated square or large triangular layouts are recommended . In many cases, it has been found that designs developed to minimize fouling often develop a fouling layer which is more easily removed . Fouling Resistances There are no published methods for predicting fouling resistances a priori . The accumulated experience of exchanger designers and users was assembled more than 40 years ago based primarily upon segmental-baffled exchanger bundles and may be found in the Standards of Tubular Exchanger Manufacturers Association (TEMA) . In the absence of other information, the fouling resistances contained therein may be used . TYPICAL HEAT-TRANSFER COEFFICIENTS Typical overall heat-transfer coefficients are given in Tables 11-3 through 11-8 . Values from these tables may be used for preliminary estimating purposes . They should not be used in place of the design methods described elsewhere in this section, although they may serve as a useful check on the results obtained by those design methods . THERMAL DESIGN FOR SOLIDS PROCESSING Solids in divided form, such as powders, pellets, and lumps, are heated and/or cooled in chemical processing for a variety of objectives such as solidification or fusing (Sec . 11), drying and water removal (Sec . 20), solvent recovery (Secs . 13 and 20), sublimation (Sec . 17), chemical reactions (Sec . 20), and oxidation . For process and mechanical-design considerations, see the referenced sections . Thermal design concerns itself with sizing the equipment to effect the heat transfer necessary to carry on the process . The design equation is the familiar one basic to all modes of heat transfer, namely, A = Q/U ∆t

(11-47)

where A = effective heat-transfer surface, Q = quantity of heat required to be transferred, ∆t = temperature difference of the process, and U = overall heat-transfer coefficient . It is helpful to define the modes of heat transfer and the corresponding overall coefficient, Uco, as Uco = overall heat-transfer coefficient for (indirect through-a-wall) conduction, Ucv = overall heat-transfer coefficient for the little-used convection mechanism, Uct = heat-transfer coefficient for the contactive mechanism in which the gaseous-phase heat carrier passes directly through the solids bed, and Ura = heat-transfer coefficient for radiation. There are two general methods for determining numerical values for Uco, Ucv, Uct, and Ura . One is by analysis of actual operating data . Values so obtained are used on geometrically similar systems of a size not too different from the equipment from which the data were obtained . The second

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT

11-23

TABLE 11-3 Typical Overall Heat-Transfer Coefficients in Tubular Heat Exchangers U = Btu/(°F ⋅ ft2 ⋅ h)

Shell side

Tube side

Design U

Includes total dirt

Liquid-liquid media Aroclor 1248 Cutback asphalt Demineralized water Ethanol amine (MEA or DEA) 10–25% solutions Fuel oil Fuel oil Gasoline Heavy oils Heavy oils Hydrogen-rich reformer stream Kerosene or gas oil Kerosene or gas oil Kerosene or jet fuels Jacket water Lube oil (low viscosity) Lube oil (high viscosity) Lube oil Naphtha Naphtha Organic solvents Organic solvents Organic solvents Tall oil derivatives, vegetable oil, etc . Water Water Wax distillate Wax distillate

Jet fuels Water Water Water or DEA, or MEA solutions Water Oil Water Heavy oils Water Hydrogen-rich reformer stream Water Oil Trichlorethylene Water Water Water Oil Water Oil Water Brine Organic solvents Water

100–150 10–20 300–500 140–200

0 .0015 .01 .001 .003

15–25 10–15 60–100 10–40 15–50 90–120

.007 .008 .003 .004 .005 .002

25–50 20–35 40–50 230–300 25–50 40–80 11–20 50–70 25–35 50–150 35–90 20–60 20–50

.005 .005 .0015 .002 .002 .003 .006 .005 .005 .003 .003 .002 .004

Caustic soda solutions (10–30%) Water Water Oil

100–250

.003

200–250 15–25 13–23

.003 .005 .005

100–200 40–60 60–80

.002 .006 .004

Water Dowtherm vapor Tall oil and derivatives

Tube side Dowtherm liquid Steam Water Water Oil Water Water or brine Water or brine Water Oil Water Oil Water Feed water No . 6 fuel oil No . 2 fuel oil Water Water Aromatic vapor-stream azeotrope

Includes total dirt

80–120 40–50 20–50 80–200 25–40

.0015 .0055 .003 .003 .004

100–200 20–60 50–120 30–65 20–30 50–75 20–30 80–120 400–1000 15–25 60–90 150–200 20–50

.003 .003 .003 .004 .005 .005 .005 .003 .0005 .0055 .0025 .003 .004

40–80

.005

40–80 10–50 20–40 5–20 80–125

.005 .005 .005 .005 .003

150–300 150–300 40–60

.0015 .0015 .0015

200–300 250–400

.0015 .0015

Gas-liquid media Air, N2, etc . (compressed) Air, N2, etc ., A Water or brine Water or brine Water

Water or brine Water or brine Air, N2 (compressed) Air, N2, etc ., A Hydrogen containing natural-gas mixtures Vaporizers

Anhydrous ammonia Chlorine Chlorine

Condensing vapor-liquid media Alcohol vapor Asphalt (450°F .) Dowtherm vapor

Shell side Dowtherm vapor Gas-plant tar High-boiling hydrocarbons V Low-boiling hydrocarbons A Hydrocarbon vapors (partial condenser) Organic solvents A Organic solvents high NC, A Organic solvents low NC, V Kerosene Kerosene Naphtha Naphtha Stabilizer reflux vapors Steam Steam Steam Sulfur dioxide Tall-oil derivatives, vegetable oils (vapor) Water

Design U

Steam condensing Steam condensing Light heat-transfer oil Steam condensing Steam condensing

Propane, butane, etc . Water

NC = noncondensable gas present . V = vacuum . A = atmospheric pressure . Dirt (or fouling factor) units are (h ⋅ ft2 ⋅ °F)/Btu . To convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5 .6783; to convert hours per square foot-degree Fahrenheit-British thermal units to square meters per second-kelvin-joules, multiply by 0 .1761 .

TABLE 11-4

Typical Overall Heat-Transfer Coefficients in Refinery Service Btu/(°F ⋅ ft2 ⋅ h)

Fluid A B C D E F G H J K

Propane Butane 400°F . end-point gasoline Virgin light naphtha Virgin heavy naphtha Kerosene Light gas oil Heavy gas oil Reduced crude Heavy fuel oil (tar)

API gravity

Fouling factor (one stream)

50 70 45 40 30 22 17 10

0 .001 .001 .001 .001 .001 .001 .002 .003 .005 .005

Reboiler, steamheated

Condenser, watercooled∗

160 155 120 140 95 85 70 60

95 90 80 85 75 60 50 45

Exchangers, liquid to liquid (tube-side fluid designation appears below)

Reboiler (heating liquid designated below)

C

G

H

C

G†

K

85 80 70 70 65 60 60 55 55 50

85 75 65 55 55 55 50 50 45 40

80 75 60 55 50 50 50 45 40 35

110 105 65 75 55

95 90 50 60 45 45 40 40

35 35 30 35 30 25 25 20

50

Condenser (cooling liquid designated below) D

F

G

J

80

55

40

30

50 50 45 40

35 35 30 30

30 30 30 20

75 70 70 70

Fouling factor, water side 0 .0002; heating or cooling streams are shown at top of columns as C, D, F, G, etc .; to convert British thermal units per hour-square footdegrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5 .6783; to convert hours per square foot-degree Fahrenheit-British thermal units to square meters per second-kelvin-joules, multiply by 0 .1761 . ∗Cooler, water-cooled, rates are about 5 percent lower . † With heavy gas oil (H) as heating medium, rates are about 5 percent lower .

11-24

HEAT-TRANSFER EQUIPMENT

TABLE 11-5 Overall Coefficients for Air-Cooled Exchangers on Bare-Tube Basis Btu/(°F ⋅ ft2 ⋅ h) Condensing

Coefficient

Liquid cooling

Coefficient

Ammonia Freon-12 Gasoline Light hydrocarbons Light naphtha Heavy naphtha Reformer reactor effluent Low-pressure steam Overhead vapors

110 70 80 90 75 65

Engine-jacket water Fuel oil Light gas oil Light hydrocarbons Light naphtha Reformer liquid streams Residuum Tar

125 25 65 85 70

Gas cooling Air or flue gas Hydrocarbon gas

70 135 65 Operating pressure, lb ./sq . in . gage

Pressure drop, lb ./sq . in .

50 100 100 35 125 1000

0.1 to 0.5 2 5 1 3 5

70 15 7

small in relation to the overall size of the equipment. Also peculiar to solids heat transfer is that the ∆t varies for the different heat-transfer mechanisms. With a knowledge of these mechanisms, the ∆t term generally is readily estimated from temperature limitations imposed by the burden characteristics and/or the construction. Conductive Heat Transfer Heat-transfer equipment in which heat is transferred by conduction is constructed so that the solids load (burden) is separated from the heating medium by a wall. For a high proportion of applications, ∆t is the log-mean temperature difference. Values of Uco are reported in Secs. 11, 15, 17, and 19. A predictive equation for Uco is    2cα  h U co =    h − 2cα /d m   d m 

(11-48)

Coefficient

Ammonia reactor stream

10 20 30 35 55 80 85

Bare-tube external surface is 0.262 ft2/ft. Fin-tube surface/bare-tube surface ratio is 16.9. To convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783; to convert poundsforce per square inch to kilopascals, multiply by 6.895.

where h = wall film coefficient, c = volumetric heat capacity, dm = depth of the burden, and α = thermal diffusivity. Relevant thermal properties of various materials are given in Table 11-9. For details of terminology, equation development, numerical values of terms in typical equipment and use, see Holt [Chem. Eng. 69: 107 (Jan. 8, 1962)]. Equation (11-48) is applicable to burdens in the solid, liquid, or gaseous phase, either static or in laminar motion; it is applicable to solidification equipment and to divided-solids equipment such as metal belts, moving trays, stationary vertical tubes, and stationary-shell fluidizers. Fixed- (or packed-) bed operation occurs when the fluid velocity is low or the particle size is large so that fluidization does not occur. For such operation, Jakob (Heat Transfer, vol. 2, Wiley, New York, 1957) gives hDt/k = b1bDt0.17(DpG/µ)0.83(cµ/k)

method is predictive and is based on the material properties and certain operating parameters. Relative values of the coefficients for the various modes of heat transfer at temperatures up to 980°C (1800°F) are as follows (Holt, Paper 11, Fourth National Heat Transfer Conference, Buffalo, 1960): Convective 1 Radiant 2 Conductive 20 Contactive 200 Because heat-transfer equipment for solids is generally an adaptation of a primarily material-handling device, the area of heat transfer is often

where b1 = 1.22 (SI) or 1.0 (USCS), h = Uco = overall coefficient between the inner container surface and the fluid stream, 2

3

 Dp   Dp   Dp   Dp  b = 0 .2366 + 0 .0092  − 11 .837  + 18 .229  − 4 .0672   Dt   Dt   Dt   Dt 

where Dp = particle diameter, Dt = vessel diameter (note that Dp/Dt has units of feet per foot in the equation), G = superficial mass velocity, k = fluid

Clean-surface coefficients

Heating applications: Steam Steam Steam Steam Steam Steam Steam Steam Steam High temperature hot water High temperature heat-transfer oil Dowtherm or Aroclor Cooling applications: Water Water Water Water

Design coefficients, considering usual fouling in this service

Natural convection

Forced convection

Natural convection

Forced convection

250–500 50–70 40–60 20–40

300–550 110–140 100–130 70–90

100–200 40–45 35–40 15–30

150–275 60–110 50–100 60–80

15–35 35–45 35–45 2–4 20–40 115–140

50–70 45–55 45–55 5–10 70–90 200–250

15–25 20–35 25–35 1–3 15–30 70–100

40–60 35–45 40–50 4–8 60–80 110–160

Tar or asphalt

12–30

45–65

10–20

30–50

Tar or asphalt

15–30

50–60

12–20

30–50

110–135 10–15 8–12 7–10

195–245 25–45 20–30 18–26

65–95 7–10 5–8 4–7

105–155 15–25 10–20 8–15

Cold side Watery solution Light oils Medium lube oil Bunker C or No. 6 fuel oil Tar or asphalt Molten sulfur Molten paraffin Air or gases Molasses or corn sirup Watery solutions

Watery solution Quench oil Medium lube oil Molasses or corn sirup Air or gases Watery solution Watery solution

4

(11-49b)

TABLE 11-6 Panel Coils Immersed in Liquid: Overall Average Heat-Transfer Coefficients* U expressed in Btu/(h ⋅ ft2 ⋅ °F)

Hot side

(11-49a)

Water 2–4 5–10 1–3 4–8 Freon or ammonia 35–45 60–90 20–35 40–60 Calcium or sodium brine 100–120 175–200 50–75 80–125 ∗Tranter Manufacturing, Inc. note: To convert British thermal units per hour-square foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5.6783.

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT

11-25

TABLE 11-7 Jacketed Vessels: Overall Coefficients Overall U ∗ Fluid in vessel

Wall material

Btu/(h ⋅ ft2 ⋅ °F)

J/(m2 ⋅ s ⋅ K)

Steam Steam Steam Steam Steam

Water Aqueous solution Organics Light oil Heavy oil

Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel

150–300 80–200 50–150 60–160 10–50

850–1700 450–1140 285–850 340–910 57–285

Brine Brine Brine Brine Brine

Water Aqueous solution Organics Light oil Heavy oil

Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel

40–180 35–150 30–120 35–130 10–30

230–1625 200–850 170–680 200–740 57–170

Heat-transfer oil Heat-transfer oil Heat-transfer oil Heat-transfer oil Heat-transfer oil

Water Aqueous solution Organics Light oil Heavy oil

Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel

50–200 40–170 30–120 35–130 10–40

285–1140 230–965 170–680 200–740 57–230

Steam Steam Steam Steam Steam

Water Aqueous solution Organics Light oil Heavy oil

Glass-lined CS Glass-lined CS Glass-lined CS Glass-lined CS Glass-lined CS

70–100 50–85 30–70 40–75 10–40

400–570 285–480 170–400 230–425 57–230

Brine Brine Brine Brine Brine

Water Aqueous solution Organics Light oil Heavy oil

Glass-lined CS Glass-lined CS Glass-lined CS Glass-lined CS Glass-lined CS

30–80 25–70 20–60 25–65 10–30

170–450 140–400 115–340 140–370 57–170

30–80 25–70 25–65 20–70 10–35

170–450 140–400 140–370 115–400 57–200

Jacket fluid

Water Glass-lined CS Heat-transfer oil Heat-transfer oil Aqueous solution Glass-lined CS Heat-transfer oil Organics Glass-lined CS Heat-transfer oil Light oil Glass-lined CS Heat-transfer oil Heavy oil Glass-lined CS ∗Values listed are for moderate nonproximity agitation. CS = carbon steel.

thermal conductivity, µ = fluid viscosity, and c = fluid specific heat. Other correlations are those of Leva [Ind. Eng. Chem. 42: 2498 (1950)]: h = 0 .813

h = 0 .125

k − 6 D p / Dt  D pG  e  µ  Dt

k  D pG  Dt  µ 

0 .90

for

Dp Dt

0 .75

for

0 .35
30

(11-56)

where θ = solids-bed passage time through the shell, min; Sr = shell slope; L = shell length; Y = percent fill; and b′ = proportionality constant . Vibratory devices which constantly agitate the solids bed maintain a relatively constant value for Uco such that Uco = a′csαe

where NRe is based on particle diameter and superficial fluid velocity . Values of a and m are as follows:

(11-55b)

where the second term of Eq . (11-55b) is positive for counterflow of air, negative for concurrent flow, and zero for indirect rotary shells . From these equations a predictive equation is developed for rotary-shell devices, which is analogous to Eq . (11-54): U co =

11-27

(11-58)

a

m

1 .58 0 .95 0 .92 0 .90

−0 .40 −0 .30 −0 .28 −0 .28

Glaser and Thodos [Am. Inst. Chem. Eng. J. 4: 63 (1958)] give a correlation involving individual particle shape and bed porosity . Kunii and Suzuki [Int. J. Heat Mass Transfer 10: 845 (1967)] discuss heat and mass transfer in packed beds of fine particles . Particle-to-fluid heat-transfer coefficients in gas fluidized beds are predicted by the relation (F . A . Zenz and D . F . Othmer, Fluidization and Fluid Particle Systems, Reinhold, original from University of Michigan, 1960) hD p k

= 0 .017( D pGmf /µ)1 .21

(11-59a)

where Gmf is the superficial mass velocity at incipient fluidization . A more general equation is given by Frantz [Chem. Eng. 69(20): 89 (1962)]: hD p k

= 0 .015(DpG/µ)1 .6(cµ/k)0 .67

(11-59b)

where h is based on true gas temperature . Bed-to-wall coefficients in dilute-phase transport generally can be predicted by an equation of the form of Eq . (5-50) . For example, Bonilla et al . (American Institute of Chemical Engineers Heat Transfer Symp ., Atlantic City, N .J ., December 1951) found for 1- to 2-µm chalk particles in water up to 8 percent by volume that the coefficient on Eq . (5-50) is 0 .029 where k, ρ, and c were arithmetic weighted averages and the viscosity was taken equal to the coefficient of rigidity . Farber and Morley [Ind. Eng. Chem. 49: 1143 (1957)] found the coefficient on Eq . (5-50) to be 0 .025 for the upward flow of air transporting silica-alumina catalyst particles at rates less than 2 kg solids/kg air (2 lb solids/lb air) . Physical properties used were those of the transporting gas . See Zenz and Othmer (Fluidization and Fluid Particle Systems, Reinhold, original from University of Michigan, 1960) for additional details covering wider porosity ranges . The thermal performance of cylindrical rotating shell units is based upon a volumetric heat-transfer coefficient U ct =

Q Vr ( ∆t )

(11-60a)

11-28

HEAT-TRANSFER EQUIPMENT

where Vr = volume . This term indirectly includes an area factor so that thermal performance is governed by a cross-sectional area rather than by a heated area . Use of the heated area is possible, however: U ct =

Q (∆ 3t 2 ) A

U ct =

or

Q (∆ 3t 4 ) A

(11-60b)

For heat transfer directly to solids, predictive equations give directly the volume V or the heat-transfer area A, as determined by heat balance and air flow rate . For devices with gas flow normal to a fluidized-solids bed, A=

Q ∆t p (cρ g )( Fg )

(11-61)

where ∆tp = ∆3t4 as explained above, cρ = volumetric specific heat, and Fg = gas flow rate . For air, cρ at normal temperature and pressure is about 1100 J/(m3 ⋅ K) [0 .0167 Btu/( ft3 ⋅ °F)]; so A=

bQ ( ∆ 3t 4 ) Fg

(11-62)

where b = 0 .0009 (SI) or 60 (USCS) . Another such equation—for stationary vertical-shell and some horizontal rotary-shell and pneumatic-transport devices in which the gas flow is parallel with and directionally concurrent with the fluidized bed—is the same as Eq . (11-62) with ∆3t4 replaced by ∆3t2 . If the operation involves drying or chemical reaction, the heat load Q is much greater than for sensible-heat transfer only . Also the gas flow rate to provide moisture carry-off and stoichiometric requirements must be considered and simultaneously provided . A good treatise on the latter is given by Pinkey and Plint (Miner. Process. June 1968, p . 17) . Evaporative cooling is a special patented technique that often can be advantageously employed in cooling solids by contactive heat transfer . The drying operation is terminated before the desired final moisture content is reached, and the solids temperature is at a moderate value . The cooling operation involves contacting the burden (preferably fluidized) with air at normal temperature and pressure . The air adiabatically absorbs and carries off a large part of the moisture and, in doing so, picks up heat from the warm (or hot) solids particles to supply the latent heat demand of evaporation . For entering solids at temperatures of 180°C (350°F) and less with normal heat capacity values of 0 .85 to 1 .0 kJ/(kg ⋅ K) [0 .2 to 0 .25 Btu/(lb ⋅ °F)], the effect can be calculated by the following procedure: 1 . Use 285 m3 (1000 ft3) of air flow at normal temperature and pressure at 40 percent relative humidity to carry off 0 .45 kg (1 lb) of water [latent heat 2326 kJ/kg (1000 Btu/lb)] and to lower temperature by 22°C to 28°C (40°F to 50°F) . 2 . Use the lowered solids temperature as t3 and calculate the remainder of the heat to be removed in the regular manner by Eq . (11-62) . The required air quantity for (2) must be equal to or greater than that for (1) . When the solids heat capacity is higher (as is the case for most organic materials), the temperature reduction is inversely proportional to the heat capacity . A nominal result of this technique is that the required air flow rate and equipment size are about two-thirds of that when evaporative cooling is not used . See Sec . 20 for equipment available . Convective Heat Transfer Equipment using the true convective mechanism when the heated particles are mixed with (and remain with) the cold particles is used so infrequently that performance and sizing equations are not available . Such a device is the pebble heater as described by Norton (Chem. Metall. Eng. July 1946) . For operation data, see Sec . 9 . Convective heat transfer is often used as an adjunct to other modes, particularly to the conductive mode . It is often more convenient to consider the agitative effect a performance improvement influence on the thermal diffusivity factor a, modifying it to ae, the effective value . A pseudo-convective heat-transfer operation is one in which the heating gas (generally air) is passed over a bed of solids . Its use is almost exclusively limited to drying operations (see Sec . 12, tray and shelf dryers) . The operation, sometimes termed direct, is more akin to the conductive mechanism . For this operation, Tsao and Wheelock [Chem. Eng. 74(13): 201 (1967)] predict the heat-transfer coefficient when radiative and conductive effects are absent by h = bG

0 .8

(11-63)

where b = 14 .31 (SI) or 0 .0128 (USCS), h = convective heat transfer, and G = gas flow rate . The drying rate is given by h(Td − Tw ) (11-64) λ 2 where Kcυ = drying rate, for constant-rate period, kg/(m ⋅ s) [lb/(h ⋅ ft2)]; Td and Tw = respective dry-bulb and wet-bulb temperatures of the air; and K cυ =

λ = latent heat of evaporation at temperature Tw . Note here that the temperature-difference determination of the operation is a simple linear one and of a steady-state nature . Also note that the operation is a function of the air flow rate . Further, the solids are granular with a fairly uniform size, have reasonable capillary voids, are of a firm texture, and have the particle surface wetted . The coefficient h is also used to predict (in the constant-rate period) the total overall air-to-solids heat-transfer coefficient Ucυ by 1/Ucυ = 1/h + x/k

(11-65)

where k = solids thermal conductivity and x is evaluated from z( Xc − Xo ) Xc − Xe

x=

(11-65a)

where z = bed (or slab) thickness and is the total thickness when drying and/or heat transfer is from one side only but is one-half of the thickness when drying and/or heat transfer is simultaneously from both sides; Xo, Xc, and Xe are, respectively, the initial (or feed-stock), critical, and equilibrium (with the drying air) moisture contents of the solids, all in kg H2O/kg dry solids (lb H2O/lb dry solids) . This coefficient is used to predict the instantaneous drying rate −

W dX U cυ (Td − Tw ) = A dθ λ

(11-66)

By rearrangement, this can be made into a design equation as follows: A=−

W λ (dX /d θ) U cυ (Td − Tw )

(11-67)

where W = weight of dry solids in the equipment, λ = latent heat of evaporation, and θ = drying time . The reader should refer to the full reference article by Tsao and Wheelock for other solids conditions qualifying the use of these equations . Radiative Heat Transfer Heat-transfer equipment using the radiative mechanism for divided solids is constructed as a “table” which is stationary, as with trays, or moving, as with a belt, and/or agitated, as with a vibrated pan, to distribute and expose the burden in a plane parallel to (but not in contact with) the plane of the radiant-heat sources . Presence of air is not necessary (see Sec . 12 for vacuum-shelf dryers and Sec . 22 for resublimation) . In fact, if air in the intervening space has a high humidity or CO2 content, it acts as an energy absorber, thereby depressing the performance . For the radiative mechanism, the temperature difference is evaluated as Dt = T e4 − T r4

(11-68)

where Te = absolute temperature of the radiant-heat source, K (°R), and Tr = absolute temperature of the bed of divided solids, K (°R) . Numerical values for Ura for use in the general design equation may be calculated from experimental data by U ra =

Q A (Te4 − Tr4 )

(11-69)

The literature to date offers practically no such values . However, enough proprietary work has been performed to present a reliable evaluation for the comparison of mechanisms (see Introduction: Modes of Heat Transfer) . For the radiative mechanism of heat transfer to solids, the rate equation for parallel-surface operations is qra = b(Te4 − Tr4 )i f

(11-70)

where b = (5 .67)(10−8) (SI) or (0 .172)(10−8) (USCS), qra = radiative heat flux, and if = an interchange factor which is evaluated from 1/if = 1/es + 1/er − 1

(11-70a)

where e s = coefficient of emissivity of the source and er = “emissivity” (or “absorptivity”) of the receiver, which is the divided-solids bed . For the emissivity values, particularly of the heat source es, an important consideration is the wavelength at which the radiant source emits as well as the flux density of the emission . Data for these values are available from Polentz [Chem. Eng. 65(7): 137; (8): 151 (1958)] and Adlam (Radiant Heating, Industrial Press, New York, p . 40) . Both give radiated flux density versus wavelength at varying temperatures . Often the seemingly cooler but longer wavelength source is the better selection . Emitting sources are (1) pipes, tubes, and platters carrying steam, 2100 kPa (300 lbf/in2); (2) electric conducting glass plates, 150°C to 315°C (300°F to 600°F) range; (3) lightbulb type (tungsten-filament resistance

THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT heater); (4) modules of refractory brick for gas burning at high temperatures and high fluxes; and (5) modules of quartz tubes, also operable at high temperatures and fluxes . For some emissivity values see Table 11-10 . For predictive work, where Ura is desired for sizing, this can be obtained by dividing the flux rate qra by ∆t: U ra = qra /(Te4 − Tr4 ) = i f b

TABLE 11-10

(11-71)

11-29

where b = (5 .67)(10−8) (SI) or (0 .172)(10−8) (USCS) . Hence A=

Q U ra (Te4 − Tr4 )

(11-72)

where A = bed area of solids in the equipment .

Normal Total Emissivity of Various Surfaces A . Metals and Their Oxides Surface

Aluminum Highly polished plate, 98 .3% pure Polished plate Rough plate Oxidized at 1110°F Aluminum-surfaced roofing Calorized surfaces, heated at 1110°F . Copper Steel Brass Highly polished: 73 .2% Cu, 26 .7% Zn 62 .4% Cu, 36 .8% Zn, 0 .4% Pb, 0 .3% Al 82 .9% Cu, 17 .0% Zn Hard rolled, polished: But direction of polishing visible But somewhat attacked But traces of stearin from polish left on Polished Rolled plate, natural surface Rubbed with coarse emery Dull plate Oxidized by heating at 1110°F Chromium; see Nickel Alloys for Ni-Cr steels Copper Carefully polished electrolytic copper Commercial, emeried, polished, but pits remaining Commercial, scraped shiny but not mirror-like Polished Plate, heated long time, covered with thick oxide layer Plate heated at 1110°F Cuprous oxide Molten copper Gold Pure, highly polished Iron and steel Metallic surfaces (or very thin oxide layer): Electrolytic iron, highly polished Polished iron Iron freshly emeried Cast iron, polished Wrought iron, highly polished Cast iron, newly turned Polished steel casting Ground sheet steel Smooth sheet iron Cast iron, turned on lathe Oxidized surfaces: Iron plate, pickled, then rusted red Completely rusted Rolled sheet steel Oxidized iron Cast iron, oxidized at 1100°F Steel, oxidized at 1100°F Smooth oxidized electrolytic iron Iron oxide Rough ingot iron

t, °F .∗

Emissivity∗

440–1070 73 78 390–1110 100

0 .039–0 .057 0 .040 0 .055 0 .11–0 .19 0 .216

390–1110 390–1110

0 .18–0 .19 0 .52–0 .57

476–674 494–710 530

0 .028–0 .031 0 .033–0 .037 0 .030

70 73 75 100–600 72 72 120–660 390–1110 100–1000

0 .038 0 .043 0 .053 0 .096 0 .06 0 .20 0 .22 0 .61–0 .59 0 .08–0 .26

176

0 .018

66

0 .030

72 242

0 .072 0 .023

77 390–1110 1470–2010 1970–2330

0 .78 0 .57 0 .66–0 .54 0 .16–0 .13

440–1160

0 .018–0 .035

350–440 800–1880 68 392 100–480 72 1420–1900 1720–2010 1650–1900 1620–1810

0 .052–0 .064 0 .144–0 .377 0 .242 0 .21 0 .28 0 .435 0 .52–0 .56 0 .55–0 .61 0 .55–0 .60 0 .60–0 .70

68 67 70 212 390–1110 390–1110 260–980 930–2190 1700–2040

0 .612 0 .685 0 .657 0 .736 0 .64–0 .78 0 .79 0 .78–0 .82 0 .85–0 .89 0 .87–0 .95

Surface Sheet steel, strong rough oxide layer Dense shiny oxide layer Cast plate: Smooth Rough Cast iron, rough, strongly oxidized Wrought iron, dull oxidized Steel plate, rough High temperature alloy steels (see Nickel Alloys) Molten metal Cast iron Mild steel Lead Pure (99 .96%), unoxidized Gray oxidized Oxidized at 390°F Mercury Molybdenum filament Monel metal, oxidized at 1110°F Nickel Electroplated on polished iron, then polished Technically pure (98 .9% Ni, + Mn), polished Electropolated on pickled iron, not polished Wire Plate, oxidized by heating at 1110°F Nickel oxide Nickel alloys Chromnickel Nickelin (18–32 Ni; 55–68 Cu; 20 Zn), gray oxidized KA-2S alloy steel (8% Ni; 18% Cr), light silvery, rough, brown, after heating After 42 hr . heating at 980°F NCT-3 alloy (20% Ni; 25% Cr), brown, splotched, oxidized from service NCT-6 alloy (60% Ni; 12% Cr), smooth, black, firm adhesive oxide coat from service Platinum Pure, polished plate Strip Filament Wire Silver Polished, pure Polished Steel, see Iron Tantalum filament Tin—bright tinned iron sheet Tungsten Filament, aged Filament Zinc Commercial, 99 .1% pure, polished Oxidized by heating at 750°F . Galvanized sheet iron, fairly bright Galvanized sheet iron, gray oxidized

t, °F .∗ 75 75

Emissivity∗ 0 .80 0 .82

73 73 100–480 70–680 100–700

0 .80 0 .82 0 .95 0 .94 0 .94–0 .97

2370–2550 2910–3270

0 .29 0 .28

260–440 75 390 32–212 1340–4700 390–1110

0 .057–0 .075 0 .281 0 .63 0 .09–0 .12 0 .096–0 .292 0 .41–0 .46

74

0 .045

440–710

0 .07–0 .087

68 368–1844 390–1110 1200–2290

0 .11 0 .096–0 .186 0 .37–0 .48 0 .59–0 .86

125–1894

0 .64–0 .76

70

0 .262

420–914 420–980

0 .44–0 .36 0 .62–0 .73

420–980

0 .90–0 .97

520–1045

0 .89–0 .82

440–1160 1700–2960 80–2240 440–2510

0 .054–0 .104 0 .12–0 .17 0 .036–0 .192 0 .073–0 .182

440–1160 100–700

0 .0198–0 .0324 0 .0221–0 .0312

2420–5430 76

0 .194–0 .31 0 .043 and 0 .064

80–6000 6000

0 .032–0 .35 0 .39

440–620 750 82 75

0 .045–0 .053 0 .11 0 .228 0 .276

260–1160

0 .81–0 .79

1900–2560 206–520 209–362

0 .526 0 .952 0 .959–0 .947

B . Refractories, Building Materials, Paints, and Miscellaneous Asbestos Board Paper Brick Red, rough, but no gross irregularities Silica, unglazed, rough Silica, glazed, rough Grog brick, glazed See Refractory Materials below .

74 100–700 70 1832 2012 2012

0 .96 0 .93–0 .945 0 .93 0 .80 0 .85 0 .75

Carbon T-carbon (Gebr . Siemens) 0 .9% ash (this started with emissivity at 260°F . of 0 .72, but on heating changed to values given) Carbon filament Candle soot Lampblack-waterglass coating

11-30

HEAT-TRANSFER EQUIPMENT

TABLE 11-10

Normal Total Emissivity of Various Surfaces (Continued ) B . Refractories, Building Materials, Paints, and Miscellaneous Surface

t, °F .∗

Emissivity∗

Surface

t, °F .∗

Emissivity∗

Same 260–440 0 .957–0 .952 Oil paints, sixteen different, all colors 212 0 .92–0 .96 Thin layer on iron plate 69 0 .927 Aluminum paints and lacquers Thick coat 68 0 .967 10% Al, 22% lacquer body, on rough or Lampblack, 0 .003 in . or thicker 100–700 0 .945 smooth surface 212 0 .52 Enamel, white fused, on iron 66 0 .897 26% Al, 27% lacquer body, on rough or Glass, smooth 72 0 .937 smooth surface 212 0 .3 Gypsum, 0 .02 in . thick on smooth or Other Al paints, varying age and Al blackened plate 70 0 .903 content 212 0 .27–0 .67 Marble, light gray, polished 72 0 .931 Al lacquer, varnish binder, on rough plate 70 0 .39 Oak, planed 70 0 .895 Al paint, after heating to 620°F 300–600 0 .35 Oil layers on polished nickel (lube oil) 68 Paper, thin Polished surface, alone 0 .045 Pasted on tinned iron plate 66 0 .924 +0 .001-in . oil 0 .27 On rough iron plate 66 0 .929 +0 .002-in . oil 0 .46 On black lacquered plate 66 0 .944 +0 .005-in . oil 0 .72 Plaster, rough lime 50–190 0 .91 Infinitely thick oil layer 0 .82 Porcelain, glazed 72 0 .924 Oil layers on aluminum foil (linseed oil) Quartz, rough, fused 70 0 .932 Al foil 212 0 .087† Refractory materials, 40 different 1110–1830 +1 coat oil 212 0 .561 poor radiators  0 .65 − 0 .75    0 .70 +2 coats oil 212 0 .574  0 .80 − 0 .85  Paints, lacquers, varnishes good radiators   Snowhite enamel varnish or rough iron  0 .85 − 0 .90  plate 73 0 .906 Roofing paper 69 0 .91 Black shiny lacquer, sprayed on iron 76 0 .875 Rubber Black shiny shellac on tinned iron sheet 70 0 .821 Hard, glossy plate 74 0 .945 Black matte shellac 170–295 0 .91 Soft, gray, rough (reclaimed) 76 0 .859 Black lacquer 100–200 0 .80–0 .95 Serpentine, polished 74 0 .900 Flat black lacquer 100–200 0 .96–0 .98 Water 32–212 0 .95–0 .963 White lacquer 100–200 0 .80–0 .95 ∗When two temperatures and two emissivities are given, they correspond, first to first and second to second, and linear interpolation is permissible . °C = (°F − 32)/1 .8 . † Although this value is probably high, it is given for comparison with the data by the same investigator to show the effect of oil layers . See Aluminum, Part A of this table .

} }{

These are important considerations in the application of the foregoing equations: 1 . Since the temperature of the emitter is generally known (preselected or readily determined in an actual operation), the absorptivity value er is the unknown . This absorptivity is partly a measure of the ability of radiant heat to penetrate the body of a solid particle (or a moisture film) instantly, as compared with diffusional heat transfer by conduction . Such instant penetration greatly reduces processing time and case-hardening effects . Moisture release and other mass transfer, however, still progress by diffusional means . 2 . In one of the major applications of radiative devices (drying), the surfaceheld moisture is a good heat absorber in the 2- to 7-µm wavelength range . Therefore, the absorptivity, color, and nature of the solids are of little importance . 3 . For drying, it is important to provide a small amount of venting air to carry away the water vapor . This is needed for two reasons . First, water vapor is a good absorber of 2- to 7-µm energy . Second, water vapor accumulation depresses further vapor release by the solids . If the air over the solids is kept fairly dry by venting, very little heat is carried off, because dry air does not absorb radiant heat . 4 . For some of the devices, when the overall conversion efficiency has been determined, the application is primarily a matter of computing the required heat load . It should be kept in mind, however, that there are two conversion efficiencies that must be differentiated . One measure of efficiency is that with which the source converts input energy to output radiated energy . The other is the overall efficiency that measures the proportion of input energy that is actually absorbed by the solids . This latter is, of course, the one that really matters . Other applications of radiant-heat processing of solids are the toasting, puffing, and baking of foods and the low-temperature roasting and preheating of plastic powder or pellets . Since the determination of heat loads for these operations is not well established, bench and pilot tests are generally necessary . Such processes require a fast input of heat and higher heat fluxes than can generally be provided by indirect equipment . Because of this, infraredequipment size and space requirements are often much lower . Although direct contactive heat transfer can provide high temperatures and heat concentrations and at the same time be small in size, its use may not always be preferable because of undesired side effects such as drying, contamination, case hardening, shrinkage, off color, and dusting . When radiating and receiving surfaces are not in parallel, as in rotary-kiln devices, and the solids burden bed may be only intermittently exposed and/or agitated, the calculation and procedures become very complex, with photometric methods of optics requiring consideration . The following equation for heat transfer, which allows for convective effects, is commonly used by designers of high-temperature furnaces:

where b = 5 .67 (SI) or 0 .172 (USCS); Q = total furnace heat transfer; σ = an emissivity factor with recommended values of 0 .74 for gas, 0 .75 for oil, and 0 .81 for coal; A = effective area for absorbing heat (here the solids burden exposed area); Tg = exiting combustion gas absolute temperature; and Ts = absorbing surface temperature . In rotary devices, reradiation from the exposed shell surface to the solids bed is a major design consideration . A treatise on furnaces, including radiative heat-transfer effects, is given by Ellwood and Danatos [Chem. Eng. 73(8): 174 (1966)] . For discussion of radiation heat-transfer computational methods, heat fluxes obtainable, and emissivity values, see Schornshort and Viskanta (ASME Paper 68-H 7-32), Sherman (ASME Paper 56-A-111), and the following subsection .

qra = Q/A = bs [(Tg/100)4 − (Ts/100)4]

FIG. 11-34 Scraper blade of scraped-surface exchanger . (Henry Vogt Machine Co., Inc.)

(11-73)

SCRAPED-SURFACE EXCHANGERS Scraped-surface exchangers have a rotating element with spring-loaded scraper blades to scrape the inside surface (Fig . 11-34) . Generally a doublepipe construction is used; the scraping mechanism is in the inner pipe,

TEMA-STYLE SHELL-AND-TUBE HEAT EXCHANGERS where the process fluid flows; and the cooling or heating medium is in the outer pipe . The most common size has 6-in inside and 8-in outside pipes . Also available are 3- by 4-in, 8- by 10-in, and 12- by 14-in sizes (in × 25 .4 = mm) . These double-pipe units are commonly connected in series and arranged in double stands . For chilling and crystallizing with an evaporating refrigerant, a 27-in shell with seven 6-in pipes is available (Henry Vogt Machine Co .) . In direct contact with the scraped surface is the process fluid which may deposit crystals upon chilling or be extremely fouling or of very high viscosity . Motors, chain

11-31

drives, appropriate guards, and so on are required for the rotating element . For chilling service with a refrigerant in the outer shell, an accumulator drum is mounted on top of the unit . Scraped-surface exchangers are particularly suitable for heat transfer with crystallization, heat transfer with severe fouling of surfaces, heat transfer with solvent extraction, and heat transfer of high-viscosity fluids . They are extensively used in paraffin-wax plants and in petrochemical plants for crystallization .

TEMA-STYLE SHELL-AND-TUBE HEAT EXCHANGERS TYPES AND DEFINITIONS

Exchanger

TEMA-style shell-and-tube-type exchangers constitute the bulk of the unfired heat-transfer equipment in chemical-process plants, although increasing emphasis has been developing in other designs . These exchangers are illustrated in Fig . 11-35, and their features are summarized in Table 11-11 . TEMA Numbering and Type Designation Recommended practice for the designation of TEMA-style shell-and-tube heat exchangers by numbers and letters has been established by the Tubular Exchanger Manufacturers Association . This information from the sixth edition of the TEMA Standards is reproduced in the following paragraphs . It is recommended that heat exchanger size and type be designated by numbers and letters . 1 . Size.  Sizes of shells (and tube bundles) shall be designated by numbers describing shell (and tube-bundle) diameters and tube lengths as follows: 2. Diameter.  The nominal diameter shall be the inside diameter of the shell in inches, rounded off to the nearest integer. For kettle reboilers the nominal diameter shall be the port diameter followed by the shell diameter, each rounded off to the nearest integer. 3. Length.  The nominal length shall be the tube length in inches. Tube length for straight tubes shall be taken as the actual overall length. For U tubes the length shall be taken as the straight length from end of tube to bend tangent. 4. Type.  Type designation shall be by letters describing stationary head, shell (omitted for bundles only), and rear head, in that order, as indicated in Fig. 11-1. Typical Examples 1. Split-ring floating heat exchanger with removable channel and cover, single-pass shell, 591-mm (23¼-in) inside diameter with tubes 4.9 m (16 ft) long. SIZE 23–192 TYPE AES. 2. U-tube exchanger with bonnet-type stationary head, split-flow shell, 483-mm (19-in) inside diameter with tubes 21-m (7-ft) straight length. SIZE 19–84 TYPE GBU. 3. Pull-through floating-heat-kettle type of reboiler having stationary head integral with tube sheet, 584-mm (23-in) port diameter and 940-mm (37-in) inside shell diameter with tubes 4.9-m (16-ft) long. SIZE 23/37–192 TYPE CKT. 4. Fixed-tube sheet exchanger with removable channel and cover, bonnet-type rear head, two-pass shell, 841-mm (33⅓-in) diameter with tubes 2 .4 m (8 ft) long . SIZE 33–96 TYPE AFM . 5 . Fixed-tube sheet exchanger having stationary and rear heads integral with tube sheets, single-pass shell, 432-mm (17-in) inside diameter with tubes 4 .9 m (16 ft) long . SIZE 17–192 TYPE CEN . Functional Definitions Heat-transfer equipment can be designated by type (e .g ., fixed tube sheet, outside packed head, etc .) or by function (chiller, condenser, cooler, etc .) . Almost any type of unit can be used to perform any of or all the listed functions . Many of these terms have been defined by Donahue [Pet. Process. 103 (March 1956)] . Equipment Chiller Condenser Partial condenser

Final condenser Cooler

Function Cools a fluid to a temperature below that obtainable if only water were used as a coolant . It uses a refrigerant such as ammonia or Freon . Condenses a vapor or mixture of vapors, either alone or in the presence of a noncondensible gas . Condenses vapors at a point high enough to provide a temperature difference sufficient to preheat a cold stream of process fluid . This saves heat and eliminates the need for providing a separate preheater (using flame or steam) . Condenses the vapors to a final storage temperature of approximately 37 .8°C (100°F) . It uses water cooling, which means that the transferred heat is lost to the process . Cools liquids or gases by means of water .

Heater Reboiler Thermosiphon reboiler Forced-circulation reboiler Steam generator Superheater Vaporizer Waste-heat boiler

Performs a double function: (1) heats a cold fluid by (2) using a hot fluid which it cools . None of the transferred heat is lost . Imparts sensible heat to a liquid or a gas by means of condensing steam or Dowtherm . Connected to the bottom of a fractionating tower, it provides the reboil heat necessary for distillation . The heating medium may be either steam or a hot-process fluid . Natural circulation of the boiling medium is obtained by maintaining sufficient liquid head to provide for circulation . A pump is used to force liquid through the reboiler . Generates steam for use elsewhere in the plant by using the available high-level heat in tar or a heavy oil . Heats a vapor above the saturation temperature . A heater that vaporizes part of the liquid . Produces steam; similar to steam generator, except that the heating medium is a hot gas or liquid produced in a chemical reaction .

GENERAL DESIGN CONSIDERATIONS Selection of Flow Path In selecting the flow path for two fluids through an exchanger, several general approaches are used . The tube-side fluid is more corrosive or dirtier or at a higher pressure . The shell-side fluid is a liquid of high viscosity or a gas . When alloy construction for one of the two fluids is required, a carbonsteel shell combined with alloy tube-side parts is less expensive than alloy in contact with the shell-side fluid combined with carbon-steel headers . Cleaning of the inside of tubes is more readily done than cleaning of exterior surfaces . For gauge pressures in excess of 2068 kPa (300 lbf/in2) for one of the fluids, the less expensive construction has the high-pressure fluid in the tubes . For a given pressure drop, higher heat-transfer coefficients are obtained on the shell side than on the tube side . Heat exchanger shutdowns are most often caused by fouling, corrosion, and erosion . Construction Codes “Rules for Construction of Pressure Vessels, Division 1,” which is part of Section VIII of the ASME Boiler and Pressure Vessel Code (American Society of Mechanical Engineers), serves as a construction code by providing minimum standards . New editions of the code are usually issued every 3 years . Interim revisions are made semiannually in the form of addenda . Compliance with ASME Code requirements is mandatory in much of the United States and Canada . Originally these rules were not prepared for heat exchangers . However, the welded joint between tube sheet and shell of the fixed-tube-sheet heat exchanger is now included . A nonmandatory appendix on from the tube to tube-sheet joints is also included . Additional rules for heat exchangers are being developed . Standards of Tubular Exchanger Manufacturers Association, 6th ed ., 1978 (commonly referred to as the TEMA Standards), serve to supplement and define the ASME Code for all shell-and-tube type of heat exchanger applications (other than double-pipe construction) . TEMA Class R design is “for the generally severe requirements of petroleum and related processing applications . Equipment fabricated in accordance with these standards is designed for safety and durability under the rigorous service and maintenance conditions in such applications .” TEMA Class C design is “for the generally moderate requirements of commercial and general process applications,” while TEMA Class B is “for chemical process service .” The mechanical design requirements are identical for all three classes of construction . The differences between the TEMA classes are minor and were listed by Rubin [Hydrocarbon Process 59: 92 (June 1980)] .

11-32

HEAT-TRANSFER EQUIPMENT

FIG. 11-35 TEMA-type designations for shell-and-tube heat exchangers . (Standards of Tubular Exchanger Manufacturers Association, 6th ed., 1978.)

TEMA-STYLE SHELL-AND-TUBE HEAT EXCHANGERS TABLE 11-11

11-33

Features of TEMA Shell-and-Tube-Type Exchangers*

Type of design T .E .M .A . rear-head type Relative cost increases from A (least expensive) through E (most expensive) Provision for differential expansion Removable bundle Replacement bundle possible Individual tubes replaceable Tube cleaning by chemicals inside and outside Interior tube cleaning mechanically Exterior tube cleaning mechanically: Triangular pitch Square pitch Hydraulic-jet cleaning: Tube interior Tube exterior Double tube sheet feasible Number of tube passes Internal gaskets eliminated

U-tube

Packed lantern-ring floating head

Internal floating head (split backing ring)

Outside-packed floating head

Pull-through floating head

L or M or N

U

W

S

P

T

B Expansion joint in shell No No Yes

A Individual tubes free to expand

C Floating head

E Floating head

D Floating head

E Floating head

Yes Yes Only those in outside row†

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Yes Yes

Yes Special tools required

Yes Yes

Yes Yes

Yes Yes

Yes Yes

No No

No‡ Yes

No‡ Yes

No‡ Yes

No‡ Yes

No‡ Yes

Yes No Yes No practical limitations Yes

Special tools required Yes Yes Any even number possible Yes

Yes Yes No Limited to one or two passes Yes

Yes Yes No No practical limitations§ No

Yes Yes Yes No practical limitations Yes

Yes Yes No No practical limitations§ No

Fixed tube sheet

note: Relative costs A and B are not significantly different and interchange for long lengths of tubing . *Modified from page a-8 of the Patterson-Kelley Co . Manual No . 700A, Heat Exchangers . † U-tube bundles have been built with tube supports which permit the U-bends to be spread apart and tubes inside of the bundle replaced . ‡ Normal triangular pitch does not permit mechanical cleaning . With a wide triangular pitch, which is equal to 2 (tube diameter plus cleaning lane)/ 3, mechanical cleaning is possible on removable bundles . This wide spacing is infrequently used . § For odd number of tube side passes, floating head requires packed joint or expansion joint.

Among the topics of the TEMA Standards are nomenclature, fabrication tolerances, inspection, guarantees, tubes, shells, baffles and support plates, floating heads, gaskets, tube sheets, channels, nozzles, end flanges and bolting, material specifications, and fouling resistances. Shell and Tube Heat Exchangers for General Refinery Services, API Standard 660, 4th ed., 1982, is published by the American Petroleum Institute to supplement both the TEMA Standards and the ASME Code. Many companies in the chemical and petroleum processing fields have their own standards to supplement these various requirements. The Interrelationships between Codes, Standards, and Customer Specifications for Process Heat Transfer Equipment is a symposium volume which was edited by F. L. Rubin and published by ASME in December 1979. (See discussion of pressure vessel codes in Sec. 6.) Design pressures and temperatures for exchangers usually are specified with a margin of safety beyond the conditions expected in service. Design pressure is generally about 172 kPa (25 lbf/in2) greater than the maximum expected during operation or at pump shutoff. Design temperature is commonly 14°C (25°F) greater than the maximum temperature in service. Tube Bundle Vibration Damage from tube vibration has become an increasing problem as plate baffled heat exchangers are designed for higher flow rates and pressure drops. The most effective method of dealing with this problem is the avoidance of cross-flow by use of tube support baffles which promote only longitudinal flow. However, even then, strict attention must be paid to the bundle area under the shell inlet nozzle where flow is introduced through the side of the shell. TEMA has devoted an entire section in its standards to this topic. In general, the mechanisms of tube vibration are as follows: Vortex Shedding The vortex-shedding frequency of the fluid in crossflow over the tubes may coincide with a natural frequency of the tubes and excite large resonant vibration amplitudes. Fluid-Elastic Coupling Fluid flowing over tubes causes them to vibrate with a whirling motion. The mechanism of fluid-elastic coupling occurs when a “critical” velocity is exceeded and the vibration then becomes selfexcited and grows in amplitude. This mechanism frequently occurs in process heat exchangers which suffer vibration damage. Pressure Fluctuation Turbulent pressure fluctuations which develop in the wake of a cylinder or are carried to the cylinder from upstream may provide a potential mechanism for tube vibration. The tubes respond to the portion of the energy spectrum that is close to their natural frequency. Acoustic Coupling When the shell-side fluid is a low-density gas, acoustic resonance or coupling develops when the standing waves in the shell are in phase with vortex shedding from the tubes. The standing waves are perpendicular to the axis of the tubes and to the direction of cross-flow. Damage to the tubes is rare. However, the noise can be extremely painful.

Testing Upon completion of shop fabrication and also during maintenance operations, it is desirable hydrostatically to test the shell side of tubular exchangers so that visual examination of tube ends can be made. Leaking tubes can be readily located and serviced. When leaks are determined without access to the tube ends, it is necessary to reroll or reweld all the tube–tube-sheet joints with possible damage to the satisfactory joints. Testing for leaks in heat exchangers was discussed by Rubin [Chem. Eng. 68: 160–166 (July 24, 1961)]. Performance testing of heat exchangers is described in the American Institute of Chemical Engineers’ Standard Testing Procedure for Heat Exchangers, Sec. 1, “Sensible Heat Transfer in Shell-and-Tube-Type Equipment.” PRINCIPAL TYPES OF CONSTRUCTION Figure 11-36 shows details of the construction of the TEMA types of shelland-tube heat exchangers. These and other types are discussed in the following paragraphs. Fixed-Tube-Sheet Heat Exchangers Fixed-tube-sheet exchangers (Fig. 11-36b) are used more often than any other type, and the frequency of use has been increasing in recent years. The tubesheets are welded to the shell. Usually these extend beyond the shell and serve as flanges to which the tube-side headers are bolted. This construction requires that the shelland-tube-sheet materials be weldable to each other. When such welding is not possible, a “blind”-gasket type of construction is utilized. The blind gasket is not accessible for maintenance or replacement once the unit has been constructed. This construction is used for steam surface condensers, which operate under vacuum. The tube-side header (or channel) may be welded to the tubesheet, as shown in Fig. 11-35 for type C and N heads. This type of construction is less costly than types B and M or A and L and still offers the advantage that tubes may be examined and replaced without disturbing the tube-side piping connections. There is no limitation on the number of tube-side passes. Shell-side passes can number one or more, although shells with more than two shell-side passes are rarely used. Tubes can completely fill the heat exchanger shell. Clearance between the outermost tubes and the shell is only the minimum necessary for fabrication. Between the inside of the shell and the baffles some clearance must be provided so that baffles can slide into the shell. Fabrication tolerances then require some additional clearance between the outside of the baffles and the outermost tubes. The edge distance between the outer tube limit (OTL) and the baffle diameter must be sufficient to prevent vibration of the tubes from breaking through the baffle holes. The outermost tube must be contained within the OTL. Clearances between the inside shell

11-34

HEAT-TRANSFER EQUIPMENT

(a)

(b) FIG. 11-36

Heat exchanger component nomenclature . (a) Internal-floating-head exchanger (with floating-head backing device) . Type AES . (b) Fixed-tube-sheet exchanger . Type BEM . (Standards of the Tubular Exchanger Manufacturers Association, 6th ed., 1978.)

diameter and OTL are 13 mm (½ in) for 635 mm (25 in) inside-diameter (ID) shells and up, 11 mm (7/16 in) for 254 through 610 mm (10 through 24 in) pipe shells, and slightly less for smaller-diameter pipe shells . Tubes can be replaced . Tube-side headers, channel covers, gaskets, etc ., are accessible for maintenance and replacement . Neither the shell-side baffle structure nor the blind gasket is accessible . During tube removal, a tube may break within the shell . When this occurs, it is most difficult to remove or to replace the tube . The usual procedure is to plug the appropriate holes in the tubesheets . Differential expansion between the shell and the tubes can develop because of differences in length caused by thermal expansion . Various types of expansion joints are used to eliminate excessive stresses caused by expansion . The need for an expansion joint is a function of both the amount of differential expansion and the cycling conditions to be expected during operation . A number of types of expansion joints are available (Fig . 11-37) . 1 . Flat plates. Two concentric flat plates with a bar at the outer edges . The flat plates can flex to make some allowance for differential expansion . This design is generally used for vacuum service and gauge pressures below 103 kPa (15 lbf/in2) . All are subject to severe stress during differential expansion . 2 . Flanged-only heads. The flat plates are flanged (or curved) . The diameter of these heads is generally 203 mm (8 in) or greater than the shell diameter . The welded joint at the shell is subject to the stress referred to before, but the joint connecting the heads is subjected to less stress during expansion because of the curved shape . 3 . Flared shell or pipe segments. The shell may be flared to connect with a pipe section, or a pipe may be halved and quartered to produce a ring . 4 . Formed heads. A pair of dished-only or elliptical or flanged and dished heads can be used . These are welded together or connected by a ring . This type of joint is similar to the flanged-only-head type but apparently is subject to less stress .

5 . Flanged and flued heads. A pair of flanged-only heads is provided with concentric reverse flue holes . These heads are relatively expensive because of the cost of the flue operation . The curved shape of the heads reduces the amount of stress at the welds to the shell and also connecting the heads . 6 . Toroidal. The toroidal joint has a mathematically predictable smooth stress pattern of low magnitude, with maximum stresses at sidewalls of the corrugation and minimum stresses at top and bottom . The foregoing designs were discussed as ring expansion joints by Kopp and Sayre, “Expansion Joints for Heat Exchangers” (ASME Misc . Pap ., 6: 211) . All are statically indeterminate but are subjected to analysis by introducing various simplifying assumptions . Some joints in current industrial use are of lighter wall construction than is indicated by the method of this paper . 7 . Bellows. Thin-wall bellows joints are produced by various manufacturers . These are designed for differential expansion and are tested for axial and transverse movement as well as for cyclical life . Bellows may be of stainless steel, nickel alloys, or copper . (Aluminum, Monel, phosphor bronze, and titanium bellows have been manufactured .) Welding nipples of the same composition as the heat exchanger shell are generally furnished . The bellows may be hydraulically formed from a single piece of metal or may consist of welded pieces . External insulation covers of carbon steel are often provided to protect the light-gauge bellows from damage . The cover also prevents insulation from interfering with movement of the bellows (see item 8) . 8 . Toroidal bellows. For high-pressure service, the bellows type of joint has been modified so that movement is taken up by thin-wall smalldiameter bellows of a toroidal shape . The thickness of parts under high pressure is reduced considerably (see item 6) . Improper handling during manufacture, transit, installation, or maintenance of the heat exchanger equipped with the thin-wall-bellows type or toroidal type of expansion joint can damage the joint . In larger units these light-wall joints are particularly susceptible to damage, and some designers prefer the use of the heavier walls of formed heads .

TEMA-STYLE SHELL-AND-TUBE HEAT EXCHANGERS

11-35

(c)

(d)

(e) FIG. 11-36 (Continued ) Heat exchanger component nomenclature . (c) Outside packed floating-head exchanger . Type AEP . (d) U-tube heat exchanger . Type CFU . (e) Kettle-type floating-head reboiler . Type AKT . (Standards of the Tubular Exchanger Manufacturers Association, 6th ed., 1978.)

11-36

HEAT-TRANSFER EQUIPMENT

(f )

FIG. 11-36 (Continued )

Heat exchanger component nomenclature . ( f ) Exchanger with packed floating tube sheet and lantern ring . Type AJW . (Standards of the Tubular Exchanger Manufacturers Association, 6th ed., 1978.)

Chemical-plant exchangers requiring expansion joints most commonly have used the flanged-and flued-head type . There is a trend toward more common use of the light-wall bellows type . U-Tube Heat Exchanger (Fig. 11-36d) The tube bundle consists of a stationary tubesheet, U tubes (or hairpin tubes), baffles or support plates, and appropriate tie rods and spacers . The tube bundle can be removed from the heat exchanger shell . A tube-side header (stationary head) and a shell with integral shell cover, which is welded to the shell, are provided . Each tube is free to expand or contract without any limitation being placed upon it by the other tubes . The U-tube bundle has the advantage of providing minimum clearance between the outer tube limit and the inside of the shell for any of the removable tube bundle constructions . Clearances are of the same magnitude as for fixed-tube-sheet heat exchangers . The number of tube holes in a given shell is less than that for a fixed-tubesheet exchanger because of limitations on bending tubes of a very short radius . The U-tube design offers the advantage of reducing the number of joints . In high-pressure construction this feature becomes of considerable importance in reducing both initial and maintenance costs . The use of U-tube construction has increased significantly with the development of hydraulic tube cleaners, which can remove fouling residues from both the straight and the U-bend portions of the tubes . Mechanical cleaning of the inside of the tubes was described by John [Chem. Eng. 66: 187–192 (Dec . 14, 1959)] . Rods and conventional mechanical tube cleaners cannot pass from one end of the U tube to the other . Powerdriven tube cleaners, which can clean both the straight legs of the tubes and the bends, are available .

Hydraulic jetting with water forced through spray nozzles at high pressure for cleaning tube interiors and exteriors of removal bundles is reported by Canaday (“Hydraulic Jetting Tools for Cleaning Heat Exchangers,” ASME Pap . 58-A-217, unpublished) . The tank suction heater, as illustrated in Fig . 11-38, contains a U-tube bundle . This design is often used with outdoor storage tanks for heavy fuel oils, tar, molasses, and similar fluids whose viscosity must be lowered to permit easy pumping . Usually the tube-side heating medium is steam . One end of the heater shell is open, and the liquid being heated passes across the outside of the tubes . Pumping costs can be reduced without heating the entire contents of the tank . Bare-tube and integral low-fin tubes are provided with baffles . Longitudinal fin-tube heaters are not baffled . Fins are most often used to minimize the fouling potential in these fluids . Kettle-type reboilers, evaporators, etc ., are often U-tube exchangers with enlarged shell sections for vapor-liquid separation . The U-tube bundle replaces the floating-heat bundle of Fig . 11-36e. The U-tube exchanger with copper tubes, cast-iron header, and other parts of carbon steel is used for water and steam services in office buildings, schools, hospitals, hotels, etc . Nonferrous tubesheets and admiralty or 90-10 copper-nickel tubes are the most frequently used substitute materials . These standard exchangers are available from a number of manufacturers at costs far below those of custom-built process industry equipment . Packed Lantern-Ring Exchanger (Fig. 11-36f ) This construction is the least costly of the straight-tube removable bundle types . The shell- and tube-side fluids are each contained by separate rings of packing separated by a lantern ring and are installed at the floating tubesheet . The lantern ring is provided with weep holes . Any leakage passing the packing goes through

TEMA-STYLE SHELL-AND-TUBE HEAT EXCHANGERS

FIG. 11-37

Expansion joints.

the weep holes and then drops to the ground . Leakage at the packing will not result in mixing within the exchanger of the two fluids . The width of the floating tubesheet must be great enough to allow for the packings, the lantern ring, and differential expansion . Sometimes a small skirt is attached to a thin tubesheet to provide the required bearing surface for packings and the lantern ring . The clearance between the outer tube limit and the inside of the shell is slightly larger than that for fixed-tube-sheet and U-tube exchangers . The use of a floating-tube-sheet skirt increases this clearance . Without the skirt the clearance must make allowance for tube-hole distortion during tube rolling near the outside edge of the tubesheet or for tube-end welding at the floating tubesheet . The packed lantern ring construction is generally limited to design temperatures below 191°C (375°F) and to the mild services of water, steam, air, lubricating oil, etc . Design gauge pressure does not exceed 2068 kPa (300 lbf/in2) for pipe shell exchangers and is limited to 1034 kPa (150 lbf/in2) for 610- to 1067-mm- (24- to 42-in-) diameter shells . Outside Packed Floating-Head Exchanger (Fig. 11-36c) The shellside fluid is contained by rings of packing, which are compressed within a stuffing box by a packing follower ring . This construction was frequently used in the chemical industry, but in recent years usage has decreased . The removable-bundle construction accommodates differential expansion between shell and tubes and is used for shell-side service up to 4137 kPa gauge pressure (600 lbf/in2) at 316°C (600°F) . There are no limitations upon the number of tube-side passes or upon the tube-side design pressure and

FIG. 11-38

Tank suction heater.

11-37

temperature . The outside packed floating-head exchanger was the most commonly used type of removable-bundle construction in chemical-plant service . The floating-tube-sheet skirt, where in contact with the rings of packing, has a fine machine finish . A split shear ring is inserted into a groove in the floating-tube-sheet skirt . A slip-on backing flange, which in service is held in place by the shear ring, bolts to the external floating-head cover . The floating-head cover is usually a circular disk . With an odd number of tube-side passes, an axial nozzle can be installed in such a floating-head cover . If a side nozzle is required, the circular disk is replaced by either a dished head or a channel barrel (similar to Fig . 11-36f ) bolted between floating-head cover and floating-tube-sheet skirt . The outer tube limit approaches the inside of the skirt but is farther removed from the inside of the shell than for any of the previously discussed constructions . Clearances between shell diameter and bundle OTL are 22 mm (⅞ in) for small-diameter pipe shells, 44 mm (1¾ in) for large-diameter pipe shells, and 58 mm (21/16 in) for moderate-diameter plate shells . Internal Floating-Head Exchanger (Fig. 11-36a) The internal floating-head design is used extensively in petroleum refinery service, but in recent years there has been a decline in usage . The tube bundle is removable, and the floating tubesheet moves (or floats) to accommodate differential expansion between shell and tubes . The outer tube limit approaches the inside diameter of the gasket at the floating tubesheet . Clearances (between shell and OTL) are 29 mm (1⅛ in) for pipe shells and 37 mm (17/16 in) for moderate-diameter plate shells. A split backing ring and bolting usually hold the floating-head cover at the floating tubesheet. These are located beyond the end of the shell and within the larger-diameter shell cover. The shell cover, split backing ring, and floating-head cover must be removed before the tube bundle can pass through the exchanger shell. With an even number of tube-side passes, the floating-head cover serves as return cover for the tube-side fluid. With an odd number of passes, a nozzle pipe must extend from the floating-head cover through the shell cover. Provision for both differential expansion and tube bundle removal must be made. Pull-Through Floating-Head Exchanger (Fig. 11-36e) Construction is similar to that of the internal floating-head split-backing-ring exchanger except that the floating-head cover bolts directly to the floating tubesheet. The tube bundle can be withdrawn from the shell without removing either shell cover or floating-head cover. This feature reduces maintenance time during inspection and repair. The large clearance between the tubes and the shell must provide for both the gasket and the bolting at the floating-head cover. This clearance is about 2 to 2½ times that required by the split-ring design. Sealing strips or dummy tubes are often installed to reduce bypassing of the tube bundle. Falling-Film Exchangers Falling-film shell-and-tube heat exchangers have been developed for a wide variety of services and are described by Sack [Chem. Eng. Prog. 63: 55 (July 1967)]. The fluid enters at the top of the vertical tubes. Distributors or slotted tubes put the liquid in film flow in the inside surface of the tubes, and the film adheres to the tube surface while falling to the bottom of the tubes. The film can be cooled, heated, evaporated, or frozen by means of the proper heat-transfer medium outside the tubes. Tube distributors have been developed for a wide range of applications. Fixed tubesheets, with or without expansion joints, and outside packed head designs are used. Principal advantages are the high rate of heat transfer, no internal pressure drop, short time of contact (very important for heat-sensitive materials), easy accessibility to tubes for cleaning, and, in some cases, prevention of leakage from one side to another. These falling-film exchangers are used in various services as described in the following paragraphs. Liquid Coolers and Condensers Dirty water can be used as the cooling medium. The top of the cooler is open to the atmosphere for access to tubes. These can be cleaned without shutting down the cooler by removing the distributors one at a time and scrubbing the tubes. Evaporators These are used extensively for the concentration of ammonium nitrate, urea, and other chemicals sensitive to heat when minimum contact time is desirable. Air is sometimes introduced in the tubes to lower the partial pressure of liquids whose boiling points are high. These evaporators are built for pressure or vacuum and with top or bottom vapor removal. Absorbers These have a two-phase flow system. The absorbing medium is put in film flow during its fall downward on the tubes as it is cooled by a cooling medium outside the tubes. The film absorbs the gas that is introduced into the tubes. This operation can be cocurrent or countercurrent. Freezers By cooling the falling film to its freezing point, these exchangers convert a variety of chemicals to the solid phase. The most common application is the production of sized ice and paradichlorobenzene. Selective freezing is used for isolating isomers. By melting the solid material and refreezing in several stages, a higher degree of purity of product can be obtained.

11-38

HEAT-TRANSFER EQUIPMENT

TUBE-SIDE CONSTRUCTION Tube-Side Header The tube-side header (or stationary head) contains one or more flow nozzles . The bonnet (Fig . 11-35B) bolts to the shell . It is necessary to remove the bonnet to examine the tube ends . The fixed-tube-sheet exchanger of Fig . 11-36b has bonnets at both ends of the shell . The channel (Fig . 11-35A) has a removable channel cover . The tube ends can be examined by removing this cover without disturbing the piping connections to the channel nozzles . The channel can bolt to the shell as shown in Fig . 11-36a and c. Type C and type N channels of Fig . 11-35 are welded to the tubesheet . This design is comparable in cost with the bonnet but has the advantages of permitting access to the tubes without disturbing the piping connections and of eliminating a gasketed joint . Special High-Pressure Closures (Fig. 11-35D) The channel barrel and the tubesheet are generally forged . The removable channel cover is seated in place by hydrostatic pressure, while a shear ring subjected to shearing stress absorbs the end force . For pressures above 6205 kPa (900 lbf/in2) these designs are generally more economical than bolted constructions, which require larger flanges and bolting as pressure increases in order to contain the end force with bolts in tension . Relatively light-gauge internal pass partitions are provided to direct the flow of tube-side fluids but are designed only for the differential pressure across the tube bundle . Tube-Side Passes Most exchangers have an even number of tube-side passes . The fixed-tube-sheet exchanger (which has no shell cover) usually has a return cover without any flow nozzles, as shown in Fig . 11-35M; types L and N are also used . All removable-bundle designs (except for the U tube) have a floating-head cover directing the flow of tube-side fluid at the floating tubesheet . Tubes Standard heat exchanger tubing has ¼-, ⅜-, ½-, ⅝-, ¾-, 1-, 1¼-, and 1½-in outside diameter (in × 25 .4 = mm) . Wall thickness is measured in Birmingham wire gauge (BWG) units . A comprehensive list of tubing characteristics and sizes is given in Table 11-12 . The most commonly used tubes in chemical plants and petroleum refineries are 19- and 25-mm (¾- and 1-in) outside diameter (OD) . Standard tube lengths are 8, 10, 12, 16, and 20 ft, with 20 ft now the most common ( ft × 0 .3048 = m) . Manufacturing tolerances for steel, stainless-steel, and nickel-alloy tubes are such that the tubing is produced to either average or minimum wall thickness . Seamless carbon-steel tube of minimum wall thickness may vary from 0 to 20 percent above the nominal wall thickness . Average-wall seamless tubing has an allowable variation of ±10 percent . Welded carbon-steel tube is produced to closer tolerances (0 to +18 percent on minimum wall; ±9 percent on average wall) . Tubing of aluminum, copper, and their alloys can be drawn easily and usually is made to minimum wall specifications . Common practice is to specify the exchanger surface in terms of total external square feet of tubing . The effective outside heat-transfer surface is based on the length of tubes measured between the inner faces of tubesheets . In most heat exchangers, there is little difference between the total and the effective surface . Significant differences are usually found in high-pressure and double-tube-sheet designs . Integrally finned tube, which is available in a variety of alloys and sizes, is being used in shell-and-tube heat exchangers . The fins are radially extruded from thick-walled tube to a height of 1 .6 mm (1/16 in) spaced at 1 .33 mm (19 fins per inch) or to a height of 3 .2 mm (⅛ in) spaced at 2.3 mm (11 fins per inch). The external surface is approximately 2½ times the outside surface of a bare tube with the same outside diameter. Also available are 0.93-mm-high (0.037-in-high) fins spaced 0.91 mm (28 fins per inch) with an external surface about 3.5 times the surface of the bare tube. Bare ends of nominal tube diameter are provided, while the fin height is slightly less than this diameter. The tube can be inserted into a conventional tube bundle and rolled or welded to the tubesheet by the same means used for bare tubes. An integrally finned tube rolled into a tubesheet with double serrations and flared at the inlet is shown in Fig. 11-39. Internally finned tubes have been manufactured but have limited application. Longitudinal fins are commonly used in double-pipe exchangers upon the outside of the inner tube. U-tube and conventional removable tube bundles are also made from such tubing. The ratio of external to internal surface generally is about 10:1 or 15:1. Transverse fins upon tubes are used in low-pressure gas services. The primary application is in air-cooled heat exchangers (as discussed under that heading), but shell-and-tube exchangers with these tubes are in service. Rolled Tube Joints Expanded tube—tube-sheet joints are standard. Properly rolled joints have uniform tightness to minimize tube fractures, stress corrosion, tube-sheet ligament pushover and enlargement, and dishing of the tubesheet. Tubes are expanded into the tubesheet for a length of two tube diameters, or 50 mm (2 in), or tube-sheet thickness minus 3 mm (⅛ in). Generally tubes are rolled for the last of these alternatives. The expanded portion should never extend beyond the shell-side face of the

tubesheet, since removing such a tube is extremely difficult. Methods and tools for tube removal and tube rolling were discussed by John [Chem. Eng. 66: 77–80 (Dec. 28, 1959)], and rolling techniques by Bach [Pet. Refiner 39: 8, 104 (1960)]. Tube ends may be projecting, flush, flared, or beaded (listed in order of usage). The flare or bell-mouth tube end is usually restricted to water service in condensers and serves to reduce erosion near the tube inlet. For moderate general process requirements at gauge pressures less than 2058 kPa (300 lbf/in2) and less than 177°C (350°F), tube-sheet holes without grooves are standard. For all other services with expanded tubes, at least two grooves in each tube hole are common. The number of grooves is sometimes changed to one or three in proportion to tube-sheet thickness. Expanding the tube into the grooved tube holes provides a stronger joint but results in greater difficulties during tube removal. Welded Tube Joints When suitable materials of construction are used, the tube ends may be welded to the tubesheets. Welded joints may be seal-welded “for additional tightness beyond that of tube rolling” or may be strength-welded. Strength-welded joints have been found satisfactory in very severe services. Welded joints may or may not be rolled before or after welding. The variables in tube-end welding were discussed in two unpublished papers (Emhardt, “Heat Exchanger Tube-to-Tubesheet Joints,” ASME Pap. 69-WA/HT-47; and Reynolds, “Tube Welding for Conventional and Nuclear Power Plant Heat Exchangers,” ASME Pap. 69-WA/HT-24), which were presented at the November 1969 meeting of the American Society of Mechanical Engineers. Tube-end rolling before welding may leave lubricant from the tube expander in the tube hole. Fouling during normal operation followed by maintenance operations will leave various impurities in and near the tube ends. Satisfactory welds are rarely possible under such conditions, since tube-end welding requires extreme cleanliness in the area to be welded. Tube expansion after welding has been found useful for low and moderate pressures. In high-pressure service tube rolling has not been able to prevent leakage after weld failure. Double-Tube-Sheet Joints This design prevents the passage of either fluid into the other because of leakage at the tube–tube-sheet joints, which are generally the weakest points in heat exchangers. Any leakage at these joints admits the fluid to the gap between the tubesheets. Mechanical design, fabrication, and maintenance of double-tube-sheet designs require special consideration. SHELL-SIDE CONSTRUCTION Shell Sizes Heat exchanger shells are generally made from standardwall steel pipe in sizes up to 305-mm (12-in) diameter; from 9.5-mm (⅜-in) wall pipe in sizes from 356 to 610 mm (14 to 24 in); and from steel plate rolled at discrete intervals in larger sizes. Clearances between the outer tube limit and the shell are discussed elsewhere in connection with the different types of construction. The following formulas may be used to estimate tube counts for various bundle sizes and tube passes. The estimated values include the removal of tubes to provide an entrance area for shell nozzle sizes of one-fifth the shell diameter. Due to the large effect from other parameters such as design pressure/corrosion allowance, baffle cuts, seal strips, and so on, these are to be used as estimates only. Exact tube counts are part of the design package of most reputable exchanger design software and are normally used for the final design. Triangular tube layouts with pitch equal to 1.25 times the tube outside diameter: C = 0.75(D/d) − 36, where D = bundle OD and d = tube OD. Range of accuracy: −24 ≤ C ≤ 24. 1 Tube Pass: Nt = 1298. + 74.86C + 1.283C2 − 0.0078C3 − 0.0006C4 (11-74a) 2 Tube Pass: Nt = 1266. + 73.58C + 1.234C2 − 0.0071C3 − 0.0005C4 (11-74b) 4 Tube Pass: Nt = 1196. + 70.79C + 1.180C2 − 0.0059C3 − 0.0004C4 (11-74c) 6 Tube Pass: Nt = 1166. + 70.72C + 1.269C2 − 0.0074C3 − 0.0006C4 (11-74d) Square tube layouts with pitch equal to 1.25 times the tube outside diameter: C = (D/d) − 36, where D = bundle OD and d = tube OD. Range of accuracy: −24 ≤ C ≤ 24. 1 Tube Pass: Nt = 593.6 + 33.52C + 0.3782C2 − 0.0012C3 + 0.0001C4 (11-75a) 2 Tube Pass: Nt = 578.8 + 33.36C + 0.3847C2 − 0.0013C3 + 0.0001C4 (11-75b) 4 Tube Pass: Nt = 562.0 + 33.04C + 0.3661C2 − 0.0016C3 + 0.0002C4 (11-75c) 6 Tube Pass: Nt = 550.4 + 32.49C + 0.3873C2 − 0.0013C3 + 0.0001C4 (11-75d)

TEMA-STYLE SHELL-AND-TUBE HEAT EXCHANGERS

11-39

TABLE 11-12 Characterstics of Tubing (From Standards of the Tubular Exchanger Manufacturers Association, 8th Ed., 1999; 25 North Broadway, Tarrytown, N.Y.)

Tube O .D ., in . 1/4

3/8

1/2

5/8

3/4

7/8

1

1¼

1½

2

B .W .G . gage

Thickness, in .

Internal area, in .2

22 24 26 27 18 20 22 24 16 18 20 22 12 13 14 15 16 17 18 19 20 10 11 12 13 14 15 16 17 18 20 10 11 12 13 14 15 16 17 18 20 8 10 11 12 13 14 15 16 18 20 7 8 10 11 12 13 14 16 18 20 10 12 14 16 11 12 13 14

0 .028 0 .022 0 .018 0 .016 0 .049 0 .035 0 .028 0 .022 0 .065 0 .049 . 0 .035 0 .028 0 .109 0 .095 0 .083 0 .072 0 .065 0 .058 0 .049 0 .042 0 .035 0 .134 0 .120 0 .109 0 .095 0 .083 0 .072 0 .065 0 .058 0 .049 0 .035 0 .134 0 .120 0 .109 0 .095 0 .083 0 .072 0 .065 0 .058 0 .049 0 .035 0 .165 0 .134 0 .120 0 .109 0 .095 0 .083 0 .072 0 .065 0 .049 0 .035 0 .180 0 .165 0 .134 0 .120 0 .109 0 .095 0 .083 0 .065 0 .049 0 .035 0 .134 0 .109 0 .083 0 .065 0 .120 0 .109 0 .095 0 .083

0 .0296 0 .0333 0 .0360 0 .0373 0 .0603 0 .0731 0 .0799 0 .0860 0 .1075 0 .1269 0 .1452 0 .1548 0 .1301 0 .1486 0 .1655 0 .1817 0 .1924 0 .2035 0 .2181 0 .2299 0 .2419 0 .1825 0 .2043 0 .2223 0 .2463 0 .2679 0 .2884 0 .3019 0 .3157 0 .3339 0 .3632 0 .2894 0 .3167 0 .3390 0 .3685 0 .3948 0 .4197 0 .4359 0 .4525 0 .4742 0 .5090 0 .3526 0 .4208 0 .4536 0 .4803 0 .5153 0 .5463 0 .5755 0 .5945 0 .6390 0 .6793 0 .6221 0 .6648 0 .7574 0 .8012 0 .8365 0 .8825 0 .9229 0 .9852 1 .0423 1 .0936 1 .1921 1 .2908 1 .3977 1 .4741 2 .4328 2 .4941 2 .5730 2 .6417

Sq . ft . external surface per foot length

Sq . ft . internal surface per foot length

Weight per ft . length steel, lb∗

Tube I .D ., in .

Moment of inertia, in .4

Section modulus, in .3

Radius of gyration, in .

Constant C†

O .D . I .D .

Transverse metal area, in .3

0 .0654 0 .0654 0 .0654 0 .0654 0 .0982 0 .0982 0 .0982 0 .0982 0 .1309 0 .1309 0 .1309 0 .1309 0 .1636 0 .1636 0 .1636 0 .1636 0 .1636 0 .1636 0 .1636 0 .1636 0 .1636 0 .1963 0 .1963 0 .1963 0 .1963 0 .1963 0 .1963 0 .1963 0 .1963 0 .1963 0 .1963 0 .2291 0 .2291 0 .2291 0 .2291 0 .2291 0 .2291 0 .2291 0 .2291 0 .2291 0 .2291 0 .2618 0 .2618 0 .2618 0 .2618 0 .2618 0 .2618 0 .2618 0 .2618 0 .2618 0 .2618 0 .3272 0 .3272 0 .3272 0 .3272 0 .3272 0 .3272 0 .3272 0 .3272 0 .3272 0 .3272 0 .3927 0 .3927 0 .3927 0 .3927 0 .5236 0 .5236 0 .5236 0 .5236

0 .0508 0 .0539 0 .0560 0 .0571 0 .0725 0 .0798 0 .0835 0 .0867 0 .0969 0 .1052 0 .1126 0 .1162 0 .1066 0 .1139 0 .1202 0 .1259 0 .1296 0 .1333 0 .1380 0 .1416 0 .1453 0 .1262 0 .1335 0 .1393 0 .1466 0 .1529 0 .1587 0 .1623 0 .1660 0 .1707 0 .1780 0 .1589 0 .1662 0 .1720 0 .1793 0 .1856 0 .1914 0 .1950 0 .1987 0 .2034 0 .2107 0 .1754 0 .1916 0 .1990 0 .2047 0 .2121 0 .2183 0 .2241 0 .2278 0 .2361 0 .2435 0 .2330 0 .2409 0 .2571 0 .2644 0 .2702 0 .2775 0 .2838 0 .2932 0 .3016 0 .3089 0 .3225 0 .3356 0 .3492 0 .3587 0 .4608 0 .4665 0 .4739 0 .4801

0 .066 0 .054 0 .045 0 .040 0 .171 0 .127 0 .104 0 .083 0 .302 0 .236 0 .174 0 .141 0 .601 0 .538 0 .481 0 .426 0 .389 0 .352 0 .302 0 .262 0 .221 0 .833 0 .808 0 .747 0 .665 0 .592 0 .522 0 .476 0 .429 0 .367 0 .268 1 .062 0 .969 0 .893 0 .792 0 .703 0 .618 0 .563 0 .507 0 .433 0 .314 1 .473 1 .241 1 .129 1 .038 0 .919 0 .814 0 .714 0 .650 0 .498 0 .361 2 .059 1 .914 1 .599 1 .450 1 .330 1 .173 1 .036 0 .824 0 .629 0 .455 1 .957 1 .621 1 .257 0 .997 2 .412 2 .204 1 .935 1 .701

0 .194 0 .206 0 .214 0 .218 0 .277 0 .305 0 .319 0 .331 0 .370 0 .402 0 .430 0 .444 0 .407 0 .435 0 .459 0 .481 0 .495 0 .509 0 .527 0 .541 0 .555 0 .482 0 .510 0 .532 0 .560 0 .584 0 .606 0 .620 0 .634 0 .652 0 .680 0 .607 0 .635 0 .657 0 .685 0 .709 0 .731 0 .745 0 .759 0 .777 0 .805 0 .670 0 .732 0 .760 0 .782 0 .810 0 .834 0 .856 0 .870 0 .902 0 .930 0 .890 0 .920 0 .982 1 .010 1 .032 1 .060 1 .084 1 .120 1 .152 1 .180 1 .232 1 .282 1 .334 1 .370 1 .760 1 .782 1 .810 1 .834

0 .00012 0 .00010 0 .00009 0 .00008 0 .00068 0 .00055 0 .00046 0 .00038 0 .0021 0 .0018 0 .0014 0 .0012 0 .0061 0 .0057 0 .0053 0 .0049 0 .0045 0 .0042 0 .0037 0 .0033 0 .0028 0 .0129 0 .0122 0 .0116 0 .0107 0 .0098 0 .0089 0 .0083 0 .0076 0 .0067 0 .0050 0 .0221 0 .0208 0 .0196 0 .0180 0 .0164 0 .0148 0 .0137 0 .0125 0 .0109 0 .0082 0 .0392 0 .0350 0 .0327 0 .0307 0 .0280 0 .0253 0 .0227 0 .0210 0 .0166 0 .0124 0 .0890 0 .0847 0 .0742 0 .0688 0 .0642 0 .0579 0 .0521 0 .0426 0 .0334 0 .0247 0 .1354 0 .1159 0 .0931 0 .0756 0 .3144 0 .2904 0 .2586 0 .2300

0 .00098 0 .00083 0 .00071 0 .00065 0 .0036 0 .0029 0 .0025 0 .0020 0 .0086 0 .0071 0 .0056 0 .0046 0 .0197 0 .0183 0 .0170 0 .0156 0 .0145 0 .0134 0 .0119 0 .0105 0 .0091 0 .0344 0 .0326 0 .0309 0 .0285 0 .0262 0 .0238 0 .0221 0 .0203 0 .0178 0 .0134 0 .0505 0 .0475 0 .0449 0 .0411 0 .0374 0 .0337 0 .0312 0 .0285 0 .0249 0 .0187 0 .0784 0 .0700 0 .0654 0 .0615 0 .0559 0 .0507 0 .0455 0 .0419 0 .0332 0 .0247 0 .1425 0 .1355 0 .1187 0 .1100 0 .1027 0 .0926 0 .0833 0 .0682 0 .0534 0 .0395 0 .1806 0 .1545 0 .1241 0 .1008 0 .3144 0 .2904 0 .2588 0 .2300

0 .0791 0 .0810 0 .0823 0 .0829 0 .1166 0 .1208 0 .1231 0 .1250 0 .1555 0 .1604 0 .1649 0 .1672 0 .1865 0 .1904 0 .1939 0 .1972 0 .1993 0 .2015 0 .2044 0 .2067 0 .2090 0 .2229 0 .2267 0 .2299 0 .2340 0 .2376 0 .2411 0 .2433 0 .2455 0 .2484 0 .2531 0 .2662 0 .2703 0 .2736 0 .2778 0 .2815 0 .2850 0 .2873 0 .2896 0 .2925 0 .2972 0 .3009 0 .3098 0 .3140 0 .3174 0 .3217 0 .3255 0 .3291 0 .3314 0 .3367 0 .3414 0 .3836 0 .3880 0 .3974 0 .4018 0 .4052 0 .4097 0 .4136 0 .4196 0 .4250 0 .4297 0 .4853 0 .4933 0 .5018 0 .5079 0 .6660 0 .6697 0 .6744 0 .6784

46 52 56 58 94 114 125 134 168 198 227 241 203 232 258 283 300 317 340 359 377 285 319 347 384 418 450 471 492 521 567 451 494 529 575 616 655 680 706 740 794 550 656 708 749 804 852 898 927 997 1060 970 1037 1182 1250 1305 1377 1440 1537 1626 1706 1860 2014 2180 2300 3795 3891 4014 4121

1 .289 1 .214 1 .168 1 .147 1 .354 1 .230 1 .176 1 .133 1 .351 1 .244 1 .163 1 .126 1 .536 1 .437 1 .362 1 .299 1 .263 1 .228 1 .186 1 .155 1 .126 1 .556 1 .471 1 .410 1 .339 1 .284 1 .238 1 .210 1 .183 1 .150 1 .103 1 .442 1 .378 1 .332 1 .277 1 .234 1 .197 1 .174 1 .153 1 .126 1 .087 1 .493 1 .366 1 .316 1 .279 1 .235 1 .199 1 .168 1 .149 1 .109 1 .075 1 .404 1 .359 1 .273 1 .238 1 .211 1 .179 1 .153 1 .116 1 .085 1 .059 1 .218 1 .170 1 .124 1 .095 1 .136 1 .122 1 .105 1 .091

0 .0195 0 .0158 0 .0131 0 .0118 0 .0502 0 .0374 0 .0305 0 .0244 0 .0888 0 .0694 0 .0511 0 .0415 0 .177 0 .158 0 .141 0 .125 0 .114 0 .103 0 .089 0 .077 0 .065 0 .259 0 .238 0 .219 0 .195 0 .174 0 .153 0 .140 0 .126 0 .108 0 .079 0 .312 0 .285 0 .262 0 .233 0 .207 0 .182 0 .165 0 .149 0 .127 0 .092 0 .433 0 .365 0 .332 0 .305 0 .270 0 .239 0 .210 0 .191 0 .146 0 .106 0 .605 0 .562 0 .470 0 .426 0 .391 0 .345 0 .304 0 .242 0 .185 0 .134 0 .575 0 .476 0 .369 0 .293 0 .709 0 .648 0 .569 0 .500

∗ Weights are based on low-carbon steel with a density of 0 .2836 lb/cu . in . For other metals multiply by the following factors: aluminum, 0 .35; titanium, 0 .58; A .I .S .I . 400 Series S/steels, 0 .99; A .I .S .I . 300 Series S/steels, 1 .02; aluminum bronze, 1 .04; aluminum brass, 1 .06; nickel-chrome-iron, 1 .07; Admiralty, 1 .09; nickel, 1 .13; nickelcopper, 1 .12; copper and cupro-nickels, 1 .14 . †

Liquid velocity =

lb per tube hour ft/s (sp gr of water at 60°F = 1 .0) C × sp gr of liquid

11-40

HEAT-TRANSFER EQUIPMENT A double-split-flow design is shown in Fig . 11-35H. The longitudinal baffles may be solid or perforated . The divided flow design (Fig . 11-35J) mechanically is like the one-pass shell except for the addition of a nozzle . Divided flow is used to meet lowpressure-drop requirements . The kettle reboiler is shown in Fig . 11-35K. When nucleate boiling is to be done on the shell side, this common design provides adequate dome space for separation of vapor and liquid above the tube bundle and surge capacity beyond the weir near the shell cover . BAFFLES AND TUBE BUNDLES The tube bundle is the most important part of a tubular heat exchanger . The tubes generally constitute the most expensive component of the exchanger and are the one most likely to corrode . Tubesheets, baffles, or support plates, tie rods, and usually spacers complete the bundle . Minimum baffle spacing is generally one-fifth of the shell diameter and not less than 50 .8 mm (2 in) . Maximum baffle spacing is limited by the requirement to provide adequate support for the tubes . The maximum unsupported tube span in inches equals 74d 0 .75 (where d is the tube OD in inches) . The unsupported tube span is reduced by about 12 percent for aluminum, copper, and their alloys . Baffles are provided for heat-transfer purposes . When shell-side baffles are not required for heat-transfer purposes, as may be the case in condensers or reboilers, tube supports are installed . Segmental Baffles Segmental or cross-flow baffles are standard . Single, double, and triple segmental baffles are used . Baffle cuts are illustrated in Fig . 11-40 . The double segmental baffle reduces cross-flow velocity

FIG. 11-39 Integrally finned tube rolled into tube sheet with double serrations and flared inlet . (Woverine Division, UOP, Inc.)

Shell-Side Arrangements The one-pass shell (Fig . 11-35E) is the most commonly used arrangement . Condensers from single-component vapors often have the nozzles moved to the center of the shell for vacuum and steam services . A solid longitudinal baffle is provided to form a two-pass shell (Fig . 11-35F) . It may be insulated to improve thermal efficiency . (See further discussion on baffles .) A two-pass shell can improve thermal effectiveness at a cost lower than for two shells in series . For split flow (Fig . 11-35G), the longitudinal baffle may be solid or perforated . The latter feature is used with condensing vapors .

(a)

(b)

(c)

Tubesheet Tube

(d) Baffle FIG. 11-40 Plate baffles . (a) Baffle cuts for single segmental baffles . (b) Baffle cuts for double segmental baffles . (c) Baffle cuts for triple segmental baffles . (d ) Helical baffle construction .

TEMA-STYLE SHELL-AND-TUBE HEAT EXCHANGERS for a given baffle spacing . The triple segmental baffle reduces both crossflow and long-flow velocities and has been identified as the “window-cut” baffle . Baffle cuts are expressed as the ratio of segment opening height to shell inside diameter . Cross-flow baffles with horizontal cut are shown in Fig . 11-36a, c, and f. This arrangement is not satisfactory for horizontal condensers, since the condensate can be trapped between baffles, or for dirty fluids in which the dirt might settle out . Vertical-cut baffles are used for side-to-side flow in horizontal exchangers with condensing fluids or dirty fluids . Baffles are notched to ensure complete drainage when the units are taken out of service . (These notches permit some bypassing of the tube bundle during normal operation .) Tubes are most commonly arranged on an equilateral triangular pitch . Tubes are arranged on a square pitch primarily for mechanical cleaning purposes in removable-bundle exchangers . Maximum baffle cut is limited to about 45 percent for single segmental baffles so that every pair of baffles will support each tube . Tube bundles are generally provided with baffles cut so that at least one row of tubes passes through all the baffles or support plates . These tubes hold the entire bundle together . In pipe-shell exchangers with a horizontal baffle cut and a horizontal pass rib for directing tube-side flow in the channel, the maximum baffle cut, which permits a minimum of one row of tubes to pass through all baffles, is approximately 33 percent in small shells and 40 percent in larger pipe shells . Maximum shell-side heat-transfer rates in forced convection are apparently obtained by cross-flow of the fluid at right angles to the tubes . To maximize this type of flow, some heat exchangers are built with segmental-cut baffles and with “no tubes in the window” (or the baffle cutout) . Maximum baffle spacing may thus equal maximum unsupported-tube span, while conventional baffle spacing is limited to one-half of this span . The maximum baffle spacing for no tubes in the window of single segmental baffles is unlimited when intermediate supports are provided . These are cut on both sides of the baffle and therefore do not affect the flow of the shell-side fluid . Each support engages all the tubes; the supports are spaced to provide adequate support for the tubes . Rod Baffles Rod or bar baffles have either rods or bars extending through the lanes between rows of tubes . A baffle set can consist of a baffle with rods in all the vertical lanes and another baffle with rods in all the horizontal lanes between the tubes . The shell-side flow is uniform and parallel to the tubes . Stagnant areas do not exist . One device uses four baffles in a baffle set . Only half of either the vertical or the horizontal tube lanes in a baffle have rods . The new design apparently provides a maximum shell-side heat-transfer coefficient for a given pressure drop . Tie Rods and Spacers Tie rods are used to hold the baffles in place with spacers, which are pieces of tubing or pipe placed on the rods to locate the baffles . Occasionally baffles are welded to the tie rods, and spacers are eliminated . Properly located tie rods and spacers serve both to hold the bundle together and to reduce bypassing of the tubes . In very large fixed-tube-sheet units, in which concentricity of shells decreases, baffles are occasionally welded to the shell to eliminate bypassing between the baffle and the shell . Metal baffles are standard . Occasionally plastic baffles are used either to reduce corrosion or in vibratory service, in which metal baffles may cut the tubes . Impingement Baffle The tube bundle is customarily protected against impingement by the incoming fluid at the shell inlet nozzle when the shell-side fluid is at a high velocity, is condensing, or is a two-phase fluid . Minimum entrance area about the nozzle is generally equal to the inlet nozzle area . Exit nozzles also require adequate area between the tubes and the nozzles . A full bundle without any provision for shell inlet nozzle area can increase the velocity of the inlet fluid by as much as 300 percent with a consequent loss in pressure . Impingement baffles are generally made of rectangular plate, although circular plates are more desirable . Rods and other devices are sometimes used to protect the tubes from impingement . To maintain a maximum tube count, the impingement plate is often placed in a conical nozzle opening or in a dome cap above the shell . Impingement baffles or flow distribution devices are recommended for axial tube-side nozzles when entrance velocity is high . Vapor Distribution Relatively large shell inlet nozzles, which may be used in condensers under low pressure or vacuum, require provision for uniform vapor distribution . Tube-Bundle Bypassing Shell-side heat-transfer rates are maximized when bypassing of the tube bundle is at a minimum . The most significant bypass stream is generally between the outer tube limit and the inside of the shell . The clearance between tubes and shell is at a minimum for fixed-tube-sheet construction and is greatest for straight-tube removable bundles .

11-41

Arrangements to reduce tube-bundle bypassing include these: Dummy tubes. These tubes do not pass through the tubesheets and can be located close to the inside of the shell . Tie rods with spacers. These hold the baffles in place but can be located to prevent bypassing . Sealing strips. These longitudinal strips either extend from baffle to baffle or may be inserted in slots cut into the baffles . Dummy tubes or tie rods with spacers may be located within the pass partition lanes (and between the baffle cuts) to ensure maximum bundle penetration by the shell-side fluid . When tubes are omitted from the tube layout to provide the entrance area about an impingement plate, the need for sealing strips or other devices to cause proper bundle penetration by the shell-side fluid is increased . Helical Baffles An increasingly popular variant to the segmental baffle is the helical baffle . These are quadrant-shaped plate baffles installed at an angle to the axial bundle centerline to produce a pseudo-spiraling flow down the length of the tube bundle (Fig . 11-40d) . This baffle has the advantage of producing shell-side heat-transfer coefficients similar to those of the segmental baffle with much less shell-side pressure loss for the same size of shell . In the case of equal pressure drops, the helical baffle exchanger will be smaller than the segmental baffle exchanger; or, for identical shell sizes, the helical baffle exchanger will permit a much higher throughput of flow for the same process inlet/outlet temperatures . A great amount of proprietary research has been conducted by a few companies into the workings of helical baffled heat exchangers . The only known open literature method for estimating helical baffle performance has been “Comparison of Correction Factors for Shell-and-Tube Heat Exchangers with Segmental or Helical Baffles” by Stehlik, Nemcansky, Kral, and Swanson [Heat Transfer Engineering 15(1): 55–65 (1994)] . Unique design variables for helical baffles include the baffle angle, adjacent baffle contact diameter (which sets the baffle spacing and is usually about one-half of the shell ID), and the number of baffle starts (i .e ., number of intermediate baffle starts) . Of course, consideration is also given to the tube layout, tube pitch, use of seal strips, and all the other configuration characteristics common to any plate baffled bundle . A helical baffle bundle built in this way produces two distinct flow regions . The area outside of the adjacent baffle contact diameter tends to produce a stable helical cross-flow . However, inside the diameter where adjacent baffles touch is a second region where vortical flow is induced but in which the intensity of the rotational component tends to decrease as one approaches the center of the bundle . For a fixed flow rate and helix angle, this tendency may be minimized by proper selection of the baffle contact diameter . With the correct selection, stream temperatures may be made to be close to uniform across the bundle cross section through the shell . However, below a critical velocity ( for the baffle configuration and fluid state), the tendency for nonuniformity of temperatures increases as velocity decreases until everincreasing portions of the central core surface area pinch out with respect to temperature and become ineffective for further heat transfer . The design approach involves varying the baffle spacing for the primary purpose of balancing the flows in the two regions and maximizing the effectiveness of the total surface area . In many cases, a shallower helix angle is chosen in conjunction with the baffle spacing in order to minimize the central core component while still achieving a reduced overall bundle pressure drop . Longitudinal Flow Baffles In fixed-tube-sheet construction with multipass shells, the baffle is usually welded to the shell as positive assurance against bypassing results . Removable tube bundles have a sealing device between the shell and the longitudinal baffle . Flexible light-gauge sealing strips and various packing devices have been used . Removable U-tube bundles with four tube-side passes and two shell-side passes can be installed in shells with the longitudinal baffle welded in place . In split-flow shells, the longitudinal baffle may be installed without a positive seal at the edges if design conditions are not seriously affected by a limited amount of bypassing . Fouling in petroleum refinery service has necessitated rough treatment of tube bundles during cleaning operations . Many refineries avoid the use of longitudinal baffles, since the sealing devices are subject to damage during cleaning and maintenance operations . CORROSION IN HEAT EXCHANGERS Some of the special considerations in regard to heat exchanger corrosion are discussed in this subsection . An extended presentation in Sec . 23 covers corrosion and its various forms as well as materials of construction . Materials of Construction The most common material of construction for heat exchangers is carbon steel . Stainless-steel construction throughout is sometimes used in chemical-plant service and on rare occasions in petroleum refining . Many exchangers are constructed from dissimilar metals . Such combinations are functioning satisfactorily in certain

11-42

HEAT-TRANSFER EQUIPMENT

TABLE 11-13 Construction

Dissimilar Materials in Heat-Exchanger

Part Tubes Tube sheets Tube-side headers Baffles Shell

Relative use

1

2

3

4

5

6

Relative cost

A

B

C

D

C

E

●

● ●

● ● ●

● ● ● ●

● ●

● ●

●

● ●

Carbon steel replaced by an alloy when ● appears. Relative use: from 1 (most popular) through 6 (least popular) combinations. Relative cost: from A (least expensive) to E (most expensive).

services . Extreme care in their selection is required since electrolytic attack can develop . Carbon-steel and alloy combinations appear in Table 11-13 . “Alloys” in chemical- and petrochemical-plant service in approximate order of use are stainless-steel series 300, nickel, Monel, copper alloy, aluminum, Inconel, stainless-steel series 400, and other alloys . In petroleum refinery service, the frequency order shifts, with copper alloy ( for water-cooled units) in first place and low-alloy steel in second place . In some segments of the petroleum industry, copper alloy, stainless series 400, low-alloy steel, and aluminum are becoming the most commonly used alloys . Copper-alloy tubing, particularly inhibited admiralty, is generally used with cooling water . Copper-alloy tubesheets and baffles are generally of naval brass . Aluminum alloy (and in particular alclad aluminum) tubing is sometimes used in water service . The alclad alloy has a sacrificial aluminum-alloy layer metallurgically bonded to a core alloy . Tube-side headers for water service are made in a wide variety of materials: carbon steel, copper alloy, cast iron, and lead-lined or plastic-lined or specially painted carbon steel . Bimetallic Tubes When corrosive requirements or temperature conditions do not permit the use of a single alloy for the tubes, bimetallic (or duplex) tubes may be used . These can be made from almost any possible combination of metals . Tube sizes and gauges can be varied . For thin gauges the wall thickness is generally divided equally between the two components . In heavier gauges the more expensive component may comprise from onefifth to one-third of the total thickness . The component materials comply with applicable ASTM specifications, but after manufacture the outer component may increase in hardness beyond specification limits, and special care is required during the tuberolling operation . When the harder material is on the outside, precautions must be taken to expand the tube properly . When the inner material is considerably softer, rolling may not be practical unless ferrules of the soft material are used . To eliminate galvanic action, the outer tube material may be stripped from the tube ends and replaced with ferrules of the inner tube material . When the end of a tube with a ferrule is expanded or welded to a tubesheet, the tube-side fluid can contact only the inner tube material, while the outer material is exposed to the shell-side fluid . Bimetallic tubes are available from a small number of tube mills and are manufactured only on special order and in large quantities . Clad Tubesheets Usually tubesheets and other exchanger parts are made of a solid metal . Clad or bimetallic tubesheets are used to reduce costs or because no single metal is satisfactory for the corrosive conditions . The alloy material (e .g ., stainless steel, Monel) is generally bonded or clad to a carbon-steel backing material . In fixed-tube-sheet construction, a copper alloy–clad tubesheet can be welded to a steel shell, while most copper-alloy tubesheets cannot be welded to steel in a manner acceptable to ASME Code authorities . Clad tubesheets in service with carbon-steel backer material include stainless-steel types 304, 304L, 316, 316L, and 317, Monel, Inconel, nickel, naval rolled brass, copper, admiralty, silicon bronze, and titanium . Naval rolled brass and Monel clad on stainless steel are also in service . Ferrous-alloy-clad tubesheets are generally prepared by a weld overlay process in which the alloy material is deposited by welding upon the face of the tubesheet . Precautions are required to produce a weld deposit free of defects, since these may permit the process fluid to attack the base metal below the alloy . Copper-alloy-clad tubesheets are prepared by brazing the alloy to the carbon-steel backing material . Clad materials can be prepared by bonding techniques, which involve rolling, heat treatment, explosive bonding, etc . When properly manufactured, the two metals do not separate because of thermal expansion differences

encountered in service . Applied tube-sheet facings prepared by tack welding at the outer edges of alloy and base metal or by bolting together the two metals are in limited use . Nonmetallic Construction Shell-and-tube exchangers are available with glass tubes 14 mm (0 .551 in) in diameter and 1 mm (0 .039 in) thick with tube lengths from 2 .015 m (79 .3 in) to 4 .015 m (158 in) . Steel shell exchangers have a maximum design pressure of 517 kPa (75 lbf/in2) . Glass shell exchangers have a maximum design gauge pressure of 103 kPa (15 lbf/in2) . Shell diameters are 229 mm (9 in), 305 mm (12 in), and 457 mm (18 in) . Heattransfer surface ranges from 3 .16 to 51 m2 (34 to 550 ft2) . Each tube is free to expand, since a Teflon sealer sheet is used at the tube–tube sheet joint . Impervious graphite heat exchanger equipment is made in a variety of forms, including outside packed-head shell-and-tube exchangers . They are fabricated with impervious graphite tubes and tube-side headers and metallic shells . Single units containing up to 1300 m2 (14,000 ft2) of heattransfer surface are available . Teflon heat exchangers of special construction are described later in this section . Fabrication Expanding the tube into the tubesheet reduces the tube wall thickness and work-hardens the metal . The induced stresses can lead to stress corrosion. Differential expansion between tubes and shell in fixedtube-sheet exchangers can develop stresses, which lead to stress corrosion . When austenitic stainless-steel tubes are used for corrosion resistance, a close fit between the tube and the tube hole is recommended to minimize work hardening and the resulting loss of corrosion resistance . To facilitate removal and replacement of tubes, it is customary to rollerexpand the tubes to within 3 mm (⅛ in) of the shell-side face of the tubesheet. A 3-mm- (⅛-in-) long gap is thus created between the tube and the tube hole at this tube-sheet face. In some services this gap has been found to be a focal point for corrosion. It is standard practice to provide a chamfer at the inside edges of tube holes in tubesheets to prevent cutting of the tubes and to remove burrs produced by drilling or reaming the tubesheet. In the lower tubesheet of vertical units, this chamfer serves as a pocket to collect material, dirt, etc., and acts as a corrosion center. Adequate venting of exchangers is required both for proper operation and to reduce corrosion. Improper venting of the water side of exchangers can cause alternate wetting and drying and accompanying chloride concentration, which is particularly destructive to the series 300 stainless steels. Certain corrosive conditions require that special consideration be given to complete drainage when the unit is taken out of service. Particular consideration is required for the upper surfaces of tubesheets in vertical heat exchangers, for sagging tubes, and for shell-side baffles in horizontal units. SHELL-AND-TUBE EXCHANGER COSTS Basic costs of shell-and-tube heat exchangers made in the United States of carbon-steel construction in 1958 are shown in Fig. 11-41. Cost data for shell-and-tube exchangers from 15 sources were correlated and found to be consistent when scaled by the Marshall and Swift index [Woods et al., Can. J. Chem. Eng. 54: 469–489 (December 1976)]. Costs of shell-and-tube heat exchangers can be estimated from Fig. 11-41 and Tables 11-14 and 11-15. These 1960 costs should be updated by use of the Marshall and Swift Index, which appears in each issue of Chemical Engineering. Note that during periods of high and low demand for heat exchangers the prices in the marketplace may vary significantly from those determined by this method. Small heat exchangers and exchangers bought in small quantities are likely to be more costly than indicated. Standard heat exchangers (which are sometimes off-the-shelf items) are available in sizes ranging from 1.9 to 37 m2 (20 to 400 ft2) at costs lower than for custom-built units. Steel costs are approximately one-half, admiralty tube-side costs are two-thirds, and stainless costs are three-fourths of those for equivalent custom-built exchangers. Kettle-type reboiler costs are 15 to 25 percent greater than for equivalent internal floating-head or U-tube exchangers. The higher extra cost is applicable with relatively large kettle-to-port-diameter ratios and with increased internals (e.g., vapor-liquid separators, foam breakers, sight glasses). To estimate exchanger costs for varying construction details and alloys, first determine the base cost of a similar heat exchanger of basic construction (carbon steel, Class R, 150 lbf/in2) from Fig. 11-41. From Table 11-14, select appropriate extras for higher pressure rating and for alloy construction of tubesheets and baffles, shell and shell cover, and channel and floating-head cover. Compute these extras in accordance with the notes at the bottom of the table. For tubes other than welded carbon steel, compute the extra cost by multiplying the exchanger surface by the appropriate cost per square foot from Table 11-15.

TEMA-STYLE SHELL-AND-TUBE HEAT EXCHANGERS

11-43

FIG. 11-41 Costs of basic exchangers—all steel, TEMA Class R, 150 lbf/in2, 1958 . To convert pounds-force per square inch

to kilopascals, multiply by 6 .895; to convert square feet to square meters, multiply by 0 .0929; to convert inches to millimeters, multiply by 25 .4; and to convert feet to meters, multiply by 0 .3048 .

TABLE 11-14

Extras for Pressure and Alloy Construction and Surface and Weights* Percent of steel base price, 1500-lbf/in2 working pressure Shell diameters, in

Pressure† 300 lbf/in2 450 lbf/in2 600 lbf/in2 Alloy All-steel heat exchanger Tube sheets and baffles Naval rolled brass Monel 1¼ Cr, ½ Mo 4–6 Cr, ½ Mo 11–13 Cr (stainless 410) Stainless 304 Shell and shell cover Monel 1¼ Cr, ½ Mo 4–6 Cr, ½ Mo 11–13 Cr (stainless 410) Stainless 304 Channel and floating-head cover Monel 1¼ Cr, ½ Mo 4–6 Cr, ½ Mo 11–13 Cr (stainless 410) Stainless 304

12

14

16

18

20

22

24

27

30

33

36

39

42

7 18 28

7 19 29

8 20 31

8 21 33

9 22 35

9 23 37

10 24 39

11 27 40

11 29 41

12 31 32

13 32 44

14 33 45

15 35 50

100

100

100

100

100

100

100

100

100

100

100

100

100

14 24 6 19 21 22

17 31 7 22 24 27

19 35 7 24 26 29

21 37 7 25 27 30

22 39 8 26 27 31

22 39 8 26 27 31

22 40 8 26 27 31

22 40 8 25 27 31

22 41 9 25 27 30

23 41 10 25 27 30

24 41 10 26 27 30

24 41 10 26 27 31

25 42 11 26 28 31

45 20 28 29 32

48 22 31 33 34

51 24 33 35 36

52 25 35 36 37

53 25 35 36 38

52 25 35 36 37

52 24 34 35 37

51 22 32 34 35

49 20 30 32 33

47 19 28 30 31

45 18 27 29 30

44 17 26 27 29

44 17 26 27 28

40 23 36 37 37

42 24 37 38 39

42 24 38 39 39

43 25 38 39 39

42 24 37 38 38

41 24 36 37 37

40 23 34 35 36

37 22 31 32 33

34 21 29 30 31

32 21 27 28 29

31 21 26 27 28

40 20 25 26 26

30 20 24 25 26

Surface Surface, ft2, internal floating 251 302 438 565 726 890 1040 1470 1820 2270 2740 3220 3700 head, ¾-in OD by 1-in square ‡ pitch, 16 ft 0 in, tube 1-in OD by 1¼-in square pitch, 218 252 352 470 620 755 876 1260 1560 1860 2360 2770 3200 16-ft 0-in tube§ Weight, lb, internal floating head, 2750 3150 4200 5300 6600 7800 9400 11,500 14,300 17,600 20,500 24,000 29,000 1-in OD, 14 BWG tube ∗Modified from E . N . Sieder and G . H . Elliot, Pet. Refiner 39(5): 223 (1960) . † Total extra is 0 .7 × pressure extra on shell side plus 0 .3 × pressure extra on tube side . ‡ Fixed-tube-sheet construction with ¾-in OD tube on 15/16-in triangular pitch provides 36 percent more surface . § Fixed-tube-sheet construction with 1-in OD tube on 1¼-in triangular pitch provides 18 percent more surface . For an all-steel heat exchanger with mixed design pressures the total extra for pressure is 0 .7 × pressure extra on shell side plus 0 .3 × pressure extra tube side . For an exchanger with alloy parts and a design pressure of 150 lbf/in2, the alloy extras are added . For shell and shell cover the combined alloy-pressure extra is the alloy extra times the shell-side pressure extra/100 . For channel and floating-head cover the combined alloy-pressure extra is the alloy extra times the tube-side pressure extra/100 . For tube sheets and baffles the combined alloy-pressure extra is the alloy extra times the higher-pressure extra times 0 .9/100 . (The 0 .9 factor is included since baffle thickness does not increase because of pressure .) note: To convert pounds-force per square inch to kilopascals, multiply by 6.895; to convert square feet to square meters, multiply by 0.0929; and to convert inches to millimeters, multiply by 25.4.

11-44

HEAT-TRANSFER EQUIPMENT TABLE 11-15

Base Quantity Extra Cost for Tube Gauge and Alloy Dollars per square foot ¾-in OD tubes

Carbon steel Admiralty (T-11) 1¼ Cr, ½ Mo (T-5) 4–6 Cr Stainless 410 welded Stainless 410 seamless Stainless 304 welded Stainless 304 seamless Stainless 316 welded Stainless 316 seamless 90-10 cupronickel Monel Low fin Carbon steel Admiralty 90-10 cupronickel

1-in OD tubes

16 BWG

14 BWG

12 BWG

16 BWG

14 BWG

12 BWG

0 0 .78 1 .01 1 .61 2 .62 3 .10 2 .50 3 .86 3 .40 7 .02 1 .33 4 .25

0 .02 1 .20 1 .04 1 .65 3 .16 3 .58 3 .05 4 .43 4 .17 7 .95 1 .89 5 .22

0 .06 1 .81 1 .11 1 .74 4 .12 4 .63 3 .99 5 .69 5 .41 10 .01 2 .67 6 .68

0 0 .94 0 .79 1 .28 2 .40 2 .84 2 .32 3 .53 3 .25 6 .37 1 .50 4 .01

0 .01 1 .39 0 .82 1 .32 2 .89 3 .31 2 .83 4 .08 3 .99 7 .27 2 .09 4 .97

0 .07 2 .03 0 .95 1 .48 3 .96 4 .47 3 .88 5 .46 5 .36 9 .53 2 .90 6 .47

0 .22 0 .58 0 .72

0 .23 0 .75 0 .96

0 .18 0 .70 0 .86

0 .19 0 .87 1 .06

note: To convert inches to millimeters, multiply by 25.4.

When points for 20-ft-long tubes do not appear in Fig . 11-41, use 0 .95 times the cost of the equivalent 16-ft-long exchanger . Length variation of steel heat exchangers affects costs by approximately $1 per square foot . Shell diameters for a given surface are approximately equal for U-tube and floating-head construction .

Low-fin tubes (1/16-in-high fins) provide 2 .5 times the surface per lineal foot . The surface required should be divided by 2 .5; then use Fig . 11-41 to determine the basic cost of the heat exchanger . Actual surface times extra costs ( from Table 11-15) should then be added to determine cost of the fin-tube exchanger .

HAIRPIN/DOUBLE-PIPE HEAT EXCHANGERS PRINCIPLES OF CONSTRUCTION Hairpin heat exchangers (often also referred to as “double pipes”) are characterized by a construction form that imparts a U-shaped appearance to the heat exchanger . In its classical sense, the term double pipe refers to a heat exchanger consisting of a pipe within a pipe, usually of a straight-leg construction with no bends . However, due to the need for removable bundle construction and the ability to handle differential thermal expansion while avoiding the use of expansion joints (often the weak point of the exchanger), the current U-shaped configuration has become the standard in the industry (Fig . 11-42) . A further departure from the classical definition comes when more than one pipe or tube is used to make a tube bundle, complete with tubesheets and tube supports similar to the TEMA-style exchanger . Hairpin heat exchangers consist of two shell assemblies housing a common set of tubes and interconnected by a return-bend cover referred to as the bonnet. The shell is supported by means of bracket assemblies designed to cradle both shells simultaneously . These brackets are configured to permit the modular assembly of many hairpin sections into an exchanger bank for inexpensive future expansion capability and for providing the very long thermal lengths demanded by special process applications . The bracket construction permits support of the exchanger without fixing the supports to the shell . This provides for thermal movement of the shells within the brackets and prevents the transfer of thermal stresses into the process piping . In special cases the brackets may be welded to the shell . However, this is usually avoided due to the resulting loss of flexibility in field installation and equipment reuse at other sites and an increase in piping stresses . The hairpin heat exchanger, unlike the removable-bundle TEMA styles, is designed for bundle insertion and removal from the return end rather than from the tubesheet end . This is accomplished by means of removable split rings which slide into grooves machined around the outside of each tubesheet and lock the tubesheets to the external closure flanges . This provides a distinct advantage in maintenance since bundle removal takes place

FIG. 11-42 Double-pipe exchanger section with longitudinal fins. (Brown Fin-tube Co.)

at the exchanger end farthest from the plant process piping without disturbing any gasketed joints of this piping . FINNED DOUBLE PIPES The design of the classical single-tube double-pipe heat exchanger is an exercise in pure longitudinal flow with the shell-side and tube-side coefficients differing primarily due to variations in flow areas . Adding longitudinal fins gives the more common double-pipe configuration (Table 11-16) . Increasing the number of tubes yields the multitube hairpin . MULTITUBE HAIRPINS For years, the slightly higher mechanical design complexity of the hairpin heat exchanger relegated it to only the smallest process requirements with shell sizes not exceeding 100 mm . In the early 1970s the maximum available sizes were increased to between 300 and 400 mm depending upon the manufacturer . At present, due to recent advances in design technology, hairpin exchangers are routinely produced in shell sizes between 51 mm (2 in) and 762 mm (30 in) for a wide range of pressures and temperatures and have been made in larger sizes as well . Table 11-17 gives common hairpin tube counts and areas for 19-mm- (¾-in-) OD tubes arranged on a 24-mm (15/16-in) triangular tube layout . The hairpin width and the centerline distance of the two legs (shells) of the hairpin heat exchanger are limited by the outside diameter of the closure flanges at the tubesheets . This diameter, in turn, is a function of the design pressures . As a general rule, for low to moderate design pressures (less than 15 bar), the center-to-center distance is approximately 1 .5 to

TABLE 11-16 Shell pipe OD

Double-Pipe Hairpin Section Data Inner pipe OD

Fin height

Fin count

Surface-areaper-unit length sq m/m sq ft/ft

mm

in

mm

in

mm

in

(max)

60.33 88.9 114.3 114.3 114.3 141.3 168.3

2.375 3.500 4.500 4.500 4.500 5.563 6.625

 25.4  48.26  48.26  60.33  73.03  88.9 114.3

1.000 1.900 1.900 2.375 2.875 3.500 4.500

12.7 12.7 25.4 19.05 12.70 17.46 17.46

0.50 0.50 1.00 0.75 0.50 0.6875 0.6875

24 36 36 40 48 56 72

0.692 1.07 1.98 1.72 1.45 2.24 2.88

2.27 3.51 6.51 5.63 4.76 7.34 9.44

AIR-COOLED HEAT EXCHANGERS TABLE 11-17

Multitube Hairpin Section Data Shell OD

Size

11-45

mm

Shell thickness in

mm

in

Tube count 19 mm

Surface area for 6 .1-m (20-ft) nominal length m2

ft2

2 .98 6 .73 10 .5 16 .7

32 .1 72 .4 113 .2 179 .6

03-MT 04-MT 05-MT 06-MT

88 .9 114 .3 141 .3 168 .3

3 .500 4 .500 5 .563 6 .625

5 .49 6 .02 6 .55 7 .11

0 .216 0 .237 0 .258 0 .280

4 9 14 22

08-MT 10-MT 12-MT 14-MT

219 .1 273 .1 323 .9 355 .6

8 .625 10 .75 12 .75 14 .00

8 .18 9 .27 9 .53 9 .53

0 .322 0 .365 0 .375 0 .375

42 70 109 136

32 .0 54 .0 84 .7 107

344 .3 581 .3 912 .1 1159

16-MT 18-MT 20-MT 22-MT

406 .4 457 .2 508 .0 558 .8

16 .00 18 .00 20 .00 22 .00

9 .53 9 .53 9 .53 9 .53

0 .375 0 .375 0 .375 0 .375

187 230 295 367

148 182 235 294

1594 1960 2529 3162

24-MT 26-MT 28-MT 30-MT

609 .6 660 .4 711 .2 762 .0

24 .00 26 .00 28 .00 30 .00

9 .53 9 .53 9 .53 11 .11

0 .375 0 .375 0 .375 0 .4375

450 526 622 733

362 427 508 602

3902 4591 5463 6475

1 .8 times the shell outside diameter, with this ratio decreasing slightly for the larger sizes . One interesting consequence of this fact is the inability to construct a hairpin tube bundle having the smallest radius bends common to a conventional U-tube, TEMA shell, and tube bundle . In fact, in the larger hairpin sizes the tubes might be better described as curved rather than bent . The smallest U-bend diameters are greater than the outside diameter of shells less than 300 mm in size . The U-bend diameters are greater than 300 mm in larger shells . As a general rule, mechanical tube cleaning around the radius of a U-bend may be accomplished with a flexible shaft-cleaning tool for bend diameters greater than 10 times the tube’s inside diameter . This permits the tool to pass around the curve of the tube bend without binding . In all these configurations, maintaining longitudinal flow on both the shell side and the tube side allows the decision for placement of a fluid stream on either one side or the other to be based upon design efficiency (mass flow rates, fluid properties, pressure drops, and velocities), and not because there is any greater tendency to foul on one side than the other . Experience has shown that, in cases where fouling is influenced by flow velocity, overall fouling in tube bundles is less in properly designed longitudinal flow bundles where areas of low velocity can be avoided without flowinduced tube vibration . This same freedom of stream choice is not as readily applied when a segmental baffle is used . In those designs, the baffle’s creation of low velocities and stagnant flow areas on the outside of the bundle can result in increased shell-side fouling at various locations of the bundle . The basis for choosing the stream side in those cases will be similar to the common shell-and-tube

heat exchanger . At times a specific selection of stream side must be made regardless of the tube support mechanism in expectation of an unresolvable fouling problem . However, this is often the exception rather than the rule . DESIGN APPLICATIONS One benefit of the hairpin exchanger is its ability to handle high tube-side pressures at a lower cost than other removable-bundle exchangers . This is due in part to the lack of pass partitions at the tubesheets which complicate the gasketing design process . Present mechanical design technology has allowed the building of dependable, removable-bundle, hairpin multitubes at tube-side pressures of 825 bar (12,000 psi) . The best-known use of the hairpin exchanger is its operation in true countercurrent flow, which yields the most efficient design for processes that have a close temperature approach or temperature cross . However, maintaining countercurrent flow in a tubular heat exchanger usually implies one tube pass for each shell pass . As recently as 30 years ago, the lack of inexpensive, multiple-tube pass capability often diluted the advantages gained from countercurrent flow . The early attempts to solve this problem led to investigations into the area of heat-transfer augmentation . This familiarity with augmentation techniques inevitably led to improvements in the efficiency and capacity of the small heat exchangers . The result has been the application of the hairpin heat exchanger to the solution of unique process problems, such as dependable, once-through, convective boilers offering high-exit qualities, especially in cases of process temperature crosses .

AIR-COOLED HEAT EXCHANGERS INTRODUCTION TO AIR-COOLED HEAT EXCHANGERS Atmospheric air has been used for many years to cool and condense fluids in areas of water scarcity . During the 1960s the use of air-cooled heat exchangers grew rapidly in the United States and elsewhere . In Europe, where seasonal variations in ambient temperatures are relatively small, air-cooled exchangers are used for the greater part of process cooling . In some new plants all cooling is done with air . Increased use of air-cooled heat exchangers has resulted from lack of available water, significant increases in water costs, and concern for water pollution . Air-cooled heat exchangers include a tube bundle, which generally has spiral-wound fins upon the tubes, and a fan, which moves air across the tubes and is provided with a driver . Electric motors are the most commonly used drivers; typical drive arrangements require a V belt or a direct rightangle gear . A plenum and structural supports are basic components . Louvers are often used . A bay generally has two tube bundles installed in parallel . These may be in the same or different services . Each bay is usually served by two

(or more) fans and is furnished with a structure, a plenum, and other attendant equipment . The location of air-cooled heat exchangers must take into consideration the large space requirements and the possible recirculation of heated air because of the effect of prevailing winds upon buildings, fired heaters, towers, various items of equipment, and other air-cooled exchangers . Inlet air temperature at the exchanger can be significantly higher than the ambient air temperature at a nearby weather station . See Air-Cooled Heat Exchangers for General Refinery Services, API Standard 661, 2d ed ., January 1978, for information on refinery process air-cooled heat exchangers . Forced and Induced Draft The forced-draft unit, illustrated in Fig . 11-43, pushes air across the finned-tube surface . The fans are located below the tube bundles . The induced-draft design has the fan above the bundle, and the air is pulled across the finned-tube surface . In theory, a primary advantage of the forced-draft unit is that less power is required . This is true when the air temperature rise exceeds 30°C (54°F) . Air-cooled heat exchangers are generally arranged in banks with several exchangers installed side by side . The height of the bundle aboveground

11-46

HEAT-TRANSFER EQUIPMENT

FIG. 11-43

Forced-draft air-cooled heat exchanger . [Chem. Eng. 114 (Mar . 27, 1978) .]

must be one-half of the tube length to produce an inlet velocity equal to the face velocity . This requirement applies both to ground-mounted exchangers and to those pipe-rack-installed exchangers which have a fire deck above the pipe rack . The forced-draft design offers better accessibility to the fan for on-stream maintenance and fan blade adjustment . The design also provides a fan and V-belt assembly, which are not exposed to the hot-air stream that exits from the unit . Structural costs are lower, and mechanical life is longer . Induced-draft design provides more even distribution of air across the bundle, since air velocity approaching the bundle is relatively low . This design is better suited for exchangers designed for a close approach of product outlet temperature to ambient-air temperature . Induced-draft units are less likely to recirculate the hot exhaust air, since the exit air velocity is several times that of the forced-draft unit . Induced-draft design more readily permits the installation of the air-cooled equipment above other mechanical equipment such as pipe racks or shelland-tube exchangers . In a service in which sudden temperature change would cause upset and loss of product, the induced-draft unit gives greater protection in that only a fraction of the surface (as compared with the forced-draft unit) is exposed to rainfall, sleet, or snow . Tube Bundle The principal parts of the tube bundle are the finned tubes and the header . Most commonly used is the plug header, which is a welded box illustrated in Fig . 11-44 . The finned tubes are described in a

FIG. 11-44

subsequent paragraph . The components of a tube bundle are identified in the figure . The second most commonly used header is a cover-plate header . The cover plate is bolted to the top, bottom, and end plates of the header . Removing the cover plate provides direct access to the tubes without the necessity of removing individual threaded plugs . Other types of headers include the bonnet-type header, which is constructed similarly to the bonnet of shell-and-tube heat exchangers; manifoldtype headers, which are made from pipe and have tubes welded into the manifold; and billet-type headers, made from a solid piece of material with machined channels for distributing the fluid . Serpentine-type tube bundles are sometimes used for very viscous fluids . A single continuous flow path through pipe is provided . Tube bundles are designed to be rigid and self-contained and are mounted so that they expand independently of the supporting structure . The face area of the tube bundle is its length times width . The net free area for air flow through the bundle is about 50 percent of the face area of the bundle . The standard air face velocity (FV) is the velocity of standard air passing through the tube bundle and generally ranges from 1 .5 to 3 .6 m/s (300 to 700 ft/min) . Tubing The 25 .4-mm (1-in) OD tube is most commonly used . Fin heights vary from 12 .7 to 15 .9 mm (0 .5 to 0 .625 in), fin spacing from 3 .6 to 2 .3 mm (7 to 11 per linear inch), and tube triangular pitch from 50 .8 to

Typical construction of a tube bundle with plug headers: (1) tube sheet; (2) plug sheet; (3) top and bottom plates; (4) end plate; (5) tube; (6) pass partition; (7) stiffener; (8) plug; (9) nozzle; (10) side frame; (11) tube spacer; (12) tube-support cross member; (13) tube keeper; (14) vent; (15) drain; (16) instrument connection . (API Standard 661 .)

AIR-COOLED HEAT EXCHANGERS 63 .5 mm (2 .0 to 2 .5 in) . The ratio of extended surface to bare-tube outside surface varies from about 7 to 20 . The 38-mm (1½-in) tube has been used for flue gas and viscous oil service . Tube size, fin heights, and fin spacing can be further varied . Tube lengths vary and may be as great as 18 .3 m (60 ft) . When tube length exceeds 12 .2 m (40 ft), three fans are generally installed in each bay . Frequently used tube lengths vary from 6 .1 to 12 .2 m (20 to 40 ft) . Finned-Tube Construction The following are descriptions of commonly used finned-tube constructions (Fig . 11-45) . 1 . Embedded. The rectangular-cross-section aluminum fin is wrapped under tension and mechanically embedded in a groove 0 .25 ± 0 .05 mm (0 .010 ± 0 .002 in) deep, spirally cut into the outside surface of a tube . 2 . Integral (or extruded). An aluminum outer tube from which fins have been formed by extrusion is mechanically bonded to an inner tube or liner . 3 . Overlapped footed. L-shaped aluminum fin is wrapped under tension over the outside surface of a tube, with the tube fully covered by the overlapped feet under and between the fins . 4 . Footed. L-shaped aluminum fin is wrapped under tension over the outside surface of a tube with the tube fully covered by the feet between the fins . 5 . Bonded. Tube fins are bonded to the outside surface by hot-dip galvanizing, brazing, or welding . Typical metal design temperatures for these finned-tube constructions are 399°C (750°F) embedded, 288°C (550°F) integral, 232°C (450°F) overlapped footed, and 177°C (350°F) footed . Tube ends are left bare to permit insertion of the tubes into appropriate holes in the headers or tubesheets . Tube ends are usually roller-expanded into these tube holes . Fans Axial-flow fans are large-volume, low-pressure devices . Fan diameters are selected to give velocity pressures of approximately 2 .5 mm (0 .1 in) of water . Total fan efficiency ( fan, driver, and transmission device) is about 75 percent, and fan drives usually have a minimum of 95 percent mechanical efficiency . Usually fans are provided with four or six blades . Larger fans may have more blades . Fan diameter is generally slightly less than the width of the bay . At the fan-tip speeds required for economic performance, a large amount of noise is produced . The predominant source of noise is vortex shedding at the trailing edge of the fan blade . Noise control of air-cooled exchangers is required by the Occupational Safety and Health Act (OSHA) . API Standard 661 (Air-Cooled Heat Exchangers for General Refinery Services, 2d ed ., January 1978) has the purchaser specifying sound-pressure-level (SPL) values per fan at a location designated by the purchaser and also specifying soundpower-level (PWL) values per fan . These are designated at the following octave-band-center frequencies: 63, 125, 250, 1000, 2000, 4000, 8000, and also the dBa value (the dBa is a weighted single-value sound pressure level) . Reducing the fan-tip speed results in a straight-line reduction in air flow while the noise level decreases . The API Standard limits fan-tip speed to 61 m/s (12,000 ft/min) for typical constructions . Fan design changes that

FIG. 11-45 Finned-tube construction .

11-47

reduce noise include increasing the number of fan blades, increasing the width of the fan blades, and reducing the clearance between fan tip and fan ring . Both the quantity of air and the developed static pressure of fans in aircooled heat exchangers are lower than indicated by fan manufacturers’ test data, which are applicable to testing-facility tolerances and not to heat exchanger constructions . The axial-flow fan is inherently a device for moving a consistent volume of air when blade setting and speed of rotation are constant . Variation in the amount of air flow can be obtained by adjusting the blade angle of the fan and the speed of rotation . The blade angle can be (1) permanently fixed, (2) hand-adjustable, or (3) automatically adjusted . Air delivery and power are a direct function of blade pitch angle . Fan mounting should provide a minimum of one-half to three-fourths diameter between fan and ground on a forced-draft heat exchanger and one-half diameter between tubes and fan on an induced-draft cooler . Fan blades can be made of aluminum, molded plastic, laminated plastic, carbon steel, stainless steel, and Monel . Fan Drivers Electric motors or steam turbines are most commonly used . These connect with gears or V belts . (Gas engines connected through gears and hydraulic motors either direct-connected or connected through gears are in use .) Fans may be driven by a prime mover such as a compressor with a V-belt takeoff from the flywheel to a jack shaft and then through a gear or V belt to the fan . Direct motor drive is generally limited to small-diameter fans . V-belt drive assemblies are generally used with fans 3 m (10 ft) and less in diameter and motors of 22 .4 kW (30 hp) and less . Right-angle gear drive is preferred for fans over 3 m (10 ft) in diameter, for electric motors over 22 .4 kW (30 hp), and with steam-turbine drives . Fan Ring and Plenum Chambers The air must be distributed from the circular fan to the rectangular face of the tube bundle . The air velocity at the fan is between 3 .8 and 10 .2 m/s (750 and 2000 ft/in) . The plenumchamber depth ( from fan to tube bundle) is dependent upon the fan dispersion angle (Fig . 11-46), which should have a maximum value of 45° . The fan ring is made to commercial tolerances for the relatively largediameter fan . These tolerances are greater than those upon closely machined fan rings used for small-diameter laboratory-performance testing . Fan performance is directly affected by this increased clearance between the blade tip and the ring, and adequate provision in design must be made for the reduction in air flow . API Standard 661 requires that fan-tip clearance be a maximum of 0 .5 percent of the fan diameter for diameters between 1 .9 and 3 .8 m (6 .25 and 12 .5 ft) . Maximum clearance is 9 .5 mm (⅜ in) for smaller fans and 19 mm (¾ in) for larger fans . The depth of the fan ring is critical . Worsham (ASME Pap . 59-PET-27, Petroleum Mechanical Engineering Conference, Houston, 1959) reports an increase in flow varying from 5 to 15 percent with the same power consumption when the depth of a fan ring was doubled . The percentage increase was proportional to the volume of air and static pressure against which the fan was operating .

11-48

HEAT-TRANSFER EQUIPMENT

FIG. 11-47 Contained internal recirculation (with internal louvers) . [Hydrocarbon Process 59: 148–149 (October 1980) .]

FIG. 11-46

Fan dispersion angle . (API Standard 661 .)

When a selection is made, the stall-out condition, which develops when the fan cannot produce any more air regardless of power input, should be considered . Air Flow Control Process operating requirements and weather conditions are considered in determining the method of controlling air flow . The most common methods include simple on-off control, on-off step control (in the case of multiple-driver units), two-speed-motor control, variablespeed drivers, controllable fan pitch, manually or automatically adjustable louvers, and air recirculation . Winterization is the provision of design features, procedures, or systems for air-cooled heat exchangers to avoid process-fluid operating problems resulting from low-temperature inlet air . These include fluid freezing, pour point, wax formation, hydrate formation, laminar flow, and condensation at the dew point (which may initiate corrosion) . The freezing points for some commonly encountered fluids in refinery service are benzene, 5 .6°C (42°F); p-xylene, 15 .5°C (55 .9°F); cyclohexane, 6 .6°C (43 .8°F); phenol, 40 .9°C (105 .6°F); monoethanolamine, 10 .3°C (50 .5°F); and diethanolamine, 25 .1°C (77 .2°F) . Water solutions of these organic compounds are likely to freeze in air-cooled exchangers during winter service . Paraffinic and olefinic gases (C1 through C4) saturated with water vapor form hydrates when cooled . These hydrates are solid crystals which can collect and plug exchanger tubes . Air flow control in some services can prevent these problems . Cocurrent flow of air and process fluid during winter may be adequate to prevent problems . (Normal design has countercurrent flow of air and process fluid .) In some services when the hottest process fluid is in the bottom tubes, which are exposed to the lowest-temperature air, winterization problems may be eliminated . Following are references which deal with problems in low-temperature environments: Brown and Benkley, “Heat Exchangers in Cold Service—A Contractor’s View,” Chem. Eng. Prog. 70: 59–62 (July 1974); Franklin and Munn, “Problems with Heat Exchangers in Low Temperature Environments,” Chem. Eng. Prog. 70: 63–67 (July 1974); Newell, “Air-Cooled Heat Exchangers in Low Temperature Environments: A Critique,” Chem. Eng. Prog. 70: 86–91 (October 1974); Rubin, “Winterizing Air Cooled Heat Exchangers,” Hydrocarbon Process 59: 147–149 (October 1980); Shipes, “Air-Cooled Heat Exchangers in Cold Climates,” Chem. Eng. Prog. 70: 53–58 (July 1974) . Air Recirculation Recirculation of air which has been heated as it crosses the tube bundle provides the best means of preventing operating problems due to low-temperature inlet air . Internal recirculation is the movement of air within a bay so that the heated air which has crossed the bundle is directed by a fan with reverse flow across another part of the bundle . Wind skirts and louvers are generally provided to minimize the entry of low-temperature air from the surroundings . Contained internal recirculation uses louvers within the bay to control the flow of warm air in the bay, as illustrated in Fig . 11-47 . Note that low-temperature inlet air has access to the tube bundle . External recirculation is the movement of the heated air within the bay to an external duct, where this air mixes with inlet air, and the mixture serves as the cooling fluid within the bay . Inlet air does not have direct access to the tube bundle; an adequate mixing chamber is essential . Recirculation over the end of the exchanger is illustrated in Fig . 11-48 . Over-the-side recirculation also is used . External recirculation systems maintain the desired low temperature of the air crossing the tube bundle .

Trim Coolers Conventional air-cooled heat exchangers can cool the process fluid to within 8 .3°C (15°F) of the design dry-bulb temperature . When a lower process outlet temperature is required, a trim cooler is installed in series with the air-cooled heat exchanger . The water-cooled trim cooler can be designed for a 5 .6°C to 11 .1°C (10°F to 20°F) approach to the wet-bulb temperature, which in the United States is about 8 .3°C (15°F) less than the dry-bulb temperature . In arid areas the difference between dryand wet-bulb temperatures is much greater . Humidification Chambers The air-cooled heat exchanger is provided with humidification chambers in which the air is cooled to a close approach to the wet-bulb temperature before entering the finned-tube bundle of the heat exchanger . Evaporative Cooling The process fluid can be cooled by using evaporative cooling with the sink temperature approaching the wet-bulb temperature . Steam Condensers Air-cooled steam condensers have been fabricated with a single tube-side pass and several rows of tubes . The bottom row has a higher temperature difference than the top row, since the air has been heated as it crosses the rows of tubes . The bottom row condenses all the entering steam before the steam has traversed the length of the tube . The top row, with a lower-temperature driving force, does not condense all the entering steam . At the exit header, uncondensed steam flows from the top row into the bottom row . Since noncondensible gases are always present in steam, these accumulate within the bottom row because steam is entering from both ends of the tube . Performance suffers .

FIG. 11-48

External recirculation with adequate mixing chamber . [Hydrocarbon Process 59: 148–149 (October 1980) .]

COMPACT AND NONTUBULAR HEAT EXCHANGERS TABLE 11-18

Air-Cooled Heat-Exchanger Costs (1970)

Surface (bare tube), sq . ft .

500

1000

2000

3000

5000

Cost for 12-row-deep bundle, dollars/square foot

9 .0

7 .6

6 .8

5 .7

5 .3

Factor for bundle depth: 6 rows 4 rows 3 rows

1 .07 1 .2 1 .25

1 .07 1 .2 1 .25

1 .07 1 .2 1 .25

1 .12 1 .3 1 .5

1 .12 1 .3 1 .5

Base: Bare-tube external surface 1 in . o .d . by 12 B .W .G . by 24 ft . 0 in . steel tube with 8 aluminum fins per inch ⅝-in . high . Steel headers . 150 lb ./sq . in . design pressure . V-belt drive and explosion-proof motor . Bare-tube surface 0 .262 sq . ft ./ft . Fin-tube surface/bare-tube surface ratio is 16 .9 . Factors: 20 ft . tube length 1 .05 30 ft . tube length 0 .95 18 B .W .G . admiralty tube 1 .04 16 B .W .G . admiralty tube 1 .12 note: To convert feet to meters, multiply by 0.3048; to convert square feet to square meters, multiply by 0.0929; and to convert inches to millimeters, multiply by 25.4.

Various solutions have been used . These include orifices to regulate the flow into each tube, a “blow-through steam” technique with a vent condenser, complete separation of each row of tubes, and inclined tubes . Air-Cooled Overhead Condensers Air-cooled overhead condensers (AOCs) have been designed and installed above distillation columns as integral parts of distillation systems . The condensers generally have inclined tubes, with air flow over the finned surfaces induced by a fan . Prevailing wind affects both structural design and performance . AOCs provide the additional advantages of reducing ground-space requirements and piping and pumping requirements and of providing smoother column operation . The downflow condenser is used mainly for nonisothermal condensation . Vapors enter through a header at the top and flow downward . The reflux condenser is used for isothermal and small-temperature-change conditions . Vapors enter at the bottom of the tubes . AOC usage first developed in Europe but became more prevalent in the United States during the 1960s . A state-of-the-art article was published by Dehne [Chem. Eng. Prog. 64: 51 (July 1969)] . Air-Cooled Heat Exchanger Costs The cost data in Table 11-18 are unchanged from those published in the 1963 edition of this text . In 1969 Guthrie [Chem. Eng. 75: 114 (Mar . 24, 1969)] presented cost data for fielderected air-cooled exchangers . These costs are only 25 percent greater than those of Table 11-18 and include the costs of steel stairways, indirect subcontractor charges, and field erection charges . Since minimal field costs would be this high (i .e ., 25 percent of purchase price), the basic costs appear to be unchanged . (Guthrie indicated a cost band of ±25 percent .) Preliminary design and the cost estimation of air-cooled heat exchangers have been discussed by J . E . Lerner [“Simplified Air Cooler Estimating,” Hydrocarbon Process 52: 93–100 (February 1972)] . Design Considerations 1 . Design dry-bulb temperature. The typically selected value is the temperature which is equaled or exceeded 2½ percent of the time during the warmest consecutive 4 months . Since air temperatures at industrial sites are frequently higher than those used for these weather data reports, it is good practice to add 1°C to 3°C (2°F to 6°F) to the tabulated value . 2 . Air recirculation. Prevailing winds and the locations and elevations of buildings, equipment, fired heaters, etc ., require consideration . All aircooled heat exchangers in a bank are of one type, i .e ., all forced-draft or all induced-draft . Banks of air-cooled exchangers must be placed far enough apart to minimize air recirculation . 3 . Wintertime operations. In addition to the previously discussed problems of winterization, provision must be made for heavy rain, strong winds, freezing of moisture upon the fins, etc . 4 . Noise. Two identical fans have a noise level 3 dBa higher than one fan, while eight identical fans have a noise level 9 dBa higher than a single fan . Noise level at the plant site is affected by the exchanger position, reflective

11-49

surfaces near the fan, hardness of these surfaces, and noise from adjacent equipment . The extensive use of air-cooled heat exchangers contributes significantly to plant noise level . 5 . Ground area and space requirements. Comparisons of the overall space requirements for plants using air cooling versus water cooling are not consistent . Some air-cooled units are installed above other equipment— pipe racks, shell-and-tube exchangers, etc . Some plants avoid such installations because of safety considerations, as discussed later . 6 . Safety. Leaks in air-cooled units are transmitted directly to the atmosphere and can cause fire hazards or toxic-fume hazards . However, the large air flow through an air-cooled exchanger greatly reduces any concentration of toxic fluids . Segal [Pet. Refiner 38: 106 (April 1959)] reports that air-fin coolers “are not located over pumps, compressors, electrical switchgear, control houses and, in general, the amount of equipment such as drums and shell-and-tube exchangers located beneath them are minimized .” Pipe-rack-mounted air-cooled heat exchangers with flammable fluids generally have concrete fire decks which isolate the exchangers from the piping . 7 . Atmospheric corrosion. Air-cooled heat exchangers should not be located where corrosive vapors and fumes from vent stacks will pass through them . 8 . Air-side fouling. Air-side fouling is generally negligible . 9 . Process-side cleaning. Either chemical or mechanical cleaning on the inside of the tubes can readily be accomplished . 10 . Process-side design pressure. The high-pressure process fluid is always in the tubes . Tube-side headers are relatively small compared with water-cooled units when the high pressure is generally on the shell side . High-pressure design of rectangular headers is complicated . The plugtype header is normally used for design gauge pressures to 13,790 kPa (2000 lbf/in2) and has been used to 62,000 kPa (9000 lbf/in2) . The use of threaded plugs at these pressures creates problems . Removable cover plate headers are generally limited to gauge pressures of 2068 kPa (300 lbf/in2) . The expensive billet-type header is used for high-pressure service . 11 . Bond resistance. Vibration and thermal cycling affect the bond resistance of the various types of tubes in different manners and thus affect the amount of heat transfer through the fin tube . 12 . Approach temperature. The approach temperature, which is the difference between the process-fluid outlet temperature and the design drybulb air temperature, has a practical minimum of 8°C to 14°C (15°F to 25°F) . When a lower process-fluid outlet temperature is required, an air humidification chamber can be provided to reduce the inlet air temperature toward the wet-bulb temperature . A 5 .6°C (10°F) approach is feasible . Since typical summer wet-bulb design temperatures in the United States are 8 .3°C (15°F) lower than dry-bulb temperatures, the outlet process-fluid temperature can be 3°C (5°F) below the dry-bulb temperature . 13 . Mean-temperature-difference (MTD) correction factor. When the outlet temperatures of both fluids are identical, the MTD correction factor for a 1:2 shell-and-tube exchanger (one pass shell side, two or more passes tube side) is approximately 0 .8 . For a single-pass, air-cooled heat exchanger the factor is 0 .91 . A two-pass exchanger has a factor of 0 .96, while a three-pass exchanger has a factor of 0 .99 when passes are arranged for counterflow . 14 . Maintenance cost. Maintenance for air-cooled equipment as compared with shell-and-tube coolers (complete with cooling-tower costs) indicates that air-cooling maintenance costs are approximately 0 .3 to 0 .5 times those for water-cooled equipment . 15 . Operating costs. Power requirements for air-cooled heat exchangers can be lower than at the summer design condition provided that an adequate means of air flow control is used . The annual power requirement for an exchanger is a function of the means of air flow control, the exchanger service, the air-temperature rise, and the approach temperature . When the mean annual temperature is 16 .7°C (30°F) lower than the design dry-bulb temperature and when both fans in a bay have automatically controllable pitch of fan blades, the annual power required has been found to be 22, 36, and 54 percent, respectively, of that needed at the design condition for three process services [Frank L . Rubin, “Power Requirements Are Lower for Air-Cooled Heat Exchangers with AV Fans,” Oil Gas J., pp . 165–167 (Oct . 11, 1982)] . Alternatively, when fans have two-speed motors, these deliver one-half of the design flow of air at half speed and use only one-eighth of the power of the full-speed condition .

COMPACT AND NONTUBULAR HEAT EXCHANGERS COMPACT HEAT EXCHANGERS With equipment costs rising and limited available plot space, compact heat exchangers are gaining a larger portion of the heat exchanger market . Numerous types use special enhancement techniques to achieve the required heat transfer in smaller plot areas and, in many cases, require lower

initial investment . As with all items that afford a benefit, a series of restrictions limit the effectiveness or application of these special heat exchanger products . In most products discussed, some of these considerations are presented, but a thorough review with reputable suppliers of these products is the only positive way to select a compact heat exchanger . The following guidelines will assist in prequalifying one of these .

11-50

HEAT-TRANSFER EQUIPMENT

FIG. 11-49

Plate-and-frame heat exchanger . Hot fluid flows down between alternate plates, and cold fluid flows up between alternate plates . (Thermal Division, Alfa-Laval, Inc.)

PLATE-AND-FRAME EXCHANGERS There are two major types: gasketed and welded-plate heat exchangers . Each is discussed individually . GASKETED-PLATE EXCHANGERS Description This type is the fastest growing of the compact exchangers and the most recognized (see Fig . 11-49) . A series of corrugated alloy material channel plates, bounded by elastomeric gaskets, are hung off and guided by longitudinal carrying bars, then compressed by large-diameter tightening bolts between two pressure-retaining frame plates (cover plates) . The frame and channel plates have portholes which allow the process fluids to enter alternating flow passages (the space between two adjacent-channel plates) . Gaskets around the periphery of the channel plate prevent leakage to the atmosphere and prevent process fluids from coming in contact with the frame plates . No interfluid leakage is possible in the port area because of a dual-gasket seal . The frame plates are typically epoxy-painted carbon-steel material and can be designed per most pressure vessel codes . Design limitations are found in Table 11-19 . The channel plates are always an alloy material with 304SS as a minimum (see Table 11-19 for other materials) . Channel plates are typically 0 .4 to 0 .8 mm thick and have corrugation depths of 2 to 10 mm . Special wide-gap (WG PHE) plates are available, in limited sizes, for slurry applications with depths of approximately 16 mm . The channel plates are compressed to achieve metal-to-metal contact for pressure-retaining integrity . These narrow gaps and the high number of contact points that change the fluid flow direction combine to create a very high turbulence between the plates . This means high individual

heat-transfer coefficients (up to 14,200 W/m2 · °C), but very high pressure drops per length as well . To compensate, the channel plate lengths are usually short, most under 2 m and few over 3 m in length . In general, the same pressure drops as conventional exchangers are used without loss of the enhanced heat transfer . Expansion of the initial unit is easily performed in the field without special considerations . The original frame length typically has an additional capacity of 15 to 20 percent more channel plates (i .e ., surface area) . In fact, if a known future capacity is available during fabrication stages, a longer carrying bar could be installed, and increasing the surface area would be easily handled later . When the expansion is needed, simply loosen the carrying bolts, pull back the frame plate, add the additional channel plates, and tighten the frame plate . API 662 Part I now covers the design of these types of heat exchangers . Applications Most plate heat exchanger (PHE) applications historically have been liquid-liquid services, but there has been significant development in the use of PHE for vacuum condensing as well as evaporation and column reboiling . Industrial users typically have chevron-style channel plates while some food applications are washboard style . Fine particulate slurries in concentrations up to 70 percent by weight are possible with standard channel spacings . Wide-gap units are used with larger particle sizes . Typical particle size should not exceed 75 percent of the single plate (not total channel) gap . Close temperature approaches and tight temperature control possible with PHEs and the ability to sanitize the entire heat-transfer surface easily were a major benefit in the food industry . Multiple services in a single frame are possible . Gasket selection is one of the most critical and limiting factors in PHE use . Table 11-20 gives some guidelines for fluid compatibility . Even trace

COMPACT AND NONTUBULAR HEAT EXCHANGERS TABLE 11-19

11-51

Compact Exchanger Applications Guide

Design conditions Design temperature, °C Minimum metal temp ., °C Design pressure, MPa Inspect for leakage Mechanical cleaning Chemical cleaning Expansion capability Repair Temperature cross Surface area/unit, m2 Holdup volume Materials Mild steel Stainless Titanium Hastalloy Nickel Alloy 20 Incoloy 825 Monel Impervious graphite

G . PHE

W . PHE

WG . PHE

BHE

DBL

MLT

STE

180 −30 3 Yes Yes Yes Yes Yes Yes 2800 Low

150 −30 2 .5 Partial Yes/no Yes Yes Yes/no Yes 900 Low

150 −30 0 .7 Yes Yes Yes Yes Yes Yes 250 Low

185 −160 3 .1 No No Yes No No Yes 50 Low

+500 −160 +20 Yes Yes Yes No Yes Yes 10 Med

+500 −160 +20 Yes Yes Yes No Yes Yes 150 Med

+500 −160 +20 Yes Yes/no Yes No Partial Yes 60 Low

G . PHE

W . PHE

WG . PHE

BHE

DBL

MLT

STE

No Yes Yes Yes Yes Yes Yes Yes No

No Yes Yes No No No No No No

No Yes No No No No No No No

Yes Yes Yes Yes Yes Yes Yes Yes No

Yes Yes Yes Yes Yes Yes Yes Yes No

Yes Yes Yes Yes Yes Yes Yes Yes No

G . PHE

W . PHE

WG . PHE

BHE

DBL

MLT

STE

A D A/B A/B B/D D D D D B A A A B

A A/D A/B A/B D D A A/B D C D C A B

A D A/B A/B A/B B D D D D B C A A

A A B D C D A A/B D D D A A D

A A A A A A A A A/D A/D A/D B A A

A A A A A/B B/C A A A A B B A A/B

A A A/B A/B C D B/C C A A A A A B/C

No Yes Yes Yes Yes Yes Yes Yes Yes

Service Clean fluids Gasket incompatibility Medium viscosity High viscosity Slurries and pulp ( fine) Slurries and pulp (coarse) Refrigerants Thermal fluids Vent condensers Process condenser Vacuum reboil/condenser Evaporator Tight temp . control High scaling

CP

SHE

THE

+400 −160 10 Yes Yes Yes No Partial Yes 450 Med

+500 −160 +20 Yes Yes Yes No Yes No∗ High High

CP

SHE

THE

No Yes Yes Yes Yes Yes Yes Yes No

Yes Yes Yes Yes Yes Yes Yes Yes No

Yes Yes Yes Yes Yes Yes Yes Yes Yes

CP

SHE

THE

A A A/B A/B B B A A B/C A/B B/C B/C B B

A A A A A A A A A B B C A B

A A A A A/D A/D A A A A A/C A C A/D

450 −160 4 .2 Partial Yes Yes No Yes Yes 850 Low

∗Multipass . Adapted from Alfa-Laval literature . A—Very good C—Fair B—Good D—Poor

fluid components need to be considered . The higher the operating temperature and pressure, the shorter the anticipated gasket life . Always consult the supplier on gasket selection and obtain an estimated or guaranteed lifetime . TABLE 11-20 Elastomer Selection Guide Uses Nitrile (NBR)

Avoid

Oil resistant Fat resistant Food stuffs Mineral oil Water

Oxidants Acids Aromatics Alkalies Alcohols

Resin cured butyl (IIR)

Acids Lyes Strong alkalies Strong phosphoric acid Dilute mineral acids Ketones Amines Water

Fats and fatty acids Petroleum oils Chlorinated hydrocarbons Liquids with dissolved chlorine Mineral oil Oxygen rich demin . water Strong oxidants

Ethylene-propylene (EPDM)

Oxidizing agents Dilute acids Amines Water (Mostly any IIR fluid)

Oils Hot & conc . acids Very strong oxidants Fats & fatty acids Chlorinated hydrocarbons

Viton (FKM, FPM)

Water Petroleum oils Many inorganic acids (Most all NBR fluids)

Amines Ketones Esters Organic acids Liquid ammonia

The major applications are, but not limited to, the following: Temperature cross applications Close approaches Viscous fluids Sterilized surface required Polished surface required Future expansion required Space restrictions Barrier coolant services Slurry applications

(lean/rich solvent) ( freshwater/seawater) (emulsions) ( food, pharmaceutical) (latex, pharmaceutical) (closed-loop coolers) (TiO2, Kaolin, precipitated  calcium carbonate, and beet sugar raw juice)

Design Plate exchangers are becoming so commonplace that there is now an API 662 document available for the specification of these products . In addition, commercial computer programs are available from HTRI among others . Standard channel-plate designs, unique to each manufacturer, are developed with limited modifications of each plate’s corrugation depths and included angles . Manufacturers combine their different style plates to custom-fit each service . Due to the possible combinations, it is impossible to present a way to exactly size PHEs . However, it is possible to estimate areas for new units and to predict performance of existing units with different conditions (chevron-type channel plates are presented) . The fixed length and limited corrugation included angles on channel plates makes the NTU (number of heat transfer units) method of sizing practical . (Water-like fluids are assumed for the following examples .) NTU =

∆t of either side LMTD

(11-76)

11-52

HEAT-TRANSFER EQUIPMENT

Most plates have NTU values of 0 .5 to 4 .0, with 2 .0 to 3 .0 as the most common (multipass shell-and-tube exchangers are typically less than 0 .75) . The more closely the fluid profile matches that of the channel plate, the smaller the required surface area . Attempting to increase the service NTU beyond the plate’s NTU capability causes oversurfacing (inefficiency) . True sizing from scratch is impractical since a pressure balance on a channel-to-channel basis, from channel closest to inlet to farthest, must be achieved and when mixed plate angles are used; this is quite a challenge . Computer sizing is not just a benefit, it is a necessity for supplier’s selection . Averaging methods are recommended to perform any sizing calculations . From the APV heat-transfer handbook Design and Application of ParaflowPlate Heat Exchangers and J . Marriott’s article “Where and How to Use Plate Heat Exchangers,” Chemical Engineering, April 5, 1971, there are the equations for plate heat transfer . Nu =

h De = 0 .28 × (Re) 0 .65 × (Pr)0 .4 k

(11-77)

where De = 2 × depth of single-plate corrugation . Also G=

W Np × w × De

(11-78)

The width of the plate w is measured from inside to inside of the channel gasket . If it is not available, use the tear-sheet drawing width and subtract 2 times the bolt diameter and subtract another 50 mm . For depth of corrugation ask the supplier, or take the compressed plate pack dimension, divide by the number of plates, and subtract the plate thickness from the result . The number of passages Np is the number of plates minus 1, then divided by 2 . Typical overall coefficients to start a rough sizing are listed below . Use these in conjunction with the NTU calculated for the process . The closer the NTU matches the plate (say, between 2 .0 and 3 .0), the higher the range of listed coefficients that can be used . The narrower (smaller) the depth of corrugation, the higher the coefficient (and pressure drop), but also the lower the ability to carry through any particulate . Water/water Steam/water Glycol/glycol Amine/amine Crude/emulsion

5700–7400 W/(m2 ∙ °C) 5700–7400 W/(m2 ∙ °C) 2300–4000 W/(m2 ∙ °C) 3400–5000 W/(m2 ∙ °C) 400–1700 W/(m2 ∙ °C)

Pressure drops typically can match conventional tubular exchangers . Again from the APV handbook, an average correlation is as follows: ∆P =

2 fG 2 L g ρDe

(11-79)

where f = 2 .5(G De/µ) g = gravitational constant Fouling factors are typically one-tenth of TEMA values or an oversurfacing of 10 to 20 percent is used (J . Kerner, “Sizing Plate Exchangers,” Chemical Engineering, November 1993) . LMTD is calculated as a 1 pass-1 pass shell and tube with no F correction factor required in most cases . Overall coefficients are determined as for shell-and-tube exchangers; that is, sum all the resistances, then invert . The resistances include the hot-side coefficient, the cold-side coefficient, the fouling factor (usually only a total value, not individual values per fluid side), and the wall resistance . -0 .3

WELDED- AND BRAZED-PLATE EXCHANGERS The title of this group of plate exchangers has been used for a great variety of designs for various applications from normal gasketed-plate exchanger services to air-preheater services on fired heaters or boilers . The intent here is to discuss more traditional heat exchanger designs, not the heat recovery designs on fired equipment flue-gas streams . Many similarities exist between these products, but the manufacturing techniques are quite different due to the normal operating conditions these units experience . To overcome the gasket limitations, PHE manufacturers have developed welded-plate exchangers . There are numerous approaches to this solution: weld plate pairs together with the other fluid side conventionally gasketed; weld up both sides but use a horizonal stacking-of-plates method of assembly; entirely braze the plates together with copper or nickel brazing; diffusion bond and then pressure-form plates and bond-etched passage plates . The act of welding the plates together removed one of the largest limitations of the plate-and-frame: the many gaskets and their compatibility limitations to process fluids .

Most methods of welded-plate manufacturing do not allow for inspection of the heat-transfer surface or mechanical cleaning of that surface, and they have limited ability to repair or plug off damaged channels . Consider these limitations when the fluid is heavily fouling, has solids, or in general, the need for repair or the potential of plugging for severe services . One of the previous types has an additional issue of the brazing material to consider for fluid compatibility . The brazing compound entirely coats both fluids’ heat-transfer surfaces . The second type, a Compabloc (CP) from Alfa-Laval AB, has the advantage of removable cover plates, similar to air-cooled exchanger headers, to observe both fluids’ surface areas . The fluids flow at 90° angles to each other on a horizontal plane . LMTD correction factors approach 1 .0 for Compabloc just as for the other welded and gasketed PHEs . Hydroblast cleaning of Compabloc surfaces is also possible . The Compabloc has higher operating conditions than PHEs or W-PHE . The performances and estimating methods of welded PHEs match those of gasketed PHEs in most cases, but normally the Compabloc, with larger depth of corrugations, can be lower in overall coefficient . Some extensions of the design operating conditions are possible with welded PHEs; most notable is that cryogenic applications are possible . Pressure vessel code acceptance is available on most units . Applications of welded plate exchangers, especially the Compabloc type, are increasingly being accepted in the chemical industry as a reliable process heat exchanger . Typical applications include, but not limited to, these: 1 . Crude oil preheat trains 2 . Oil and gas facilities, crude and gas sweetening applications 3 . Process condensers and reboilers on chemical industry distillation columns 4 . Refined product coolers and primary petrochemical manufacturing heat exchangers 5 . Pharmaceutical condensers 6 . Other areas where space and weight are primary concerns COMBINATION WELDED-PLATE EXCHANGERS Plate exchangers are well known for their high efficiency but suffer from limitations on operating pressure . Several companies have rectified this limitation by placing the welded plate exchanger inside a pressure vessel to withstand the pressure, such as Alfa Laval’s Packinox design . One popular application is the feed effluent exchange in a catalytic reforming plant for oil refineries . Large volumes of gases with some liquids require cross-exchange to feed a reactor system . Close temperature approaches and lower pressure drops are required as well as a very clean service . These combined units provide an economic alternative to shell-and-tube exchangers . SPIRAL-PLATE HEAT EXCHANGER (SHE) Description The spiral-plate heat exchanger (SHE) may be one exchanger selected primarily for its virtues and not for its initial cost . SHEs offer high reliability and on-line performance in many severely fouling services such as slurries . The SHE is formed by rolling two strips of plate, with welded-on spacer studs, upon each other into clock-spring shape . This forms two passages . Passages are sealed off on one end of the SHE by welding a bar to the plates; hot and cold fluid passages are sealed off on opposite ends of the SHE . A single rectangular flow passage is now formed for each fluid, producing very high shear rates compared to tubular designs . Removable covers are provided on each end to access and clean the entire heat-transfer surface . Pure countercurrent flow is achieved, and the LMTD correction factor is essentially = 1 .0 . Since there are no dead spaces in a SHE, the helical flow pattern combines to entrain any solids and create high turbulence, creating a self-cleaning flow passage . There are no thermal expansion problems in spirals . Since the center of the unit is not fixed, it can torque to relieve stress . The SHE can be expensive when only one fluid requires a high-alloy material . Since the heat-transfer plate contacts both fluids, it is required to be fabricated out of the higher alloy . SHEs can be fabricated out of any material that can be cold-worked and welded . The channel spacings can be different on each side to match the flow rates and pressure drops of the process design . The spacer studs are also adjusted in their pitch to match the fluid characteristics . As the operating pressure or design conditions require, the plate thickness increases from a minimum of 2 mm to a maximum (as required by pressure) up to 10 mm if the shell is integrally rolled . For high pressures, the SHE is inserted in a standard pressure vessel with cover flanges . This means relatively thick material separates the two fluids compared to the tubing of conventional exchangers . Pressure vessel code conformance is a common request . API 664 was recently issued covering this type of heat exchanger and its use .

COMPACT AND NONTUBULAR HEAT EXCHANGERS Applications The most common applications that fit SHE are slurries . The single rectangular channel provides an ideal geometry to sweep the surface clear of blockage and causes none of the distribution problems associated with other exchanger types . A localized restriction causes an increase in local velocity which aids in keeping the unit free-flowing, eliminating plugging problems that plague other heat exchanger types . Only fibers that are long and stringy cause SHE to have a blockage it cannot clear itself . As an additional antifoulant measure, SHEs have been coated with a phenolic lining . This provides some degree of corrosion protection as well, but this is not guaranteed due to pinholes in the lining process . There are three types of SHE to fit different applications: Type I is the spiral-spiral flow pattern . It is used for all heating and cooling services and can accommodate temperature crosses such as lean/rich services in one unit . The removable covers on each end enable access to one side at a time to perform maintenance on that fluid side . Never remove a cover with one side under pressure as the unit will telescope out like a collapsible cup . Type II units are the condenser and reboiler designs . One side is spiral flow, and the other side is in cross-flow . These SHEs provide very stable designs for vacuum condensing and reboiling services . A SHE can be fitted with special mounting connections for reflux-type vent-condenser applications . The vertically mounted SHE directly attaches onto the column or tank . Type III units are a combination of the type I and type II where part is in spiral flow and part is in cross-flow . This SHE can condense and subcool in a single unit . The unique channel arrangement has been used to provide on-line cleaning, by switching fluid sides to clean the fouling (caused by the fluid that previously flowed there) off the surface . Phosphoric acid coolers use pond water for cooling and both sides foul; water, as you expect, and phosphoric acid deposit crystals . By reversing the flow sides, the water dissolves the acid crystals and the acid clears up the organic fouling . SHEs are also used as oleum coolers, sludge coolers/heaters, slop oil heaters, and in other services where multiple-flow-passage designs have not performed well . Design A thorough article by P . E . Minton of Union Carbide called “Designing Spiral-Plate Heat Exchangers” appeared in Chemical Engineering on May 4, 1970 . It covers the design in detail . Also an article in Chemical Engineering Progress titled “Applications of Spiral Plate Heat Exchangers” by A . Hargis, A . Beckman, and J . Loicano appeared in July 1967 and provides formulas for heat-transfer and pressure-drop calculations . Spacings are from 6 .35 to 31 .75 mm (in 6 .35-mm increments) with 9 .5 mm the most common . Stud densities are 60 × 60 to 110 × 110 mm, with the former the most common . The width (measured to the spiral flow passage) is from 150 to 2500 mm (in 150-mm increments) . By varying the spacing and the width, separately for each fluid, velocities can be maintained at optimum rates to reduce fouling tendencies or utilize the allowable pressure drop most effectively . Diameters can reach 2500 mm . The total surface areas exceed 465 m2 . Materials that work harder are not suitable for spirals since hot-forming is not possible and heat treatment after forming is impractical . Nu =

H De = 0 .0315 (Re) 0 .8 (Pr)0 .25 (µ/µw )0 .17 k

(11-80)

where De = 2 × spacing and flow area = width × spacing ∆P =

LV 2ρ × 1 .45 (1 .45 for 60- × 60-mm studs) 1 .705E03

(11-81)

The LMTD and overall coefficient are calculated as in the PHE section above . BRAZED-PLATE-FIN HEAT EXCHANGERS Brazed-aluminum-plate-fin heat exchangers (or core exchangers or cold boxes, as they are sometimes called) were first manufactured for the aircraft industry during World War II . In 1950, the first tonnage air-separation plant with these compact, lightweight, reversing heat exchangers began producing oxygen for a steel mill . Aluminum-plate-fin exchangers are used in the process and gas-separation industries, particularly for services below −45°C . Core exchangers are made up of a stack of rectangular sheets of aluminum separated by a wavy, usually perforated, aluminum fin . Two ends are sealed off to form a passage (see Fig . 11-50) . The layers have the wavy fins and sealed ends alternating at 90° to each . Aluminum half-pipe-type headers are attached to the open ends to route the fluids into the alternating passages . Fluids usually flow at this same 90° angle to one another . Variations in the fin height, number of passages, and length and width of the prime sheet allow for the core exchanger to match the needs of the intended service .

FIG. 11-50

11-53

Exploded view of a typical plate-fin arrangement . (Trane Co.)

Design conditions range in pressures from full vacuum to 96 .5 bar g and in temperatures from −269°C to 200°C . This is accomplished while meeting the quality standards of most pressure vessel codes . API 662 Part 2 has been developed for this type of heat exchanger . Design and Application Brazed plate heat exchangers have two design standards available . One is ALPEMA, the Aluminum Plate-Fin Heat Exchanger Manufacturers’ Association, and the other is the API 662 document for plate heat exchangers . Applications are varied for this highly efficient, compact exchanger . Mainly it is seen in the cryogenic fluid services of air-separation plants, in refrigeration trains as in ethylene plants, and in natural-gas processing plants . Fluids can be all vapor, liquid, condensing, or vaporizing . Multifluid exchangers and multiservice cores, that is, one exchanger with up to 10 different fluids, are common for this type of product . Cold boxes are a group of cores assembled into a single structure or module, prepiped for minimum field connections . (Data were obtained from ALTEC International, now Chart Industries . For detailed information refer to GPSA Engineering Handbook, Sec . 9 .) PLATE-FIN TUBULAR EXCHANGER (PFE) Description These shell-and-tube exchangers are designed to use a group of tightly spaced plate fins to increase the shell-side heat-transfer performance as fins do on double-pipe exchangers . In this design, a series of very thin plates ( fins), usually of copper or aluminum, are punched to the same pattern as the tube layout, spaced very close together, and mechanically bonded to the tube . Fin spacing is 315 to 785 FPM ( fins per meter) with 550 FPM most common . The fin thicknesses are 0 .24 mm for aluminum and 0 .19 mm for copper . Surface-area ratios over bare prime-tube units can be 20:1 to 30:1 . The cost of the additional plate-fin material, without a reduction in shell diameter in many cases, and increased fabrication has to be offset by the total reduction of plot space and prime tube surface area . The more costly the prime tube or plot space, the better the payout for this design . A rectangular tube layout is normally used with no tubes in the window (NTIW) . The window area (where no tubes are) of the plate fins is cut out . This causes a larger shell diameter for a given tube count compared to conventional tubular units . A dome area on the top and bottom of the inside of the shell has been created for the fluid to flow along the tube length . To exit the unit, the fluid must flow across the plate-finned tube bundle with extremely low pressure loss . The units from the outside and from the tube side appear as in any conventional shell-and-tube exchanger . Applications Two principal applications are rotating equipment oil coolers and compressor intercoolers and after-coolers . Although seemingly different applications, both rely on the shell-side finning to enhance the heat transfer of low heat-transfer characteristic fluids, viscous oils, and gases . By the nature of the fluids and their applications, both are clean servicing . The tightly spaced fins would be a maintenance problem otherwise . Design The economics usually work out in the favor of gas coolers when the centrifugal machine’s flow rate reaches about 5000 scfm . The pressure loss can be kept to 7 .0 kPa in most cases . When the ratio of Atht to Ashs is 20:1, this is another point to consider in these plate-fin designs . Vibration is practically impossible with this design, and uses in reciprocating compressors are possible because of this . Marine and hydraulic-oil coolers use these characteristics to enhance the coefficient of otherwise poorly performing fluids . The higher metallurgies in marine applications such as 90/10 Cu-Ni allow the higher cost of plate-fin design to be offset by the reduced amount of alloy material being used . On small hydraulic coolers, these fins usually allow one to two size smaller coolers for the package and save skid space and initial cost . Always check on metallurgy compatibility and cleanliness of the shellside fluid! (Data are provided by Bos-Hatten and ITT-Standard .) PRINTED-CIRCUIT HEAT EXCHANGERS These are a variation of the welded or brazed plate heat exchangers that uses a chemical etching process to form the flow channels and diffusion bonding

11-54

HEAT-TRANSFER EQUIPMENT

technique to secure the plates together . These units have the high heattransfer characteristics and extended operating conditions that welded or brazed units have, but the diffusion process makes the bond the same strength as that of the prime plate material . The chemical etching, similar to that used in printed circuitry, allows greater flexibility in flow channel patterns than any other heat exchanger . This type of heat exchanger is perhaps the most compact design of all due to the infinite variations in passage size, layout, and direction . Headers are welded on the core block to direct the fluids into the appropriate passages . The all-metal design allows very high operating conditions for both temperature and pressure . The diffusion bonding provides a nearhomogeneous material for fluids that are corrosive or require high purity . These exchangers can handle gases, liquids, and two-phase applications . They have the greatest potential in cryogenic, refrigeration, gas processing, and corrosive chemical applications . Other applications are possible with the exception of fluids containing solids: the narrow passages, as in most plate exchangers, are conducive to plugging . SPIRAL-TUBE EXCHANGER (STE) Description These exchangers are typically a series of stacked helical-coil tubes connected to manifolds, then inserted into a casing or shell . They have many advantages similar to those of spiral-plate designs, such as avoiding differential expansion problems, acceleration effects of the helical flow increasing the heat-transfer coefficient, and compactness of plot area . They are typically selected because of their economical design . The most common form has both sides in helical flow patterns, pure countercurrent flow is followed, and the LMTD correction factor approaches 1 .0 . Temperature crosses are possible in single units . As with the spiral-plate unit, different configurations are possible for special applications . Tube material includes any that can be formed into a coil, but usually copper, copper alloys, and stainless steel are most common . The casing or shell material can be cast iron, cast steel, cast bronze, fabricated steel, stainless steel, and other high-alloy materials . Units are available with pressure vessel code conformance . The data provided here have been supplied by Graham Mfg . for their units called Heliflow . Applications The common Heliflow applications are tank-vent condensers, sample coolers, pump-seal coolers, and steam-jet vacuum condensers . Instant water heaters, glycol/water services, and cryogenic vaporizers use the spiral tube’s ability to reduce thermally induced stresses caused in these applications . Many other applications are well suited for spiral tube units, but many believe only small surface areas are possible with these units . Graham Mfg . states that units are available to 60 m2 . Their ability to polish the surfaces, double-wall the coil, use finned coil, and insert static mixers, among other configurations in design, make them quite flexible . Tube-side design pressures can be up to 69,000 kPa . A cross-flow design on the external surface of the coil is particularly useful in steam-jet ejector condensing service . These Heliflow units can be made very cost-effective, especially in small units . The main difference, compared to spiral plate, is that the tube side cannot be cleaned except chemically and that multiple flow passages make tubeside slurry applications (or fouling) impractical . Design The fluid flow is similar to that of the spiral-plate exchangers, but through parallel tube passages . Graham Mfg . has a liquid-liquid sizing pamphlet available from its local distributor . An article by M . A . Noble, J . S . Kamlani, and J . J . McKetta (“Heat Transfer in Spiral Coils,” Petroleum Engineer, April 1952, p . 723) discusses sizing techniques . The tube-side fluid must be clean or at least chemically cleanable . With a large number of tubes in the coil, cleaning of inside surfaces is not totally reliable . Fluids that attack stressed materials such as chlorides should be reviewed as to proper coil-material selection . Fluids that contain solids can be a problem due to erosion of relatively thin coil materials, unlike for the thick plates in spiral-plate units and multiple, parallel fluid passages compared to a single passage in spiral-plate units . GRAPHITE HEAT EXCHANGERS Impervious graphite exchangers now come in a variety of geometries to suit the particular requirements of the service . They include cubic block form, drilled cylinder block, shell-and-tube, and plate-and-frame . Description Graphite is one of three crystalline forms of carbon . The other two are diamond and charcoal . Graphite has a hexagonal crystal structure, diamond is cubic, and charcoal is amorphous . Graphite is inert to most chemicals and resists corrosion attack . It is, however, porous and it must be impregnated with a resin sealer to be used . Two main resins used are phenolic and PTFE with furan (one currently being phased out of production) . Selection of resins includes chemical compatibility, operating

temperatures, and type of unit to be used . For proper selection, consult with a graphite supplier . Shell-and-tube units in graphite were started by Karbate in 1939 . The European market started using block design in the 1940s . Both technologies utilize the high thermal conductivity of the graphite material to compensate for the poor mechanical strength . The thicker materials needed to sustain pressure do not adversely impede the heat transfer . Maximum design pressures range from 0 .35 to 1 .0 kPa depending on the type and size of exchanger . Design temperature is dependent on the fluid and resin selection, the maximum is 230°C . In all situations, the graphite heat-transfer surface is contained within a metal structure or a shell (graphite-lined on process side) to maintain the design pressure . For shell-and-tube units, the design is a packed floating tubesheet at both ends within a shell and channel . For stacked block design, the standardize blocks are glued together with special adhesives and compressed within a framework that includes manifold connections for each fluid . The cylindrical block unit is a combination of the above two with blocks glued together and surrounded by a pressure-retaining shell . Pressure vessel code conformance of the units is possible due to the metallic components of these designs . Since welding of graphite is not possible, the selection and application of the adhesives used are critical to the proper operation of these units . Tube–tubesheet joints are glued since rolling of tubes into tubesheet is not possible . The packed channels and gasketed manifold connections are two areas of additional concern when one is selecting sealants for these units . Applications and Design The major applications for these units are in the acid-related industries . Sulfuric, phosphoric, and hydrochloric acids require either very costly metals or impervious graphite . Usually graphite is the more cost-effective material used . Applications are increasing in the herbicide and pharmaceutical industries as new products with chlorine and fluorine compounds expand . Services are coolers, condensers, and evaporators, basically all services requiring this material . Types of units are shelland-tube, block-type (circular and rectangular), and plate-and-frame type of exchangers . The designs of the shell-and-tube units are the same as any others, but the design characteristics of tubes, spacing, and thickness are unique to the graphite design . The block and plate and frame also can be evaluated by using techniques previously addressed; but again the unique characteristics of the graphite materials require input from a reputable supplier . Most designs will need the supplier to provide the most cost-effective design for the immediate and future operation of the exchangers . Also consider the entire system design as some condensers and/or evaporators can be integral with their associated column . CASCADE COOLERS Cascade coolers are a series of standard pipes, usually manifolded in parallel and connected in series by vertically or horizontally oriented U bends . Process fluid flows inside the pipe entering at the bottom, and water trickles from the top downward over the external pipe surface . The water is collected from a trough under the pipe sections, cooled, and recirculated over the pipe sections . The pipe material can be any of the metallics and also glass, impervious graphite, and ceramics . The tube-side coefficient and pressure drop are as in any circular duct . The water coefficient (with Re number less than 2100) is calculated from the following equation by W . H . McAdams, T . B . Drew, and G . S . Bays, Jr ., from ASME Trans. 62: 627–631 (1940) . h = 218 × (G′/Do)⅓

(W/m2 ∙ °C)

(11-82)

where G′ = m/(2L) m = water rate, kg/h L = length of each pipe section, m Do = outside diameter of pipe, m LMTD corrections are per Fig . 11-4i or j depending on U-bend orientation . BAYONET-TUBE EXCHANGERS This type of exchanger gets its name from its design, which is similar to a bayonet sword and its associated scabbard or sheath . The bayonet tube is a smaller-diameter tube inserted into a larger-diameter tube that has been capped at one end . The fluid flow typically enters the inner tube, exiting, hitting the cap of the larger tube, and returning to the opposite direction in the annular area . The design eliminates any thermal expansion problems . It also creates a unique nonfreeze-type tube side for steam heating of cryogenic fluids; the inner tube steam keeps the annulus condensate from freezing against the cold shell-side fluid . This design can be expensive on a surfacearea basis due to the need for a double-channel design, and only the outer tube surface is used to transfer heat . LMTD calculations for nonisothermal fluid are quite extensive, and those applications are far too few to attempt

HEAT EXCHANGERS FOR SOLIDS to define it . The heat transfer is like the annular calculation of a double-pipe unit . The shell side is a conventional baffled shell-and-tube design . A rigorous treatment of the design of bayonet exchangers, “Understanding Bayonet Heat Exchangers” by Richard L . Shilling, is available through Heat Transfer Research, Inc . ATMOSPHERIC SECTIONS These consist of a rectangular bundle of tubes in similar fashion to air cooler bundles, placed just under the cooled water distribution section of a cooling tower . It, in essence, combines the exchanger and cooling tower into a single piece of equipment . This design is practical only for single-service cooler/ condenser applications, and expansion capabilities are not provided . The process fluid flows inside the tubes, and the cooling tower provides cool water that flows over the outside of the tube bundle . Water quality is critical for these applications to prevent fouling or corrosive attack on the outside of the tube surfaces and to prevent blockage of the spray nozzles . The initial and operating costs are lower than those for a separate cooling tower and exchanger . Principal applications now are in the HVAC, refrigeration, and industrial systems . Sometimes these are called wet surface air coolers. h = 1729 [(m2/h)/face area m2]⅓

11-55

NONMETALLIC HEAT EXCHANGERS Another growing field is that of nonmetallic heat exchanger designs which typically are of the shell-and-tube or coiled-tubing type . The graphite units were previously discussed, but numerous other materials are available . The materials include Teflon, PVDF, glass, ceramic, and others as the need arises . When using these types of products, one should consider the following topics and discuss the application openly with experienced suppliers . 1 . The tube-to-tubesheet joint, how is it made? Many use O-rings to add another material to the selection process . Preference should be given to a fusing technique of similar material . 2 . What size tube or flow passage is available? Small tubes plug unless filtration is installed . The size of filtering is needed from the supplier . 3 . These materials are very sensitive to temperature and pressure . Thermal or pressure shocks must be avoided . 4 . Thermal conductivity of these materials is very low and affects the overall coefficient . When several materials are compatible, explore all of them, as final cost is not always the same as raw material costs .

(11-83)

HEAT EXCHANGERS FOR SOLIDS This section describes equipment for heat transfer to or from solids by the indirect mode . Such equipment is constructed so that the solids load (burden) is separated from the heat-carrier medium by a wall; the two phases are never in direct contact . Heat transfer is by conduction based on diffusion laws . Equipment in which the phases are in direct contact is covered in other sections of this text, principally in Sec . 20 . Some of the devices covered here handle the solids burden in a static or laminar-flow bed . Other devices can be considered as continuously agitated kettles in their heat-transfer aspect . For the latter, unit-area performance rates are higher . Computational and graphical methods for predicting performance are given for both major heat-transfer aspects in Sec . 10 . In solids heat processing with indirect equipment, the engineer should remember that the heattransfer capability of the wall is many times that of the solids burden . Hence the solids properties and bed geometry govern the rate of heat transfer . This is more fully explained earlier in this section . Only limited resultant (not predictive) and “experience” data are given here . EQUIPMENT FOR SOLIDIFICATION A frequent operation in the chemical field is the removal of heat from a material in a molten state to effect its conversion to the solid state . When the operation is carried on batchwise, it is termed casting, but when done continuously, it is termed flaking . Because of rapid heat transfer and temperature variations, jacketed types are limited to an initial melt temperature of 232°C (450°F) . Higher temperatures [to 316°C (600°F)] require extreme care in jacket design and cooling-liquid flow pattern . Best performance and greatest capacity are obtained by (1) holding precooling to the minimum and (2) optimizing the cake thickness . The latter cannot always be done from the heat-transfer standpoint, as size specifications for the end product may dictate thickness . Table Type This is a simple flat metal sheet with slightly upturned edges and jacketed on the underside for coolant flow . For many years this was the mainstay of food processors . Table types are still widely used when production is done in small batches, when considerable batch-to-batch variation occurs, for pilot investigation, and when the cost of continuous devices is unjustifiable . Slab thicknesses are usually in the range of 13 to 25 mm (½ to 1 in) . These units are homemade, with no standards available . Initial cost is low, but operating labor is high . Agitated-Pan Type A natural evolution from the table type is a circular flat surface with jacketing on the underside for coolant flow and the added feature of a stirring means to sweep over the heat-transfer surface . This device is the agitated-pan type (Fig . 11-51) . It is a batch-operation device . Because of its age and versatility, it still serves a variety of heat-transfer operations for the chemical-process industries . While the most prevalent designation is agitatedpan dryer (in this mode, the burden is heated rather than cooled), considerable use is made of it for solidification applications . In this field, it is particularly suitable for processing burdens that change phase (1) slowly, by “thickening,” (2) over a wide temperature range, (3) to an amorphous solid form, or (4) to a soft semigummy form (versus the usual hard crystalline structure) .

The stirring produces the end product in the desired divided-solids form . Hence, it is frequently termed a granulator or a crystallizer . A variety of factory-made sizes in various materials of construction are available . Initial cost is modest, while operating cost is rather high (as is true of all batch devices), but the ability to process “gummy” burdens and/or simultaneously effect two unit operations often yields an economical application . Vibratory Type This construction (Fig . 11-52) takes advantage of the burden’s special needs and the characteristic of vibratory actuation . A flammable burden requires the use of an inert atmosphere over it and a suitable nonhazardous fluid in the jacket . The vibratory action permits construction of rigid self-cleaning chambers with simple flexible connections . When solidification has been completed and vibrators started, the intense vibratory motion of the whole deck structure (as a rigid unit) breaks free the friable cake [up to 76 mm (3 in) thick], shatters it into lumps, and conveys it up over the dam to discharge . Heat-transfer performance is good, with overall coefficient U of about 68 W/(m2 ⋅ °C) [12 Btu/(h ⋅ ft2 ⋅ °F)] and values of heat flux q on the order of 11,670 W/m2 [3700 Btu/(h ⋅ ft2)] . Application of timing-cycle controls and a surge hopper for the discharge solids facilitates automatic operation of the caster and continuous operation of subsequent equipment . Belt Types The patented metal-belt type (Fig . 11-53a), termed the “water-bed” conveyor, features a thin wall, a well-agitated fluid side for a thin water film (there are no rigid welded jackets to fail), a stainless-steel or Swedish-iron conveyor belt “floated” on the water with the aid of guides, no removal knife, and cleanability . It is mostly used for cake thicknesses of 3 .2 to 15 .9 mm (⅛ to ⅝ in) at speeds up to 15 m/min (50 ft/min), with

FIG. 11-51

type.

Heat-transfer equipment for solidification (with agitation); agitated-pan

11-56

HEAT-TRANSFER EQUIPMENT

FIG. 11-52 Heat-transfer equipment for batch solidification; vibrating-conveyor type . (Courtesy of Jeffrey Mfg. Co.)

property of Teflon . Another development [Food Process. Mark. 69 (March 1969)] is extending the capability of belt solidification by providing use of subzero temperatures . Rotating-Drum Type This type (Fig . 11-55a and b) is not an adaptation of a material-handling device (though volumetric material throughput is a first consideration) but is designed specifically for heat-transfer service . It is well engineered, established, and widely used . The twindrum type (Fig . 11-55b) is best suited to thin [0 .4- to 6-mm (1 ⁄ 64- to ¼-in)] cake production . For temperatures to 149°C (300°F) the coolant water is piped in and siphoned out . Spray application of coolant water to the inside is employed for high-temperature work, permitting feed temperatures to at least 538°C (1000°F), or double those values for jacketed equipment . Vaporizing refrigerants are readily applicable for very low temperature work . The burden must have a definite solidification temperature to ensure proper pickup from the feed pan . This limitation can be overcome by side feeding through an auxiliary rotating spreader roll . Application limits are further extended by special feed devices for burdens having oxidationsensitive and/or supercooling characteristics . The standard double-drum model turns downward, with adjustable roll spacing to control sheet thickness . The newer twin-drum model (Fig . 11-55b) turns upward and, though subject to variable cake thickness, handles viscous and indefinite solidification temperature-point burden materials well .

45 .7-m (150-ft) pulley centers common . For 25- to 32-mm (1- to 1¼-in) cake, another belt on top to give two-sided cooling is frequently used . Applications are in food operations for cooling to harden candies, cheeses, gelatins, margarines, gums, etc .; and in chemical operations for solidification of sulfur, greases, resins, soaps, waxes, chloride salts, and some insecticides . Heat transfer is good, with sulfur solidification showing values of q = 5800 W/m2 [1850 Btu/(h ⋅ ft2)] and U = 96 W/(m2 ⋅ °C) [17 Btu/(h ⋅ ft2 ⋅ °F)] for a 7 .9-mm (5/16-in) cake . The submerged metal belt (Fig . 11-53b) is a special version of the metal belt to meet the peculiar handling properties of pitch in its solidification process . Although adhesive to a dry metal wall, pitch will not stick to the submerged wetted belt or rubber edge strips . Submergence helps to offset the very poor thermal conductivity through two-sided heat transfer . A fairly recent application of the water-cooled metal belt to solidification duty is shown in Fig . 11-54 . The operation is termed pastillizing from the form of the solidified end product, termed pastilles. The novel feature is a one-step operation from the molten liquid to a fairly uniformly sized and shaped product without intermediate operations on the solid phase . Another development features a nonmetallic belt [Plast. Des. Process 13 (July 1968)] . When rapid heat transfer is the objective, a glass-fiber, Teflon-coated construction in a thickness as little as 0 .08 mm (0 .003 in) is selected for use . No performance data are available, but presumably the thin belt permits rapid heat transfer while taking advantage of the nonsticking

(a)

(b) FIG. 11-53 Heat-transfer equipment for continuous solidification . (a) Cooled metal belt . (Courtesy of Sandvik, Inc.) (b) Submerged metal belt . (Courtesy of Sandvik, Inc.)

HEAT EXCHANGERS FOR SOLIDS

11-57

Rotating-Shelf Type The patented Roto-shelf type (Fig . 11-55c) features (1) a large heat-transfer surface provided over a small floor space and in a small building volume, (2) easy floor cleaning, (3) nonhazardous machinery, (4) stainless-steel surfaces, (5) good control range, and (6) substantial capacity by providing as needed 1 to 10 shelves operated in parallel . It is best suited for thick-cake production and burden materials having an indefinite solidification temperature . Solidification of liquid sulfur into 13- to 19-mm- (½- to ¾-in-) thick lumps is a successful application . Heat transfer, by liquid-coolant circulation through jackets, limits feed temperatures to 204°C (400°F) . Heat-transfer rate, controlled by the thick cake rather than by equipment construction, should be equivalent to the belt type . Thermal performance is aided by applying water sprayed directly to the burden top to obtain two-sided cooling . FIG. 11-54 Heat-transfer equipment for solidification; belt type for the operation of pastillization . (Courtesy of Sandvik, Inc.)

Drums have been successfully applied to a wide range of chemical products, both inorganic and organic, pharmaceutical compounds, waxes, soaps, insecticides, food products to a limited extent (including lard cooling), and even flake-ice production . A novel application is that of using a water-cooled roll to pick up from a molten-lead bath and turn out a 1 .2-m- (4-ft-) wide continuous sheet, weighing 4 .9 kg/m2 (1 lb/ft2), which is ideal for a sound barrier . This technique is more economical than other sheeting methods [Mech. Eng. 631 (March 1968)] . Heat-transfer performance of drums, in terms of reported heat flux, is: for an 80°C (176°F) melting-point wax, 7880 W/m2 [2500 Btu/(h ⋅ ft2)]; for a 130°C (266°F) melting-point organic chemical, 20,000 W/m2 [6500 Btu/ (h ⋅ ft2)]; and for high-melting-point [318°C (604°F)] caustic soda (watersprayed in drum), 95,000 to 125,000 W/m2 [30,000 to 40,000 Btu/(h ⋅ ft2)], with overall coefficients of 340 to 450 W/(m2 ⋅ °C) [60 to 80 Btu/(h ⋅ ft2 ⋅ °F)] . An innovation that is claimed often to increase these performance values by as much as 300 percent is the addition of hoods to apply impinging streams of heated air to the solidifying and drying solids surface as the drums carry it upward [Chem. Eng. 74: 152 (June 19, 1967)] . Similar rotating-drum indirect heat-transfer equipment is also extensively used for drying duty on liquids and thick slurries of solids (see Sec . 20) .

EQUIPMENT FOR FUSION OF SOLIDS The thermal duty here is the opposite of solidification operations . The indirect heat-transfer equipment suitable for one operation is not suitable for the other because of the material-handling aspects rather than the thermal aspects . Whether the temperature of transformation is a definite or ranging one is of little importance in the selection of equipment for fusion . The burden is much agitated, but the beds are deep . Only fair overall coefficient values may be expected, although heat flux values are good . Horizontal-Tank Type This type (Fig . 11-56a) is used to transfer heat for melting or cooking dry powdered solids, rendering lard from meatscrap solids, and drying divided solids . Heat-transfer coefficients are 17 to 85 W/(m2 ⋅ °C) [3 to 15 Btu/(h ⋅ ft2 ⋅ °F)] for drying and 28 to 140 W/(m2 ⋅ °C) [5 to 25 Btu/(h ⋅ ft2 ⋅ °F)] for vacuum and/or solvent recovery . Vertical Agitated-Kettle Type Shown in Fig . 11-56b, this type is used to cook, melt to the liquid state, and provide or remove reaction heat for solids that vary greatly in “body” during the process so that material handling is a real problem . The virtues are simplicity and 100 percent cleanability . These often outweigh the poor heat-transfer aspect . These devices are available from the small jacketed type illustrated to huge cast-iron directunderfired bowls for calcining gypsum . Temperature limits vary with construction; the simpler jackets allow temperatures to 371°C (700°F) (as with Dowtherm), which is not true of all jacketed equipment .

(a)

(b)

(c)

FIG. 11-55 Heat-transfer equipment for continuous solidification . (a) Single drum . (b) Twin drum . (c) Roto shelf . (Courtesy of Buflovak Division, Blaw-Knox Food & Chemical Equipment, Inc.)

11-58

HEAT-TRANSFER EQUIPMENT

(a)

(b)

(c)

FIG. 11-56 Heat-transfer equipment for fusion of solids . (a) Horizontal-tank type . (Courtesy of Struthers Wells Corp.) (b) Agitated kettle . (Courtesy of Read-Standard Division, Capital Products Co.) (c) Double-drum mill . (Courtesy of Farrel-Birmingham Co.)

Mill Type Figure 11-56c shows one model of roll construction used . Note the ruggedness, as it is a power device as well as one for indirect heat transfer, employed to knead and heat a mixture of dry powdered-solid ingredients with the objective of reacting and reforming via fusion to a consolidated product . In this compounding operation, frictional heat generated by the kneading may require heat-flow reversal (by cooling) . Heatflow control and temperature-level considerations often predominate over heat-transfer performance . Power and mixing considerations, rather than heat transfer, govern . The two-roll mill shown is employed in compounding raw plastic, rubber, and rubberlike elastomer stocks . Multiple-roll mills less knives (termed calenders) are used for continuous sheet or film production in widths up to 2 .3 m (7 .7 ft) . Similar equipment is employed in the chemical compounding of inks, dyes, paint pigments, and the like . HEAT-TRANSFER EQUIPMENT FOR SHEETED SOLIDS Cylinder Heat-Transfer Units Sometimes called “can” dryers or drying rolls, these devices are differentiated from drum dryers in that they are used for solids in flexible continuous-sheet form, whereas drum dryers are used for liquid or paste forms . The construction of the individual cylinders, or drums, is similar in most respects to that of drum dryers . Special designs are used to obtain uniform distribution of steam within large drums when uniform heating across the drum surface is critical . A cylinder dryer may consist of one large cylindrical drum, such as the so-called Yankee dryer, but more often it comprises a number of drums arranged so that a continuous sheet of material may pass over them in series . Typical of this arrangement are Fourdrinier paper machine dryers, cellophane dryers, slashers for textile piece goods and fibers, etc . The multiple cylinders are arranged in various ways . Generally, they are staggered in two horizontal rows . In any one row, the cylinders are placed close together . The sheet material contacts the undersurface of the lower rolls and passes over the upper rolls, contacting 60 to 70 percent of the cylinder surface . The cylinders may also be arranged in a single horizontal row, in more than two horizontal rows, or in one or more vertical rows . When it is desired to contact only one side of the sheet with the cylinder surface, unheated guide rolls are used to conduct the sheeting from one cylinder to the next . For sheet materials that shrink on processing, it is frequently necessary to drive the cylinders at progressively slower speeds through the dryer . This requires elaborate individual electric drives on each cylinder .

Cylinder dryers usually operate at atmospheric pressure . However, the Minton paper dryer is designed for operation under vacuum . The drying cylinders are usually heated by steam, but occasionally single cylinders may be gas-heated, as in the case of the Pease blueprinting machine . Upon contacting the cylinder surface, wet sheet material is first heated to an equilibrium temperature somewhere between the wet-bulb temperature of the surrounding air and the boiling point of the liquid under the prevailing total pressure . The heat-transfer resistance of the vapor layer between the sheet and the cylinder surface may be significant . These cylinder units are applicable to almost any form of sheet material that is not injuriously affected by contact with steam-heated metal surfaces . They are used chiefly when the sheet possesses certain properties such as a tendency to shrink or lacks the mechanical strength necessary for most types of continuous-sheeting air dryers . Applications are to dry films of various sorts, paper pulp in sheet form, paper sheets, paperboard, textile piece goods and fibers, etc . In some cases, imparting a special finish to the surface of the sheet may be an objective . The heat-transfer performance capacity of cylinder dryers is not easy to estimate without a knowledge of the sheet temperature, which, in turn, is difficult to predict . According to published data, steam temperature is the largest single factor affecting capacity . Overall evaporation rates based on the total surface area of the dryers cover a range of 3 .4 to 23 kg water/(h ⋅ m2) [0 .7 to 4 .8 lb water/(h ⋅ ft2)] . The value of the coefficient of heat transfer from steam to sheet is determined by the conditions prevailing on the inside and on the surface of the dryers . Low coefficients may be caused by (1) poor removal of air or other noncondensibles from the steam in the cylinders, (2) poor removal of condensate, (3) accumulation of oil or rust on the interior of the drums, and (4) accumulation of a fiber lint on the outer surface of the drums . In a test reported by Lewis et al . [Pulp Pap. Mag. Can. 22 (February 1927)] on a sulfite-paper dryer, in which the actual sheet temperatures were measured, a value of 187 W/(m2 ⋅ °C) [33 Btu/(h ⋅ ft2 ⋅ °F)] was obtained for the coefficient of heat flow between the steam and the paper sheet . Operating-cost data for these units are meager . Power costs may be estimated by assuming 1 hp per cylinder for diameters of 1 .2 to 1 .8 m (4 to 6 ft) . Data on labor and maintenance costs are also lacking . The size of commercial cylinder dryers covers a wide range . The individual rolls may vary in diameter from 0 .6 to 1 .8 m (2 to 6 ft) and up to 8 .5 m (28 ft) in width . In some cases, the width of rolls decreases throughout the dryer in order to conform to the shrinkage of the sheet . A single-cylinder dryer,

HEAT EXCHANGERS FOR SOLIDS

11-59

such as the Yankee dryer, generally has a diameter between 2 .7 and 4 .6 m (9 and 15 ft) . HEAT-TRANSFER EQUIPMENT FOR DIVIDED SOLIDS Most equipment for this service is some adaptation of a material-handling device whether or not the transport ability is desired . The old vertical tube and the vertical shell ( fluidizer) are exceptions . Material-handling problems, plant transport needs, power, and maintenance are prime considerations in equipment selection and frequently overshadow heat-transfer and capital-cost considerations . Material handling is generally the most important aspect . Material-handling characteristics of the divided solids may vary during heat processing . The body changes are usually important in drying, occasionally significant for heating, and only on occasion important for cooling . The ability to minimize the effects of changes is a major consideration in equipment selection . Dehydration operations are better performed on contactive apparatus (see Sec . 12) that provides air to carry off released water vapor before a semiliquid form develops . Some types of equipment are convertible from heat removal to heat supply by simply changing the temperature level of the fluid or air . Other types require an auxiliary change . Still others require constructional changes . Temperature limits for the equipment generally vary with the thermal operation . The kind of thermal operation has a major effect on heat-transfer values . For drying, overall coefficients are substantially higher in the presence of substantial moisture for the constant-rate period than in finishing . However, a stiff “body” occurrence due to moisture can prevent a normal “mixing” with an adverse effect on the coefficient . Fluidized-Bed Type Known as the cylindrical fluidizer, this operates with a bed of fluidized solids (Fig . 11-57) . It is an indirect heat-transfer version of the contactive type in Sec . 17 . An application disadvantage is the need for batch operation unless some short circuiting can be tolerated . Solids-cooling applications are few, as they can be more effectively accomplished by the fluidizing gas via the contactive mechanism that is referred to in Sec . 11 . Heating applications are many and varied . These are subject to one shortcoming, which is the dissipation of the heat input by carry-off in the fluidizing gas . Heat-transfer performance for the indirect mode to solids has been outstanding, with overall coefficients in the range of 570 to 850 W/(m2 ⋅ °C) [100 to 150 Btu/(h ⋅ ft2 ⋅ °F)] . This device with its thin film does for solids what the falling-film and other thin-film techniques do for fluids, as shown by Holt (Pap . 11, 4th National Heat-Transfer Conference, August 1960) . In a design innovation with high heat-transfer capability, heat is supplied indirectly to the fluidized solids through the walls of in-bed, horizontally placed, finned tubes [Petrie, Freeby, and Buckham, Chem. Eng. Prog. 64(7): 45 (1968)] . Moving-Bed Type This concept uses a single-pass tube bundle in a vertical shell with the divided solids flowing by gravity in the tubes . It is little used for solids . A major difficulty in divided-solids applications is the problem of charging and discharging with uniformity . A second is poor heattransfer rates . Because of these limitations, this tube bundle type is not the workhorse for solids that it is for liquid- and gas-phase heat exchange . However, there are applications in which the nature of a specific chemical reactor system requires indirect heating or cooling of a moving bed of divided solids . One of these is the segregation process which through a

FIG. 11-57 Heat-transfer equipment for divided solids; stationary vertical-shell type . The indirect fluidizer .

FIG. 11-58 Stationary vertical-tube type of indirect heat-transfer equipment with

divided solids inside tubes, laminar solids flow, and steady-state heat conditions .

gaseous reaction frees chemically combined copper in an ore to a free copper form which permits easy, efficient subsequent recovery [Pinkey and Plint, Miner. Process. pp . 17–30 (June 1968)] . The apparatus construction and principle of operation are shown in Fig . 11-58 . The functioning is abetted by a novel heat-exchange provision of a fluidized sand bed in the jacket . This provides a much higher unit heat-input rate (coefficient value) than would the usual low-density hot-combustion-gas flow . Agitated-Pan Type This device (Fig . 11-52) is not an adaptation of a material-handling device but was developed many years ago primarily for heat-transfer purposes . As such, it has found wide application . In spite of its batch operation with high attendant labor costs, it is still used for processing divided solids when no phase change is occurring . Simplicity and easy cleanout make the unit a wise selection for handling small, experimental, and even some production runs when quite a variety of burden materials are heat-processed . Both heating and cooling are feasible with it, but greatest use has been for drying [see Sec . 12 and Uhl and Root, Chem. Eng. Prog. 63(7): 8 (1967)] . Because it can be readily covered (as shown in the illustration) and a vacuum drawn or special atmosphere provided, this device features versatility to widen its use . For drying granular solids, the heat-transfer rate ranges from 28 to 227 W/(m2 ⋅ °C) [5 to 40 Btu/(h ⋅ ft2 ⋅ °F)] . For atmospheric applications, thermal efficiency ranges from 65 to 75 percent . For vacuum applications, it is about 70 to 80 percent . These devices are available from several sources, fabricated of various metals used in chemical processes . Kneading Devices These are closely related to the agitated pan but differ as being primarily mixing devices with heat transfer a secondary consideration . Heat transfer is provided by jacketed construction of the main body and is effected by a coolant, hot water, or steam . These devices are applicable for the compounding of divided solids by mechanical rather than chemical action . Application is largely in the pharmaceutical and food processing industries . For a more complete description, illustrations, performance, and power requirements, refer to Sec . 19 . Shelf Devices Equipment having heated and/or cooled shelves is available but is little used for divided-solids heat processing . Most extensive use of stationary shelves is for freezing of packaged solids for food industries and for freeze drying by sublimation (see Sec . 22) . Rotating-Shell Devices These (see Fig . 11-59) are installed horizontally, whereas stationary-shell installations are vertical . Material-handling aspects are of greater importance than thermal performance . Thermal results are customarily given in terms of overall coefficient on the basis of the total area provided, which varies greatly with the design . The effective use, chiefly percent fill factor, varies widely, affecting the reliability of

11-60

HEAT-TRANSFER EQUIPMENT

(a)

(b)

(c)

(d) FIG. 11-59

Rotating shells as indirect heat-transfer equipment . (a) Plain . (Courtesy of BSP Corp.) (b) Flighted . (Courtesy of BSP Corp.) (c) Tubed . (d) Deep-finned type . (Courtesy of Link-Belt Co.)

stated coefficient values . For performance calculations see Sec . 10 on heatprocessing theory for solids . These devices are variously used for cooling, heating, and drying and are the workhorses for heat-processing divided solids in the large-capacity range . Different modifications are used for each of the three operations . The plain type (Fig . 11-59a) features simplicity and yet versatility through various end-construction modifications enabling wide and varied applications . Thermal performance is strongly affected by the “body” characteristics of the burden because of its dependency for material handling on frictional contact . Hence, performance ranges from well-agitated beds with good thin-film heat-transfer rates to poorly agitated beds with poor thickfilm heat-transfer rates . Temperature limits in application are (1) low-range cooling with shell dipped in water, 400°C (750°F) and less; (2) intermediate cooling with forced circulation of tank water, to 760°C (1400°F); (3) primary cooling, above 760°C (1400°F), water copiously sprayed and loading kept light; (4) low-range heating, below steam temperature, hot-water dip; and (5) high-range heating by tempered combustion gases or ribbon radiant-gas burners . The flighted type (Fig . 11-59b) is a first-step modification of the plain type . The simple flight addition improves heat-transfer performance . This type is most effective on semifluid burdens which slide readily . Flighted models are restricted from applications in which soft-cake sticking occurs, breakage must be minimized, and abrasion is severe . A special flighting is one having the cross section compartmented into four lesser areas with ducts between . Hot gases are drawn through the ducts en route from the outer oven to the stack to provide about 75 percent more heating surface, improving efficiency and capacity with a modest cost increase . Another similar unit has the flights made in a triangular-duct cross section with hot gases drawn through . The tubed-shell type (Fig . 11-59c) is basically the same device more commonly known as a steam-tube rotary dryer (see Sec . 20) . The rotation, combined with slight inclination from the horizontal, moves the shellside solids through it continuously . This type features good mixing with the objective of increased heat-transfer performance . Tube-side fluid may be water, steam, or combustion gas . Bottom discharge slots in the shell are used so that heat-transfer-medium supply and removal can be made through the ends; these restrict wide-range loading and make the tubed type inapplicable for floody materials . These units are seldom applicable for sticky, soft-caking, scaling, or heat-sensitive burdens . They are not recommended for abrasive materials . This type has high thermal efficiency

because heat loss is minimized . Heat-transfer coefficient values are as follows: water, 34 W/(m2 ⋅ °C) [6 Btu/(h ⋅ ft2 ⋅ °F)]; steam, same, with heat flux reliably constant at 3800 W/m2 [1200 Btu/(h ⋅ ft2)]; and gas, 17 W/(m2 ⋅ °C) [3 Btu/(h ⋅ ft2 ⋅ °F)], with a high temperature difference . Although from the preceding discussion the device may seem rather limited, it is nevertheless widely used for drying, with condensing steam predominating as the heat-carrying fluid . But with water or refrigerants flowing in the tubes, it is also effective for cooling operations . The units are custom-built by several manufacturers in a wide range of sizes and materials . A few fabricators that specialize in this type of equipment have accumulated a vast store of data for determining application sizing . The patented deep-finned type in Fig . 11-59d is named the Rotofin cooler . It features loading with a small layer thickness, excellent mixing to give a good effective diffusivity value, and a thin fluid-side film . Unlike other rotating-shell types, it is installed horizontally, and the burden is moved positively by the fins acting as an Archimedes spiral . Rotational speed and spiral pitch determine travel time . For cooling, this type is applicable to both secondary and intermediate cooling duties . Applications include solids in small lumps [9 mm (¾ in)] and granular size [6 mm and less (¼ to 0 in)] with no larger pieces to plug the fins, solids that have a free-flowing body characteristic with no sticking or caking tendencies, and drying of solids that have a low moisture and powder content unless special modifications are made for substantial vapor and dust handling . Thermal performance is very good, with overall coefficients to 110 W/(m2 ⋅ °C) [20 Btu/(h ⋅ ft2 ⋅ °F)], with one-half of these coefficients nominal for cooling based on the total area provided (nearly double those reported for other indirect rotaries) . Conveyor-Belt Devices The metal-belt type (Fig . 11-55) is the only device in this classification of material-handling equipment that has had serious effort expended on it to adapt it to indirect heat-transfer service with divided solids . It features a lightweight construction of a large area with a thin metal wall . Indirect-cooling applications have been made with poor thermal performance, as could be expected with a static layer . Auxiliary plowlike mixing devices, which are considered an absolute necessity to secure any worthwhile results for this service, restrict applications . Spiral-Conveyor Devices Figure 11-60 illustrates the major adaptations of this widely used class of material-handling equipment to indirect heat-transfer purposes . These conveyors can be considered for heat-transfer purposes as continuously agitated kettles . The adaptation of Fig . 11-60d offers a batch-operated version for evaporation duty . For this service, all are package-priced and package-shipped items requiring few, if any, auxiliaries .

HEAT EXCHANGERS FOR SOLIDS The jacketed solid-flight type (Fig . 11-60a) is the standard low-cost (partsbasis-priced) material-handling device, with a simple jacket added and employed for secondary-range heat transfer of an incidental nature . Heattransfer coefficients are as low as 11 to 34 W/(m2 ⋅ °C) [2 to 6 Btu/(h ⋅ ft2 ⋅ °F)] on sensible heat transfer and 11 to 68 W/(m2 · °C) [2 to 12 Btu/(h ⋅ ft2 ⋅ °F)] on drying because of substantial static solids-side film . The small-spiral–large-shaft type (Fig . 11-60b) is inserted in a solidsproduct line as pipe banks are in a fluid line, solely as a heat-transfer device . It features a thin burden ring carried at a high rotative speed and subjected to two-sided conductance to yield an estimated heat-transfer coefficient of 285 W/(m2 ⋅ °C) [50 Btu/(h ⋅ ft2 ⋅ °F)], thereby ranking thermally next to the shell-fluidizer type . This device for powdered solids is comparable with the Votator of the fluid field . Figure 11-60c shows a fairly new spiral device with a medium-heavy annular solids bed and having the combination of a jacketed, stationary outer shell with moving paddles that carry the heat-transfer fluid . A unique feature of this device to increase volumetric throughput, by providing an overall greater temperature drop, is that the heat medium is supplied to and withdrawn from the rotor paddles by a parallel piping arrangement in the rotor shaft . This is a unique flow arrangement compared with the usual series flow . In addition, the rotor carries burden-agitating spikes which give it the trade name of Porcupine Heat-Processor (Chem. Equip. News, April 1966; and Uhl and Root, AIChE Prepr . 21, 11th National Heat-Transfer Conference, August 1967) . The large-spiral hollow-flight type (Fig . 11-60d) is an adaptation, with external bearings, full fill, and salient construction points as shown, that

(a)

is highly versatile in application . Heat-transfer coefficients are 34 to 57 W/ (m2 ⋅ °C) [6 to 10 Btu/(h ⋅ ft2 ⋅ °F)] for poor, 45 to 85 W/(m2 ⋅ °C) [8 to 15 Btu/ (h ⋅ ft2 ⋅ °F)] for fair, and 57 to 114 W/(m2 ⋅ °C) [10 to 20 Btu/(h ⋅ ft2 ⋅ °F)] for wet conductors . A popular version of this employs two such spirals in one material-handling chamber for a pugmill agitation of the deep solids bed . The spirals are seldom heated . The shaft and shell are heated . Another deep-bed spiral-activated solids-transport device is shown by Fig . 11-60e. The flights carry a heat-transfer medium as well as the jacket . A unique feature of this device, which is purported to increase heat-transfer capability in a given equipment space and cost, is the dense-phase fluidization of the deep bed that promotes agitation and moisture removal on drying operations . Double-Cone Blending Devices The original purpose of these devices was mixing (see Sec . 19) . Adaptations have been made; so many models now are primarily for indirect heat-transfer processing . A jacket on the shell carries the heat-transfer medium . The mixing action, which breaks up agglomerates (but also causes some degradation), provides very effective burden exposure to the heat-transfer surface . On drying operations, the vapor release (which in a static bed is a slow diffusional process) takes place relatively quickly . To provide vapor removal from the burden chamber, a hollow shaft is used . Many of these devices carry the hollow-shaft feature a step further by adding a rotating seal and drawing a vacuum . This increases thermal performance notably and makes the device a natural for solvent-recovery operations . These devices are replacing the older tank and spiral-conveyor devices . Better provisions for speed and ease of fill and discharge (without powered

(c)

(b)

(d)

(e) FIG. 11-60

11-61

Spiral-conveyor adaptations as heat-transfer equipment . (a) Standard jacketed solid flight . (Courtesy of Jeffrey Mfg. Co.) (b) Small spiral, large shaft . (Courtesy of Fuller Co.) (c) “Porcupine” medium shaft . (Courtesy of Bethlehem Corp.) (d) Large spiral, hollow flight . (Courtesy of Rietz Mfg. Co.) (e) Fluidized-bed large spiral, helical flight . (Courtesy of Western Precipitation Division, Joy Mfg. Co.)

11-62

HEAT-TRANSFER EQUIPMENT

FIG. 11-61

Performance of tubed blender heat-transfer device .

rotation) minimize downtime to make this batch-operated device attractive . Heat-transfer coefficients ranging from 28 to 200 W/(m2 ⋅ °C) [5 to 35 Btu/ (h ⋅ ft2 ⋅ °F)] are obtained . However, if caking on the heat-transfer walls is serious, then values may drop to 5 .5 or 11 W/(m2 ⋅ °C) [1 or 2 Btu/(h ⋅ ft2 ⋅ °F)], constituting a misapplication . The double cone is available in a fairly wide range of sizes and construction materials . The users are the fine-chemical, pharmaceutical, and biological-preparation industries . A novel variation is a cylindrical model equipped with a tube bundle to resemble a shell-and-tube heat exchanger with a bloated shell [Chem. Process. 20 (Nov . 15, 1968)] . Conical ends provide for redistribution of burden between passes . The improved heat-transfer performance is shown by Fig . 11-61 . Vibratory-Conveyor Devices Figure 11-62 shows the various adaptations of vibratory material-handling equipment for indirect heat-transfer service on divided solids . The basic vibratory-equipment data are given in Sec . 21 . These indirect heat-transfer adaptations feature simplicity,

nonhazardous construction, nondegradation, nondusting, no wear, ready conveying-rate variation [1 .5 to 4 .5 m/min (5 to 15 ft/min)], and good heattransfer coefficient—115 W/(m2 ⋅ °C) [20 Btu/(h ⋅ ft2 ⋅ °F)] for sand . They usually require feed rate and distribution auxiliaries . They are suited for heating and cooling of divided solids in powdered, granular, or moist forms but no sticky, liquefying, or floody ones . Terminal-temperature differences less than 11°C (20°F) on cooling and 17°C (30°F) on heating or drying operations are seldom practical . These devices are for medium and light capacities . The heavy-duty jacketed type (Fig . 11-62a) is a special custom-built adaptation of a heavy-duty vibratory conveyor shown in Fig . 11-60 . Its application is to continuously cool the crushed material [ from about 177°C (350°F)] produced by the vibratory-type “caster” of Fig . 11-53 . It does not have the liquid dam and is made in longer lengths that employ L, switchback, and S arrangements on one floor . The capacity rate is 27,200 to 31,700 kg/h (30 to 35 ton/h) with heat-transfer coefficients in the order of 142 to 170 W/(m2 ⋅ °C) [25 to 30 Btu/(h ⋅ ft2 ⋅ °F)] . For heating or drying applications, it employs steam to 414 kPa (60 lbf/in2) . The jacketed or coolant-spraying type (Fig . 11-62b) is designed to ensure a very thin, highly agitated liquid-side film and the same initial coolant temperature over the entire length . It is frequently employed for transporting substantial quantities of hot solids, with cooling as an incidental consideration . For heating or drying applications, hot water or steam at a gauge pressure of 7 kPa (1 lbf/in2) may be employed . This type is widely used because of its versatility, simplicity, cleanability, and good thermal performance . The light-duty jacketed type (Fig . 11-62c) is designed for use of air as a heat carrier . The flow through the jacket is highly turbulent and is usually counterflow . On long installations, the air flow is parallel to every two sections for greater heat-carrying capacity and a fairly uniform surface temperature . The outstanding feature is that a wide range of temperature control is obtained by merely changing the heat-carrier temperature level from as low as atmospheric moisture condensation will allow to 204°C (400°F) . On heating operations, a very good thermal efficiency can be obtained by insulating the machine and recycling the air . While the heat-transfer rating is good, the heat-removal capacity is limited . Cooler units are often used in series with like units operated as dryers or when clean water is unavailable . Drying applications are for heat-sensitive [49°C to 132°C (120°F to 270°F)] products; when temperatures higher than steam at a gauge pressure of 7 kPa (1 lbf/in2) can provide are wanted but heavy-duty equipment is too costly; when the

(a)

(d) (b)

(c) FIG. 11-62

(e)

Vibratory-conveyor adaptations as indirect heat-transfer equipment . (a) Heavy-duty jacketed for liquid coolant or high-pressure steam . (b) Jacketed for coolant spraying . (c) Light-duty jacketed construction . (d) Jacketed for air or steam in tiered arrangement . (e) Jacketed for air or steam with Mix-R-Step surface . (Courtesy of Jeffrey Mfg. Co.)

THERMAL INSULATION

11-63

FIG. 11-63 Elevator type as heat-transfer equipment . (Courtesy of Carrier Conveyor Corp.)

FIG. 11-64

jacket corrosion hazard of steam is unwanted; when headroom space is at a premium; and for highly abrasive burden materials such as fritted or crushed glasses and porcelains . The tiered arrangement (Fig . 11-62d) employs the units of Fig . 11-62 with either air or steam at a gauge pressure of 7 kPa (1 lbf/in2) as a heat medium . These are custom-designed and built to provide a large amount of heat-transfer surface in a small space with the minimum of transport and to provide a complete processing system . These receive a damp material, resize while in process by granulators or rolls, finish dry, cool, and deliver to packaging or tableting . The applications are primarily in the fine chemical, food, and pharmaceutical manufacturing fields . The Mix-R-Step type in Fig . 11-62e is an adaptation of a vibratory conveyor . It features better heat-transfer rates, practically doubling the coefficient values of the standard flat surface and trebling heat-flux values, as the layer depth can be increased from the normal 13 to 25 and 32 mm (½ to 1 and 1¼ in) . It may be provided on decks jacketed for air, steam, or water spray . It is also often applicable when an infrared heat source is mounted overhead to supplement the indirect or as the sole heat source . Elevator Devices The vibratory elevating-spiral type (Fig . 11-63) adapts divided-solids-elevating material-handling equipment to heat-transfer service . It features a large heat-transfer area over a small floor space and employs a reciprocating shaker motion to effect transport . Applications, layer depth, and capacities are restricted, as burdens must be of such “body” character as to convey uphill by the microhopping transport principle . The type lacks self-emptying ability . Complete washdown and cleaning is a feature not inherent in any other elevating device . A typical application is the cooling of a low-density plastic powder at the rate of 544 kg/h (1200 lb/h) . Another elevator adaptation is that for a spiral-type elevating device developed for ground cement and thus limited to fine powdery burdens . The spiral operates inside a cylindrical shell, which is externally cooled by a falling film of water . The spiral not only elevates the material in a thin layer against the wall but keeps it agitated to achieve high heat-transfer rates . Specific operating data are not available [Chem. Eng. Prog. 68(7): 113 (1968)] . The falling-water film, besides being ideal thermally, by virtue of no jacket pressure very greatly reduces the hazard that the cooling water may contact the water-sensitive burden in process . Surfaces wet by water are accessible for cleaning . A fair range of sizes are available, with material-handling capacities to 60 ton/h . Pneumatic Conveying Devices See Sec . 21 for descriptions, ratings, and design factors of these devices . Use is primarily for transport purposes, and heat transfer is a very secondary consideration . Applications have largely been for plastics in powder and pellet forms .

By modifications, needed cooling operations have been simultaneously effected with transport to stock storage [Plast. Des. Process 28 (December 1968)] . Heat-transfer aspects and performance were studied and reported on by Depew and Farbar (ASME Pap . 62-HT-14, September 1962) . Heat-transfer coefficient characteristics are similar to those shown in Sec . 11 for the indirectly heated fluid bed . Another frequent application on plastics is a small, rather incidental but necessary amount of drying required for plastic pellets and powders on receipt when shipped in bulk to the users . Pneumatic conveyors modified for heat transfer can handle this readily . A pneumatic transport device designed primarily for heat-sensitive products is shown in Fig . 11-64 . This was introduced into the United States after 5 years’ use in Europe [Chem. Eng. 76: 54 (June 16, 1969)] . Both the shell and the rotor carry steam as a heating medium to effect indirect transfer as the burden briefly contacts those surfaces rather than from the transport air, as is normally the case . The rotor turns slowly (1 to 10 r/min) to control, by deflectors, product distribution and prevent caking on walls . The carrier gas can be inert, as nitrogen, and also recycled through appropriate auxiliaries for solvent recovery . Application is limited to burdens that (1) are fine and uniformly grained for the pneumatic transport, (2) dry very fast, and (3) have very little, if any, sticking or decomposition characteristics . Feeds can carry 5 to 100 percent moisture (dry basis) and discharge at 0 .1 to 2 percent . Wall temperatures range from 100 to 170°C (212 to 340°F) for steam and lower for a hot-water heat source . Pressure drops are on the order of 500 to 1500 mmH2O (20 to 60 inH2O) . Steam consumption approaches that of a contractive-mechanism dryer down to a low value of 2 .9 kg steam/kg water (2 .9 lb steam/lb water) . Available burden capacities are 91 to 5900 kg/h (200 to 13,000 lb/h) . Vacuum-Shelf Types These are very old devices, being a version of the table type . Early-day use was for drying (see Sec . 12) . Heat transfer is slow even when supplemented by vacuum, which is 90 percent or more of present-day use . The newer vacuum blender and cone devices are taking over many applications . The slow heat-transfer rate is quite satisfactory in a major application, freeze drying, which is a sublimation operation (see Sec . 22 for description) in which the water must be retained in the solid state during its removal . Then slow diffusional processes govern . Another extensive application is in freezing packaged foods for preservation purposes . Available sizes range from shelf areas of 0 .4 to 67 m2 (4 to 726 ft2) . These are available in several manufacturers’ standards, either as system components or with auxiliary gear as packaged systems .

A pneumatic transport adaptation for heat-transfer duty . (Courtesy of Werner & Pfleiderer Corp.)

THERMAL INSULATION Materials or combinations of materials which have air- or gas-filled pockets or void spaces that retard the transfer of heat with reasonable effectiveness are thermal insulators . Such materials may be particulate and/or fibrous, with or without binders, or may be assembled, such as multiple heatreflecting surfaces that incorporate air- or gas-filled void spaces .

The ability of a material to retard the flow of heat is expressed by its thermal conductivity ( for unit thickness) or conductance ( for a specific thickness) . Low values for thermal conductivity or conductance (or high thermal resistivity or resistance value) are characteristics of thermal insulation .

11-64

HEAT-TRANSFER EQUIPMENT

TABLE 11-21 Thicknesses of Piping Insulation Insulation, nominal thickness in mm Nominal ironpipe size, in

Outer diameter

1 25

1½ 38

2 51

2½ 64

3 76

3½ 89

4 102

Approximate wall thickness in

mm

in

mm

in

mm

in

mm

in

mm

in

mm

in

mm

in

mm

½ ¾ 1 1¼ 1½

0 .84 1 .05 1 .32 1 .66 1 .90

21 27 33 42 48

1 .01 0 .90 1 .08 0 .91 1 .04

26 23 27 23 26

1 .57 1 .46 1 .58 1 .66 1 .54

40 37 40 42 39

2 .07 1 .96 2 .12 1 .94 2 .35

53 50 54 49 60

2 .88 2 .78 2 .64 2 .47 2 .85

73 71 67 63 72

3 .38 3 .28 3 .14 2 .97 3 .35

86 83 80 75 85

3 .88 3 .78 3 .64 3 .47 3 .85

99 96 92 88 98

4 .38 4 .28 4 .14 3 .97 4 .42

111 109 105 101 112

2 2½ 3 3½ 4

2 .38 2 .88 3 .50 4 .00 4 .50

60 73 89 102 114

1 .04 1 .04 1 .02 1 .30 1 .04

26 26 26 33 26

1 .58 1 .86 1 .54 1 .80 1 .54

40 47 39 46 39

2 .10 2 .36 2 .04 2 .30 2 .04

53 60 52 58 52

2 .60 2 .86 2 .54 2 .80 2 .54

66 73 65 71 65

3 .10 3 .36 3 .04 3 .36 3 .11

79 85 77 85 79

3 .60 3 .92 3 .61 3 .86 3 .61

91 100 92 98 92

4 .17 4 .42 4 .11 4 .36 4 .11

106 112 104 111 104

4½ 5 6 7 8

5 .00 5 .56 6 .62 7 .62 8 .62

127 141 168 194 219

1 .30 0 .99 0 .96

33 25 24

1 .80 1 .49 1 .46 1 .52 1 .52

46 38 37 39 39

2 .30 1 .99 2 .02 2 .02 2 .02

58 51 51 51 51

2 .86 2 .56 2 .52 2 .52 2 .65

73 65 64 64 67

3 .36 3 .06 3 .02 3 .15 3 .15

85 78 77 80 80

3 .86 3 .56 3 .65 3 .65 3 .65

98 90 93 93 93

4 .48 4 .18 4 .15 4 .15 4 .15

114 106 105 105 105

9 .62 10 .75 11 .75 12 .75 14 .00

244 273 298 324 356

1 .52 1 .58 1 .58 1 .58 1 .46

39 40 40 40 37

2 .15 2 .08 2 .08 2 .08 1 .96

55 53 53 53 50

2 .65 2 .58 2 .58 2 .58 2 .46

67 66 66 66 62

3 .15 3 .08 3 .08 3 .08 2 .96

80 78 78 78 75

3 .65 3 .58 3 .58 3 .58 3 .46

93 91 91 91 88

4 .15 4 .08 4 .08 4 .08 3 .96

105 104 104 104 101

1 .46

37

1 .96

50

2 .46

62

2 .96

75

3 .46

88

3 .96

101

9 10 11 12 14 Over 14, up to and including 36

Heat is transferred by radiation, conduction, and convection . Radiation is the primary mode and can occur even in a vacuum . The amount of heat transferred for a given area is relative to the temperature differential and emissivity from the radiating to the absorbing surface . Conduction is due to molecular motion and occurs within gases, liquids, and solids . The tighter the molecular structure, the higher the rate of transfer . As an example, steel conducts heat at a rate approximately 600 times that of typical thermal insulation materials . Convection is due to mass motion and occurs only in fluids . The prime purpose of a thermal insulation system is to minimize the amount of heat transferred .

vapor transmission (to prevent surface condensation), and those above 27°C (80°F) should prevent water entry and allow moisture to escape . Metal finishes are more durable, require less maintenance, reduce heat loss, and, if uncoated, increase the surface temperature on hot systems .

INSULATION MATERIALS Materials Thermal insulations are produced from many materials or combinations of materials in various forms, sizes, shapes, and thicknesses . The most commonly available materials fall within the following categories: Fibrous or cellular—mineral: Alumina, asbestos, glass, perlite, rock, silica, slag, or vermiculite Fibrous or cellular—organic: Cane, cotton, wood, and wood bark (cork) Cellular organic plastics. Elastomer, polystyrene, polyisocyanate, polyisocyanurate, and polyvinyl acetate Cements: Insulating and/or finishing Heat-reflecting metals (reflective): Aluminum, nickel, stainless steel Available forms. Blanket ( felt and batt), block, cements, loose fill, foil and sheet, formed or foamed in place, flexible, rigid, and semirigid . The actual thicknesses of piping insulation differ from the nominal values . Dimensional data of ASTM Standard C585 appear in Table 11-21 . Thermal Conductivity (K Factor) Depending on the type of insulation, the thermal conductivity (K factor) can vary with age, manufacturer, moisture content, and temperature . Typical published values are shown in Fig . 11-65 . Mean temperature is equal to the arithmetic average of the temperatures on both sides of the insulating material . Actual system heat loss (or gain) will normally exceed calculated values because of projections, axial and longitudinal seams, expansion-contraction openings, moisture, workers’ skill, and physical abuse . Finishes Thermal insulations require an external covering ( finish) to provide protection against entry of water or process fluids, mechanical damage, and ultraviolet degradation of foamed materials . In some cases the finish can reduce the flame-spread rating and/or provide fire protection . The finish may be a coating (paint, asphaltic, resinous, or polymeric), a membrane (coated felt or paper, metal foil, or laminate of plastic, paper, foil, or coatings), or sheet material ( fabric, metal, or plastic) . Finishes for systems operating below 2°C (35°F) must be sealed and retard vapor transmission . Those from 2°C (35°F) through 27°C (80°F) should retard

FIG. 11-65 Thermal conductivity of insulating materials .

THERMAL INSULATION

11-65

FIG. 11-66 Dewar flask .

SYSTEM SELECTION A combination of insulation and finish produces the thermal insulation system . Selection of these components depends on the purpose for which the system is to be used . No single system performs satisfactorily from the cryogenic through the elevated-temperature range . Systems operating below freezing have a low vapor pressure, and atmospheric moisture is pushed into the insulation system, while the reverse is true for hot systems . Some general guidelines for system selection follow . Cryogenic [-273 to -101çC (-459 to -150çF)] High Vacuum This technique is based on the Dewar flask, which is a double-walled vessel with reflective surfaces on the evacuated side to reduce radiation losses . Figure 11-66 shows a typical laboratory-size Dewar . Figure 11-67 shows a

FIG. 11-68 Insulating materials and applicable temperature ranges .

semiportable type . Radiation losses can be further reduced by filling the cavity with powders such as perlite or silica prior to pulling the vacuum . Multilayer Multilayer systems consist of series of radiation-reflective shields of low emittance separated by fillers or spacers of very low conductance and exposed to a high vacuum . Foamed or Cellular Cellular plastics such as polyurethane and polystyrene do not hold up or perform well in the cryogenic temperature range because of permeation of the cell structure by water vapor, which in turn increases the heat-transfer rate . Cellular glass holds up better and is less permeable . Low Temperature [-101 to -1çC (-150 to +30çF)] Cellular glass, glass fiber, polyurethane foam, and polystyrene foam are frequently used for this service range . A vapor-retarder finish with a perm rating less than 0 .02 is required . In addition, it is good practice to coat all contact surfaces of the insulation with a vapor-retardant mastic to prevent moisture migration when the finish is damaged or is not properly maintained . Closed-cell insulation should not be relied on as the vapor retarder . Hairline cracks can develop, cells can break down, glass-fiber binders are absorbent, and moisture can enter at joints between all materials . Moderate and High Temperature [over 2çC (36çF)] Cellular or fibrous materials are normally used . See Fig . 11-68 for nominal temperature range . Nonwicking insulation is desirable for systems operating below 100°C (212°F) . Other Considerations Autoignition can occur if combustible fluids are absorbed by wicking-type insulations . Chloride stress corrosion of austenitic stainless steel can occur when chlorides are concentrated on metal surfaces at or above approximately 60°C (140°F) . The chlorides can come from sources other than the insulation . Some calcium silicates are formulated to exceed the requirements of the MIL-I-24244A specification . Fire resistance of insulations varies widely . Calcium silicate, cellular glass, glass fiber, and mineral wool are fire-resistant but do not perform equally under actual fire conditions . A steel jacket provides protection, but aluminum does not . Traced pipe performs better with a nonwicking insulation which has low thermal conductivity . Underground systems are very difficult to keep dry permanently . Methods of insulation include factory-preinsulated pouring types and conventionally applied types . Corrosion can occur under wet insulation . A protective coating, applied directly to the metal surface, may be required . ECONOMIC THICKNESS OF INSULATION

FIG. 11-67

Hydrogen bottle .

Optimal economic insulation thickness may be determined by various methods . Two of these are the minimum total cost method and the incremental cost method (or marginal cost method) . The minimum total cost method involves actual calculations of lost energy and insulation costs for each insulation thickness . The thickness producing the lowest total cost is the

11-66

HEAT-TRANSFER EQUIPMENT determined . The energy saved for each increment is then found . The value of this energy varies directly with the temperature level [e .g ., steam at 538°C (1000°F) has a greater value than condensate at 100°C (212°F)] . The final increment selected for use is required either to provide a satisfactory return on investment or to have a suitable payback period . Recommended Thickness of Insulation Indoor insulation thickness appears in Table 11-22, and outdoor thickness appears in Table 11-23 . These selections were based upon calcium silicate insulation with a suitable aluminum jacket . However, the variation in thickness for fiberglass, cellular glass, and rock wool is minimal . Fiberglass is available for maximum temperatures of 260, 343, and 454°C (500, 650, and 850°F) . Rock wool, cellular glass, and calcium silicate are used up to 649°C (1200°F) . The tables were based upon the cost of energy at the end of the first year, a 10 percent inflation rate on energy costs, a 15 percent interest cost, and a present-worth pretax profit of 40 percent per annum on the last increment of insulation thickness . Dual-layer insulation was used for 3½-in and greater

optimal economic solution . The optimum thickness is determined to be the point where the last dollar invested in insulation results in exactly $1 in energy cost savings (“ETI—Economic Thickness for Industrial Insulation,” Conservation Pap . 46, Federal Energy Administration, August 1976) . The incremental cost method provides a simplified and direct solution for the least-cost thickness . The total cost method does not in general provide a satisfactory means for making most insulation investment decisions, since an economic return on investment is required by investors and the method does not properly consider this factor . Return on investment is considered by Rubin (“Piping Insulation—Economics and Profits,” in Practical Considerations in Piping Analysis, ASME Symposium, vol . 69, 1982, pp . 27–46) . The incremental method used in this reference requires that each incremental ½ in of insulation provide the predetermined return on investment . The minimum thickness of installed insulation is used as a base for calculations . The incremental installed capital cost for each additional ½ in of insulation is

TABLE 11-22

Indoor Insulation Thickness, 80°F Still Ambient Air* Minimum pipe temperature, °F

Pipe size, in

Insulation thickness, in

Energy cost, $/million Btu 1

2

3

4

5

6

7

8

¾

1½ 2 2½ 3

950

600

550

400 1100 1750

350 1000 1050

300 900 950

250 800 850

250 750 800 1200

1

1½ 2 2½ 3

1200

800

600 1200

500 1000

450 900 1200

400 800 1050 1100

350 700 1000 1150

300 700 900 950

1½

1½ 2 2½ 3

1100

750

550 1000

450 850 1050

400 700 900

400 650 800 1150

350 600 750 1100

300 500 650 1000

2

1½ 2 2½ 3

1050

700

500 1050 1100

450 850 950 1200

400 750 1000 1050

350 700 750 950

300 600 700 850

300 600 650 800

3

1½ 2 2½ 3

950

650 1100

500 900 1050

400 700 850 1050

350 600 750 950

300 550 650 800

300 500 500 750

250 450 500 700

4

1½ 2 2½ 3 3½

950

600 1100

500 850 1200

400 700 1000 1050

350 600 850 900

300 550 750 800

300 500 700 750 1150

250 450 650 700 1050

6

1½ 2 2½ 3 3½ 4

600

350 1100

300 850 900 1150

250 700 800 1000

250 600 650 850

200 550 600 750 1100

200 500 550 700 1000

200 500 550 600 900 1200

8

2 2½ 3 3½ 4

1000 1050

800 850

650 700 1050

550 600 900 1200

500 550 800 1100

450 500 750 1000 1150

400 450 700 900 1100

10

2 2½ 3 3½ 4

1100 1200

850 900 1050

700 750 900

650 700 750 1200

550 600 700 1050

500 550 600 950

450 500 550 900 1200

12

2 2½ 3 3½ 4 4½

1150

750 1000

600 800 1200

500 650 1000

400 550 900 1200

400 500 800 1100 1150 1200

350 450 700 1000 1050 1100

300 400 650 900 950 1000

14

2 2½ 3 3½ 4 4½

1050

650 1000

550 800 1100

450 650 950

400 550 800 1150 1200

350 500 700 1000 1050 1200

300 450 650 950 1000 1100

300 400 600 850 900 1000

THERMAL INSULATION TABLE 11-22

Indoor Insulation Thickness, 80°F Still Ambient Air* (Continued ) Minimum pipe temperature, °F

Pipe size, in

Insulation thickness, in

Energy cost, $/million Btu 1

2

3

4

5

6

7

8

16

2 2½ 3 3½ 4 4½

950

650 1000 1200

500 800 950

400 700 800

350 600 700 1150 1200

300 550 600 1050 1100 1150

300 500 550 950 1000 1050

300 450 500 850 900 950

18

2 2½ 3 3½ 4 4½

1000

650 950 1150

500 750 900

400 600 750

350 550 650 1200

350 500 550 1100 1150 1200

300 450 500 1000 1050 1100

300 400 500 900 950 1000

20

2 2½ 3 3½ 4 4½

1050

700 1000 1150

550 800 900

450 600 750

400 550 650

350 500 550 1100 1150

350 450 500 1000 1050 1200

300 400 500 950 1000 1100

24

2 2½ 3 3½ 4 4½

950

600 1150

500 900 1050

400 750 900

350 650 750 1100 1150

300 550 700 1000 1050 1150

300 500 600 900 950 1050

250 450 550 800 850 950

∗Aluminum-jacketed calcium silicate insulation with an emissivity factor of 0 .05 . To convert inches to millimeters, multiply by 25 .4, to convert dollars per 1 million British thermal units to dollars per 1 million kilojoules, multiply by 0 .948, °C = 5/9 (°F − 32) .

TABLE 11-23

Outdoor Insulation Thickness, 7.5-mi/h Wind, 60°F Air* Minimum pipe temperature, °F Energy cost, $/million Btu

Pipe size, in

Thickness, in

1

2

3

4

5

6

7

8

¾

1 1½ 2 2½

450 800

300 500

250 400 1150 1100

250 300 950 1000

200 250 850 900

200 250 750 800

150 200 700 750

150 200 650 700

1

1 1½ 2 2½ 3

400 1000

300 650

250 500 1100

200 400 900 1200

200 350 800 1050 1100

150 300 700 950 1000

150 300 600 850 900

150 250 600 800 850

1½

1 1½ 2 2½ 3

350 900

250 600 100

200 450 850 1150

200 350 700 950

150 300 600 800 1200

150 300 550 750 1050

150 250 500 700 1000

150 250 450 600 900

2

1 1½ 2 2½ 3

350 900

250 550 1150

200 450 900 1000

150 400 750 850 1050

150 300 650 750 950

150 300 600 650 850

150 250 550 600 750

150 250 500 550 700

3

1 1½ 2 2½ 3 3½

300 750

200 500 950 1150

150 400 750 950 1150

150 300 600 750 1000

150 250 500 650 850

150 250 450 600 750

150 250 400 500 650

150 200 350 500 600 1150

4

1 1½ 2 2½ 3 3½

250 750

200 500 950

150 350 750 1050 1100

150 300 600 900 950

150 250 500 700 750

150 250 450 650 700 1200

150 200 400 600 650 1100

150 200 350 550 600 1000

11-67

11-68

HEAT-TRANSFER EQUIPMENT TABLE 11-23

Outdoor Insulation Thickness, 7.5-mi/h Wind, 60°F Air* (Continued ) Minimum pipe temperature, °F Energy cost, $/million Btu

Pipe size, in

Thickness, in

1

2

3

4

5

6

7

8

6

1 1½ 2 2½ 3 3½ 4 4½

250 450

150 300 900 1050

150 200 700 800 1050

150 200 600 650 900

150 150 500 600 750 1150

150 150 450 500 700 1050

150 150 400 450 600 950 1200

150 150 350 400 550 850 1150 1200

8

1 2 2½ 3 3½ 4

250

200 850 900

150 650 700 1100

150 550 600 950

150 450 500 800 1150

150 400 450 750 1000

150 350 400 700 950 1050

150 350 400 600 850 1000

10

2 2½ 3 3½ 4 4½

200

150 1000 1200

150 800 950

150 650 800

150 550 700 1100

150 500 600 1000

150 450 550 900 1150 1200

150 400 500 800 1050 1100

12

1½ 2 2½ 3 3½ 4 4½

250 950

150 600 900

150 500 700 1100

150 400 550 900

150 350 500 800 1100 1150 1200

150 300 400 700 1000 1050 1100

150 250 400 650 900 950 1000

150 250 350 550 850 900 950

14

1½ 2 2½ 3 3½ 4 4½

250 850

150 550 850

150 400 650 1000

150 350 550 850 1200

150 300 500 700 1000 1050

150 250 400 650 950 1000 1100

150 250 400 550 850 900 1000

150 250 400 500 800 850 950

1½ 2 2½ 3 3½ 4 4½

250 800

150 500 900 1000

150 350 700 850

150 300 550 700 1200

150 300 500 600 1000 1100 1150

150 250 450 500 950 1000 1000

150 250 400 450 850 900 950

150 200 350 400 800 850 900

1½ 2 2½ 3 3½

250 850

150 550 800 1000

150 400 650 800

150 350 500 650

150 300 450 550 1100

150 250 400 500 1000

150 250 350 450 900

150 200 350 400 850

1½ 2 2½ 3 3½ 4 4½

150 900

150 550 850 1000

150 450 650 800

150 350 550 650

150 300 450 550 1150 1200

150 300 400 500 1050 1100 1200

150 250 350 450 950 1000 1100

150 250 350 400 900 950 1050

1½ 2 2½ 3 3½ 4 4½ 5

150 800

150 500 950 1150

150 400 750 950

150 300 650 750 1150 1200

150 250 550 650 1000 1050

150 250 500 600 900 950 1050

150 200 450 550 800 850 950

150 200 400 500 750 800 850

16

18

20

24

∗Aluminum-jacketed calcium silicate insulation with an emissivity factor of 0 .05 . To convert inches to millimeters, multiply by 25 .4; to convert miles per hour to kilometers per hour, multiply by 1 .609; and to convert dollars per 1 million British thermal units to dollars per 1 million kilojoules, multiply by 0 .948; °C = 5/9 (°F − 32) .

thicknesses . The tables and a full explanation of their derivation appear in a paper by F . L . Rubin (“Piping Insulation—Economics and Profits,” in Practical Considerations in Piping Analysis, ASME Symposium, vol . 69, 1982, pp . 27–46) . Alternatively, the selected thicknesses have a payback period on the last nominal ½-in increment of 1 .44 years as presented in a later paper by Rubin [“Can You Justify More Piping Insulation?” Hydrocarbon Process 152–155 (July 1982)] . Example 11-1

For 24-in pipe at 371°C (700°F) with an energy cost of $4/million Btu, select 2-in thickness for indoor and 2½-in thickness for outdoor locations . [A 2½-in thickness would be chosen at 399°C (750°F) indoors and 3½-in outdoors .]

Example 11-2 For 16-in pipe at 343°C (650°F) with energy valued at $5/million Btu, select 2½-in insulation indoors [use 3-in thickness at 371°C (700°F)] . Outdoors choose 3-in insulation [use 3½-in dual-layer insulation at 538°C (1000°F)] . Example 11-3 For 12-in pipe at 593°C (1100°F) with an energy cost of $6/million Btu, select 3½-in thickness for an indoor installation and 4½-in thickness for an outdoor installation . INSTALLATION PRACTICE Pipe Depending on the diameter, pipe is insulated with cylindrical half, third, or quarter sections or with flat segmental insulation . Fittings and

AIR CONDITIONING valves are insulated with preformed insulation covers or with individual pieces cut from sectional straight pipe insulation . Method of Securing Insulation with factory-applied jacketing may be secured with adhesive on the overlap, staples, tape, or wire, depending on the type of jacket and the outside diameter . Insulation which has a separate jacket is wired or banded in place before the jacket ( finish) is applied . Double Layer Pipe expansion is a significant factor at temperatures above 600°F (316°C) . Above this temperature, insulation should be applied in a double layer with all joints staggered to prevent excessive heat loss and high surface temperature at joints opened by pipe expansion . This procedure also minimizes thermal stresses in the insulation . Finish Covering for cylindrical surfaces ranges from asphalt-saturated or saturated and coated organic and asbestos paper, through laminates of such papers and plastic films or aluminum foil, to medium-gauge aluminum, galvanized steel, or stainless steel . Fittings and irregular surfaces may be covered with fabric-reinforced mastics or preformed metal or plastic covers . Finish selection depends on function and location . Vapor-barrier finishes may be in sheet form or a mastic, which may or may not require reinforcing, depending on the method of application; and additional protection may be required to prevent mechanical abuse and/or provide fire resistance . Criteria for selecting other finishes should include protection of insulation against water entry, mechanical abuse, or chemical attack . Appearance, life-cycle cost, and fire resistance may also be determining

11-69

factors . Finish may be secured with tape, adhesive, bands, or screws . Fasteners which will penetrate vapor-retarder finishes should not be used . Tanks, Vessels, and Equipment Flat, curved, and irregular surfaces such as tanks, vessels, boilers, and breechings are normally insulated with flat blocks, beveled lags, curved segments, blankets, or spray-applied insulation . Since no general procedure can apply to all materials and conditions, it is important that manufacturers’ specifications and instructions be followed for specific insulation applications . Method of Securing On small-diameter cylindrical vessels, the insulation may be secured by banding around the circumference . On larger cylindrical vessels, banding may be supplemented with angle-iron ledges to support the insulation and prevent slipping . On large flat and cylindrical surfaces, banding or wiring may be supplemented with various types of welded studs or pins . Breather springs may be required with bands to accommodate expansion and contraction . Finish The materials are the same as for pipe and should satisfy the same criteria . Breather springs may be required with bands . Additional References: ASHRAE Handbook and Product Directory: Fundamentals, American Society of Heating, Refrigerating and Air Conditioning Engineers, Atlanta, Ga ., 1981 . Turner and Malloy, Handbook of Thermal Insulation Design Economics for Pipes and Equipment, Krieger, New York, 1980 . Turner and Malloy, Thermal Insulation Handbook, McGraw-Hill, New York, 1981 .

AIR CONDITIONING INTRODUCTION

VENTILATION

Air conditioning is the process of treating air to simultaneously control its temperature, humidity, cleanliness, and distribution to meet the requirements of the conditioned spaces . Detailed discussions of various air cleaning and air distribution systems can be found in the HVAC Applications volume of the ASHRAE Handbook (American Society of Heating, Refrigerating, and Air-Conditioning Engineers Inc ., 1791 Tullie Circle NE, Atlanta, Ga .) . Air conditioning applications may include human comfort as well as the maintenance of proper conditions for manufacturing, processing, or preserving a wide variety of material and equipment . Industrial environments may use localized air conditioning to maintain safe working conditions for the health and efficiency of workers, even when overall space conditions cannot be made entirely comfortable for economical or other practical reasons .

Odors or pollutants arising from occupants, cooking, or building material outgassing in residential or commercial buildings must be controlled to maintain a pleasant and safe living or working environment . Acceptable air quality can be maintained by localized exhaust of pollutants at their source, dilution with outdoor air that is free of such pollutants, or a combination of the two processes . Recommended outdoor air requirements for different types of nonresidential buildings are given in ASHRAE Standard 62 .1, Ventilation for Acceptable Indoor Air Quality . Ventilation air requirements will vary because of the amounts of pollutant produced by different occupant activities and structural materials, but the ventilation rates are typically between 15 and 25 cfm of outdoor air per person for non-manufacturing commercial environments . Outdoor ventilation air requires much more energy to condition than the recirculated air from the nearly constant temperature conditioned space . Occupancy sensors (which typically detect CO2 levels) are often used to reduce space conditioning costs by regulating the amount of outdoor air when space occupancy may be highly variable, such as in schools, theaters, or office complexes occupied less than 50 h per week . Local or state building codes may restrict how ventilation systems must be designed for fire or smoke control . Industrial air conditioning systems must often address harmful gases, vapors, dusts, or fumes that are released into the work environment . These contaminants are best controlled by exhaust systems located near the source before they can enter the working environment . Dilution ventilation may be acceptable where nontoxic contaminants come from widely dispersed points . Combinations of local exhaust and dilution ventilation may provide the least expensive installation . Dilution alone may not be appropriate for cases involving toxic materials or large volumes of contaminants, or where the employees must work near the contaminant source . Chapter 32 of the ASHRAE Handbook HVAC Applications provides extensive information on the design and efficacy of a variety of exhaust systems . Safety codes from OSHA or local government bodies may have requirements that must take priority .

COMFORT AIR CONDITIONING Human comfort is influenced primarily by air temperature and humidity, local air velocity, radiant heat exchange, clothing insulation value, and metabolic rate . Chapter 48 of the 2012 ASHRAE Handbook HVAC Applications has an extensive discussion of noise control, another important consideration in air conditioning system design . Chapter 9 of the 2013 ASHRAE Handbook HVAC Fundamentals relates ambient air temperature and moisture content to human comfort, accounting for a wide variety of clothing and activity levels . It also provides results from extensive research efforts that address the impact of air velocity, radiative exchange, vertical temperature variations, age, gender, and a variety of other factors . The standard that addresses human comfort design criteria is ASHRAE Standard 55, Thermal Environmental Conditions for Human Occupancy . Because of the differences typically found in a given conditioned space regarding occupant manner of dress, age, gender, activity levels, and personal preferences, an 80 percent occupant comfort satisfaction rate is about the maximum that can realistically be obtained . INDUSTRIAL AIR CONDITIONING

AIR CONDITIONING EQUIPMENT

Industrial buildings should be designed according to their intended use . For instance, the manufacture or processing of hygroscopic materials (e .g ., paper, textiles, and foods) will require tight control of humidity . The production of many electronic components often requires clean rooms with stringent limitations on particulate matter in the air . The processing of many fresh foods requires low temperatures, while the ambient in a facility for manufacturing refractories or forged metal products might be acceptable at much higher temperatures . Chapter 14 of the 2011 ASHRAE Handbook HVAC Applications provides extensive tables of suggested temperature and humidity conditions for many industrial air conditioning applications as well as special space conditioning considerations that may be needed for a wide variety of industrial processes .

Basically, an air conditioning system consists of a fan unit that forces air through a series of devices which act upon the air to clean it, increase or decrease its temperature, and increase or decrease its water vapor content . Air conditioning equipment can generally be classified into two broad types: central (also called field-erected) and unitary . CENTRAL COOLING AND HEATING SYSTEMS At least a dozen types of central air conditioning and air distribution systems are commonly used in commercial and industrial applications . They usually have large cooling and heating equipment located in a central location from which many different spaces or zones are served . Chilled-water

11-70

HEAT-TRANSFER EQUIPMENT

coils or direct-expansion refrigerant coils are most commonly used for cooling the airstream . Spray washers using chilled water are sometimes used where continuous humidity control and air cleaning are especially important . Steam or hot-water coils usually provide the heating effect where the steam or hot water is generated in a boiler . Humidification may be provided by steam injection into the airstream, target-type water nozzles, pan humidifiers, air washers, or sprayed coils . Air cleaning is most commonly provided by cleanable or throwaway filters . Electronic air cleaners may be used when a low air pressure drop is important . Air handling units are available in capacities up to 50,000 ft3/min with the cooling/heating coils, filters, and humidity control systems in a prefabricated package . These units can be located on a rooftop of a low-rise structure and connected to the chiller and boiler for fast field installation with minimal design of components . The principal types of refrigeration equipment used in central systems are reciprocating (up to 300 tons); helical rotary (up to 750 tons); absorption (up to 2000 tons); and centrifugal (up to 10,000 tons) . The mechanical drives are most commonly electric motors, but larger systems may use turbines or engines depending on the system size and the availability or cost of various fuels . The heat rejected from the condensers usually calls for wet cooling towers for larger systems or air-cooled condensers for smaller units . Modular condensing units with the compressor(s), direct expansion condensers with fans, and chilled-water heat exchangers are available in capacities up to several hundred tons . UNITARY REFRIGERANT-BASED AIR CONDITIONING SYSTEMS Unitary systems range from window-mounted air conditioners and heat pumps to residential and small commercial systems to commercial selfcontained systems . The various types of unitary systems are described in detail in the HVAC Systems and Equipment volume of the ASHRAE Handbook . A detailed analysis of the proposed installation is necessary to select the type of air conditioning equipment that is best for an application . Each type of system has its own particular advantages and disadvantages . Important factors to be considered in the selection of air conditioning equipment are the required precision of temperature and humidity control; investment, owning, and operating costs; and space requirements . Building characteristics are also important, such as whether it is new or existing, multiple-story, size, available space for ducts, etc . For example, rooftop air conditioners or low-profile water source units may offer advantages for existing buildings where extensive air ducts would be difficult to install . A central system would usually be employed for large industrial processes where precise temperature and humidity control may be required . LOAD CALCULATION The first step in the design of most air conditioning systems is to determine the peak load at suitably severe design operating conditions . Since both outdoor and indoor temperatures influence the size of the equipment, the designer must exercise good judgment in selecting appropriate conditions for sizing the system . The efficiency of most systems is highest at full-load conditions, so oversizing cooling equipment will increase the first cost as well as operating costs . The most severe historical local outdoor conditions should almost never be used for sizing a system, or it will operate at a small fraction of its full capacity almost all the time . ASHRAE has compiled extensive weather data for over 6000 locations around the world based on 30 years of hourly recordings at each site . Data are presented in statistical format, such as dry-bulb temperatures exceeded 2 .0, 1 .0, or 0 .4 percent of the

time; the mean coincident wet-bulb temperature at those dry-bulb conditions; wind speeds exceeded 5, 2 .5, and 1 .0 percent of the time, and similarly compiled dew point temperatures . These data provide a good understanding of the number of hours per year that the capacity of the system may be exceeded . The statistical data permit loads to be computed for peak sensible or latent conditions, as well as for sizing cooling towers or other humiditysensitive equipment . Due to the size of this weather data set, an abbreviated data set is included in the ASHRAE Handbook Fundamentals, with the complete data set available on the CD that comes with the Handbook. In addition, the weather data have been standardized in ANSI/ASHRAE Standard 169 . These data allow for different design conditions to be used for critical applications (such as a hospital) or for much less critical applications (such as an exercise gym) . After appropriate design temperature and humidity conditions are selected, the next step is to calculate the space cooling load . The sensible heat load consists of (1) transmission through the building exterior envelope; (2) solar and sky radiation through windows and skylights; (3) heat gains from infiltration of outside air; (4) heat gains from people, lights, appliances, and power equipment (including the A/C fan motors); and (5) heat from materials brought in at higher than room temperature . The latent heat load accounts for moisture (1) given off from people, appliances, and products and (2) from infiltration of outside air . The total space load is the sum of the sensible and latent loads . The total cooling equipment load consists of the total space load plus the sensible and latent loads from the outside ventilation air . The procedure for load calculation in nonresidential buildings should account for thermal storage in the mass of the structure, occupancy patterns, and other uses of energy that affect the load . The load can be strongly dependent on the use of the building . For example, lighting, computers, and copy equipment might be major load components for an office building that will require cooling even in winter . Load calculations are now performed almost exclusively with computer software . Basic loads for simple buildings can be determined using spreadsheet software, while large buildings with variable occupancy, large internal loads, and extensive window areas usually require much more elaborate computer models . Most computer models incorporate hourly weather data so load variations and changes in equipment performance with outdoor conditions can both be properly accounted for . Chapter 19 of the ASHRAE Handbook Fundamentals presents a summary of the various types of computerized load models that are currently available . References 2011 ASHRAE Handbook . Heating, Ventilating, and Air-Conditioning Applications. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc ., Atlanta, Ga . 2012 ASHRAE Handbook . Heating, Ventilating, and Air-Conditioning Systems and Equipment. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc ., Atlanta, Ga . 2013 ASHRAE Handbook . Fundamentals. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc ., Atlanta, Ga . ANSI/ASHRAE Standard 55-2013 . Thermal Environmental Conditions for Human Occupancy. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc ., Atlanta, Ga . ANSI/ASHRAE/IESNA Standard 62 .1-2013 . Ventilation for Acceptable Indoor Air Quality. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc ., Atlanta, Ga . ANSI/ASHRAE Standard 169-2013 . Weather Data for Building Design Standards. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc ., Atlanta, Ga .

REFRIGERATION INTRODUCTION Refrigeration is a process in which heat is transferred from a lower- to a higher-temperature level by doing work on a system . In some systems heat transfer is used to provide the energy to drive the refrigeration cycle . All refrigeration systems are heat pumps (“pump energy from a lower to a higher potential”) . The term heat pump is mostly used to describe refrigeration system applications where heat rejected to the condenser is of primary interest . There are many means to obtain the refrigerating effect, but here three are discussed: mechanical vapor refrigeration cycles, absorption, and steam-jet cycles due to their significance for industry .

Basic Principles Since refrigeration is the practical application of the thermodynamics, comprehending the basic principles of thermodynamics is crucial for a full understanding of refrigeration . Section 4 includes a through approach to the theory of thermodynamics . Since our goal is to understand refrigeration processes, cycles are of crucial interest . The Carnot refrigeration cycle is reversible and consists of adiabatic (isentropic due to reversible character) compression (1-2), isothermal rejection of heat (2-3), adiabatic expansion (3-4), and isothermal addition of heat (4-1) . The temperature-entropy diagram is shown in Fig . 11-69 . The Carnot cycle is an unattainable ideal which serves as a standard of comparison, and it provides a convenient guide to the temperatures that should be maintained to achieve maximum effectiveness .

REFRIGERATION

11-71

The measure of the system performance is the coefficient of performance (COP) . For refrigeration applications COPR is the ratio of heat removed from the low-temperature level (Qlow) to the energy input (W): COPR =

Qlow W

(11-84)

For the heat pump (HP) operation, heat rejected at the high temperature Qhigh is the objective, thus COPHP = FIG. 11-69 Temperature–entropy diagram of the Carnot cycle .

Qhigh W

Q +W = COPR + 1 W

=

(11-85)

For a Carnot cycle (where ∆Q = T ∆s), the COP for the refrigeration application becomes (note that T is absolute temperature [K]) COPR =

Tlow Thigh − Tlow

(11-86)

Thigh

(11-87)

and for heat pump application COPHP =

FIG. 11-70

Methods of transforming low-pressure vapor into high-pressure vapor in refrigeration systems (Stoecker, Refrigeration, and Air-Conditioning .)

FIG. 11-71

Basic refrigeration systems .

Thigh − Tlow

The COP in real refrigeration cycles is always less than that for the ideal (Carnot) cycle, and there is constant effort to achieve this ideal value . Basic Refrigeration Methods Three basic methods of refrigeration (mentioned above) use similar processes for obtaining the refrigeration effect: evaporation in the evaporator, condensation in the condenser where heat is rejected to the environment, and expansion in a flow restrictor . The main difference lies in the way compression is being done (Fig . 11-70): using mechanical work (in compressor), thermal energy ( for absorption and desorption), or pressure difference (in ejector) . In Fig . 11-71 basic refrigeration systems are displayed in greater detail . A more elaborate approach is presented in the text .

11-72

HEAT-TRANSFER EQUIPMENT

FIG. 11-74 Refrigeration system with a heat exchanger to subcool the liquid from

the condenser .

FIG. 11-72

The pressure-enthalpy diagram for the vapor compression cycle .

MECHANICAL REFRIGERATION (VAPOR COMPRESSION SYSTEMS) Vapor Compression Cycles The most widely used refrigeration principle is vapor compression . Isothermal processes are realized through isobaric evaporation and condensation in the tubes . The standard vapor compression refrigeration cycle (counterclockwise Rankine cycle) is marked in Fig . 11-71a by 1, 2, 3, 4 . Work that could be obtained in a turbine is small, and a turbine is substituted for an expansion valve . For reasons of proper compressor function, wet compression is substituted for compression of dry vapor . Although the T−s diagram is very useful for thermodynamic analysis, the pressure enthalpy diagram is used much more in refrigeration practice because both evaporation and condensation are isobaric processes so that the heat exchanged is equal to the enthalpy difference ∆Q = ∆h. For the ideal, isentropic compression, the work could be also presented as enthalpy difference ∆W = ∆h. The vapor compression cycle (Rankine) is presented in Fig . 11-72 in p-h coordinates . Figure 11-73 presents the actual versus standard vapor-compression cycle . In reality, flow through the condenser and evaporator must be accompanied by a pressure drop . There is always some subcooling in the condenser and superheating of the vapor entering the compressor-suction line, both due to continuing process in the heat exchangers and the influence of the

environment . Subcooling and superheating are usually desirable to ensure only liquid enters the expansion device . Superheating is recommended as a precaution against droplets of liquid being carried over into the compressor . There are many ways to increase cycle efficiency (COP) . Some of them are better suited to one, but not for the other refrigerant . Sometimes, for the same refrigerant, the impact on COP could be different for various temperatures . One typical example is the use of a liquid-to-suction heat exchanger (Fig . 11-74) . The suction vapor coming from the evaporator could be used to subcool the liquid from the condenser . Graphic interpretation in the T−s diagram for such a process is shown in Fig . 11-75 . The result of the use of suction line heat exchanger is to increase the refrigeration effect ∆Q and to increase the work by ∆W. The change in COP is then ∆COP = COP′ − COP =

Q + ∆Q P + ∆P − Q /P

(11-88)

When dry, or superheated, vapor is used to subcool the liquid, the COP in R12 systems will increase, and the COP in NH3 systems will decrease . For R22 systems it could have both effects, depending on the operating regime . Generally, this measure is advantageous (COP is improved) for fluids with high specific heat of liquid (less inclined saturated-liquid line on the p-h diagram), small heat of evaporation hfg when vapor-specific heat is low (isobars in superheated regions are steep) and when the difference between evaporation and condensation temperatures is high . Measures to increase COP should be studied for every refrigerant . Sometimes the purpose of the suction-line heat exchanger is not only to improve the COP, but also to ensure that only the vapor reaches the compressor, particularly in the case of a malfunctioning expansion valve . The system shown in Fig . 11-74 is direct expansion where dry or slightly superheated vapor leaves the evaporator . Such systems are predominantly used in small applications because of their simplicity and light weight . For the systems where efficiency is crucial (large industrial systems), recirculating systems (Fig . 11-76) are more appropriate . Ammonia refrigeration plants are almost exclusively built as recirculating systems . The main advantage of recirculating versus direct expansion systems is better utilization of evaporator surface area . The diagram reflecting the influence of quality on the local heat-transfer coefficients is shown

FIG. 11-75 Refrigeration system with a heat exchanger to subcool the liquid from FIG. 11-73

Actual vapor compression cycle compared with standard cycle .

the condenser .

REFRIGERATION

11-73

The mass flow rate at the flash-tank inlet mi consists of three components (mi = m1 + msup + mflash): m1 = liquid at pm feeding low-temperature evaporator msup = liquid at pm to evaporate in flash tank to cool superheated discharge mflash = flashed refrigerant, used to cool remaining liquid The vapor component is

FIG. 11-76 Recirculation system .

mm =

Qm h3 − h6

(11-89)

(11-90)

FIG. 11-77

(11-91)

(1 − xm) × mi = m1 + msup

(11-92)

and the liquid component is

in Fig . 11-89 . It is clear that heat-transfer characteristics will be better if the outlet quality is lower than 1 . Circulation could be achieved either by pumping (mechanical or gas) or by using gravity (thermosyphon effect: density of pure liquid at the evaporator entrance is higher than density of the vaporliquid mixture leaving the evaporator) . The circulation ratio (ratio of actual mass flow rate to the evaporated mass flow rate) is higher than 1 and up to 5 . Higher values are not recommended due to a small increase in heat-transfer rate for a significant increase in pumping costs . Multistage Systems When the evaporation and condensing pressure (or temperature) difference is large, it is prudent to separate compression into two stages . The use of multistage systems opens up the opportunity to use flash-gas removal and intercooling as measures to improve system performance . One typical two-stage system with two evaporating temperatures and both flash-gas removal and intercooling is shown in Fig . 11-77 . The purpose of the flash-tank intercooler is to (1) separate vapor created in the expansion process, (2) cool superheated vapor from compressor discharge, and (3) eventually separate existing droplets at the exit of the medium-temperature evaporator . The first measure will decrease the size of the low-stage compressor because it will not wastefully compress the portion of flow which cannot perform the refrigeration, and the second measure will decrease the size of the high-stage compressor due to lowering the specific volume of the vapor from the low-stage compressor discharge, positively affecting operating temperatures of the high-stage compressor due to the cooling effect . If the refrigerating requirement at a low-evaporating temperature is Ql and at the medium level is Qm, then the mass flow rates (m1 and mm, respectively) needed are Ql Ql m1 = = h1 − h8 h1 − h7

mflash = xm × mi

The liquid part of flow to cool superheated compressor discharge is determined by msup =

h −h Ql h −h × 2 3 = m1 × 2 3 hfgm h1 − h8 h3 − h7

(11-93)

h6 − h7 h3 − h7

(11-94)

Since the quality xm is xm =

The mass flow rate through the condenser and high-stage compressor mh is finally mh = mm + mi

(11-94a)

The optimum intermediate pressure for the two-stage refrigeration cycle is determined as the geometric mean between evaporation pressure pl and condensing pressure ph (Fig . 11-78): pm =

ph pl

(11-95)

based on equal pressure ratios for low- and high-stage compressors . The optimum interstage pressure is slightly higher than the geometric mean of the suction and the discharge pressures, but, due to the very flat optimum of power versus interstage pressure relation geometric mean, it is widely accepted for determining the intermediate pressure . The required pressure of the intermediate-level evaporator may dictate interstage pressure other than determined as optimal .

Typical two-stage system with two evaporating temperatures, flash-gas removal, and intercooling .

11-74

HEAT-TRANSFER EQUIPMENT

FIG. 11-80

FIG. 11-78 Pressure–enthalpy diagram for typical two-stage system with two evaporating temperatures, flash-gas removal, and intercooling .

Two-stage systems should be seriously considered when the evaporating temperature is below −20°C . Such designs will save on power and reduce compressor discharge temperatures, but will increase the initial cost . Cascade System This is a reasonable choice in cases where the evaporating temperature is very low (below −60°C) . When condensing pressures are to be in the rational limits, the same refrigerant has a high specific volume at very low temperatures, requiring a large compressor . The evaporating pressure may be below atmospheric, which could cause moisture and air infiltration into the system if there is a leak . In other words, when the temperature difference between the medium that must be cooled and the environment is too high to be served with one refrigerant, it is wise to use different refrigerants in the high and low stages . Figure 11-79 shows a cascade system schematic diagram . There are basically two independent systems linked via a heat exchanger: the evaporator of the high-stage system and the condenser of the low-stage system . EQUIPMENT Compressors These could be classified by one criterion (the way the increase in pressure is obtained) as positive-displacement and dynamic types, as shown in Fig . 11-80 (see Sec . 10 for drawings and mechanical description of the various types of compressors) . Positive-displacement compressors (PDCs) are the machines that increase the pressure of the vapor by reducing the volume of the chamber . Typical PDCs are reciprocating (in a variety of types) or rotary as screw (with one and two rotors), vane, scroll, and so on . Centrifugal compressors or turbocompressors are machines where the pressure is raised, converting some of the kinetic energy obtained by a rotating mechanical element which continuously adds angular momentum to a steadily flowing fluid, similar to a fan or pump .

FIG. 11-79 Cascade system .

Types of refrigeration compressors .

Generally, reciprocating compressors dominate in the range up to 300kW refrigeration capacity . Centrifugal compressors are more accepted for the range over 500 kW, while screw compressors are in between with a tendency to go toward smaller capacities . The vane and the scroll compressors are finding their places primarily in very low-capacity range (domestic refrigerators and air conditioners), although vane compressors could be found in industrial compressors . Frequently, screw compressors operate as boosters, for the base load, while reciprocating compressors accommodate the variation of capacity in the high stage . The major reason for such design is the advantageous operation of screw compressors near full load and in design conditions, while reciprocating compressors seem to have better efficiencies at part-load operation than screw compressors . Using other criteria, compressors are classified as open, semihermetic (accessible), or hermetic. Open type is characterized by shaft extension out of the compressor, where it is coupled to the driving motor . When the electric motor is in the same housing with the compressor mechanism, it could be either hermetic or accessible (semihermetic) . Hermetic compressors have welded enclosures, not designed to be repaired, and are generally manufactured for smaller capacities (seldom over 30 kW), while semihermetic or an accessible type is located in the housing which is tightened by screws . Semihermetic compressors have all the advantages of hermetic (no sealing of moving parts, e .g ., no refrigerant leakage at the seal shaft, no external motor mounting, no coupling alignment) and could be serviced, but it is more expensive . Compared to other applications, refrigeration capacities in the chemical industry are usually high . That leads to wide use of centrifugal, screw, or high-capacity rotary compressors . Most centrifugal and screw compressors use economizers to minimize power and suction volume requirements . Generally, there is far greater use of open-drive type of compressors in the chemical plants than in air conditioning, commercial, or food refrigeration . Very frequently, compressor lube oil systems are provided with auxiliary oil pumps, filters, coolers, and other equipment to permit maintenance and repair without shutdown . Positive-Displacement Compressors Reciprocating compressors are built in different sizes (up to about 1-MW refrigeration capacity per unit) . Modern compressors are high-speed, mostly direct-coupled, single-acting, from 1 to mostly 8, and occasionally up to 16 cylinders . Two characteristics of compressors for refrigeration are the most important: refrigerating capacity and power . Typical characteristics are as presented in Fig . 11-81 . Refrigerating capacity Qe is the product of the mass flow rate of refrigerant m and the refrigerating effect R which is ( for isobaric evaporation) R = hevaporator outlet − hevaporator inlet . Power P required for the compression, necessary for the motor selection, is the product of mass flow rate m and work of compression W. The latter is, for the isentropic compression, W = hdischarge − hsuction . Both of these characteristics could be calculated for the ideal (without losses) and for the actual compressor . Ideally, the mass flow rate is equal to the product of the compressor displacement Vi per unit time and the gas density ρ: m = Vi × ρ . The compressor displacement rate is the volume swept through by the pistons (product of the cylinder number n and volume of cylinder V = stroke × d 2π/4) per second . In reality, the actual compressor delivers less refrigerant . The ratio of the actual flow rate (entering compressor) to the displacement rate is the volumetric efficiency ηva . The volumetric efficiency is less than unity due to reexpansion of the compressed vapor in clearance volume, pressure drop (through suction and discharge valves, strainers, manifolds, etc .), internal gas leakage (through the clearance between piston rings and cylinder walls, etc .), valve inefficiencies, and expansion of the vapor in the suction cycle caused by the heat exchanged (hot cylinder walls, oil, motor, etc .) .

REFRIGERATION

FIG. 11-81 Typical capacity and power-input curves for reciprocating compressor .

Similar to volumetric efficiency, isentropic (adiabatic) efficiency ηa is the ratio of the work required for isentropic compression of the gas to work input to the compressor shaft . The adiabatic efficiency is less than 1 mainly due to pressure drop through the valve ports and other restricted passages and the heating of the gas during compression . Figure 11-82 presents the compression on a pressure-volume diagram for an ideal compressor with clearance volume (thin lines) and actual compressor (thick lines) . Compression in an ideal compressor without clearance is extended using dashed lines to the points Id (end of discharge), line Id − Is (suction), and Is (beginning of suction) . The area surrounded by the lines of

compression, discharge, reexpansion, and intake presents the work needed for compression . The actual compressor only appears to demand less work for compression due to smaller area in the p-V diagram . The mass flow rate for an ideal compressor is higher, which cannot be seen in the diagram . In reality, an actual compressor will have adiabatic compression and reexpansion and higher discharge and lower suction pressures due to pressure drops in valves and lines . The slight increase in the pressure at the beginning of the discharge and suction is due to forces needed to initially open valves . When the suction pressure is lowered, the influence of the clearance will increase, causing in the extreme cases the entire volume to be used for reexpansion, which drives the volumetric efficiency to zero . There are various options for capacity control of reciprocating refrigeration compressors: 1 . Open the suction valves by some external force (oil from the lubricating system, discharge gas, electromagnets, …) . 2 . Gas bypass: return the discharge gas to suction (within the compressor or outside the compressor) . 3 . Control the suction pressure by throttling in the suction line . 4 . Control the discharge pressure . 5 . Add reexpansion volume . 6 . Change the stroke . 7 . Change the compressor speed . The first method is used most frequently . The next preference is for the last method, mostly used in small compressors due to problems with speed control of electric motors . Other means of capacity control are very seldom utilized due to thermodynamic inefficiencies and design difficulties . Energy losses in a compressor, when capacity regulation is provided by lifting the suction valves, are due to friction of gas flowing into and out of the unloaded cylinder . This is shown in Fig . 11-83 where the comparison is made for ideal partial-load operation, reciprocating, and screw compressors . Rotary compressors are also PDC types, but where refrigerant flow rotates during compression . Unlike the reciprocating type, rotary compressors have a built-in volume ratio which is defined as the volume in the cavity when the suction port is closed (Vs = m × υs) over the volume in the cavity when the discharge port is uncovered (Vd = m × υd) . The built-in volume ratio determines for a given refrigerant and conditions the pressure ratio, which is pd  υ s  = ps  υd 

n

where n represents the politropic exponent of compression .

FIG. 11-82 Pressure–volume diagram of an ideal (thin line) and actual (thick line) reciprocating

compressor .

11-75

(11-96)

11-76

HEAT-TRANSFER EQUIPMENT now widely used for high-stage applications . There are several methods for capacity regulation of screw compressors . One is variable-speed drive, but a more economical first-cost concept is a slide valve that is used in some form by practically all screw compressors . The slide is located in the compressor casting below the rotors, allowing internal gas recirculation without compression . The slide valve is operated by a piston located in a hydraulic cylinder and actuated by high-pressure oil from both sides . When the compressor is started, the slide valve is fully open and the compressor is unloaded . To increase capacity, a solenoid valve on the hydraulic line opens, moving the piston in the direction of increasing capacity . To increase part-load efficiency, the slide valve is designed to consist of two parts, one traditional slide valve for capacity regulation and other for built-in volume adjustment . Single-screw compressors are a newer design (early 1960s) compared to twin-screw compressors, and are manufactured in the range of capacity from 100 kW to 4 MW . The compressor screw is cylindrical with helical grooves mated with two star wheels (gate rotors) rotating in opposite direction from each other . Each tooth acts as the piston in the rotating “cylinder” formed by the screw flute and cylindrical main-rotor casting . As compression occurs concurrently in both halves of the compressor, radial forces are oppositely directed, resulting in negligible net-radial loads on the rotor bearings (unlike twin-screw compressors), but there are some loads on the star wheel shafts . Scroll compressors are currently used in relatively small-size installations, predominantly for residential air conditioning (up to 50 kW) . They are recognized for low-noise operation . Two scrolls ( freestanding, involute spirals bounded on one side by a flat plate) facing each other form a closed volume while one moves in a controlled orbit around a fixed point on the other fixed scroll . The suction gas which enters from the periphery is trapped by the scrolls . The closed volumes move radially inward until the discharge port is reached, when vapor is pressed out . The orbiting scroll is driven by a shortthrow crank mechanism . As in screw compressors, internal leakage should be kept low, and it occurs in gaps between cylindrical surfaces and between the tips of the involute and the opposing scroll baseplate . Similar to the screw compressor, the scroll compressor is a constantvolume-ratio machine . Losses occur when operating conditions of the compressor do not match the built-in volume ratio (see Fig . 11-84) . Vane compressors are used in small, hermetic units, but sometimes as booster compressors in industrial applications . Two basic types are the fixed (roller) or single-vane type and the rotating or multiple-vane type . In the single-vane type, the rotor (called roller) is eccentrically placed in the cylinder so these two are always in contact . The contact line makes the first separation between the suction and discharge chambers while the vane (spring-loaded divider) makes the second . In the multiple-vane compressors, the rotor and the cylinder are not in the contact . The rotor has two or more sliding vanes which are held against the cylinder by centrifugal force . In the vane rotary compressors, no suction valves are needed . Since the gas enters the compressor continuously, gas pulsations are at a minimum . Vane compressors have a high volumetric efficiency because of the small clearance volume and consequent low reexpansion losses . Rotary vane compressors have a low weight-to-displacement ratio, which makes them suitable for transport applications . Centrifugal Compressors These are sometimes called turbocompressors and mostly serve refrigeration systems in the capacity range of 200 to 10,000 kW . The main component is a spinning impeller wheel, backwardcurved, which imparts energy to the gas being compressed . Some of the kinetic energy converts into pressure in a volute . Refrigerating centrifugal compressors are predominantly multistage, compared to other turbocompressors, which produce high-pressure ratios .

FIG. 11-83 Typical power-refrigeration capacity data for different types of compressors during partial unloaded operation .

In other words, in a reciprocating compressor the discharge valve opens when the pressure in the cylinder is slightly higher than the pressure in the high-pressure side of the system, while in rotary compressors the discharge pressure will be established only by inlet conditions ( ps , Vs) and the built-in volume ratio regardless of the system discharge pressure . Very seldom are the discharge and system (condensing) pressures equal, causing the situation shown in Fig . 11-84 . When condensing pressure p is lower than discharge pd, shown as case (a), “overcompression” will cause energy losses presented by the horn on the diagram . If the condensing pressure is higher, in the moment when the discharge port uncovers there will be flow of refrigerant backward into the compressor, causing losses shown in Fig . 11-84b; and the last stage will be only discharge without compression . The case when the compressor discharge pressure is equal to the condensing pressure is shown in Fig . 11-84c. Double helical rotary (twin) screw compressors consist of two mating, helically grooved rotors (male and female) with asymmetric profile, in a housing formed by two overlapped cylinders, with inlet and outlet ports . Developed relatively recently (in the 1930s), the first twin-screw compressors were used for air, and later (in the 1950s) became popular for refrigeration . Screw compressors have some advantages over reciprocating compressors ( fewer moving parts and greater compactness) but also some drawbacks (lower efficiency at off-design conditions, as discussed above, higher manufacturing cost due to complicated screw geometry, large separators and coolers for oil which is important as a sealant) . Figure 11-85 shows the oil circuit of a screw compressor . Oil cooling could be provided by water, glycol, or refrigerant either in the heat exchanger utilizing thermosyphon effect or using the direct expansion concept . To overcome some inherent disadvantages, screw compressors have been initially used predominantly as booster (low-stage) compressors, and following development in capacity control and decreasing prices, they are

FIG. 11-84

Vs

Vs

Vs

(a)

(b)

(c)

Matching compressor built-in pressure ratio with actual pressure difference .

REFRIGERATION

FIG. 11-85

Oil cooling in a screw compressor .

The torque T (N ∙ m) the impeller ideally imparts to the gas is T = m (utang . out rout − utang . in rin)

(11-97)

where m (kg/s) = mass flow rate rout (m) = radius of exit of impeller rin (m) = radius of entrance of impeller utang .out (m/s) = tangential velocity of refrigerant leaving impeller utang .in (m/s) = tangential velocity of refrigerant entering impeller When refrigerant enters essentially radially, utang . in = 0 and torque becomes T = m × utang .out × rout

(11-98)

The power P (in watts) is the product of torque and rotative speed w [l/s] and so is P = T × w = m × utang . out × rout × w

(11-99)

which for utang . ou = rout × w becomes 2

P = m × utang .out

(11-100)

P = m × ∆h

(11-101)

Lines of constant efficiencies show the maximum efficiency . Unstable operation sequence, called surging, occurs when compressors fail to operate in the range left of the surge envelope . It is characterized by noise and wide fluctuations of load on the compressor and the motor . The period of the cycle is usually 2 to 5 s, depending upon the size of the installation . The capacity could be controlled by (1) adjusting the prerotation vanes at the impeller inlet, (2) varying the speed, (3) varying the condenser pressure, and (4) bypassing discharge gas . The first two methods are predominantly used . Condensers These are heat exchangers that convert refrigerant vapor to a liquid . Heat is transferred in three main phases: (1) desuperheating, (2) condensing, and (3) subcooling . In reality condensation occurs even in the superheated region, and subcooling occurs in the condensation region . Three main types of refrigeration condensers are air-cooled, water-cooled, and evaporative . Air-cooled condensers are used mostly in air conditioning and for smaller refrigeration capacities . The main advantage is the availability of cooling medium (air), but heat-transfer rates for the air side are far below values when water is used as a cooling medium . Condensation always occurs inside tubes, while the air side uses extended surface ( fins) . The most common types of water-cooled refrigerant condensers are (1) shell-and-tube, (2) shell-and-coil, (3) tube-in-tube, and (4) brazedplate . Shell-and-tube condensers are built up to 30-MW capacity . Cooling water flows through the tubes in a single-pass or multipass circuit . Fixedtubesheet and straight-tube construction are common . Horizontal layout is typical, but sometimes vertical is used . Heat-transfer coefficients for the vertical types are lower due to poor condensate drainage, but less water of lower purity can be utilized . Condensation always occurs on the tubes, and often the lower portion of the shell is used as a receiver . In shell-and-coil condensers, water circulates through one or more continuous or assembled coils contained within the shell while refrigerant condenses outside . The tubes cannot be mechanically cleaned or replaced . Tube-in-tube condensers could be found in versions where condensation occurs either in the inner tube or in the annulus . Condensing coefficients are more difficult to predict, especially in the cases where tubes are formed in spiral . Mechanical cleaning is more complicated, sometimes impossible, and tubes are not replaceable . Brazed-plate condensers are constructed of plates brazed together to make up an assembly of separate channels . The plates are typically stainless steel, wave-style corrugated, enabling high heat-transfer rates . Performance calculation is difficult, with very few correlations available . The main advantage is the highest performance/volume (mass) ratio and the lowest refrigerant charge . The last mentioned advantage seems to be the most important feature for many applications where minimization of charge inventory is crucial . Evaporative condensers (Fig . 11-87) are widely used due to lower condensing temperatures than in the air-cooled condensers and also lower than the water-cooled condenser combined with the cooling tower . Water demands are far lower than for water-cooled condensers . The chemical industry uses shell-and-tube condensers widely, although the use of air-cooled condensing equipment and evaporative condensers is on the increase .

or for isentropic compression

The performance of a centrifugal compressor (discharge to suctionpressure ratio versus the flow rate) for different speeds is shown in Fig . 11-86 .

FIG. 11-86 Performance of the centrifugal compressor .

11-77

FIG. 11-87 Evaporative condenser with desuperheating coil .

11-78

HEAT-TRANSFER EQUIPMENT

Generally, cooling water is of a lower quality than normal, having also higher mud and silt content . Sometimes even replaceable copper tubes in shell-and-tube heat exchangers are required . It is advisable to use cupronickel instead of copper tubes (when water is high in chlorides) and to use conservative water-side velocities (less than 2 m/s for copper tubes) . Evaporative condensers are used quite extensively . In most cases, commercial evaporative condensers are not totally suitable for chemical plants due to the hostile atmosphere, which usually abounds in vapor and dusts that can cause either chemical (corrosion) or mechanical problems (plugging of spray nozzles) . Air-cooled condensers are similar to evaporative ones in that the service dictates the use of either more expensive alloys in the tube construction or conventional materials of greater wall thickness . Heat rejected in the condenser QCd consists of heat absorbed in the evaporator QEevap and energy W supplied by the compressor: QCd = QEevap + W

(11-102)

For the actual systems, compressor work will be higher than for ideal systems for the isentropic efficiency and other losses . In the case of hermetic or accessible compressors where an electric motor is cooled by the refrigerant, condenser capacity should be QCd = QEevap + PEM

(11-103)

It is common that compressor manufacturers provide data for the ratio of the heat rejected at the condenser to the refrigeration capacity, as shown in Fig . 11-88 . The solid line represents data for the open compressors while the dotted line represents the hermetic and accessible compressors . The difference between solid and dotted line is due to all losses (mechanical and electrical in the electric motor) . Condenser design is based on the value QCd = QEevap × heat rejection ratio

(11-104)

Thermal and mechanical design of heat exchangers (condensers and evaporators) is presented earlier in this section . Evaporators These are heat exchangers where refrigerant is evaporated while cooling the product, fluid, or body . Refrigerant could be in direct contact with the body that is being cooled, or some other medium could be used as secondary fluid . Mostly air, water, and antifreeze are fluids that are cooled . Design is strongly influenced by the application . Evaporators for air cooling will have in-tube evaporation of the refrigerant, while liquid chillers could have refrigerant evaporation inside or outside the tube . The heattransfer coefficient for evaporation inside the tube (versus length or quality) is shown in Fig . 11-89 . Fundamentals of the heat transfer in evaporators, as well as design aspects, are presented in Sec . 11 . We point out only some specific aspects of refrigeration applications .

FIG. 11-88 Typical values of the heat rejection ratio of the heat rejected at the con-

denser to the refrigerating capacity .

FIG. 11-89

Heat-transfer coefficient for boiling inside the tube .

Refrigeration evaporators could be classified according to the method of feed as either direct (dry) expansion or flooded (liquid overfeed) . In dry expansion the evaporator’s outlet is dry or slightly superheated vapor . This limits the liquid feed to the amount that can be completely vaporized by the time it reaches the end of the evaporator . In the liquid overfeed evaporator, the amount of liquid refrigerant circulating exceeds the amount evaporated by the circulation number . Decision on the type of the system to be used is one of the first in the design process . A direct-expansion evaporator is generally applied in smaller systems where compact design and low first costs are crucial . Control of the refrigerant mass flow is then obtained by either a thermoexpansion valve or a capillary tube . Figure 11-89 suggests that the evaporator surface is the most effective in the regions with quality that is neither low nor high . In dry-expansion evaporators, inlet qualities are 10 to 20 percent, but when controlled by the thermoexpansion valve, vapor at the outlet is not only dry, but even superheated . In recirculating systems, saturated liquid (x = 0) is entering the evaporator . Either the pump or gravity will deliver more refrigerant liquid than will evaporate, so outlet quality could be lower than 1 . The ratio of refrigerant flow rate supplied to the evaporator overflow rate of refrigerant vaporized is the circulation ratio n. When n increases, the coefficient of heat transfer will increase due to the wetted outlet of the evaporator and the increased velocity at the inlet (Fig . 11-90) . In the range of n = 2 to 4, the overall U value for air cooler increases roughly by 20 to 30 percent compared to the directexpansion case . Circulation rates higher than 4 are not efficient . The price for an increase in heat-transfer characteristics is a more complex system with more auxiliary equipment: low-pressure receivers, refrigerant pumps, valves, and controls . Liquid refrigerant is predominantly pumped by mechanical pumps; however, sometimes gas at condensing pressure is used for pumping, in the variety of concepts .

FIG. 11-90 Effect of circulation ratio on the overall heat-transfer coefficient of an air-cooling coil .

REFRIGERATION The important characteristics of the refrigeration evaporators is the presence of the oil . The system is contaminated with oil in the compressor, in spite of reasonably efficient oil separators . Some systems will recirculate oil, when miscible with refrigerant, returning it to the compressor crankcase . This is found mostly in the systems using halocarbon refrigerants . Although oils that are miscible with ammonia exist, immiscible oils are predominantly used . This inhibits the ammonia systems from recirculating the oil . In systems with oil recirculation when halocarbons are used, special consideration should be given to proper sizing and layout of the pipes . Proper pipeline configuration, slopes, and velocities (to ensure oil circulation under all operating loads) are essential for good system operation . When refrigerant is lighter than the oil in systems with no oil recirculation, oil will be at the bottom of every volume with a top outlet . Then oil must be drained periodically to avoid decreasing the performance of the equipment . It is essential for proper design to have the data for refrigerant–oil miscibility under all operating conditions . Some refrigerant–oil combinations will always be miscible, others always immiscible, but still others will have both characteristics, depending on the temperatures and pressures applied . Defrosting is the important issue for evaporators which are cooling air below freezing . Defrosting is done periodically, actuated predominantly by time relays, but other frost indicators are used (temperature, visual, or pressure-drop sensors) . Defrost technique is determined mostly by fluids available and tolerable complexity of the system . Defrosting is done by the following mechanisms when the system is off: • Hot (or cool) refrigerant gas (the predominant method in industrial applications) • Water (defrosting from the outside, unlike hot-gas defrost) • Air (only when room temperature is above freezing) • Electricity ( for small systems where hot-gas defrost will be too complex and water is not available) • Combinations of above System Analysis Design calculations are made on the basis of the close to the highest refrigeration load; however, the system operates at the design conditions very seldom . The purpose of regulating devices is to adjust the system performance to cooling demands by decreasing the effect or performance of some component . Refrigeration systems have inherent selfregulating control which the engineer can rely on to a certain extent . When the refrigeration load starts to decrease, less refrigerant will evaporate . This causes a drop in evaporation temperature (as long as compressor capacity is unchanged) due to the imbalance in vapor being taken by the compressor and produced by evaporation in the evaporator . With a drop in evaporation pressure, the compressor capacity will decrease due to (1) lower vapor density (lower mass flow for the same volumetric flow rate) and (2) a decrease in volumetric efficiency . However, when the evaporation temperature drops, for the unchanged temperature of the medium being cooled, the evaporator capacity will increase due to an increase in the mean-temperature difference between refrigerant and cooled medium, causing a positive effect (increase) on the cooling load . With a decrease in the evaporation temperature, the heat rejection factor will increase, causing an increase in heat rejected to the condenser, but the refrigerant mass flow rate will decrease because of the compressor characteristics . These will have an opposite effect on the condenser load . Even a simplified analysis demonstrates the necessity for better understanding of system performance under different operating conditions . Two methods could be used for more accurate analysis . The traditional method of refrigeration-system analysis is through determination of balance points, whereas in recent years, system analysis is performed by system simulation or mathematical modeling, using mathematical (equation-solving) rather than graphical (intersection of two curves) procedures . Systems with a small number of components such as the vapor compression refrigeration system could be analyzed both ways . Graphical presentation, better suited for understanding trends, is not appropriate for more-complex systems, more detailed component description, and frequent change of parameters . There are a variety of different mathematical models tailored to fit specific systems, refrigerants, available resources, demands, and complexity . Although limited in its applications, graphical representation is valuable as the starting tool and for clear understanding of the system performance . Refrigeration capacity qe and power P curves for the reciprocating compressor are shown in Fig . 11-91 . They are functions of temperatures of evaporation and condensation:

and

qe = qe(tevap, tcd)

(11-105a)

P = P(tevap, tcd)

(11-105b)

where qe (kW) = refrigerating capacity P (kW) = power required by the compressor tevap (°C) = evaporating temperature tcd (°C) = condensing temperature

11-79

FIG. 11-91 Refrigerating capacity and power requirement for the reciprocating

compressor .

A more detailed description of compressor performance is shown in the subsection on refrigeration compressors . Condenser performance, shown in Fig . 11-92, could be simplified as qcd = F (tcd − tamb)

(11-105c)

where qcd (kW) = capacity of condenser F (kW/°C) = capacity of condenser per unit inlet temperature difference (F = U × A) tamb (°C) = ambient temperature (or temperature of condenser cooling medium) In this analysis F will be constant, but it could be described more accurately as a function of parameters influencing heat transfer in the condenser (temperature, pressure, flow rate, fluid thermodynamic, and thermophysical characteristics, etc .) . Condenser performance should be expressed as an evaporating effect to enable matching with compressor and evaporator performance . The condenser evaporating effect is the refrigeration capacity of an evaporator served by a particular condenser . It is the function of the cycle, evaporating

FIG. 11-92 Condenser performance .

11-80

HEAT-TRANSFER EQUIPMENT

FIG. 11-93

Heat rejection ratio . FIG. 11-95

temperature, and the compressor . The evaporating effect could be calculated from the heat-rejection ratio qCd/qe: qe =

qCd heat-rejection ratio

(11-105d)

The heat rejection rate is presented in Fig . 11-93 (or Fig . 11-88) . Finally, the evaporating effect of the condenser is shown in Fig . 11-94 . The performance of the condensing unit (compressor and condenser) subsystem could be developed as shown in Fig . 11-95 by superimposing two graphs, one for compressor performance and the other for condenser evaporating effect . Evaporator performance could be simplified as qe = Fevap(tamb − tevap)

(11-106)

where qe (kW) = evaporator capacity Fe (kW/°C) = evaporator capacity per unit inlet temperature difference tamb (°C) = ambient temperature (or temperature of cooled body or fluid) . The diagram of the evaporator performance is shown in Fig . 11-96 . The character of the curvature of the lines (variable heat-transfer rate) indicates that the evaporator is cooling air . Influences of the flow rate of cooled fluid are also shown in this diagram; i .e ., higher flow rate will increase heat transfer . The same effect could be shown in the condenser performance curve . It is omitted only for the reasons of simplicity .

FIG. 11-94 Condenser evaporating effect .

Balance points of compressor and condenser determine performance of condensing unit for fixed temperature of condenser cooling fluid ( flow rate and heattransfer coefficient are constant) .

The performance of the complete system could be predicted by superimposing the diagrams for the condensing unit and the evaporator, as shown in Fig . 11-97 . Point 1 reveals a balance for constant flows and inlet temperatures of chilled fluid and fluid for condenser cooling . When this point is transferred in the diagram for the condensing unit in Fig . 11-94 or 11-95, the condensing temperature could be determined . When the temperature of entering fluid in the evaporator tamb1 is lowered to tamb2, the new operating conditions will be determined by the state at point 2 . Evaporation temperature drops from tevap1 to tevap2 . If the evaporation temperature is unchanged, the same reduction of inlet temperature could be achieved by reducing the capacity of the condensing unit from Cp to Cp∗ . The new operating point 3 shows reduction in capacity for ∆ due to the reduction in the compressor or the condenser capacity . Mathematical modeling is essentially the same process, but the description of the component performance is generally much more complex and detailed . This approach enables a user to vary more parameters more easily, look into various possibilities for intervention, and predict the response of the system from different influences . Equation solving does not necessarily have to be done by successive substitution or iteration as this procedure could suggest .

FIG. 11-96

Refrigerating capacity of evaporator .

REFRIGERATION

11-81

Absorption systems will be considered when there is low-cost, lowpressure steam or waste heat available and the evaporation temperature and refrigeration load are relatively high . Typical application range is for water chilling at 7°C to 10°C, and capacities from 300 kW to 5 MW in a single unit . The main drawback is the difficulty in maintaining a tight system with the highly corrosive lithium bromide and an operating pressure in the evaporator and the absorber below atmospheric . Ejector (steam-jet) refrigeration systems are used for similar applications, when the chilled-water outlet temperature is relatively high, when relatively cool condensing water and cheap steam at 7 bar are available, and for similar high duties (0 .3 to 5 MW) . Even though these systems usually have low first and maintenance costs, there are not many steam-jet systems running . OTHER REFRIGERATION SYSTEMS APPLIED IN THE INDUSTRY

FIG. 11-97 Performance of complete refrigeration system (1), when there is reduction in heat load (2), and when for the same ambient (or inlet in evaporator) evaporation temperature is maintained constant by reducing capacity of compressor/ condenser part (3) .

System, Equipment, and Refrigerant Selection There is no universal rule that can be used to decide which system, equipment type, or refrigerant is the most appropriate for a given application . A number of variables influence the final-design decision: • Refrigeration load • Type of installation • Temperature level of medium to be cooled • Condensing media characteristics: type (water, air, etc .), temperature level, available quantities • Energy source for driving the refrigeration unit (electricity, natural gas, steam, waste heat) • Location and space available (urban areas, sensitive equipment around, limited space, etc .) • Funds available (i .e ., initial versus run-cost ratio) • Safety requirements (explosive environment, aggressive fluids, etc .) • Other demands (compatibility with existing systems, type of load, compactness, level of automatization, operating life, possibility to use process fluid as refrigerant) Generally, vapor compression systems are considered first . They can be used for almost every task . Whenever it is possible, prefabricated elements or complete units are recommended . Reciprocating compressors are widely used for lower rates, more uneven heat loads (when frequent and wider range of capacity reduction is required) . They ask for more space and have higher maintenance costs than centrifugal compressors, but are often the most economical in first costs . Centrifugal compressors are considered for huge capacities, when the evaporating temperature is not too low . Screw compressors are considered first when space in the machine room is limited, when the system has operating long hours, and when periods between service should be longer . Direct expansions are more appropriate for smaller systems which should be compact and where there is just one or few evaporators . Overfeed (recirculation) systems should be considered for all applications where first cost for additional equipment (surge drums, low-pressure receivers, refrigerant pumps, and accessories) is lower than the savings for the evaporator surface . Choice of refrigerant is complex and not straightforward . For industrial applications, advantages of ammonia (thermodynamic and economic) overcome drawbacks which are mostly related to low-toxicity refrigerants and panics created by accidental leaks when used in urban areas . Halocarbons have many advantages (not toxic, not explosive, odorless, etc .), but environmental issues and slightly inferior thermodynamic and thermophysical properties compared to ammonia or hydrocarbons as well as rising prices are giving the opportunity to use other options . When this text was written, the ozone depletion issue was not resolved, R22 was still used but facing phase-out, and R134a was considered to be the best alternative for CFCs and HCFCs, having similar characteristics to the already banned R12 . Very often, fluid to be cooled is used as a refrigerant in the chemical industry . Use of secondary refrigerants in combination with the ammonia central-refrigeration unit is becoming a viable alternative in many applications .

Absorption Refrigeration Systems Two main absorption systems are used in industrial application: lithium bromide–water and ammonia– water . Lithium bromide–water systems are limited to evaporation temperatures above freezing because water is used as the refrigerant, while the refrigerant in an ammonia–water system is ammonia and consequently can be applied for the lower-temperature requirements . The single-effect indirect-fired lithium bromide cycle is shown in Fig . 11-98 . The machine consists of five major components: The evaporator is the heat exchanger where refrigerant (water) evaporates (being sprayed over the tubes) due to low pressure in the vessel . Evaporation chills water flow inside the tubes that bring heat from the external system to be cooled . The absorber is a component where strong absorber solution is used to absorb the water vapor flashed in the evaporator . A solution pump sprays the lithium bromide over the absorber tube section . Cool water is passing through the tubes taking the refrigeration load, heat of dilution, heat to cool condensed water, and sensible heat for solution cooling . The heat exchanger is used to improve the efficiency of the cycle, reducing consumption of steam and condenser water . The generator is a component where heat brought to a system in a tube section is used to restore the solution concentration by boiling off the water vapor absorbed in the absorber . The condenser is an element where water vapor, boiled in the generator, is condensed, preparing pure water (refrigerant) for discharge to an evaporator . Heat supplied to the generator is boiling weak (dilute) absorbent solution on the outside of the tubes . Evaporated water is condensed on the outside of the condenser tubes . Water utilized to cool the condenser is usually cooled in the cooling tower . Both the condenser and generator are located in the same vessel, being at the absolute pressure of about 6 kPa . The water condensate passes through a liquid trap and enters the evaporator . Refrigerant (water) boils on the evaporator tubes and cools the water flow that brings the refrigeration load . Refrigerant that is not evaporated flows to the recirculation pump to be sprayed over the evaporator tubes . Solution with high water concentration that enters the generator increases in concentration as water evaporates . The resulting strong, absorbent solution (solution with low water concentration) leaves the generator on its way to the heat exchanger . There the stream of high water concentration that flows to the generator cools the stream of solution with low water concentration that flows to the second vessel . The solution with low water concentration is distributed over the absorber tubes . The absorber and evaporator are located in the same vessel, so the refrigerant evaporated on the evaporator tubes is readily absorbed into the absorbent solution . The pressure in the second vessel during the operation is 7 kPa (absolute) . Heats of absorption and dilution are removed by cooling water (usually from the cooling tower) . The resulting solution with high water concentration is pumped through the heat exchanger to the generator, completing the cycle . The heat exchanger increases the efficiency of the system by preheating, that is, reducing the amount of heat that must be added to the high water solution before it begins to evaporate in the generator . The absorption machine operation is analyzed with the use of a lithium bromide–water equilibrium diagram, as shown in Fig . 11-99 . Vapor pressure is plotted versus the mass concentration of lithium bromide in the solution . The corresponding saturation temperature for a given vapor pressure is shown on the left-hand side of the diagram . The line in the lower right corner of the diagram is the crystallization line . It indicates the point at which the solution will begin to change from liquid to solid, and this is the limit of the cycle . If the solution becomes overconcentrated, the absorption cycle will be interrupted owing to solidification, and capacity will not be restored until the unit is desolidified . This normally requires the addition of heat to the outside of the solution heat exchanger and the solution pump . The diagram in Fig . 11-100 presents enthalpy data for LiBr–water solutions . It is needed for the thermal calculation of the cycle . Enthalpies for

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FIG. 11-98

Two-shell lithium bromide–water cycle chiller .

water and water vapor can be determined from the table of the properties of water . The data in Fig . 11-100 are applicable to saturated or subcooled solutions and are based on a zero enthalpy of liquid water at 0°C and a zero enthalpy of solid LiBr at 25°C . Since the zero enthalpy for the water in the solution is the same as that in conventional tables of properties of water, the water property tables can be used in conjunction with the diagram in Fig . 11-99 . The coefficient of performance of the absorption cycle is defined on the same principle as for the mechanical refrigeration COPabs =

useful effect refrigeration rate = heat input heat input at generator

but note that here the denominator for COPabs is heat while for the mechanical refrigeration cycle it is work . Since these two forms of energy are not equal, COPabs is not as low (0 .6 to 0 .8) as it appears compared to COP for mechanical system (2 .5 to 3 .5) . The double-effect absorption unit is shown in Fig . 11-101 . All major components and the operation of the double-effect absorption machine are similar to those for the single-effect machine . The primary generator, located in vessel 1, is using an external heat source to evaporate water from dilute-absorbent (high water concentration) solution . Water vapor readily flows to generator II where it is condensed on the tubes . The absorbent (LiBr) intermediate solution from generator I will pass through the heat exchanger on the way to generator II where it is heated by the condensing water vapor . The throttling valve reduces pressure from vessel 1 (about 103 kPa absolute)

FIG. 11-99 Temperature–pressure–concentration diagram of saturated LiBr–water solutions (W. F. Stoecker and J. W. Jones: Refrigeration and Air-Conditioning) .

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FIG. 11-100 Enthalpy of LiBr–water solutions (W. F. Stoecker and J. W. Jones: Refrigeration and Air-Conditioning) .

to that of vessel 2 . Following the reduction of pressure, some water in the solution flashes to vapor, which is liquefied at the condenser . In the high-temperature heat exchanger, the intermediate solution heats the weak (high water concentration) solution stream coming from the lowtemperature heat exchanger . In the low-temperature heat exchanger, strong solution is being cooled before entering the absorber . The absorber is at the same pressure as the evaporator . The double-effect absorption units achieve higher COPs than the single-stage ones . The ammonia–water absorption system was extensively used until the 1950s when the LiBr–water combination became popular . Figure 11-102 shows a simplified ammonia–water absorption cycle . The refrigerant is ammonia, and the absorbent is dilute aqueous solution of ammonia . Ammonia–water systems differ from water–lithium bromide equipment to accommodate major differences: Water (here absorbent) is also volatile, so the regeneration of weak water solution to strong water solution is a fractional distillation . Different refrigerant (ammonia) causes different, much higher pressures: about 1100 to 2100 kPa absolute in condenser . Ammonia vapor from the evaporator and the weak water solution from the generator are producing strong water solution in the absorber . Strong water solution is then separated in the rectifier, producing (1) ammonia with some water vapor content and (2) very strong water solution at the bottom, in the generator . Heat in the generator vaporizes ammonia, and the weak solution returns to absorber . On its way to the absorber, the weak solution stream passes through the heat exchanger, heating the strong solution from the absorber on the way to the rectifier . The other stream, mostly

ammonia vapor but with some water vapor content, flows to the condenser . To remove water as much as possible, the vapor from the rectifier passes through the analyzer where it is additionally cooled . The remaining water escaped from the analyzer passes as liquid through the condenser and the evaporator to the absorber . Ammonia–water units can be arranged for single-stage or cascaded twostage operation . The advantage of two-stage operation is that it creates the possibility of utilizing only part of the heat on the higher-temperature level and the rest on the lower-temperature level, but the price is increased for first cost and heat required . Ammonia–water and lithium bromide–water systems operate under comparable COP . The ammonia–water system is capable of achieving evaporating temperatures below 0°C because the refrigerant is ammonia . Water as the refrigerant limits evaporating temperatures to no lower than freezing, better to 3°C . Advantage of the lithium bromide–water system is that it requires less equipment and operates at lower pressures . But this is also a drawback, because pressures are below atmospheric, causing air infiltration in the system which must be purged periodically . Due to corrosion problems, special inhibitors must be used in the lithium bromide–water system . The infiltration of air in the ammonia–water system is also possible, but when evaporating temperature is below −33°C . This can result in formation of corrosive ammonium carbonate . Further Readings: ASHRAE Handbook, Refrigeration Systems and Applications, 1994; Bogart, M ., Ammonia Absorption Refrigeration in Industrial Processes, Gulf Publishing Co . Houston, Tex ., 1981; Stoecker, W . F ., and Jones, J . W ., Refrigeration and Air-Conditioning, McGraw-Hill, New York, 1982 .

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FIG. 11-101 Double-effect absorption unit .

Steam-Jet (Ejector) Systems These systems substitute an ejector for a mechanical compressor in a vapor compression system . Since the refrigerant is water, maintaining temperatures lower than that of the environment requires that the pressure of water in the evaporator be below atmospheric . A typical arrangement for the steam-jet refrigeration cycle is shown in Fig . 11-103 . Main Components These are the main components of steam-jet refrigeration systems:

1 . Primary steam ejector. This kinetic device utilizes the momentum of a high-velocity jet to entrain and accelerate a slower-moving medium into which it is directed . High-pressure steam is delivered to the ejector nozzle . The steam expands while flowing through the nozzle where the velocity increases rapidly . The velocity of steam leaving the nozzle is around 1200 m/s . Because of this high velocity, flash vapor from the tank is continually aspired into the moving steam . The mixture of steam and flash vapor then enters the diffuser section where the velocity is gradually reduced

FIG. 11-102 Simplified ammonia–water absorption cycle .

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FIG. 11-103 Ejector (steam-jet) refrigeration cycle (with surface-type condenser) .

because of increasing cross-sectional area . The energy of the high-velocity steam compresses the vapor during its passage through the diffuser, raising its temperature above the temperature of the condenser cooling water . 2 . Condenser. This is the component of the system where the vapor condenses and the heat is rejected . The rate of heat rejected is Qcond = (Ws + Ww) hfg

(11-107)

where Qcond = heat rejection (kW) Ws = primary booster steam rate (kg/s) Ww = flash vapor rate (kg/s) hfg = latent heat (kJ/kg) The condenser design, surface area, and condenser cooling water quantity should be based on the highest cooling water temperature likely to be encountered . If the inlet cooling water temperature becomes hotter than the design value, the primary booster (ejector) may cease functioning because of the increase in condenser pressure . Two types of condensers could be used: the surface condenser (shown in Fig . 11-103) and the barometric or jet condenser (Fig . 11-104) . The surface

FIG. 11-104 Barometric condenser for steam-jet system .

condenser is of shell-and-tube design with water flowing through the tubes and steam condensed on the outside surface . In the jet condenser, condensing water and the steam being condensed are mixed directly, and no tubes are provided . The jet condenser can be barometric or a low-level type . The barometric condenser requires a height of ~10 m above the level of the water in the hot well . A tailpipe of this length is needed so that condenser water and condensate can drain by gravity . In the low-level jet type, the tailpipe is eliminated, and it becomes necessary to remove the condenser water and condensate by pumping from the condenser to the hot well . The main advantages of the jet condenser are low maintenance with the absence of tubes and the fact that condenser water of varying degrees of cleanliness may be used . 3 . Flash tank. This is the evaporator of the ejector system and is usually a large-volume vessel where large water surface area is needed for efficient evaporative cooling action . Warm water returning from the process is sprayed into the flash chamber through nozzles (sometimes cascades are used for maximizing the contact surface, since they are less susceptible to carryover problems), and the cooled effluent is pumped from the bottom of the flash tank . When the steam supply to one ejector of a group is closed, some means must be provided for preventing the pressure in the condenser and flash tank from equalizing through that ejector . A compartmental flash tank is frequently used for such purposes . With this arrangement, partitions are provided so that each booster is operating on its own flash tank . When the steam is shut off to any booster, the valve to the inlet spray water to that compartment also is closed . A float valve is provided to control the supply of makeup water to replace the water vapor that has flashed off . The flash tank should be insulated . Applications The steam-jet refrigeration is suited for the following: 1 . It is suited to processes where direct vaporization is used for concentration or drying of heat-sensitive foods and chemicals and where, besides elimination of the heat exchanger, preservation of the product quality is an important advantage . 2 . It enables the use of hard water or even seawater for heat rejection, e .g ., for absorption of gases (CO2, SO2, ClO2, etc .) in chilled water (desorption is provided simultaneously with chilling) when a direct-contact barometric condenser is used . Despite being simple, rugged, reliable, low cost, and vibration-free and requiring low maintenance, steam-jet systems are not widely accepted in water chilling for air conditioning due to characteristics of the cycle . Factors Affecting Capacity Ejector (steam-jet) units become attractive when cooling relatively high-temperature chilled water with a source of about 7 bar gauge waste steam and relatively cool condensing water . The factors involved with steam-jet capacity include the following: 1 . Steam pressure. The main boosters can operate on steam pressures from as low as 0 .15 bar up to 7 bar gauge . The quantity of steam required increases rapidly as the steam pressure drops (Fig . 11-105) . The best steam rates are obtained with about 7 bar . Above this pressure the change

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FIG. 11-107

Steam demand versus chilled-water temperature for typical steam-jet system. (ASHRAE 1983 Equipment Handbook).

FIG. 11-105 Effect of steam pressure on steam demand at 38°C condenser temperature.

(ASHRAE 1983 Equipment Handbook).

in quantity of steam required is practically negligible . Ejectors must be designed for the highest available steam pressure, to take advantage of the lower steam consumption for various steam-inlet pressures . The secondary ejector systems used for removing air require steam pressures of 2 .5 bar or greater . When the available steam pressure is lower than this, an electrically driven vacuum pump is used for either the final secondary ejector or the entire secondary group . The secondary ejectors normally require 0 .2 to 0 .3 kg/h of steam per kilowatt of refrigeration capacity . 2 . Condenser water temperature. In comparison with other vapor compression systems, steam-jet machines require relatively large water quantities for condensation . The higher the inlet water temperature, the higher the water requirements (Fig . 11-106) . The condensing water temperature has an important effect on steam rate per refrigeration effect, rapidly decreasing with colder condenser cooling water . Figure 11-107 presents data on steam rate versus condenser water inlet for given chilled-water outlet temperatures and steam pressure . 3 . Chilled-water temperature.    As the chilled-water outlet temperature decreases, the ratio of the steam/refrigeration effect decreases, thus increasing condensing temperatures and/or increasing the condensing-water requirements. Unlike other refrigeration systems, the chilled-water flow rate is of no particular importance in steam-jet system design, because there is, due to direct heat exchange, no influence of evaporator tube velocities and related temperature differences on heat-transfer rates. Widely varying return chilled-water temperatures have little effect on steam-jet equipment. Multistage Systems The majority of steam-jet systems being currently installed are multistage. Up to five-stage systems are in commercial operation. Capacity Control The simplest way to regulate the capacity of most steam vacuum refrigeration systems is to furnish several primary boosters

FIG. 11-106 Steam demand versus condenser water flow rate.

in parallel and operate only those required to handle the heat load. It is not uncommon to have as many as four main boosters on larger units for capacity variation. A simple automatic on-off type of control may be used for this purpose. By sensing the chilled-water temperature leaving the flash tank, a controller can turn steam on and off to each ejector as required. Additionally, two other control systems that will regulate steam flow or condenser-water flow to the machine are available. As the condenser-water temperature decreases during various periods of the year, the absolute condenser pressure will decrease. This will permit the ejectors to operate on less steam because of the reduced discharge pressure. Either the steam flow or the condenser water quantities can be reduced to lower operating costs at other than design periods. The arrangement selected depends on cost considerations between the two flow quantities. Some systems have been arranged for a combination of the two, automatically reducing steam flow down to a point, followed by a reduction in condenser-water flow. For maximum operating efficiency, automatic control systems are usually justifiable in keeping operating cost to a minimum without excessive operator attention. In general, steam savings of about 10 percent of rated booster flow are realized for each 2.5°C reduction in condensing-water temperature below the design point. In some cases, with relatively cold inlet condenser water it has been possible to adjust automatically the steam inlet pressure in response to chilledwater outlet temperatures. In general, however, this type of control is not possible because of the differences in temperature between the flash tank and the condenser. Under usual conditions of warm condenser-water temperatures, the main ejectors must compress water vapor over a relatively high ratio, requiring an ejector with entirely different operating characteristics. In most cases, when the ejector steam pressure is throttled, the capacity of the jet remains almost constant until the steam pressure is reduced to a point at which there is a sharp capacity decrease. At this point, the ejectors are unstable, and the capacity is severely curtailed. With a sufficient increase in steam pressure, the ejectors will once again become stable and operate at their design capacity. In effect, steam jets have a vapor-handling capacity fixed by the pressure at the suction inlet. In order for the ejector to operate along its characteristic pumping curve, it requires a certain minimum steam flow rate which is fixed for any particular pressure in the condenser. (For further information on the design of ejectors, see Sec. 6.) Further Reading and Reference: ASHRAE 1983 Equipment Handbook; Spencer, E., “New Development in Steam Vacuum Refrigeration,” ASHRAE Trans. 67: 339 (1961). Refrigerants A refrigerant is a body or substance that acts as a cooling agent by absorbing heat from another body or substance which has to be cooled. Primary refrigerants are those that are used in the refrigeration systems, where they alternately vaporize and condense as they absorb and give off heat, respectively. Secondary refrigerants are heat-transfer fluids or heat carriers. Refrigerant pairs in absorption systems are ammonia–water and lithium bromide–water, while steam (water) is used as a refrigerant in ejector systems. Refrigerants used in the mechanical refrigeration systems are far more numerous. A list of the most significant refrigerants is presented in the ASHRAE Handbook Fundamentals. More data are shown in Sec. 2, “Physical and Chemical Data.” Because of the rapid changes in the refrigerant issue, readers are advised to consult the most recent data and publications at the time of application. The first refrigerants were natural: air, ammonia, CO2, SO2, and so on. Fast expansion of refrigeration in the second and third quarters of the 20th

REFRIGERATION

11-87

FIG. 11-108 Halocarbon refrigerants .

century is marked by the new refrigerants, chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) . They are halocarbons that contain one or more of the three halogens chlorine, fluorine, and bromine (Fig . 11-108) . These refrigerants introduced many advantageous qualities compared to most of the existing refrigerants: they are odorless, nonflammable, nonexplosive, compatible with the most engineering materials, nontoxic, and have a reasonably high COP . In the last decade, the refrigerant issue is extensively discussed because of the accepted hypothesis that the chlorine and bromine atoms from halocarbons released to the environment were using up ozone in the stratosphere, depleting it especially above the polar regions . The Montreal Protocol and later agreements ban use of certain CFCs and halon compounds . Presently, all CFCs are out of production and the production, import, and use of HCFCs have been banned in the United States since 2015, except for HCFC-22 and HCFC-142b . A complete ban on all HCFCs in the United States is scheduled for 2030 . Chemical companies are trying to develop safe and efficient refrigerant for the refrigeration industry and application, but uncertainty in CFC and HCFC substitutes is still high . When this text was written, HFCs were a promising solution . That is true especially for R134a which seems to be the best alternative for R12 . Substitutes for R22 and R502 are still under debate . Numerous ecologists and chemists are for an extended ban on HFCs as well, mostly due to significant use of CFCs in the production of HFCs . Extensive research is ongoing to find new refrigerants . Many projects are aimed to design and study refrigerant mixtures, both azeotropic (mixture which behaves physically as a single, pure compound) and zeotropic having desirable qualities for the processes with temperature glides in the evaporator and the condenser . Ammonia (R717) is the single natural refrigerant being used extensively (beside halocarbons) . It is significant in industrial applications for its excellent thermodynamic and thermophysical characteristics . Many engineers are considering ammonia as a CFC substitute for various applications . Significant work is being done on reducing the refrigerant inventory and consequently problems related to leaks of this fluid with strong odor . There is growing interest in hydrocarbons in some countries, particularly in Europe . Indirect cooling (secondary refrigeration) is under reconsideration for many applications . Because of the vibrant refrigerant issue it will be a challenge for every engineer to find the best solution for the particular application, but basic principles are the same . Good refrigerant should have these characteristics: • Safe: nontoxic, nonflammable, and nonexplosive • Environmentally friendly • Compatible with materials normally used in refrigeration: oils, metals, elastomers, etc . • Desirable thermodynamic and thermophysical characteristics: • High latent heat • Low specific volume of vapor • Low compression ratio • Low viscosity • Reasonably low pressures for operating temperatures • Low specific heat of liquid • High specific heat of vapor • High conductivity and other heat-transfer related characteristics • Reasonably low compressor discharge temperatures • Easily detected if leaking • High dielectric constant • Good stability Secondary Refrigerants (Antifreezes or Brines) These are mostly liquids used for transporting heat energy from the remote heat source (process heat exchanger) to the evaporator of the refrigeration system . Antifreezes or brines do not change state in the process, but there are examples where some secondary refrigerants are either changing state themselves, or just particles which are carried in them .

Indirect refrigeration systems are more prevalent in the chemical industry than in the food industry, commercial refrigeration, or comfort air conditioning . This is even more evident in the cases where a large amount of heat is to be removed or where a low temperature level is involved . The advantage of an indirect system is centralization of refrigeration equipment, which is especially important for relocation of refrigeration equipment in a nonhazardous area, for both people and equipment . Salt Brines The typical curve of freezing point is shown in Fig . 11-109 . Brine of concentration x (water concentration is 1 − x) will not solidify at 0°C ( freezing temperature for water, point A) . When the temperature drops to B, the first crystal of ice is formed . As the temperature decreases to point C, ice crystals continue to form and their mixture with the brine solution forms the slush . At point C there will be part ice in the mixture l2/(l1 + l2) and liquid (brine) l1/(l1 + l2) . At point D there is mixture of m1 parts eutectic brine solution D1 [concentration m1/(m1 + m2)], and m2 parts of ice [concentration m2/(m1 + m2)] . Cooling the mixture below D solidifies the entire solution at the eutectic temperature . The eutectic temperature is the lowest temperature that can be reached with no solidification . It is obvious that further strengthening of brine has no effect, and can cause a different reaction—salt sometimes freezes out in the installations where the concentration is too high . Sodium chloride, an ordinary salt (NaCl), is the least expensive per volume of any brine available . It can be used in contact with food and in open systems because of its low toxicity . Heat-transfer coefficients are relatively high . However, its drawbacks are that it has a relatively high freezing point and is highly corrosive (requires inhibitors, thus must be checked on a regular schedule) . Calcium chloride (CaCl2) is similar to NaCl . It is the second-lowest-cost brine, with a somewhat lower freezing point (used for temperatures as low as −37°C) . It is highly corrosive and not appropriate for direct contact with food . Heat-transfer coefficients are rapidly reduced at temperatures below −20°C . The presence of magnesium salts in either sodium or calcium chloride is undesirable because they tend to form sludge . Air and carbon dioxide are contaminants, and excessive aeration of the brine should be prevented through the use of closed systems . Oxygen, required for corrosion, normally comes from the atmosphere and dissolves in the brine solution . Dilute brines dissolve oxygen more readily and are generally more corrosive than concentrated brines . It is believed that even a closed brine system will not prevent the infiltration of oxygen . To adjust an alkaline condition to pH 7 .0 to 8 .5, use caustic soda (to correct up to pH 7 .0) or sodium dichromate (to reduce excessive alkalinity below pH 8 .5) . Such slightly alkaline brines are generally less corrosive than neutral or acid ones, although with high alkalinity the activity may increase . If the untreated brine has the proper pH value, the acidifying effect of the dichromate may be neutralized by adding commercial flake caustic soda (76 percent pure) in quantity that corresponds to 27 percent of sodium dichromate used . Caustic soda must be thoroughly dissolved in warm water before it is added to the brine . Recommended inhibitor (sodium dichromate) concentrations are 2 kg/m3 of CaCl2 and 3 .2 kg/m3 of NaCl brine . Sodium dichromate when dissolved in water or brine makes the solution acid . Steel, iron, copper, or red brass can be used with brine circulating systems . Calcium chloride systems are generally equipped with all-iron-and-steel pumps and valves to prevent electrolysis in the event of acidity . Copper and red brass tubing is used for calcium chloride evaporators . Sodium chloride systems are using all-iron or all-bronze pumps . Organic Compounds (Inhibited Glycols) Ethylene glycol is colorless, practically odorless, and completely miscible with water . Advantages are low volatility and relatively low corrosivity when properly inhibited . Main drawbacks are relatively low heat-transfer coefficients at lower temperatures due to high viscosities (even higher than for propylene glycol) . It is somewhat toxic, but less harmful than methanol–water solutions . It is not appropriate for the food industry and should not stand in open containers .

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FIG. 11-109 Phase diagram of the brine .

Preferably waters that are classified as soft and are low in chloride and sulfate ions should be used for preparation of ethylene glycol solution . Pure ethylene glycol freezes at −12 .7°C . Exact composition and temperature for the eutectic point are unknown, since solutions in this region turn to viscous, glassy mass that makes it difficult to determine the true freezing point . For the concentrations lower than eutectic, ice forms on freezing, while on the concentrated, solid glycol separates from the solution . Ethylene glycol normally has pH of 8 .8 to 9 .2 and should not be used below pH 7 .5 . Addition of more inhibitor cannot restore the solution to its original condition . Once inhibitor has been depleted, it is recommended that the old glycol be removed from the system and the new charge be installed . Propylene glycol is very similar to ethylene glycol, but it is not toxic and is used in direct contact with food . It is more expensive and, having higher viscosity, shows lower heat-transfer coefficients . Methanol–water is an alcohol-base compound . It is less expensive than other organic compounds and, due to lower viscosity, has better heattransfer and pressure drop characteristics . It is used up to −35°C . Disadvantages are that (1) it is considered more toxic than ethylene glycol and thus more suitable for outdoor applications and (2) it is flammable and could be assumed to be a potential fire hazard . For ethylene glycol systems, copper tubing is often used (up to 3 in), while pumps, cooler tubes, or coils are made of iron, steel, brass, copper, or aluminum . Galvanized tubes should not be used in ethylene glycol systems because of reaction of the inhibitor with the zinc . Methanolewater solutions are compatible with most materials but in sufficient concentration will badly corrode aluminum . Ethanol–water is a solution of denatured grain alcohol . Its main advantage is that it is nontoxic and thus is widely used in the food and chemical industry . By using corrosion inhibiters it could be made noncorrosive for brine service . It is more expensive than methanol–water and has somewhat lower heat-transfer coefficients . As an alcohol derivate it is flammable . Secondary refrigerants shown below, listed under their generic names, are sold under different trade names . Some other secondary refrigerants appropriate for various refrigeration applications will be listed under their trade names . More data could be obtained from the manufacturer . Syltherm XLT (Dow Corning Corporation). A silicone polymer (Dimethyl Polysiloxane); recommended temperature range −70°C to 250°C; odorless; low in acute oral toxicity; noncorrosive toward metals and alloys commonly found in heat transfer systems . Syltherm 800 (Dow Corning Corporation). A silicone polymer (Dimethyl Polysiloxane); recommended temperature range −40°C to 400°C; similar to Syltherm XLT, more appropriate for somewhat higher temperatures; flash point is 160°C .

D-limonene (Florida Chemicals). A compound of optically active terpene (C10H16) derived as an extract from orange and lemon oils; limited data show very low viscosity at low temperatures—only 1 cP at −50°C; natural substance having questionable stability . Therminol D-12 (Monsanto). A synthetic hydrocarbon; clear liquid; recommended range −40°C to 250°C; not appropriate for contact with food; precautions against ignitions and fires should be taken with this product; could be found under trade names Santotherm or Gilotherm . Therminol LT (Monsanto). Akylbenzene, synthetic aromatic (C10H14); recommended range −70°C to −180°C; not appropriate for contact with food; precautions against ignitions and fire should be taken when dealing with this product . Dowtherm J (Dow Corning Corporation). A mixture of isomers of an alkylated aromatic; recommended temperature range −70°C to 300°C; noncorrosive toward steel, common metals and alloys; combustible material; flash point 58°C; low toxic; prolonged and repeated exposure to vapors should be limited to 10 ppm for daily exposures of 8 h . Dowtherm Q (Dow Corning Corporation). A mixture of dyphenylehane and alkylated aromatics; recommended temperature range −30°C to 330°C; combustible material; flash point 120°C; considered low toxic, similar to Dowtherm J . Safety in Refrigeration Systems This is of paramount importance and should be considered at every stage of installation . The design engineer should have safety as the primary concern by choosing a suitable system and refrigerant: selecting components, choosing materials and thicknesses of vessels, pipes, and relief valves of pressure vessels, proper venting of machine rooms, and arranging the equipment for convenient access for service and maintenance (piping arrangements, valve location, machine room layout, etc .) . She or he should conform to the stipulation of the safety codes, which is also important for the purposes of professional liability . During construction and installation, the installer’s good decisions and judgments are crucial for safety, because design documentation never specifies all details . This is especially important when there is reconstruction or repair while the facility has been charged . During operation the plant is in the hands of the operating personnel . They should be properly trained and familiar with the installation . Very often, accidents are caused by an improper practice, such as making an attempt to repair when proper preparation has not been made . Operators should be trained in first-aid procedures and how to respond to emergencies . Most frequently needed standards and codes are listed below, and the reader can find comments in W . F . Stoecker, Industrial Refrigeration, vol . 2, chap . 12, Business News Publishing Co ., Troy, Mich ., 1995; ASHRAE Handbook,

EVAPORATORS Refrigeration System and Applications, 1994, chap . 51 . These are some important standards and codes on safety that a refrigeration engineer should consult: ANSI/ASHRAE Standard 15-92, Safety Code for Mechanical Refrigeration, ASHRAE, Atlanta Ga ., 1992; ANSI/ASHRAE Standard 34-92, Number Designation of Refrigerants, ASHRAE, Atlanta, Ga ., 1992; ANSI/ASME Boiler and Pressure Vessel Code, ASME, New York, 1989; ANSI/ASME Code for Pressure Piping, B31, B31 .5–1987, ASME, New York, 1987; ANSI/IIAR 2—1984,

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Equipment, Design and Installation of Ammonia Mechanical Refrigeration Systems, IIAR, Chicago, 1984; IIAR Minimum Safety Criteria for a Safe Ammonia Refrigeration Systems, Bulletin 109; IIAR, IIAR Start-up, Inspection, and Maintenance of Ammonia Mechanical Refrigeration Systems, Bulletin 110, Chicago, 1988; IIAR Recommended Procedures in Event of Ammonia Spills, Bulletin 106, IIAR, Chicago, 1977; A Guide to Good Practices for the Operation of an Ammonia Refrigeration System, IIAR Bulletin R1, 1983 .

EVAPORATORS General References: Badger and Banchero, Introduction to Chemical Engineering, McGraw-Hill, New York, 1955 . Standiford, Chem. Eng. 70: 158–176 (Dec . 9, 1963) . Testing Procedure for Evaporators, American Institute of Chemical Engineers, 1979 . Upgrading Evaporators to Reduce Energy Consumption, ERDA Technical Information Center, Oak Ridge, Tenn ., 1977 . PRIMARY DESIGN PROBLEMS Heat Transfer This is the most important single factor in evaporator design, since the heating surface represents the largest part of evaporator cost . Other things being equal, the type of evaporator selected is the one having the highest heat-transfer cost coefficient under desired operating conditions in terms of joules per second per kelvin (British thermal units per hour per degree Fahrenheit) per dollar of installed cost . When power is required to induce circulation past the heating surface, the coefficient must be even higher to offset the cost of power for circulation . Vapor-Liquid Separation This design problem may be important for a number of reasons . The most important is usually prevention of entrainment because of value of product lost, pollution, contamination of the condensed vapor, or fouling or corrosion of the surfaces on which the vapor is condensed . Vapor-liquid separation in the vapor head may also be important when spray forms deposits on the walls, when vortices increase the head requirements of circulating pumps, and when short-circuiting allows vapor or unflashed liquid to be carried back to the circulating pump and heating element . Evaporator performance is rated on the basis of steam economy—kilograms of solvent evaporated per kilogram of steam used . Heat is required (1) to raise the feed from its initial temperature to the boiling temperature, (2) to provide the minimum thermodynamic energy to separate liquid solvent from the feed, and (3) to vaporize the solvent . The first can be changed appreciably by reducing the boiling temperature or by heat interchange between the feed and the residual product and/or condensate . The greatest increase in steam economy is achieved by reusing the vaporized solvent . This is done in a multiple-effect evaporator by using the vapor from one effect as the heating medium for another effect in which boiling takes place at a lower temperature and pressure . Another method of increasing the utilization of energy is to employ a thermocompression evaporator, in which the vapor is compressed so that it will condense at a temperature high enough to permit its use as the heating medium in the same evaporator . Selection Problems Aside from heat-transfer considerations, the selection of type of evaporator best suited for a particular service is governed by the characteristics of the feed and product . Points that must be considered include crystallization, salting and scaling, product quality, corrosion, and foaming . In the case of a crystallizing evaporator, the desirability of producing crystals of a definite uniform size usually limits the choice to evaporators having a positive means of circulation. Salting, which is the growth on body and heating-surface walls of a material having a solubility that increases with an increase in temperature, is frequently encountered in crystallizing evaporators . It can be reduced or eliminated by keeping the evaporating liquid in close or frequent contact with a large surface area of crystallized solid . Scaling is the deposition and growth on body walls, and especially on heating surfaces, of a material undergoing an irreversible chemical reaction in the evaporator or having a solubility that decreases with an increase in temperature . Scaling can be reduced or eliminated in the same general manner as salting . Both salting and scaling liquids are usually best handled in evaporators that do not depend on boiling to induce circulation . Fouling is the formation of deposits other than salt or scale and may be due to corrosion, solid matter entering with the feed, or deposits formed by the condensing vapor . Product Quality Considerations of product quality may require low holdup time and low-temperature operation to avoid thermal degradation . The low holdup time eliminates some types of evaporators, and other types are also eliminated because of poor heat-transfer characteristics at low temperature . Product quality may dictate special materials of construction to avoid metallic contamination or a catalytic effect on decomposition of

the product . Corrosion may also influence evaporator selection, since the advantages of evaporators having high heat-transfer coefficients are more apparent when expensive materials of construction are indicated . Corrosion and erosion are frequently more severe in evaporators than in other types of equipment because of the high liquid and vapor velocities used, the frequent presence of solids in suspension, and the necessary concentration differences . EVAPORATOR TYPES AND APPLICATIONS Evaporators may be classified as follows: 1 . Heating medium is separated from evaporating liquid by tubular heating surfaces . 2 . Heating medium is confined by coils, jackets, double walls, flat plates, etc . 3 . Heating medium is brought into direct contact with the evaporating liquid . 4 . Heating is done by solar radiation . By far the largest number of industrial evaporators employ tubular heating surfaces . Circulation of liquid past the heating surface may be induced by boiling or by mechanical means . In the latter case, boiling may or may not occur at the heating surface . Forced-Circulation Evaporators (Fig. 11-110a, b, c) Although it may not be the most economical for many uses, the forced-circulation (FC) evaporator is suitable for the widest variety of evaporator applications . The use of a pump to ensure circulation past the heating surface makes it possible to separate the functions of heat transfer, vapor-liquid separation, and crystallization . The pump withdraws liquor from the flash chamber and forces it through the heating element back to the flash chamber . Circulation is maintained regardless of the evaporation rate; so this type of evaporator is well suited to crystallizing operation, in which solids must be maintained in suspension at all times . The liquid velocity past the heating surface is limited only by the pumping power needed or available and by accelerated corrosion and erosion at the higher velocities . Tube velocities normally range from a minimum of about 1 .2 m/s (4 ft/s) in salt evaporators with copper or brass tubes and liquid containing 5 percent or more solids up to about 3 m/s (10 ft/s) in caustic evaporators having nickel tubes and liquid containing only a small amount of solids . Even higher velocities can be used when corrosion is not accelerated by erosion . Highest heat-transfer coefficients are obtained in FC evaporators when the liquid is allowed to boil in the tubes, as in the type shown in Fig . 11-110a. The heating element projects into the vapor head, and the liquid level is maintained near and usually slightly below the top tube sheet . This type of FC evaporator is not well suited to salting solutions because boiling in the tubes increases the chances of salt deposit on the walls and the sudden flashing at the tube exits promotes excessive nucleation and production of fine crystals . Consequently, this type of evaporator is seldom used except when there are headroom limitations or when the liquid forms neither salt nor scale . Swirl Flow Evaporators One of the most significant problems in the thermal design of once-through, tube-side evaporators is the poor predictability of the loss of ∆T upon reaching the critical heat flux condition . This situation may occur through flashing due to a high wall temperature or due to process needs to evaporate most of, if not all, the liquid entering the evaporator . It is the result of sensible heating of the vapor phase which accumulates at the heat-transfer surface, dries out the tube wall, and blocks the transfer of heat to the remaining liquid . In some cases, even with correctly predicted heat-transfer coefficients, the unexpected ∆T loss can reduce the actual performance of the evaporator by as much as 200 percent below the predicted performance . The best approach is to maintain a high level of mixing of the phases through the heat exchanger near the heat-transfer surface . The use of swirl flow—whereby a rotational vortex is imparted to the boiling fluid to centrifuge the liquid droplets out to the tube wall—has proved to be the most reliable means to correct for and eliminate this loss of ∆T . The

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HEAT-TRANSFER EQUIPMENT

(a)

(c)

(b)

(d)

The tendency toward scale formation is also reduced, since supersaturation in the heating element is generated only by a controlled amount of heating and not by both heating and evaporation . The type of vapor head used with the FC evaporator is chosen to suit the product characteristics and may range from a simple centrifugal separator to the crystallizing chambers shown in Fig . 11-110b and c. Figure 11-110b shows a type frequently used for common salt . It is designed to circulate a slurry of crystals throughout the system . Figure 11-110c shows a submergedtube FC evaporator in which heating, flashing, and crystallization are completely separated . The crystallizing solids are maintained as a fluidized bed in the chamber below the vapor head, and little or no solids circulate through the heater and flash chamber . This type is well adapted to growing coarse crystals, but the crystals usually approach a spherical shape, and careful design is required to avoid production of tines in the flash chamber . In a submerged-tube FC evaporator, all heat is imparted as sensible heat, resulting in a temperature rise of the circulating liquor that reduces the overall temperature difference available for heat transfer . Temperature rise, tube proportions, tube velocity, and head requirements on the circulating pump all influence the selection of circulation rate . Head requirements are frequently difficult to estimate since they consist not only of the usual friction, entrance and contraction, and elevation losses when the return to the flash chamber is above the liquid level, but also of increased friction losses due to flashing in the return line and vortex losses in the flash chamber . Circulation is sometimes limited by vapor in the pump suction line . This may be drawn in as a result of inadequate vapor-liquid separation or may come from vortices near the pump suction connection to the body or may be formed in the line itself by short-circuiting from heater outlet to pump inlet of liquor that has not flashed completely to equilibrium at the pressure in the vapor head .

(e)

(f)

(g)

Advantages of forced-circulation evaporators: 1 . High heat-transfer coefficients 2 . Positive circulation 3 . Relative freedom from salting, scaling, and fouling Disadvantages of forced-circulation evaporators: 1 . High cost 2 . Power required for circulating pump 3 . Relatively high holdup or residence time Best applications of forced-circulation evaporators: 1 . Crystalline product 2 . Corrosive solutions 3 . Viscous solutions

(h)

(i)

(j)

FIG. 11-110 Evaporator types . (a) Forced circulation . (b) Submerged-tube forced circulation . (c) Oslo-type crystallizer . (d ) Short-tube vertical . (e) Propeller calandria . ( f ) Long-tube vertical . (g) Recirculating long-tube vertical . (h) Falling film . (i, j) Horizontaltube evaporators . C = condensate; F = feed; G = vent; P = product; S = steam; V = vapor; ENT’T = separated entrainment outlet .

use of this technique almost always corrects the design to operate as well as or better than predicted . Also, the use of swirl flow eliminates the need to choose between horizontal and vertical orientation for most two-phase velocities . Both orientations work about the same in swirl flow . Many commercially viable methods of inducing swirl flow inside tubes are available in the form of either swirl flow tube inserts (twisted tapes, helical cores, spiral wire inserts) or special tube configurations (twisted tube, internal spiral fins) . All are designed to impart a natural swirl component to the flow inside the tubes . Each has been proved to solve the problem of tubeside vaporization at high vapor qualities up to and including complete tubeside vaporization . By far the largest number of forced-circulation evaporators is of the submerged-tube type, as shown in Fig . 11-110b. The heating element is placed far enough below the liquid level or return line to the flash chamber to prevent boiling in the tubes . Preferably, the hydrostatic head should be sufficient to prevent boiling even in a tube that is plugged (and hence at steam temperature), since this prevents salting of the entire tube . Evaporators of this type sometimes have horizontal heating elements (usually two-pass), but the vertical single-pass heating element is used whenever sufficient headroom is available . The vertical element usually has a lower friction loss and is easier to clean or retube than a horizontal heater . The submergedtube forced-circulation evaporator is relatively immune to salting in the tubes, since no supersaturation is generated by evaporation in the tubes .

Frequent difficulties with forced-circulation evaporators: 1 . Plugging of tube inlets by salt deposits detached from walls of equipment 2 . Poor circulation due to higher than expected head losses 3 . Salting due to boiling in tubes 4 . Corrosion-erosion

Short-Tube Vertical Evaporators (Fig. 11-110d) This is one of the earliest types still in widespread commercial use . Its principal use at present is in the evaporation of cane-sugar juice . Circulation past the heating surface is induced by boiling in the tubes, which are usually 50 .8 to 76 .2 mm (2 to 3 in) in diameter by 1 .2 to 1 .8 m (4 to 6 ft) long . The body is a vertical cylinder, usually of cast iron, and the tubes are expanded into horizontal tube sheets that span the body diameter . The circulation rate through the tubes is many times the feed rate; so there must be a return passage from above the top tube sheet to below the bottom tube sheet . Most commonly used is a central well or downtake, as shown in Fig . 11-110d. So that friction losses through the downtake do not appreciably impede circulation up through the tubes, the area of the downtake should be of the same order of magnitude as the combined cross-sectional area of the tubes . This results in a downtake almost half of the diameter of the tube sheet . Circulation and heat transfer in this type of evaporator are strongly affected by the “liquid level .” Highest heat-transfer coefficients are achieved when the level, as indicated by an external gauge glass, is only about halfway up the tubes . Slight reductions in level below the optimum result in incomplete wetting of the tube walls with a consequent increased tendency to foul and a rapid reduction in capacity . When this type of evaporator is used with a liquid that can deposit salt or scale, it is customary to operate with the liquid level appreciably higher than the optimum and usually appreciably above the top tube sheet . Circulation in the standard short-tube vertical evaporator is dependent entirely on boiling, and when boiling stops, any solids present settle out of suspension . Consequently, this type is seldom used as a crystallizing

EVAPORATORS evaporator . By installing a propeller in the downtake, this objection can be overcome . Such an evaporator, usually called a propeller calandria, is illustrated in Fig . 11-110e. The propeller is usually placed as low as possible to reduce cavitation and is shrouded by an extension of the downtake well . The use of the propeller can sometimes double the capacity of a short-tube vertical evaporator . The evaporator shown in Fig . 11-110e includes an elutriation leg for salt manufacture similar to that used on the FC evaporator of Fig . 11-110b. The shape of the bottom will, of course, depend on the particular application and on whether the propeller is driven from above or below . To avoid salting when the evaporator is used for crystallizing solutions, the liquid level must be kept appreciably above the top tube sheet .

Advantages of short-tube vertical evaporators: 1 . High heat-transfer coefficients at high temperature differences 2 . Low headroom 3 . Easy mechanical descaling 4 . Relatively inexpensive Disadvantages of short-tube vertical evaporators: 1 . Poor heat transfer at low temperature differences and low temperature 2 . High floor space and weight 3 . Relatively high holdup 4 . Poor heat transfer with viscous liquids Best applications of short-tube vertical evaporators: 1 . Clear liquids 2 . Crystalline product if propeller is used 3 . Relatively noncorrosive liquids, since body is large and expensive if built of materials other than mild steel or cast iron 4 . Mild scaling solutions requiring mechanical cleaning, since tubes are short and large in diameter

Long-Tube Vertical Evaporators (Fig. 11-110f, h, i) More total evaporation is accomplished in this type than in all the others combined because it is normally the cheapest per unit of capacity. The long-tube vertical (LTV) evaporator consists of a simple one-pass vertical shell-and-tube heat exchanger discharging into a relatively small vapor head . Normally, no liquid level is maintained in the vapor head, and the residence time of liquor is only a few seconds . The tubes are usually about 50 .8 mm (2 in) in diameter but may be smaller than 25 .4 mm (1 in) . Tube length may vary from less than 6 to 10 .7 m (20 to 35 ft) in the rising-film version and to as great as 20 m (65 ft) in the falling-film version . The evaporator is usually operated singlepass, concentrating from the feed to discharge density in just the time that it takes the liquid and evolved vapor to pass through a tube . An extreme case is the caustic high concentrator, producing a substantially anhydrous product at 370°C (700°F) from an inlet feed of 50 percent NaOH at 149°C (300°F) in one pass up 22-mm- (8/8-in-) OD nickel tubes 6 m (20 ft) long . The largest use of LTV evaporators is for concentrating black liquor in the pulp and paper industry . Because of the long tubes and relatively high heat-transfer coefficients, it is possible to achieve higher single-unit capacities in this type of evaporator than in any other . The LTV evaporator shown in Fig . 11-110f is typical of those commonly used, especially for black liquor . Feed enters at the bottom of the tube and starts to boil partway up the tube, and the mixture of liquid and vapor leaving at the top at high velocity impinges against a deflector placed above the tube sheet . This deflector is effective both as a primary separator and as a foam breaker . In many cases, as when the ratio of feed to evaporation or the ratio of feed to heating surface is low, it is desirable to provide for recirculation of product through the evaporator . This can be done in the type shown in Fig . 11-110f by adding a pipe connection between the product line and the feed line . Higher recirculation rates can be achieved in the type shown in Fig . 11-110h, which is used widely for condensed milk . By extending the enlarged portion of the vapor head still lower to provide storage space for liquor, this type can be used as a batch evaporator . Liquid temperatures in the tubes of an LTV evaporator are far from uniform and are difficult to predict . At the lower end, the liquid is usually not boiling, and the liquor picks up heat as sensible heat . Since entering liquid velocities are usually very low, true heat-transfer coefficients are low in this nonboiling zone . At some point up the tube, the liquid starts to boil, and from that point on the liquid temperature decreases because of the reduction in static, friction, and acceleration heads until the vapor-liquid mixture reaches the top of the tubes at substantially the vapor-head temperature . Thus the true temperature difference in the boiling zone is always less than the total temperature difference as measured from steam and vapor-head temperatures .

FIG. 11-111

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Temperature variations in a long-tube vertical evaporator .

Although the true heat-transfer coefficients in the boiling zone are quite high, they are partially offset by the reduced temperature difference . The point in the tubes at which boiling starts and at which the maximum temperature is reached is sensitive to operating conditions, such as feed properties, feed temperature, feed rate, and heat flux . Figure 11-111 shows typical variations in liquid temperature in tubes of an LTV evaporator operating at a constant terminal temperature difference . Curve 1 shows the normal case in which the feed is not boiling at the tube inlet . Curve 2 gives an indication of the temperature difference lost when the feed enters at the boiling point . Curve 3 is for exactly the same conditions as curve 2 except that the feed contained 0 .01 percent Teepol to reduce surface tension [Coulson and Mehta, Trans. Inst. Chem. Eng. 31: 208 (1953)] . The surface-active agent yields a more intimate mixture of vapor and liquid, with the result that liquid is accelerated to a velocity more nearly approaching the vapor velocity, thereby increasing the pressure drop in the tube . Although the surface-active agent caused an increase of more than 100 percent in the true heat-transfer coefficient, this was more than offset by the reduced temperature difference so that the net result was a reduction in evaporator capacity . This sensitivity of the LTV evaporator to changes in operating conditions is less pronounced at high than at low temperature differences and temperature levels . The falling-film version of the LTV evaporator (Fig . 11-110i) eliminates these problems of hydrostatic head . Liquid is fed to the tops of the tubes and flows down the walls as a film . Vapor-liquid separation usually takes place at the bottom, although some evaporators of this type are arranged for vapor to rise through the tube countercurrently to the liquid . The pressure drop through the tubes is usually very small, and the boiling-liquid temperature is substantially the same as the vapor-head temperature . The fallingfilm evaporator is widely used for concentrating heat-sensitive materials, such as fruit juices, because the holdup time is very small, the liquid is not overheated during passage through the evaporator, and heat-transfer coefficients are high even at low boiling temperatures . The principal problem with the falling-film LTV evaporator is feed distribution to the tubes . It is essential that all tube surfaces be wetted continually . This usually requires recirculation of the liquid unless the ratio of feed to evaporation is quite high . An alternative to the simple recirculation system of Fig . 11-110i is sometimes used when the feed undergoes an appreciable concentration change and the product is viscous and/or has a high boiling point rise . The feed chamber and vapor head are divided into a number of liquor compartments, and separate pumps are used to pass the liquor through the various banks of tubes in series, all in parallel as to steam and vapor pressures . The actual distribution of feed to the individual tubes of a falling-film evaporator may be accomplished by orifices at the inlet to each tube, by a perforated plate above the tube sheet, or by one or more spray nozzles . Both rising- and falling-film LTV evaporators are generally unsuited to salting or severely scaling liquids . However, both are widely used for black liquor, which presents a mild scaling problem, and also are used to carry solutions beyond saturation with respect to a crystallizing salt . In the latter case, deposits can usually be removed quickly by increasing the feed rate or reducing the steam rate in order to make the product unsaturated for a short time . The falling-film evaporator is not generally suited to liquids containing solids because of difficulty in plugging the feed distributors . However, it has been applied to the evaporation of saline waters saturated with CaSO4 and containing 5 to 10 percent CaSO4 seeds in suspension for scale prevention (Anderson, ASME Pap . 76-WA/Pwr-5, 1976) . Because of their simplicity of construction, compactness, and generally high heat-transfer coefficients, LTV evaporators are well suited to service with corrosive liquids . An example is the reconcentration of rayon spin-bath liquor, which is highly acid . These evaporators employ impervious graphite tubes, lead, rubber-covered or impervious graphite tube sheets, and rubberlined vapor heads . Polished stainless-steel LTV evaporators are widely used for food products . The latter evaporators are usually similar to that shown in Fig . 11-110h, in which the heating element is at one side of the vapor head to permit easy access to the tubes for cleaning .

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HEAT-TRANSFER EQUIPMENT

Advantages of long-tube vertical evaporators: 1 . Low cost 2 . Large heating surface in one body 3 . Low holdup 4 . Small floor space 5 . Good heat-transfer coefficients at reasonable temperature differences (rising film) 6 . Good heat-transfer coefficients at all temperature differences ( falling film) Disadvantages of long-tube vertical evaporators: 1 . High headroom 2 . Generally unsuitable for salting and severely scaling liquids 3 . Poor heat-transfer coefficients of rising-film version at low temperature differences 4 . Recirculation usually required for falling-film version Best applications of long-tube vertical evaporators: 1 . Clear liquids 2 . Foaming liquids 3 . Corrosive solutions 4 . Large evaporation loads 5 . High temperature differences—rising film, low temperature differences—falling film 6 . Low-temperature operation—falling film 7 . Vapor compression operation—falling film Frequent difficulties with long-tube vertical evaporators: 1 . Sensitivity of rising-film units to changes in operating conditions 2 . Poor feed distribution to falling-film units

Horizontal-Tube Evaporators (Fig. 11-110j) In these types the steam is inside and the liquor outside the tubes . The submerged-tube version of Fig . 11-110j is seldom used except for the preparation of boiler feedwater . Low entrainment loss is the primary aim: the horizontal cylindrical shell yields a large disengagement area per unit of vessel volume . Special versions use deformed tubes between restrained tube sheets that crack off much of a scale deposit when sprayed with cold water . By showering liquor over the tubes in the version of Fig . 11-110f, hydrostatic head losses are eliminated and heat-transfer performance is improved to that of the falling-film tubular type of Fig . 11-110i. Originally called the Lillie, this evaporator is now also called the spray-film or simply the horizontal-tube evaporator. Liquid distribution over the tubes is accomplished by sprays or perforated plates above the topmost tubes . Maintaining this distribution through the bundle to avoid overconcentrating the liquor is a problem unique to this type of evaporator . It is now used primarily for seawater evaporation .

Advantages of horizontal-tube evaporators: 1 . Very low headroom 2 . Large vapor-liquid disengaging area—submerged-tube type 3 . Relatively low cost in small-capacity straight-tube type 4 . Good heat-transfer coefficients 5 . Easy semiautomatic descaling—bent-tube type Disadvantages of horizontal-tube evaporators: 1 . Unsuitable for salting liquids 2 . Unsuitable for scaling liquids—straight-tube type 3 . High cost—bent-tube type 4 . Maintaining liquid distribution—film type Best applications of horizontal-tube evaporators: 1 . Limited headroom 2 . Small capacity 3 . Nonscaling nonsalting liquids—straight-tube type 4 . Severely scaling liquids—bent-tube type

Miscellaneous Forms of Heating Surface Special evaporator designs are sometimes indicated when heat loads are small, special product characteristics are desired, or the product is especially difficult to handle . Jacketed kettles, frequently with agitators, are used when the product is very viscous, batches are small, intimate mixing is required, and/or ease of cleaning is an important factor . Evaporators with steam in coiled tubes may be used for small capacities with scaling liquids in designs that permit “cold shocking,” or complete withdrawal of the coil from the shell for manual scale removal . Other designs for scaling liquids employ flat-plate heat exchangers, since in general a scale deposit can be removed more easily from a flat plate than from a curved surface . One such design, the channel-switching

evaporator, alternates the duty of either side of the heating surface periodically from boiling liquid to condensing vapor so that scale formed when the surface is in contact with boiling liquid is dissolved when the surface is next in contact with condensing vapor . Agitated thin-film evaporators employ a heating surface consisting of one large-diameter tube that may be either straight or tapered, horizontal or vertical . Liquid is spread on the tube wall by a rotating assembly of blades that either maintain a close clearance from the wall or actually ride on the film of liquid on the wall . The expensive construction limits application to the most difficult materials . High agitation [on the order of 12 m/s (40 ft/s) rotor-tip speed] and power intensities of 2 to 20 kW/m2 (0 .25 to 2 .5 hp/ft2) permit handling extremely viscous materials . Residence times of only a few seconds permit concentration of heat-sensitive materials at temperatures and temperature differences higher than in other types [Mutzenberg, Parker, and Fischer, Chem. Eng. 72: 175–190 (Sept . 13, 1965)] . High feed-toproduct ratios can be handled without recirculation . Economic and process considerations usually dictate that agitated thinfilm evaporators be operated in single-effect mode . Very high temperature differences can then be used: many are heated with Dowtherm or other high-temperature media . This enables one to achieve reasonable capacities in spite of the relatively low heat-transfer coefficients and the small surface that can be provided in a single tube [to about 20 m2 (200 ft2)] . The structural need for wall thicknesses of 6 to 13 mm (¼ to ½ in) is a major reason for the relatively low heat-transfer coefficients when evaporating waterlike materials . Evaporators without Heating Surfaces The submerged-combustion evaporator makes use of combustion gases bubbling through the liquid as the means of heat transfer . It consists simply of a tank to hold the liquid, a burner and gas distributor that can be lowered into the liquid, and a combustion control system . Since there are no heating surfaces on which scale can deposit, this evaporator is well suited to use with severely scaling liquids . The ease of constructing the tank and burner of special alloys or nonmetallic materials makes practical the handling of highly corrosive solutions . However, since the vapor is mixed with large quantities of noncondensible gases, it is impossible to reuse the heat in this vapor, and installations are usually limited to areas of low fuel cost . One difficulty frequently encountered in the use of submerged-combustion evaporators is a high entrainment loss . Also, these evaporators cannot be used when control of crystal size is important . Disk or cascade evaporators are used in the pulp and paper industry to recover heat and entrained chemicals from boiler stack gases and to effect a final concentration of the black liquor before it is burned in the boiler . These evaporators consist of a horizontal shaft on which are mounted disks perpendicular to the shaft or bars parallel to the shaft . The assembly is partially immersed in the thick black liquor so that films of liquor are carried into the hot-gas stream as the shaft rotates . Some forms of flash evaporators require no heating surface . An example is a recrystallizing process for separating salts having normal solubility curves from salts having inverse solubility curves, as in separating sodium chloride from calcium sulfate [Richards, Chem. Eng. 59(3): 140 (1952)] . A suspension of raw solid feed in a recirculating brine stream is heated by direct steam injection . The increased temperature and dilution by the steam dissolve the salt having the normal solubility curve . The other salt remains undissolved and is separated from the hot solution before it is flashed to a lower temperature . The cooling and loss of water on flashing cause recrystallization of the salt having the normal solubility curve, which is separated from the brine before the brine is mixed with more solid feed for recycling to the heater . This system can be operated as a multiple effect by flashing down to the lower temperature in stages and using flash vapor from all but the last stage to heat the recycle brine by direct injection . In this process no net evaporation occurs from the total system, and the process cannot be used to concentrate solutions unless heating surfaces are added . UTILIZATION OF TEMPERATURE DIFFERENCE Temperature difference is the driving force for evaporator operation and usually is limited, as by compression ratio in vapor compression evaporators and by available steam pressure and heat-sink temperature in singleand multiple-effect evaporators . A fundamental objective of evaporator design is to make as much of this total temperature difference available for heat transfer as is economically justifiable . Some losses in temperature difference, such as those due to boiling point rise (BPR), are unavoidable . However, even these can be minimized, such as by passing the liquor through effects or through different sections of a single effect in series so that only a portion of the heating surface is in contact with the strongest liquor . Figure 11-112 shows approximate BPR losses for a number of process liquids . A correlation for concentrated solutions of many inorganic salts

EVAPORATORS

11-93

FIG. 11-112 Boiling-point rise of aqueous solutions . °C = 5/9 (°F − 32) .

at the atmospheric pressure boiling point [Meranda and Furter, J. Ch. and E. Data 22: 315–7 (1977)] is BPR = 104 .9N21 .14

(11-108)

where N2 is the mole fraction of salts in solution . Correction to other pressures, when heats of solution are small, can be based on a constant ratio of vapor pressure of the solution to that of water at the same temperature . The principal reducible loss in ∆T is that due to friction and to entrance and exit losses in vapor piping and entrainment separators . Pressure-drop losses here correspond to a reduction in condensing temperature of the vapor and hence a loss in available ∆T. These losses become most critical at the low-temperature end of the evaporator, both because of both the increasing specific volume of the vapor and the reduced slope of the vaporpressure curve . Sizing of vapor lines is part of the economic optimization of the evaporator, extra costs of larger vapor lines being balanced against savings in ∆T, which correspond to savings in heating-surface requirements . Note that entrance and exit losses in vapor lines usually exceed by severalfold the straight-pipe friction losses, so they cannot be ignored . VAPOR-LIQUID SEPARATION Product losses in evaporator vapor may result from foaming, splashing, or entrainment . Primary separation of liquid from vapor is accomplished in the vapor head by making the horizontal plan area large enough that most of the entrained droplets can settle out against the rising flow of vapor . Allowable velocities are governed by the Souders-Brown equation V = k (ρ1 − ρυ )/ρυ, in which k depends on the size distribution of droplets and the decontamination factor F desired . For most evaporators and for F between 100 and 10,000, k ≅ 0 .245/(F − 50)0 .4 (Standiford, Chemical Engineers’ Handbook, 4th ed ., McGraw-Hill, New York, 1963, pp . 11–35) . Higher values of k (to about 0 .15) can be tolerated in the falling-film evaporator, where most of the entrainment separation occurs in the tubes, the vapor is scrubbed by liquor leaving the tubes, and the vapor must reverse direction to reach the outlet . Foaming losses usually result from the presence in the evaporating liquid of colloids or of surface-tension depressants and finely divided solids . Antifoam agents are often effective . Other means of combatting foam include

the use of steam jets impinging on the foam surface, the removal of product at the surface layer, where the foaming agents seem to concentrate, and operation at a very low liquid level so that hot surfaces can break the foam . Impingement at high velocity against a baffle tends to break the foam mechanically, and this is the reason that the long-tube vertical, forcedcirculation, and agitated-film evaporators are particularly effective with foaming liquids . Operating at lower temperatures and/or higher dissolved solids concentrations may also reduce foaming tendencies . Splashing losses are usually insignificant if a reasonable height has been provided between the liquid level and the top of the vapor head . The height required depends on the violence of boiling . Heights of 2 .4 to 3 .6 m (8 to 12 ft) or more are provided in short-tube vertical evaporators, in which the liquid and vapor leaving the tubes are projected upward . Less height is required in forced-circulation evaporators, in which the liquid is given a centrifugal motion or is projected downward as by a baffle . The same is true of long-tube vertical evaporators, in which the rising vapor-liquid mixture is projected against a baffle . Entrainment losses by flashing are frequently encountered in an evaporator . If the feed is above the boiling point and is introduced above or only a short distance below the liquid level, then entrainment losses may be excessive . This can occur in a short-tube-type evaporator if the feed is introduced at only one point below the lower tube sheet (Kerr, Louisiana Agric. Expt. Stn. Bull. 149, 1915) . The same difficulty may be encountered in forced-circulation evaporators having too high a temperature rise through the heating element and thus too wide a flashing range as the circulating liquid enters the body . Poor vacuum control, especially during start-up, can cause the generation of far more vapor than the evaporator was designed to handle, with a consequent increase in entrainment . Entrainment separators are frequently used to reduce product losses . There are a number of specialized designs available, practically all of which rely on a change in direction of the vapor flow when the vapor is traveling at high velocity . Typical separators are shown in Fig . 11-110, although not necessarily with the type of evaporator with which they may be used . The most common separator is the cyclone, which may have either a top or a bottom outlet, as shown in Fig . 11-110a and b, or may even be wrapped around the heating element of the next effect, as shown in Fig . 11-110f. The separation efficiency of a cyclone increases with an increase in inlet velocity, although at the cost of some pressure drop, which means a loss in available

11-94

HEAT-TRANSFER EQUIPMENT

temperature difference . Pressure drop in a cyclone is from 10 to 16 velocity heads [Lawrence, Chem. Eng. Prog. 48: 241 (1952)], based on the velocity in the inlet pipe . Such cyclones can be sized in the same manner as a cyclone dust collector [using velocities of about 30 m/s (100 ft/s) at atmospheric pressure] although sizes may be increased somewhat in order to reduce losses in available temperature difference . Knitted wire mesh serves as an effective entrainment separator when it cannot be easily fouled by solids in the liquor . The mesh is available in woven metal wire of most alloys and is installed as a blanket across the top of the evaporator (Fig . 11-110d) or in a monitor of reduced diameter atop the vapor head . These separators have low-pressure drops, usually on the order of 13 mm (½ in) of water, and collection efficiency is above 99 .8 percent in the range of vapor velocities from 2 .5 to 6 m/s (8 to 20 ft/s) [Carpenter and Othmer, Am. Inst. Chem. Eng. J. 1: 549 (1955)] . Chevron (hook-and-vane) type of separators is also used because of the higher-allowable velocities or because of the reduced tendency to foul with solids suspended in the entrained liquid . EVAPORATOR ARRANGEMENT Single-Effect Evaporators Single-effect evaporators are used when the required capacity is small, steam is cheap, the material is so corrosive that very expensive materials of construction are required, or the vapor is so contaminated that it cannot be reused . Single-effect evaporators may be operated in batch, semibatch, or continuous-batch modes or continuously . Strictly speaking, batch evaporators are ones in which filling, evaporating, and emptying are consecutive steps . This method of operation is rarely used since it requires that the body be large enough to hold the entire charge of feed and the heating element be placed low enough so as not to be uncovered when the volume is reduced to that of the product . The more usual method of operation is semibatch, in which feed is continually added to maintain a constant level until the entire charge reaches final density . Continuous-batch evaporators usually have a continuous feed and, over at least part of the cycle, a continuous discharge . One method of operation is to circulate from a storage tank to the evaporator and back until the entire tank is up to desired concentration and then to finish in batches . Continuous evaporators have essentially continuous feed and discharge, and concentrations of both feed and product remain substantially constant . Thermocompression The simplest means of reducing the energy requirements of evaporation is to compress the vapor from a single-effect evaporator so that the vapor can be used as the heating medium in the same evaporator . The compression may be accomplished by mechanical means or by a steam jet . To keep the compressor cost and power requirements within reason, the evaporator must work with a fairly narrow temperature difference, usually from about 5 .5°C to 11°C (10°F to 20°F) . This means that a large evaporator heating surface is needed, which usually makes the vapor compression evaporator more expensive in first cost than a multiple-effect evaporator . However, total installation costs may be reduced when purchased power is the energy source, since the need for boiler and heat sink is eliminated . Substantial savings in operating cost are realized when electric or mechanical power is available at a low cost relative to low-pressure steam, when only high-pressure steam is available to operate the evaporator, or when the cost of providing cooling water or other heat sink for a multiple-effect evaporator is high . Mechanical thermocompression may employ reciprocating, rotary positivedisplacement, centrifugal, or axial-flow compressors . Positive-displacement compressors are impractical for all but the smallest capacities, such as portable seawater evaporators . Axial-flow compressors can be built for capacities of more than 472 m3/s (1 × 106 ft3/min) . Centrifugal compressors are usually cheapest for the intermediate-capacity ranges that are normally encountered . In all cases, great care must be taken to keep entrainment at a minimum, since the vapor becomes superheated on compression and any liquid present will evaporate, leaving the dissolved solids behind . In some cases, a vapor-scrubbing tower may be installed to protect the compressor . A mechanical recompression evaporator usually requires more heat than is available from the compressed vapor . Some of this extra heat can be obtained by preheating the feed with the condensate and, if possible, with the product . Rather extensive heat-exchange systems with close approach temperatures are usually justified, especially if the evaporator is operated at high temperature to reduce the volume of vapor to be compressed . When the product is a solid, an elutriation leg such as that shown in Fig . 11-110b is advantageous, since it cools the product almost to the feed temperature . The remaining heat needed to maintain the evaporator in operation must be obtained from outside sources . While theoretical compressor power requirements are reduced slightly by going to lower evaporating temperatures, the volume of vapor to be compressed and hence compressor size and cost increase so rapidly that lowtemperature operation is more expensive than high-temperature operation .

The requirement of low temperature for fruit juice concentration has led to the development of an evaporator employing a secondary fluid, usually Freon or ammonia . In this evaporator, the vapor is condensed in an exchanger cooled by boiling Freon . The Freon, at a much higher vapor density than the water vapor, is then compressed to serve as the heating medium for the evaporator . This system requires that the latent heat be transferred through two surfaces instead of one, but the savings in compressor size and cost are enough to justify the extra cost of heating surface or the cost of compressing through a wider temperature range . Steam-jet thermocompression is advantageous when steam is available at a pressure appreciably higher than can be used in the evaporator . The steam jet then serves as a reducing valve while doing some useful work . The efficiency of a steam jet is quite low and falls off rapidly when the jet is not used at the vapor flow rate and terminal pressure conditions for which it was designed . Consequently, multiple jets are used when wide variations in evaporation rate are expected . Because of the low first cost and the ability to handle large volumes of vapor, steam-jet thermocompressors are used to increase the economy of evaporators that must operate at low temperatures and hence cannot be operated in multiple effect . The steam-jet thermocompression evaporator has a heat input larger than that needed to balance the system, and some heat must be rejected . This is usually done by venting some of the vapor at the suction of the compressor . Multiple-Effect Evaporation Multiple-effect evaporation is the principal means in use for economizing on energy consumption . Most such evaporators operate on a continuous basis, although for a few difficult materials a continuous-batch cycle may be employed . In a multiple-effect evaporator, steam from an outside source is condensed in the heating element of the first effect . If the feed to the effect is at a temperature near the boiling point in the first effect, 1 kg of steam will evaporate almost 1 kg of water . The first effect operates at (but is not controlled at) a boiling temperature high enough that the evaporated water can serve as the heating medium of the second effect . Here almost another kilogram of water is evaporated, and this may go to a condenser if the evaporator is a double-effect or may be used as the heating medium of the third effect . This method may be repeated for any number of effects . Large evaporators having 6 and 7 effects are common in the pulp and paper industry, and evaporators having as many as 17 effects have been built . As a first approximation, the steam economy of a multipleeffect evaporator will increase in proportion to the number of effects and usually will be somewhat less numerically than the number of effects . The increased steam economy of a multiple-effect evaporator is gained at the expense of evaporator first cost . The total heat-transfer surface will increase substantially in proportion to the number of effects in the evaporator . This is only an approximation since going from one to two effects means that about one-half of the heat transfer is at a higher temperature level, where heat-transfer coefficients are generally higher . On the other hand, operating at lower temperature differences reduces the heat-transfer coefficient for many types of evaporator . If the material has an appreciable boiling-point elevation, this will also lower the available temperature difference . The only accurate means of predicting the changes in steam economy and surface requirements with changes in the number of effects is by detailed heat and material balances together with an analysis of the effect of changes in operating conditions on heat-transfer performance . The approximate temperature distribution in a multiple-effect evaporator is under the control of the designer, but once built, the evaporator establishes its own equilibrium . Basically, the effects are a number of series resistances to heat transfer, each resistance being approximately proportional to 1/UnAn . The total available temperature drop is divided between the effects in proportion to their resistances . If one effect starts to scale, its temperature drop will increase at the expense of the temperature drops across the other effects . This provides a convenient means of detecting a drop in the heat-transfer coefficient in an effect of an operating evaporator . If the steam pressure and final vacuum do not change, the temperature in the effect that is scaling will decrease and the temperature in the preceding effect will increase . The feed to a multiple-effect evaporator is usually transferred from one effect to another in series so that the ultimate product concentration is reached in only one effect of the evaporator . In backward-feed operation, the raw feed enters the last (coldest) effect, the discharge from this effect becomes the feed to the next-to-the-last effect, and so on until product is discharged from the first effect . This method of operation is advantageous when the feed is cold, since much less liquid must be heated to the higher temperature existing in the early effects . It is also used when the product is so viscous that high temperatures are needed to keep the viscosity low enough to give reasonable heat-transfer coefficients . When product viscosity is high but a hot product is not needed, the liquid from the first effect is sometimes flashed to a lower temperature in one or more stages and the flash vapor added to the vapor from one or more later effects of the evaporator .

EVAPORATORS

effect of the evaporator . Product flash tanks may also be used in a backwardor mixed-feed evaporator . In a forward-feed evaporator, the principal means of heat recovery may be by use of feed preheaters heated by vapor bled from each effect of the evaporator . In this case, condensate may be either flashed as before or used in a separate set of exchangers to accomplish some of the feed preheating . A feed preheated by last-effect vapor may also materially reduce condenser water requirements . Seawater Evaporators The production of potable water from saline water represents a large and growing field of application for evaporators . Extensive work done in this field to 1972 was summarized in the annual Saline Water Conversion Reports of the Office of Saline Water, U .S . Department of the Interior . Steam economies on the order of 10 kg evaporation/kg steam are usually justified because (1) unit production capacities are high, (2) fixed charges are low on capital used for public works (i .e ., they use long amortization periods and have low interest rates, with no other return on investment considered), (3) heat-transfer performance is comparable with that of pure water, and (4) properly treated seawater causes little deterioration due to scaling or fouling . Figure 11-113a shows a multiple-effect ( falling-film) flow sheet as used for seawater . Twelve effects are needed for a steam economy of 10 . Seawater is used to condense last-effect vapor, and a portion is then treated to prevent scaling and corrosion . Treatment usually consists of acidification to break down bicarbonates, followed by deaeration, which also removes the carbon dioxide generated . The treated seawater is then heated to successively higher temperatures by a portion of the vapor from each effect and finally is fed to the evaporating surface of the first effect . The vapor generated therein and the partially concentrated liquid are passed to the second effect, and so on until the last effect . The feed rate is adjusted relative to the steam rate so that the residual liquid from the last effect can carry away all the salts in solution, in a volume about one-third of that of the feed . Condensate formed in each effect but the first is flashed down to the following effects in sequence and constitutes the product of the evaporator . As the feed-to-steam ratio is increased in the flow sheet of Fig . 11-113a, a point is reached where all the vapor is needed to preheat the feed and none is available for the evaporator tubes . This limiting case is the multistage flash evaporator, shown in its simplest form in Fig . 11-113b. Seawater is treated as before and then pumped through a number of feed heaters in series . It is

In forward-feed operation, raw feed is introduced in the first effect and passed from effect to effect parallel to the steam flow . Product is withdrawn from the last effect . This method of operation is advantageous when the feed is hot or when the concentrated product would be damaged or would deposit scale at high temperature . Forward feed simplifies operation when liquor can be transferred by pressure difference alone, thus eliminating all intermediate liquor pumps . When the feed is cold, forward feed gives a low steam economy since an appreciable part of the prime steam is needed to heat the feed to the boiling point and thus accomplishes no evaporation . If forward feed is necessary and feed is cold, steam economy can be improved markedly by preheating the feed in stages with vapor bled from intermediate effects of the evaporator . This usually represents little increase in total heating surface or cost since the feed must be heated in any event and shelland-tube heat exchangers are generally less expensive per unit of surface area than evaporator heating surface . Mixed-feed operation is used only for special applications, as when liquor at an intermediate concentration and a certain temperature is desired for additional processing . Parallel feed involves the introduction of raw feed and the withdrawal of product at each effect of the evaporator . It is used primarily when the feed is substantially saturated and the product is a solid . An example is the evaporation of brine to make common salt . Evaporators of the types shown in Fig . 11-110b or e are used, and the product is withdrawn as a slurry . In this case, parallel feed is desirable because the feed washes impurities from the salt leaving the body . Heat recovery systems are frequently incorporated in an evaporator to increase the steam economy . Ideally, product and evaporator condensate should leave the system at a temperature as low as possible . Also, heat should be recovered from these streams by exchange with feed or evaporating liquid at the highest possible temperature . This would normally require separate liquid-liquid heat exchangers, which add greatly to the complexity of the evaporator and are justifiable only in large plants . Normally, the loss in thermodynamic availability due to flashing is tolerated since the flash vapor can then be used directly in the evaporator effects . The most commonly used is a condensate flash system in which the condensate from each effect but the first (which normally must be returned to the boiler) is flashed in successive stages to the pressure in the heating element of each succeeding

(a)

(b)

(c) FIG. 11-113 Flow sheets for seawater evaporators . (a) Multiple effect ( falling film) . (b) Multistage flash (once-through) .

(c) Multistage flash (recirculating) .

11-95

11-96

HEAT-TRANSFER EQUIPMENT

given a final boost in temperature with prime steam in a brine heater before it is flashed down in series to provide the vapor needed by the feed heaters . The amount of steam required depends on the approach-temperature difference in the feed heaters and the flash range per stage . Condensate from the feed heaters is flashed down in the same manner as the brine . Since the flow being heated is identical to the total flow being flashed, the temperature rise in each heater is equal to the flash range in each flasher . This temperature difference represents a loss from the temperature difference available for heat transfer . There are thus two ways of increasing the steam economy of such plants: increasing the heating surface and increasing the number of stages . Whereas the number of effects in a multiple-effect plant will be about 20 percent greater than the steam economy, the number of stages in a flash plant will be 3 to 4 times the steam economy . However, a large number of stages can be provided in a single vessel by means of internal bulkheads . The heat-exchanger tubing is placed in the same vessel, and the tubes usually are continuous through a number of stages . This requires ferrules or special close tube-hole clearances where the tubes pass through the internal bulkheads . In a plant for a steam economy of 10, the ratio of flow rate to heating surface is usually such that the seawater must pass through about 152 m of 19-mm (500 ft of ¾-in) tubing before it reaches the brine heater . This places a limitation on the physical arrangement of the vessels . Inasmuch as it requires a flash range of about 61°C (110°F) to produce 1 kg of flash vapor for every 10 kg of seawater, the multistage flash evaporator requires handling a large volume of seawater relative to the product . In the flow sheet of Fig . 11-113b all this seawater must be deaerated and treated for scale prevention . In addition, the last-stage vacuum varies with the ambient seawater temperature, and ejector equipment must be sized for the worst condition . These difficulties can be eliminated by using the recirculating multistage flash flow sheet of Fig . 11-113c. The last few stages, called the reject stages, are cooled by a flow of seawater that can be varied to maintain a reasonable last-stage vacuum . A small portion of the last-stage brine is blown down to carry away the dissolved salts, and the balance is recirculated to the heat recovery stages. This arrangement requires a much smaller makeup of fresh seawater and hence a lower treatment cost . The multistage flash evaporator is similar to a multiple-effect forcedcirculation evaporator, but with all the forced-circulation heaters in series . This has the advantage of requiring only one large-volume forced-circulation pump, but the sensible heating and short-circuiting losses in available temperature differences remain . A disadvantage of the flash evaporator is that the liquid throughout the system is at almost the discharge concentration . This has limited its industrial use to solutions in which no great concentration differences are required between feed and product and where the liquid can be heated through wide temperature ranges without scaling . A partial remedy is to arrange several multistage flash evaporators in series, the heat rejection section of one being the brine heater of the next . This permits independent control of concentration but eliminates the principal advantage of the flash evaporator, which is the small number of pumps and vessels required . An unusual feature of the flash evaporator is that fouling of the heating surfaces reduces primarily the steam economy rather than the capacity of the evaporator . Capacity is not affected until the heat rejection stages can no longer handle the increased flashing resulting from the increased heat input . EVAPORATOR CALCULATIONS Single-Effect Evaporators The heat requirements of a single-effect continuous evaporator can be calculated by the usual methods of stoichiometry . If enthalpy data or specific heat and heat-of-solution data are not available, the heat requirement can be estimated as the sum of the heat needed to raise the feed from feed to product temperature and the heat required to evaporate the water . The latent heat of water is taken at the vapor-head pressure instead of at the product temperature in order to compensate partially for any heat of solution . If sufficient vapor pressure data are available for the solution, methods are available to calculate the true latent heat from the slope of the Dühring line [Othmer, Ind. Eng. Chem. 32: 841 (1940)] . The heat requirements in batch evaporation are the same as those in continuous evaporation except that the temperature (and sometimes pressure) of the vapor changes during the course of the cycle . Since the enthalpy of water vapor changes but little relative to temperature, the difference between continuous and batch heat requirements is almost always negligible . More important usually is the effect of variation of fluid properties, such as viscosity and boiling point rise, on heat transfer . These can only be estimated by a step-by-step calculation . In selecting the boiling temperature, consideration must be given to the effect of temperature on heat-transfer characteristics of the type of evaporator to be used . Some evaporators show a marked drop in coefficient at low temperature—more than enough to offset any gain in available temperature

difference . The condenser cooling-water temperature and cost must also be considered . Thermocompression Evaporators Thermocompression evaporator calculations [Pridgeon, Chem. Metall. Eng. 28: 1109 (1923); Peter, Chimia (Switzerland) 3: 114 (1949); Petzold, Chem. Ing. Tech. 22: 147 (1950); and Weimer, Dolf, and Austin, Chem. Eng. Prog. 76(11): 78 (1980)] are much the same as single-effect calculations with the added complication that the heat supplied to the evaporator from compressed vapor and other sources must exactly balance the heat requirements . Some knowledge of compressor efficiency is also required . Large axial-flow machines on the order of 236 m3/s (500,000 ft3/min) capacity may have efficiencies of 80 to 85 percent . Efficiency drops to about 75 percent for a 14 m3/s (30,000 ft3/min) centrifugal compressor . Steam-jet compressors have thermodynamic efficiencies on the order of only 25 to 30 percent . Flash Evaporators The calculation of a heat and material balance on a flash evaporator is relatively easy once it is understood that the temperature rise in each heater and the temperature drop in each flasher must all be substantially equal . The steam economy E, kg evaporation/kg of 1055-kJ steam (lb/lb of 1000-Btu steam) may be approximated from ∆T ∆T   E = 1−  1250  Y + R + ∆T /N

(11-109)

where ∆T is the total temperature drop between feed to the first flasher and discharge from the last flasher, °C; N is the number of flash stages; Y is the approach between vapor temperature from the first flasher and liquid leaving the heater in which this vapor is condensed, °C (the approach is usually substantially constant for all stages); and R°C is the sum of the boiling-point rise and the short-circuiting loss in the first flash stage . The expression for the mean effective temperature difference ∆t available for heat transfer then becomes ∆t =

∆T 1 − ∆T /1250 − RE /∆T N ln 1 − ∆T /1250 − RE /∆T − E /N

(11-110)

Multiple-Effect Evaporators A number of approximate methods have been published for estimating performance and heating-surface requirements of a multiple-effect evaporator [Coates and Pressburg, Chem. Eng. 67(6): 157 (1960); Coates, Chem. Eng. Prog. 45: 25 (1949); and Ray and Carnahan, Trans. Am. Inst. Chem. Eng. 41: 253 (1945)] . However, because of the wide variety of methods of feeding and the added complication of feed heaters and condensate flash systems, the only certain way to determine performance is by detailed heat and material balances . Algebraic solutions may be used, but if more than a few effects are involved, trial-and-error methods are usually quicker . These frequently involve trial-and-error within trial-and-error solutions . Usually, if condensate flash systems or feed heaters are involved, it is best to start at the first effect . The basic steps in the calculation are then as follows: 1 . Estimate temperature distribution in the evaporator, taking into account boiling-point elevations . If all heating surfaces are to be equal, the temperature drop across each effect will be approximately inversely proportional to the heat-transfer coefficient in that effect . 2 . Determine total evaporation required, and estimate steam consumption for the number of effects chosen . 3 . From assumed feed temperature ( forward feed) or feed flow (backward feed) to the first effect and assumed steam flow, calculate evaporation in the first effect . Repeat for each succeeding effect, checking intermediate assumptions as the calculation proceeds . Heat input from condensate flash can be incorporated easily since the condensate flow from the preceding effects will have already been determined . 4 . The result of the calculation will be a feed to or a product discharge from the last effect that may not agree with actual requirements . The calculation must then be repeated with a new assumption of steam flow to the first effect . 5 . These calculations should yield liquor concentrations in each effect that enable a revised estimate of boiling-point rises . They also give the quantity of heat that must be transferred in each effect . From the heat loads, assumed temperature differences, and heat-transfer coefficients, the heating-surface requirements can be determined . If the distribution of heating surface is not as desired, the entire calculation may need to be repeated with revised estimates of the temperature in each effect . 6 . If sufficient data are available, heat-transfer coefficients under the proposed operating conditions can be calculated in greater detail and surface requirements readjusted . Such calculations require considerable judgment to avoid repetitive trials but are usually well worth the effort . Sample calculations are given in

EVAPORATORS the American Institute of Chemical Engineers’ Testing Procedure for Evaporators and by Badger and Banchero, Introduction to Chemical Engineering, McGraw-Hill, New York, 1955 . These balances may be done by computer, but programming time frequently exceeds the time needed to do them manually, especially when variations in flow sheet are to be investigated . The MASSBAL program of SACDA, London, Ont ., provides a considerable degree of flexibility in this regard . Another program, not specific to evaporators, is ASPEN PLUS by Aspen Tech ., Cambridge, Mass . Many such programs include simplifying assumptions and approximations that are not explicitly stated and can lead to erroneous results . Optimization The primary purpose of evaporator design is to enable production of the necessary amount of satisfactory product at the lowest total cost . This requires economic-balance calculations that may include a great number of variables . Among the possible variables are the following: 1 . Initial steam pressure versus cost or availability . 2 . Final vacuum versus water temperature, water cost, heat-transfer performance, and product quality . 3 . Number of effects versus steam, water, and pump power cost . 4 . Distribution of heating surface between effects versus evaporator cost . 5 . Type of evaporator versus cost and continuity of operation . 6 . Materials of construction versus product quality, tube life, evaporator life, and evaporator cost . 7 . Corrosion, erosion, and power consumption versus tube velocity . 8 . Downtime for retubing and repairs . 9 . Operating-labor and maintenance requirements . 10 . Method of feeding and use of heat recovery systems . 11 . Size of recovery heat exchangers . 12 . Possible withdrawal of steam from an intermediate effect for use elsewhere . 13 . Entrainment separation requirements . The type of evaporator to be used and the materials of construction are generally selected on the basis of past experience with the material to be concentrated . The method of feeding can usually be decided on the basis of known feed temperature and the properties of feed and product . However, few of the listed variables are completely independent . For instance, if a large number of effects are to be used, with a consequent low temperature drop per effect, it is impractical to use a natural-circulation evaporator . If expensive materials of construction are desirable, it may be found that the forced-circulation evaporator is the cheapest and that only a few effects are justifiable . The variable having the greatest influence on total cost is the number of effects in the evaporator . An economic balance can establish the optimum number where the number is not limited by such factors as viscosity, corrosiveness, freezing point, boiling-point rise, or thermal sensitivity . Under present U .S . conditions, savings in steam and water costs justify the extra capital, maintenance, and power costs of about seven effects in large commercial installations when the properties of the fluid are favorable, as in black-liquor evaporation . Under government financing conditions, as for plants to supply freshwater from seawater, evaporators containing from 12 to 30 or more effects can be justified . As a general rule, the optimum number of effects increases with an increase in steam cost or plant size . Larger plants favor more effects, partly because they make it easier to install heat recovery systems that increase the steam economy attainable with a given number of effects . Such recovery systems usually do not increase the total surface needed, but do require that the heating surface be distributed between a greater number of pieces of equipment . The most common evaporator design is based on the use of the same heating surface in each effect . This is by no means essential since few evaporators are “standard” or involve the use of the same patterns . In fact, there is no reason why all effects in an evaporator must be of the same type . For instance, the cheapest salt evaporator might use propeller calandrias for the early effects and forced-circulation effects at the low-temperature end, where their higher cost per unit area is more than offset by higher heattransfer coefficients . Bonilla [Trans. Am. Inst. Chem. Eng. 41: 529 (1945)] developed a simplified method for distributing the heating surface in a multiple-effect evaporator to achieve minimum cost . If the cost of the evaporator per unit area of heating surface is constant throughout, then minimum cost and area will be achieved if the ratio of area to temperature difference A/∆T is the same for all effects . If the cost per unit area z varies, as when different tube materials or evaporator types are used, then zA/∆T should be the same for all effects . EVAPORATOR ACCESSORIES Condensers The vapor from the last effect of an evaporator is usually removed by a condenser . Surface condensers are employed when mixing of condensate with condenser cooling water is not desired . For the most part,

11-97

they are shell-and-tube condensers with vapor on the shell side and a multipass flow of cooling water on the tube side . Heat loads, temperature differences, sizes, and costs are usually of the same order of magnitude as for another effect of the evaporator . Surface condensers use more cooling water and are so much more expensive that they are never used when a directcontact condenser is suitable . The most common type of direct-contact condenser is the countercurrent barometric condenser, in which vapor is condensed by rising against a rain of cooling water . The condenser is set high enough that water can discharge by gravity from the vacuum in the condenser . Such condensers are inexpensive and are economical on water consumption . They can usually be relied on to maintain a vacuum corresponding to a saturatedvapor temperature within 2 .8°C (5°F) of the water temperature leaving the condenser [How, Chem. Eng. 63(2): 174 (1956)] . The ratio of water consumption to vapor condensed can be determined from the following equation: Water flow H u − h2 = Vapor flow h2 − h1

(11-111)

where Hυ = vapor enthalpy and h1 and h2 = water enthalpies entering and leaving the condenser . Another type of direct-contact condenser is the jet or wet condenser, which makes use of high-velocity jets of water both to condense the vapor and to force noncondensible gases out the tailpipe . This type of condenser is frequently placed below barometric height and requires a pump to remove the mixture of water and gases . Jet condensers usually require more water than the more common barometric-type condensers and cannot be throttled easily to conserve water when operating at low evaporation rates . Vent Systems Noncondensible gases may be present in the evaporator vapor as a result of leakage, air dissolved in the feed, or decomposition reactions in the feed . When the vapor is condensed in the succeeding effect, the noncondensibles increase in concentration and impede heat transfer . This occurs partially because of the reduced partial pressure of vapor in the mixture but mainly because the vapor flow toward the heating surface creates a film of poorly conducting gas at the interface . (See Thermal Design of Condensers, Multicomponent Condensers earlier in this section for means of estimating the effect of noncondensible gases on the steam-film coefficient .) The most important means of reducing the influence of noncondensibles on heat transfer is by properly channeling them past the heating surface . A positive vapor flow path from inlet to vent outlet should be provided, and the path should preferably be tapered to avoid pockets of low velocity where noncondensibles can be trapped . Excessive clearances and low-resistance channels that could bypass vapor directly from the inlet to the vent should be avoided [Standiford, Chem. Eng. Prog. 75: 59–62 (July 1979)] . In any event, noncondensible gases should be vented well before their concentration reaches 10 percent . Since gas concentrations are difficult to measure, the usual practice is to overvent . This means that an appreciable amount of vapor can be lost . To help conserve steam economy, venting is usually done from the steam chest of one effect to the steam chest of the next . In this way, excess vapor in one vent does useful evaporation at a steam economy only about 1 less than the overall steam economy . Only when there are large amounts of noncondensible gases present, as in beet sugar evaporation, is it desirable to pass the vents directly to the condenser to avoid serious losses in heat-transfer rates . In such cases, it can be worthwhile to recover heat from the vents in separate heat exchangers, which preheat the entering feed . The noncondensible gases eventually reach the condenser (unless vented from an effect above atmospheric pressure to the atmosphere or to auxiliary vent condensers) . These gases will be supplemented by air dissolved in the condenser water and by carbon dioxide given off on decomposition of bicarbonates in the water if a barometric condenser is used . These gases may be removed by the use of a water-jet-type condenser but are usually removed by a separate vacuum pump . The vacuum pump is usually of the steam-jet type if high-pressure steam is available . If high-pressure steam is not available, more expensive mechanical pumps may be used . These may be either a water-ring (Hytor) type or a reciprocating pump . The primary source of noncondensible gases usually is air dissolved in the condenser water . Figure 11-114 shows the dissolved-gas content of freshwater and seawater, calculated as equivalent air . The lower curve for seawater includes only dissolved oxygen and nitrogen . The upper curve includes carbon dioxide that can be evolved by complete breakdown of bicarbonate in seawater . Breakdown of bicarbonates is usually not appreciable in a condenser but may go almost to completion in a seawater evaporator . The large increase in gas volume as a result of possible bicarbonate breakdown is illustrative of the uncertainties involved in sizing vacuum systems .

11-98

HEAT-TRANSFER EQUIPMENT providing a relatively quiescent zone in which the salt can settle . Sufficiently high slurry densities can usually be achieved in this manner to reach the limit of pumpability . The evaporators are usually placed above barometric height so that the slurry can be discharged intermittently on a short time cycle . This permits the use of high velocities in large lines that have little tendency to plug . If the amount of salts crystallized is on the order of 1 ton/h or less, a salt trap may be used . This is simply a receiver that is connected to the bottom of the evaporator and is closed off from the evaporator periodically for emptying . Such traps are useful when insufficient headroom is available for gravity removal of the solids . However, traps require a great deal of labor, give frequent trouble with the shutoff valves, and also can upset evaporator operation completely if a trap is reconnected to the evaporator without first displacing all air with feed liquor . EVAPORATOR OPERATION

FIG. 11-114 Gas content of water saturated at atmospheric pressure . °C = 5/9 (°F − 32) .

By far the largest load on the vacuum pump is water vapor carried with the noncondensible gases . Standard power-plant practice assumes that the mixture leaving a surface condenser will have been cooled 4 .2°C (7 .5°F) below the saturation temperature of the vapor . This usually corresponds to about 2 .5 kg water vapor/kg air . One advantage of the countercurrent barometric condenser is that it can cool the gases almost to the temperature of the incoming water and thus reduce the amount of water vapor carried with the air . In some cases, as with pulp mill liquors, the evaporator vapors contain constituents more volatile than water, such as methanol and sulfur compounds . Special precautions may be necessary to minimize the effects of these compounds on heat transfer, corrosion, and condensate quality . They can include removing most of the condensate countercurrent to the vapor entering an evaporator heating element, channeling vapor and condensate flow to concentrate most of the “foul” constituents into the last fraction of vapor condensed (and keeping this condensate separate from the rest of the condensate), and flashing the warm evaporator feed to a lower pressure to remove much of the foul constituents in only a small amount of flash vapor . In all such cases, special care is needed to properly channel vapor flow past the heating surfaces so there is a positive flow from steam inlet to vent outlet with no pockets, where foul constituents or noncondensibles can accumulate . Salt Removal When an evaporator is used to make a crystalline product, a number of means are available for concentrating and removing the salt from the system . The simplest is to provide settling space in the evaporator itself . This is done in the types shown in Fig . 11-110b, c, and e by

The two principal elements of evaporator control are evaporation rate and product concentration. Evaporation rate in single- and multiple-effect evaporators is usually achieved by steam flow control . Conventional-control instrumentation is used (see Sec . 22), with the added precaution that the pressure drop across the meter and control valve, which reduces temperature difference available for heat transfer, not be excessive when maximum capacity is desired . Capacity control of thermocompression evaporators depends on the type of compressor; positive-displacement compressors can utilize speed control or variations in operating pressure level . Centrifugal machines normally utilize adjustable inlet-guide vanes . Steam jets may have an adjustable spindle in the high-pressure orifice or be arranged as multiple jets that can individually be cut out of the system . Product concentration can be controlled by any property of the solution that can be measured with the requisite accuracy and reliability . The preferred method is to impose control on the rate of product withdrawal . Feed rates to the evaporator effects are then controlled by their levels . When level control is impossible, as with the rising-film LTV, product concentration is used to control the feed rate—frequently by ratioing of feed to steam with the ratio reset by product concentration, sometimes also by feed concentration . Other controls that may be needed include vacuum control of the last effect (usually by air bleed to the condenser) and temperature-level control of thermocompression evaporators (usually by adding makeup heat or by venting excess vapor, or both, as feed or weather conditions vary) . For more control details, see N . Lior, ed ., Measurement and Control in Water Desalination, Elsevier Science Publ . Co ., New York, 1986, pp . 241–305 . Control of an evaporator requires more than proper instrumentation . Operator logs should reflect changes in basic characteristics, as by use of pseudo heat-transfer coefficients, which can detect obstructions to heat flow, hence to capacity . These are merely the ratio of any convenient measure of heat flow to the temperature drop across each effect . Dilution by wash and seal water should be monitored since it absorbs evaporative capacity . Detailed tests, routine measurements, and operating problems are covered more fully in AICE, Testing Procedure for Evaporators and by Standiford [Chem. Eng. Prog. 58(11): 80 (1962)] . By far the best application of computers to evaporators is for working up operators’ data into the basic performance parameters such as heattransfer coefficients, steam economy, and dilution .

Section 12

Psychrometry, Evaporative Cooling, and Solids Drying

John P. Hecht, Ph.D. Technical Section Head, Drying and Particle Processing, The Procter & Gamble Company; Member, American Institute of Chemical Engineers (Section Editor, Evaporative Cooling, SolidsDrying Fundamentals, Drying Equipment) Wayne E. Beimesch, Ph.D. Technical Associate Director (Retired), Corporate Engineering, The Procter & Gamble Company (Drying Equipment, Operation and Troubleshooting) Karin Nordström Dyvelkov, Ph.D. GEA Process Engineering A/S Denmark (Drying Equipment, Fluidized Bed Dryers, Spray Dryers) Ian C. Kemp, M.A. (Cantab) Scientific Leader, GlaxoSmithKline; Fellow, Institution of Chemical Engineers; Associate Member, Institution of Mechanical Engineers (Psychrometry, Solids-Drying Fundamentals, Freeze Dryers) Tim Langrish, D. Phil. School of Chemical and Biomolecular Engineering, The University of Sydney, Australia (Solids-Drying Fundamentals, Cascading Rotary Dryers) (Francis) Lee Smith, Ph.D., M. Eng. Principal, Wilcrest Consulting Associates, LLC, Katy, Texas; Partner and General Manager, Albutran USA, LLC, Katy, Texas (Evaporative Cooling) Jason A. Stamper, M. Eng. Technology Leader, Drying and Particle Processing, The Procter & Gamble Company; Member, Institute for Liquid Atomization and Spray Systems (Drying Equipment, Fluidized Bed Dryers, Spray Dryers)

PSYCHROMETRY Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculation Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relationship Between Wet-Bulb and Adiabatic Saturation Temperatures . . . . . Psychrometric Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples Illustrating Use of Psychrometric Charts . . . . . . . . . . . . . . . . . . . . . . . . Example 12-1 Determination of Moist Air Properties . . . . . . . . . . . . . . . . . . . . . . Example 12-2 Air Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-3 Evaporative Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-4 Cooling and Dehumidification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-5 Cooling Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-6 Recirculating Dryer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Psychrometric Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Psychrometric Software and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Psychrometric Calculations—Worked Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-7 Determination of Moist Air Properties . . . . . . . . . . . . . . . . . . . . . . Example 12-8 Calculation of Humidity and Wet-Bulb Condition . . . . . . . . . . . . Example 12-9 Calculation of Psychrometric Properties of Acetone/Nitrogen Mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12-3 12-4 12-5 12-6 12-6 12-6 12-6 12-7 12-10 12-10 12-11 12-11 12-11 12-12 12-12 12-12 12-13

Measurement of Humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hygrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dew Point Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wet-Bulb/Dry-Bulb Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EVAPORATIVE COOLING Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cooling Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cooling Tower Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-10 Calculation of Mass-Transfer Coefficient Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cooling Tower Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cooling Tower Operation: Water Makeup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-11 Calculation of Makeup Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fans and Pumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fogging and Plume Abatement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Natural Draft Towers, Cooling Ponds, and Spray Ponds . . . . . . . . . . . . . . . . . . . .

12-14 12-14 12-14 12-14

12-14 12-15 12-15 12-15 12-15 12-16 12-16 12-16 12-17 12-17 12-17 12-17

12-1

12-2

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

Wet Surface Air Coolers (WSACs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wet Surface Air Cooler Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common WSAC Applications and Configurations . . . . . . . . . . . . . . . . . . . . . . . . . WSAC for Closed-Circuit Cooling Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Conservation Applications—“Wet-Dry” Cooling . . . . . . . . . . . . . . . . . . . . SOLIDS-DRYING FUNDAMENTALS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanisms of Moisture Transport Within Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drying Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-12 Drying of a Pure Water Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drying Curves and Periods of Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction to Internal and External Mass-Transfer Control—Drying of a Slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concept of a Characteristic Drying Rate Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-13 Characteristic Drying Curve Application . . . . . . . . . . . . . . . . . . . Dryer Modeling, Design, and Scale-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Levels of Dryer Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heat and Mass Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scoping Design Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scaling Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detailed or Rigorous Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-14 Air Drying of a Thin Layer of Paste . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement of Drying Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performing a Mass and Energy Balance on a Large Industrial Dryer . . . . . . . . . . Drying of Nonaqueous Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Practical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Product Quality Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transformations Affecting Product Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional Readings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solids-Drying Equipment—General Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification and Selection of Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Description of Dryer Classification and Selection Criteria . . . . . . . . . . . . . . . . . . Selection of Drying Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dryer Selection Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dryer Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Batch Tray Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuous Tray and Gravity Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuous Band and Tunnel Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12-17 12-17 12-18 12-19 12-19 12-20

12-20 12-21 12-21 12-22 12-22 12-22 12-23 12-23 12-24 12-25 12-25 12-25 12-25 12-25 12-26 12-26 12-26 12-26 12-29 12-29 12-29 12-30 12-30 12-30 12-30 12-30 12-31 12-32 12-32 12-32 12-32 12-36 12-36 12-38 12-38 12-41 12-44

Example 12-15 Mass and Energy Balance on a Dryer with Partially Recycled Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Batch Agitated and Rotating Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-16 Calculations for Batch Dryer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuous Agitated and Rotary Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-17 Sizing of a Cascading Rotary Dryer . . . . . . . . . . . . . . . . . . . . . . . . . Additional Readings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluidized-Bed and Spouted-Bed Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Industrial Fluid-Bed Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design and Scale-Up of Fluid Beds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-18 Scaling a Batch Fluidized-Bed Dryer . . . . . . . . . . . . . . . . . . . . . . . Vibrating Fluidized-Bed Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pneumatic Conveying Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-19 Mass and Energy Balance for a Pneumatic Conveying Dryer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spray Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Industrial Designs and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plant Layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-20 Scoping Exercise for Size of Spray Dryer . . . . . . . . . . . . . . . . . . . . Spray Dryer Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-21 Mass and Energy Balance on a Spray Dryer . . . . . . . . . . . . . . . . . Additional Readings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drum and Thin-Film Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-22 Heat-Transfer Calculations on a Drum Dryer . . . . . . . . . . . . . . . Thin-Film Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sheet Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cylinder Dryers and Paper Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stenters (Tenters) and Textile Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12-23 Impinging Air Drying of Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Freeze Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Batch Freeze Dryers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cycle Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuous Freeze Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electromagnetic Drying Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dielectric Methods (Radiofrequency and Microwave) . . . . . . . . . . . . . . . . . . . . . . Example 12-24 Sheet Drying with Convection and Infrared . . . . . . . . . . . . . . . . Additional Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operation and Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dryer Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dryer Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environmental Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control and Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12-44 12-46 12-51 12-51 12-56 12-60 12-62 12-65 12-66 12-66 12-66 12-67 12-67 12-71 12-71 12-74 12-75 12-75 12-78 12-78 12-79 12-79 12-80 12-81 12-81 12-81 12-81 12-82 12-83 12-83 12-84 12-84 12-84 12-84 12-84 12-84 12-86 12-86 12-86 12-86 12-87 12-88 12-88 12-88

Nomenclature and Units

Symbol

Definition

SI units

U .S . Customary System units

Symbol

A aw

Area Water activity

m2 —

ft2 —

awvapor

Activity of water in vapor phase

awsolid C CP

Activity of water in solid phase Concentration Specific heat capacity at constant pressure Concentration of water in solid Diffusion coefficient of water in a solid or liquid as a function of moisture content Diffusion coefficient of water in air Diameter (particle) Power Solids or liquid mass flow rate Mass flux of water at surface Relative drying rate Gas mass flow rate Acceleration due to gravity, 9 .81 m/s2 (32 .2 ft/s2) Enthalpy of a pure substance

— —

— —

kg/m3 J/(kg ⋅ K)

lb/ft3 Btu/(lb ⋅ °F)

kg/m3 m2/s

lb/ft3 ft2/s

m2/s m W kg/s kg/(m2 ⋅ s) — kg/s m/s2

ft2/s in Btu/h lb/h lb/( ft2 ⋅ s) — lb/h ft/s2

L M m msolids N N P Pwbulk

J/kg

Btu/lb

Pwsurface

Cw D(u) Dwater/air D E F F F G g H

ΔHvap h I J K kair kc kp

Definition Heat of vaporization Heat-transfer coefficient Humid enthalpy (dry substance and associated moisture or vapor) Mass flux (of evaporating liquid) Mass-transfer coefficient Thermal conductivity of air Mass-transfer coefficient for a concentration driving force Mass-transfer coefficient for a partial pressure driving force Length; length of drying layer Molecular weight Mass Mass of dry solids Specific drying rate (−dX/dt) Rotational speed (drum, impeller, etc .) Total pressure Partial pressure of water vapor in air far from the drying material Partial pressure of water vapor in air at the solid interface

SI units

U .S . Customary System units

J/kg W/(m2 ⋅ K) J/kg

Btu/lb Btu/( ft2 ⋅ h ⋅ °F) Btu/lb

kg/(m2 ⋅ s) m/s W/(m ⋅ K) m/s

lb/( ft2 ⋅ h) lb/( ft2 ⋅ h ⋅ atm) Btu/( ft ⋅ h ⋅ °F) ft2/s

kg/(m2 ⋅ s)

lbm/( ft3 ⋅ s)

m kg/mol kg kg 1/s 1/s kg/(m ⋅ s2) kg/(m ⋅ s2)

ft lb/mol lb lb 1/s rpm lb/in2 lb/in2

kg/(m ⋅ s2)

lb/in2

Symbol P sat pure

p pw , air Q Q R r r RH S S T T, t T U U V V u u droplet W wavg dry-basis X Y Z

Definition Partial pressure/vapor pressure of component Pure component vapor pressure Partial pressure of water vapor in air Heat-transfer rate Heat flux Universal gas constant, 8314 J/(kmol ⋅ K) Droplet radius Radius; radial coordinate Relative humidity Percentage saturation Solid-fixed coordinate Absolute temperature Temperature Time Velocity Mass of water/mass of dry solid Volume Air velocity Specific volume Droplet volume Wet-basis moisture content Average wet-basis moisture content Solids moisture content (dry basis) Mass ratio Distance coordinate

U .S . Customary System units

SI units kg/(m ⋅ s2) 2

kg/(m ⋅ s ) kg/(m ⋅ s2) W W/m2 J/(mol ⋅ K)

lb/in2 2

lb/in lb/in2 Btu/h Btu/( ft2 ⋅ h) Btu/(mol ⋅ °F)

m ft m ft — — — — Depends on geometry K °R °C °F s h m/s ft/s — — m3 ft3 m/s ft/s ft3/lb m3/kg m3 ft3 — — — — — — — — m ft

Bi Gr Nu Pr

Archimedes number, (gdP3ρg/µ2) (ρP − ρG) Biot number, hL/κ Grashof number, L3ρ2βg ∆T/µ2 Nusselt number, hdP/κ Prandtl number, µCP/κ

—

—

— — — —

— — — —

Definition

SI units

Re Sc Sh Le

Reynolds number, ρ dP U/µ Schmidt number, µ/ρD Sherwood number, kY dP/D Lewis = Sc/Pr

α β ε ζ η θ κ λ µ µair ρ ρair ρs ρos ρwo τ F

Slope Psychrometric ratio Voidage (void fraction) Dimensionless distance Efficiency Dimensionless time Thermal conductivity Latent heat of evaporation Absolute viscosity Viscosity of air Density Air density Mass concentration of solids Density of dry solids Density of pure water Residence time of solids Characteristic (dimensionless) moisture content Relative humidity

— — — —

— — — —

— — — — — — W/(m ⋅ K) J/kg kg/(m ⋅ s) kg/(m ⋅ s) kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 s —

— — — — — — Btu/( ft ⋅ h ⋅ °F) Btu/lb lb/( ft ⋅ s) lb/( ft ⋅ s) lb/ft3 lb/ft3 lb/ft3 lb/ft3 lb/ft3 h —

%

%

Greek letters

Y

Subscripts g v as o s wb dew liq

Dimensionless groups Ar

Symbol

U .S . Customary System units

gas vapor adiabatic saturation reference saturation wet bulb dew point liquid

PSYCHROMETRY General References: ASHRAE 2002 Handbook: Fundamentals, SI Edition, American Society of Heating, Refrigeration, and Air-Conditioning Engineers, Atlanta, Ga ., 2002, chap . 6 . “Psychometrics,” chap . 19 .2, “Sorbents and Desiccants .” Aspen Process Manual (Internet knowledge base), Aspen Technology, 2000 onward . Humidity and Dewpoint, British Standard BS 1339 (rev .) . Humidity and dew point, Pt . 1 (2002); Terms, definitions and formulae, Pt . 2 (2005); Psychrometric calculations and tables (including spreadsheet), Pt . 3 (2004); Guide to humidity measurement . British Standards Institution, Gunnersbury, UK . Cook and DuMont, Process Drying Practice, McGraw-Hill, New York, 1991, chap . 6 . Keey, Drying of Loose and Particulate Materials, Hemisphere, New York, 1992 . Poling, Prausnitz, and O’Connell, The Properties of Gases and Liquids, 5th ed ., McGraw-Hill, New York, 2000 . Earlier editions: 1st/2d eds ., Reid and Sherwood (1958/1966); 3d ed ., Reid, Prausnitz, and Sherwood (1977); 4th ed ., Reid, Prausnitz, and Poling (1986) . Soininen, “A Perspectively Transformed Psychrometric Chart and Its Application to Drying Calculations,” Drying Technol. 4(2): 295–305 (1986) . Sonntag, “Important New Values of the Physical Constants of 1986, Vapor Pressure Formulations Based on the ITS-90, and Psychrometer Formulae,” Zeitschrift für Meteorologie 40(5): 340–344 (1990) . Treybal, Mass-Transfer Operations, 3d ed ., McGraw-Hill, New York, 1980 . Wexler, Humidity and Moisture, vol . 1, Reinhold, New York, 1965 .

Psychrometry is concerned with the determination of the properties of gas-vapor mixtures . These are important in calculations for humidification and dehumidification, particularly in cooling towers, air-conditioning systems, and dryers . The first two cases involve the air–water vapor system at near-ambient conditions, but dryers normally operate at elevated temperatures and may also use elevated or subatmospheric pressures and other gas-solvent systems .

TERMINOLOGY Terminology and nomenclature pertinent to psychrometry are given below . There is often considerable confusion between the dry and wet basis, and between mass, molar, and volumetric quantities, in both definitions and calculations . Dry- and wet-basis humidities are similar at ambient conditions but can differ significantly at elevated humidities, e .g ., in dryer exhaust streams . Complete interconversion formulas between four key humidity parameters are given in Table 12-1 for the air-water system and in Table 12-2 for a general gas-vapor system . Definitions related to humidity, vapor pressure, saturation, and volume are as follows; the most useful are absolute humidity, vapor pressure, and relative humidity . Absolute Humidity Y Mass of water (or solvent) vapor carried by unit mass of dry air (or other carrier gas) . It is also known as the humidity ratio, mixing ratio, mass ratio, or dry-basis humidity. Preferred units are lb/lb or kg/kg, but g/kg and gr/lb are often used, as are ppmw and ppbw (parts per million/billion by weight); ppmw = 106Y, ppbw = 109Y . Specific Humidity YW Mass of vapor per unit mass of gas-vapor mixture . Also known as mass fraction or wet-basis humidity, and is used much more rarely than dry-basis absolute humidity . YW = Y/(1 + Y); Y = YW/(1 − YW) . Mole Ratio z Number of moles of vapor per mole of gas (dry basis), mol/mol; z = (Mg/Mu)Y, where Mu = molecular weight of vapor and Mg = molecular weight of gas . It may also be expressed as ppmv and ppbv (parts per million/billion by volume); ppmv = 106 z, ppbv = 109 z . 12-3

12-4

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

TABLE 12-1 Interconversion Formulas for Air-Water System, to Three Significant Figures T = temperature in kelvins (K); P = total pressure in pascals (Pa or N/m2) Y (or ppmw)∗

Convert from: Convert to: Absolute humidity (mixing ratio) Y (kg ⋅ kg−1)

1

y Y=

Y=

0 .622 p P− p

Y=

0 .622 0 .002167 P /(YuT ) − 1

1

y=

p P

y=

461 .5YυT P

y=

Y 0 .622 + Y

Vapor pressure p (Pa)

p=

PY 0 .622 + Y

p = yP

Volumetric humidity Yυ (kg ⋅ m−3)

Yu =

0 .002167 PY (0 .622 + Y )T

Yυ =

Y=

mu mg

Yw =

mu m g + mu

z=

nu ng

y=

nu n g + nu

Volumetric Humidity Yt Mass of vapor per unit volume of gas-vapor mixture . It is sometimes, confusingly, called the absolute humidity, but it is really a vapor concentration; preferred units are kg/m3 or lb/ft3, but g/m3 and gr/ft3 are also used . It is inconvenient for calculations because it depends on temperature and pressure and on the units system; absolute humidity Y is always preferable for heat and mass balances . It is proportional to the specific humidity (wet basis); Yυ = YWρg, where ρg is the humid gas density (mass of gas-vapor mixture per unit volume, wet basis). Also Yu =

M u Pnu RT (n g + nu )

Vapor Pressure p Partial pressure of vapor in gas-vapor mixture, which is proportional to the mole fraction of vapor; p = yP, where P = total pressure, in the same units as p (Pa, N/m2, bar, atm, or psi) . Hence p=

nu P n g + nu

Saturation Vapor Pressure ps Pressure exerted by pure vapor at a given temperature . When the vapor partial pressure p in the gas-vapor mixture at a given temperature equals the saturation vapor pressure ps at the same temperature, the air is saturated and the absolute humidity is designated the saturation humidity Ys . Relative Humidity RH or Y The partial pressure of vapor divided by the saturation vapor pressure at the given temperature, usually expressed as a percentage . Thus RH = 100p/ps . Percentage Absolute Humidity (Percentage Saturation) S Ratio of absolute humidity to saturation humidity, given by S = 100Y/Ys = 100p (P − ps)/ [ps(P − p)]. It is used much less commonly than relative humidity . Dew Point Tdew, or Saturation Temperature The temperature at which a given mixture of water vapor and air becomes saturated on cooling; i .e ., the temperature at which water exerts a vapor pressure equal to the partial pressure of water vapor in the given mixture .

Yυ

0 .622Y 1−Y

Mole fraction y (mol ⋅ mol−1)

Mole Fraction y Number of moles of vapor per mole of gas-vapor mixture (wet basis); y = z/(1 + z); z = y/(1 - y). If a mixture contains mυ kg and nυ mol of vapor (e .g ., water) and mg kg and ng mol of noncondensible gas (e .g ., air), with mυ = nυMυ and mg = ngMg, then the four quantities above are defined by

p

p = 461 .5YυT

1

0 .002167 yP T

Yυ =

0 .002167 p T

1

Humid Volume t Volume in cubic meters (cubic feet) of 1 kg (1 lb) of dry air and the water vapor it contains . Saturated Volume vs Humid volume when the air is saturated . Terms related to heat balances are as follows: Humid Heat Cs Heat capacity of unit mass of dry air and the moisture it contains . Cs = CPg + CPvY, where CPg and CPv are the heat capacities of dry air and water vapor, respectively, and both are assumed constant . For approximate engineering calculations at near-ambient temperatures, in SI units, Cs = 1 + 1 .9Y kJ/(kg ⋅ K) and in USCS units, Cs = 0 .24 + 0 .45Y (Btu/(lb ⋅ °F) . Humid Enthalpy H Heat content at a given temperature T of unit mass of dry air and the moisture it contains, relative to a datum temperature T0, usually 0°C . As water is liquid at 0°C, the humid enthalpy also contains a term for the latent heat of water . If heat capacity is invariant with temperature, H = (CPg + CPvY)(T - T0) + λ0Y, where λ0 is the latent heat of water at 0°C, 2501 kJ/kg (1075 Btu/lb) . In practice, for accurate calculations, it is often easier to obtain the vapor enthalpy Hυ from steam tables, when H = Hg + Hv = CPgT + Hυ . Adiabatic Saturation Temperature Tas Final temperature reached by a small quantity of vapor-gas mixture into which water is evaporating . It is sometimes called the thermodynamic wet-bulb temperature. Wet-Bulb Temperature Twb Dynamic equilibrium temperature attained by a liquid surface from which water is evaporating into a flowing airstream when the rate of heat transfer to the surface by convection equals the rate of mass transfer away from the surface . It is very close to the adiabatic saturation temperature for the air-water system, but not for most other vapor-gas systems; see later . CALCULATION FORMULAS Table 12-1 gives formulas for conversion between absolute humidity, mole fraction, vapor pressure, and volumetric humidity for the air-water system, and Table 12-2 does likewise for a general gas-vapor system . Where relationships are not included in the definitions, they are given below . In USCS units, the formulas are the same except for the volumetric humidity Yυ . Because of the danger of confusion with pressure units, it is recommended that in both Tables 12-1 and 12-2, Yυ be calculated in SI units and then converted . Volumetric humidity is also related to absolute humidity and humid gas density by Yυ = YW ρg =

Y ρg 1+Y

(12-1)

TABLE 12-2 Interconversion Formulas for a General Gas-Vapor System Mg, Mu = molal mass of gas and vapor, respectively; R = 8314 J/(kmol ⋅ K); T = temperature in kelvins (K); P = total pressure in pascals (Pa or N/m2) Convert from:

Y (or ppmw)∗

Convert to: Absolute humidity (mixing ratio) Y (kg ⋅ kg−1)

1

y Y=

p

Yυ

Mu y M g (1 − Y )

Y=

pM u ( P − p) M g

Y=

Mu M g ( PM u /(Yu RT ) − 1

1

y=

p P

y=

Yυ RT PM υ

p=

Yυ RT Mυ

Mole fraction y (mol ⋅ mol−1)

y=

Y M u /M g + Y

Vapor pressure p (Pa)

p=

PY M u /M g + Y

p = yP

Volumetric humidity Yυ (kg ⋅ m−3)

Yu =

Mu PY RT M u /M g + Y

Yυ =

M υ yP RT

1 Yυ =

Mυ p RT

1

PSYCHROMETRY Two further useful formulas are as follows:

Parameter

General vapor-gas system

Density of humid gas (moist air) ρg , kg/m3

ρg =

Humid volume υ per unit mass of dry air, m3/kg

υ=

Mg  M  P − p + υ p RT  Mg 

RT RT = M g ( P − p) P

Air-water system, SI units, to 3 significant figures P − 0 .378 p ρg = 287 .1T υ=

461 .5T (0 .622 + Y ) P

Eq . no . (12-2)

(12-3)

 1 Y  × +   M g Mυ 

This equation has to be reversed and solved iteratively to obtain Yas (absolute humidity at adiabatic saturation) and hence Tas (the calculation is divergent in the opposite direction) . Approximate direct formulas are available from various sources, e .g ., British Standard BS 1339 (2002) and Liley [IJMEE 21(2), 1993] . The latent heat of evaporation evaluated at the adiabatic saturation temperature is λas, which may be obtained from steam tables; humid heat Cs is evaluated at initial humidity Y . On a psychrometric chart, the adiabatic saturation process almost exactly follows a constant-enthalpy line, as the sensible heat given up by the gas-vapor mixture exactly balances the latent heat of the liquid that evaporates back into the mixture . The only difference is due to the sensible heat added to the water to take it from the datum temperature to Tas . The adiabatic saturation line differs from the constantenthalpy line as follows, where CPL is the specific heat capacity of the liquid: Has - H = CPLTas(Yas - Y )

From Eq . (12-2), the density of dry air at 0°C (273 .15 K) and 1 atm (101,325 Pa) is 1 .292 kg/m3 (0 .08065 lb/ft3) . Note that the density of moist air is always lower than that of dry air . Equation (12-3) gives the humid volume of dry air at 0°C (273 .15 K) and 1 atm as 0 .774 m3/kg (12 .4 ft3/lb) . For moist air, the humid volume is not the reciprocal of humid gas density; υ = (1 + Y )/ρg . The saturation vapor pressure of water is given by Sonntag (1990) in Pa (N/m2) at absolute temperature T (K) . Over water: ln ps = −6096 .9385T −1 + 21 .2409642 − 2 .711193 × 10−2T + 1 .673952 × 10−5T 2 + 2 .433502 ln T

(12-4a) h(T - Twb) = ky λwb(Ywb - Y)

(12-4b)

Simpler equations for saturation vapor pressure are the Antoine equation and Magnus formula . These are slightly less accurate, but easier to calculate and also easily reversible to give T in terms of p . For the Antoine equation, given below, coefficients for numerous other solvent-gas systems are given in Poling, Prausnitz, and O’Connell, The Properties of Gases and Liquids, 5th ed ., McGraw-Hill, New York, 2000 . ln ps = C0 −

C1 T − C2

T=

C1 + C2 C 0 − ln ps

(12-5)

Values for Antoine coefficients for the air-water system are given in Table 12-3 . The standard values give vapor pressure within 0 .1 percent of steam tables over the range 50 to 100°C, but an error of nearly 3 percent at 0°C . The alternative coefficients give a close fit at 0 and 100°C and an error of less than 1 .2 percent over the intervening range . The Sonntag equation strictly only applies to water vapor with no other gases present (i .e ., in a partial vacuum) . The vapor pressure of a gas mixture, e .g ., water vapor in air, is given by multiplying the pure liquid vapor pressure by an enhancement factor f, for which various equations are available (see British Standard BS 1339 Part 1, 2002) . However, the correction is typically less than 0 .5 percent, except at elevated pressures, and it is therefore usually neglected for engineering calculations . RELATIONSHIP BETWEEN WET-BULB AND ADIABATIC SATURATION TEMPERATURES If a stream of air is intimately mixed with a quantity of water in an adiabatic system, the temperature of the air will drop and its humidity will increase . If the equilibration time or the number of transfer units approaches infinity, the air-water mixture will reach saturation . The adiabatic saturation temperature Tas is given by a heat balance between the initial unsaturated vaporgas mixture and the final saturated mixture at thermal equilibrium: Cs(T - Tas) = λas(Yas - Y)

p in Pa p in Pa

(12-8)

where ky is the corrected mass-transfer coefficient [kg/(m2 ⋅ s)], h is the heattransfer coefficient [kW/(m2 ⋅ K)], Ywb is the saturation mixing ratio at twb, and λwb is the latent heat (kJ/kg) evaluated at Twb . Again, this equation must be solved iteratively to obtain Twb and Ywb . In practice, for any practical psychrometer or wetted droplet or particle, there is significant extra heat transfer from radiation . For an Assmann psychrometer at near-ambient conditions, this is approximately 10 percent . This means that any measured real value of Twb is slightly higher than the “pure convective” value in the definition . It is often more convenient to obtain wet-bulb conditions from adiabatic saturation conditions (which are much easier to calculate) by the following formula: T − Twb T − Tas = β Ywb − Y Yas − Y

(12-9)

where the psychrometric ratio β = C s ky /h and C s is the mean value of the humid heat over the range from Tas to T . The advantage of using β is that it is approximately constant over normal ranges of temperature and pressure for any given pair of vapor and gas values . This avoids having to estimate values of heat- and mass-transfer coefficients h and ky from uncertain correlations . For the air-water system, considering convective heat transfer alone, β ~ 1 .1 . In practice, there is an additional contribution from radiation, and β is very close to 1 . As a result, the wet-bulb and adiabatic saturation temperatures differ by less than 1°C for the air-water system at near-ambient conditions (0 to 100°C, Y < 0 .1 kg/kg) and can be taken as equal for normal calculation purposes . Indeed, typically the Twb measured by a practical psychrometer or at a wetted solid surface is closer to Tas than to the “pure convective” value of Twb . However, for nearly all other vapor-gas systems, particularly for organic solvents, β < 1, and hence Twb > Tas . This is illustrated in Fig . 12-5 . The surface (wet-bulb) temperature can change as drying progresses, whereas in the airwater system it stays constant . For these systems the psychrometric ratio may be obtained by determining h/ky from heat- and mass-transfer analogies such as the Chilton-Colburn analogy . The basic form of the equation is n

Sc β =   = Le−n  Pr 

(12-6)

(12-10)

TABLE 12-3 Alternative Set of Values for Antoine Coefficients for Air-Water Systems Standard values Alternative values

(12-7)

Equation (12-7) is useful for calculating the adiabatic saturation line for a given Tas and gives an alternative iterative method for finding Tas, given T and Y; compared with Eq . (12-6), it is slightly more accurate and converges faster, but the calculation is more cumbersome . The wet-bulb temperature is the temperature attained by a fully wetted surface, such as the wick of a wet-bulb thermometer or a droplet or wet particle undergoing drying, in contact with a flowing unsaturated gas stream . It is regulated by the rates of vapor-phase heat and mass transfer to and from the wet bulb . Assuming mass transfer is controlled by diffusion effects and heat transfer is purely convective,

Over ice: ln ps = −6024 .5282T −1 + 29 .32707 + 1 .0613868 × 10−2T − 1 .3198825 × 10−5T 2 − 0 .49382577 ln T

12-5

C0

C1

C2

23 .1963 23 .19

3816 .44 3830

46 .13 K 44 .83 K

C0 p in mmHg p in mmHg

18 .3036 18 .3

C1

C2

3816 .44 3830

46 .13 K 44 .87 K

12-6

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

where Sc is the Schmidt number for mass-transfer properties, Pr is the Prandtl number for heat-transfer properties, and Le is the Lewis number κ/(Csρg D), where κ is the gas thermal conductivity and D is the diffusion coefficient for the vapor through the gas . Experimental and theoretical values of the exponent n range from 0 .56 [Bedingfield and Drew, Ind. Eng. Chem . 42: 1164 (1950)] to 23 [Chilton and Colburn, Ind. Eng. Chem . 26: 1183 (1934)] . A detailed discussion is given by Keey (1992) . Values of β for any system can be estimated from the specific heats, diffusion coefficients, and other data given in Sec . 2 . See the example below . For calculation of wet-bulb (and adiabatic saturation) conditions, the most commonly used formula in industry is the psychrometer equation . This is a simple linear formula that gives vapor pressure directly if the wet-bulb temperature is known, and it is therefore ideal for calculating humidity from a wet-bulb measurement using a psychrometer, although the calculation of wet-bulb temperature from humidity still requires an iteration p = pwb − AP (T − Twb)

(12-11)

where A is the psychrometer coefficient . For the air-water system, the following formulas based on equations given by Sonntag [Zeitschrift für Meteorologie 40(5): 340–344 (1990)] may be used to give A for Twb up to 30°C; they are based on extensive experimental data for Assmann psychrometers . Over water (wet-bulb temperature): A = 6 .5 × 10-4(1 + 0 .000944Twb)

(12-12a)

Over ice (ice-bulb temperature): Ai = 5 .72 × 10-4

(12-12b)

For other vapor-gas systems, A is given by A=

M gC s M vβλ wb

(12-13)

Here β is the psychrometric coefficient for the system . As a cross-check, for the air-water system at 20°C wet-bulb temperature, 50°C dry-bulb temperature, and absolute humidity 0 .002 kg/kg, Cs = 1 .006 + 1 .9 × 0 .002 = 1 .01 kJ/(kg ⋅ K) and λwb = 2454 kJ/kg . Since Mg = 28 .97 kg/kmol and Mυ = 18 .02 kg/kmol, Eq . (12-12) gives A as 6 .617 × 10-4/β, compared with Sonntag’s value of 6 .653 × 10−4 at this temperature, giving a value for the psychrometric coefficient β of 0 .995; that is, β ≈ 1, as expected for the air-water system . PSYCHROMETRIC CHARTS Psychrometric charts are plots of humidity, temperature, enthalpy, and other useful parameters of a gas-vapor mixture . They are helpful for rapid estimates of conditions and for visualization of process operations such as humidification and drying . They apply to a given system at a given pressure, the most common, of course, being air-water at atmospheric pressure . There are four types, of which the Grosvenor and Mollier types are most widely used . The Grosvenor chart plots temperature (abscissa) versus humidity (ordinate) . Standard charts produced by ASHRAE and other groups, or by computer programs, are usually of this type . The saturation line is a curve from bottom left to top right, and curves for constant relative humidity are approximately parallel to this . Lines from top left to bottom right may be of either constant wet-bulb temperature or constant enthalpy, depending on the chart . The two are not quite identical, so if only one is shown, correction factors are required for the other parameter . Examples are shown in Figs . 12-1 (SI units) and 12-2 (USCS units) . An additional chart for a wider temperature range in USCS units is given in Perry’s 8th Edition (Fig . 12-2b) . The Bowen chart is a plot of enthalpy (abscissa) versus humidity (ordinate) . It is convenient to be able to read enthalpy directly, especially for nearadiabatic convective drying where the operating line approximately follows a line of constant enthalpy . However, it is very difficult to read accurately because the key information is compressed in a narrow band near the saturation line . See Cook and DuMont, Process Drying Practice, McGraw-Hill, New York, 1991, chap . 6 . The Mollier chart plots humidity (abscissa) versus enthalpy (lines sloping diagonally from top left to bottom right) . Lines of constant temperature are shallow curves at a small slope to the horizontal . The chart is nonorthogonal (no horizontal lines) and hence a little difficult to plot and interpret initially . However, the area of greatest interest is expanded, and they are therefore easy to read accurately . They tend to cover a wider temperature range than Grosvenor charts, so are useful for dryer calculations . The slope of the enthalpy lines is normally −1/λ, where λ is the latent heat of evaporation . Adiabatic saturation lines are not quite parallel to constant-enthalpy lines and are slightly curved; the deviation increases as humidity increases . Figure 12-3 shows an example .

The Salen-Soininen perspective transformed chart is a triangular plot . It is tricky to plot and read, but covers a much wider range of humidity than do the other types of chart (up to 2 kg/kg) and is thus very effective for highhumidity mixtures and calculations near the boiling point, e .g ., in pulp and paper drying . See Soininen, Drying Technol. 4(2): 295–305 (1986) . Figure 12-4 shows a psychrometric chart for combustion products in air . The thermodynamic properties of moist air are given in Table 12-1 . Figure 12-4 shows a number of useful additional relationships, e .g ., specific volume and latent heat variation with temperature . Accurate figures should always be obtained from physical properties tables or by calculation using the formulas given earlier, and these charts should only be used as a quick check for verification . Figure 12-5 shows a psychrometric chart for an organic solvent system . In the past, psychrometric charts have been used to perform quite precise calculations . To do this, additive corrections are often required for enthalpy of added water or ice, and for variations in barometric pressure from the standard level (101,325 Pa, 14 .696 lbf/in2, 760 mmHg, 29 .921 inHg) . It is preferable to use formulas, which give an accurate figure at any set of conditions . Psychrometric charts and tables can be used as a rough crosscheck that the result has been calculated correctly . Table 12-4 gives values of saturation humidity, specific volume, enthalpy, and entropy of saturated moist air at selected conditions . Below the freezing point, these become virtually identical to the values for dry air, as saturation humidity is very low . For pressure corrections, an altitude increase of approximately 275 m (900 ft) gives a pressure decrease of 0 .034 bar (1 inHg) . For a recorded wet-bulb temperature of 10°C (50°F), this gives an increase in humidity of 0 .00027 kg/kg (1 .9 gr/lb) and the enthalpy increases by 0 .68 kJ/kg (0 .29 Btu/lb) . This correction increases roughly proportionately for further changes in pressure, but climbs sharply as wet-bulb temperature is increased; when Twb reaches 38°C (100°F), ΔY = 0 .0016 kg/kg (11 .2 gr/lb) and ΔH = 4 .12 kJ/kg (1 .77 Btu/lb) . Equivalent, more detailed tables in SI units can be found in the ASHRAE Handbook . Examples Illustrating Use of Psychrometric Charts In these examples the following nomenclature is used: t = dry-bulb temperature, °F tw = wet-bulb temperature, °F td = dew point temperature, °F H = moisture content, lb water/lb dry air ΔH = moisture added to or rejected from airstream, lb water/lb dry air h′= enthalpy at saturation, Btu/lb dry air D = enthalpy deviation, Btu/lb dry air h = h′+ D = true enthalpy, Btu/lb dry air hw = enthalpy of water added to or rejected from system, Btu/lb dry air qa = heat added to system, Btu/lb dry air qr = heat removed from system, Btu/lb dry air Subscripts 1, 2, 3, etc ., indicate entering and subsequent states . Example 12-1 Determination of Moist Air Properties Find the properties of moist air when the dry-bulb temperature is 80°F and the wet-bulb temperature is 67°F . Solution Read directly from Fig . 12-2 (Fig . 12-6a shows the solution diagrammatically) . Moisture content H = 78 gr/lb dry air = 0 .011 lb water/lb dry air Enthalpy at saturation h′ = 31 .6 Btu/lb dry air Enthalpy deviation D = -0 .1 Btu/lb dry air True enthalpy h = 31 .5 Btu/lb dry air Specific volume υ = 13.8 ft3/lb dry air Relative humidity = 51 percent Dew point td = 60.3°F

Example 12-2 Air Heating Air is heated by a steam coil from 30°F dry-bulb temperature and 80 percent relative humidity to 75°F dry-bulb temperature. Find the relative humidity, wet-bulb temperature, and dew point of the heated air. Determine the quantity of heat added per pound of dry air. Solution Reading directly from the psychrometric chart (Fig. 12-2), Relative humidity = 15 percent Wet-bulb temperature = 51.5°F Dew point = 25.2°F

PSYCHROMETRY

12-7

FIG. 12-1 Grosvenor psychrometric chart for the air-water system at standard atmospheric pressure, 101,325 Pa, SI units .

(Courtesy Carrier Corporation .) The enthalpy of the inlet air is obtained from Fig . 12-2 as h1 = h′1 + D1 = 10 .1 + 0 .06 = 10 .16 Btu/lb dry air; at the exit, h2 = h′2 + D2 = 21 .1 - 0 .1 = 21 Btu/lb dry air . The heat added equals the enthalpy difference, or

this is by definition an adiabatic process and there will be no change in wet-bulb temperature . The only change in enthalpy is that from the heat content of the makeup water . This can be demonstrated as follows:

qa = Δh = h2 - h1 = 21 - 10 .16 = 10 .84 Btu/lb dry air If the enthalpy deviation is ignored, the heat added qa is Δh = 21 .1 - 10 .1 = 11 Btu/lb dry air, or the result is 1 .5 percent high . Figure 12-6b shows the heating path on the psychrometric chart .

Example 12-3  Evaporative Cooling Air at 95°F dry-bulb temperature and 70°F wet-bulb temperature contacts a water spray, where its relative humidity is increased to 90 percent . The spray water is recirculated; makeup water enters at 70°F . Determine the exit dry-bulb temperature, wet-bulb temperature, change in enthalpy of the air, and quantity of moisture added per pound of dry air . Solution Figure 12-6c shows the path on a psychrometric chart . The leaving dry-bulb temperature is obtained directly from Fig . 12-2 as 72 .2°F . Since the spray water enters at the wet-bulb temperature of 70°F and there is no heat added to or removed from it,

Then

Inlet moisture H1 = 70 gr/lb dry air Exit moisture H2 = 107 gr/lb dry air ΔH = 37 gr/lb dry air Inlet enthalpy h1 = h′1 + D1 = 34 .1 - 0 .22 = 33 .88 Btu/lb dry air Exit enthalpy h2 = h′2 + D2 = 34 .1 - 0 .02 = 34 .08 Btu/lb dry air Enthalpy of added water hw = 0 .2 Btu/lb dry air ( from small diagram, 37 gr at 70°F) qa = h2 − h1 + hw = 34.08 - 33.88 + 0.2 = 0

12-8

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-2 Grosvenor psychrometric chart (medium temperature) for the air-water system at standard atmospheric pressure, 29 .92 inHg,

USCS units . (Courtesy Carrier Corporation .)

FIG. 12-3 Mollier psychrometric chart for the air-water system at standard atmospheric pressure, 101,325 Pa SI units, plots humidity (abscissa) against enthalpy (lines sloping diagonally from top left to bottom right) . (Source: Aspen Technology.)

PSYCHROMETRY

FIG. 12-4 Grosvenor psychrometric chart for air and flue gases at high temperatures, molar units [Hatta, Chem. Metall. Eng. 37: 64 (1930)] .

200 200

220

240

260

280

180

300

320

340

360

2%

380

420

400

10%

5%

180 160 160 20%

120 100 80 60

Dry bulb

140 Temperature, °C

Enthalpy, kJ/kg dry gas

140

120

40%

100

60%

80

40

60

20

40

100%

40

20

20

0

45 Adiabatic saturation

35 25

0

50 Wet bulb

10 5 50

30 Adiabatic-saturation temperature, °C

15 100

150

200 300 250 Humidity, g vapor/kg dry gas

350

400

450

FIG. 12-5 Mollier chart showing changes in Twb during an adiabatic saturation process for an organic system (nitrogen-toluene) .

500

12-9

12-10

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

TABLE 12-4 Thermodynamic Properties of Saturated Air (USCS units, at standard pressure, 29.921 inHg) Condensed water Volume, ft3/lb dry air

Entropy, Btu/(°F⋅lb dry air)

Enthalpy, Btu/lb dry air

Entropy, Btu/ Vapor (lb⋅°F) pressure, inHg Temp . sw ps T, °F

Temp . T, °F

Saturation humidity Hs

υa

υas

υs

ha

sa

sas

ss

Enthalpy, Btu/lb hw

−150 −100

6 .932 × 10−9 9 .772 × 10−7

7 .775 9 .046

.000 .000

7 .775 9 .046

36 .088 24 .037

.000 .001

36 .088 24 .036

0 .09508 0 .05897

.00000 .00000

0 .09508 0 .05897

218 .77 201 .23

0 .4800 0 .4277

3 .301 × 10−6 4 .666 × 10−5

−150 −100

−50

4 .163 × 10−5

10 .313

.001

10 .314

12 .012

.043

11 .969

0 .02766

.00012

0 .02754

181 .29

0 .3758

1 .991 × 10−3

−50

−4

7 .872 × 10 1 .315 × 10−3 2 .152 × 10−3 3 .454 × 10−3 3 .788 × 10−3 3 .788 × 10−3 5 .213 × 10−3 7 .658 × 10−3 1 .108 × 10−2

11 .578 11 .831 12 .084 12 .338 12 .388 12 .388 12 .590 12 .843 13 .096

.015 .025 .042 .068 .075 .075 .105 .158 .233

11 .593 11 .856 12 .126 12 .406 12 .463 12 .463 12 .695 13 .001 13 .329

0 .000 2 .402 4 .804 7 .206 7 .686 7 .686 9 .608 12 .010 14 .413

.835 1 .401 2 .302 3 .709 4 .072 4 .072 5 .622 8 .291 12 .05

0 .835 3 .803 7 .106 10 .915 11 .758 11 .758 15 .230 20 .301 26 .46

0 .00000 .00518 .01023 .01519 .01617 .01617 .02005 .02481 .02948

.00192 .00314 .00504 .00796 .00870 .00870 .01183 .01711 .02441

0 .00192 .00832 .01527 .02315 .02487 .02487 .03188 .04192 .05389

158 .93 154 .17 149 .31 144 .36 143 .36 0 .04 8 .09 18 .11 28 .12

0 .3244 0 .3141 0 .3039 0 .2936 0 .2916 0 .0000 .0162 .0361 .0555

0 .037645 × 10−2 0 .062858 0 .10272 0 .16452 0 .18035 0 .18037 .24767 .36240 .52159

70 80 90 100 110 120 130

1 .582 × 10−2 2 .233 × 10−2 3 .118 × 10−2 4 .319 × 10−2 5 .944 × 10−2 8 .149 × 10−2 0 .1116

13 .348 13 .601 13 .853 14 .106 14 .359 14 .611 14 .864

.339 0 .486 .692 .975 1 .365 1 .905 2 .652

13 .687 14 .087 14 .545 15 .081 15 .724 16 .516 17 .516

16 .816 19 .221 21 .625 24 .029 26 .434 28 .841 31 .248

17 .27 24 .47 34 .31 47 .70 65 .91 90 .70 124 .7

34 .09 43 .69 55 .93 71 .73 92 .34 119 .54 155 .9

.03405 0 .03854 .04295 .04729 .05155 .05573 .05985

.03437 0 .04784 .06596 .09016 .1226 .1659 .2245

.06842 0 .08638 .10890 .13745 .1742 .2216 .2844

38 .11 48 .10 58 .08 68 .06 78 .03 88 .01 98 .00

.0746 0 .0933 .1116 .1296 .1472 .1646 .1817

.73915 1 .0323 1 .4219 1 .9333 2 .5966 3 .4474 4 .5272

70 80 90 100 110 120 130

140 150

0 .1534 0 .2125

15 .117 15 .369

3 .702 5 .211

18 .819 20 .580

33 .655 36 .063

172 .0 239 .2

205 .7 275 .3

.06390 .06787

.3047 .4169

.3686 .4848

107 .99 117 .99

.1985 .2150

5 .8838 7 .5722

140 150

160 170 180 190 200

0 .2990 0 .4327 0 .6578 1 .099 2 .295

15 .622 15 .874 16 .127 16 .379 16 .632

7 .446 10 .938 16 .870 28 .580 60 .510

23 .068 26 .812 32 .997 44 .959 77 .142

38 .472 40 .882 43 .292 45 .704 48 .119

337 .8 490 .6 748 .5 1255 2629

376 .3 531 .5 791 .8 1301 2677

.07179 .07565 .07946 .08320 .08689

.5793 .8273 1 .240 2 .039 4 .179

.6511 .9030 1 .319 2 .122 4 .266

128 .00 138 .01 148 .03 158 .07 168 .11

.2313 .2473 .2631 .2786 .2940

9 .6556 12 .203 15 .294 19 .017 23 .468

160 170 180 190 200

0 10 20 30 32 32∗ 40 50 60

has

hs

0 10 20 30 32 32∗ 40 50 60

note: Compiled by John A. Goff and S. Gratch. See also Keenan and Kaye. Thermodynamic Properties of Air, Wiley, New York, 1945. Enthalpy of dry air taken as zero at 0°F. Enthalpy of liquid water taken as zero at 32°F. To convert British thermal units per pound to joules per kilogram, multiply by 2326; to convert British thermal units per pound dry air-degree Fahrenheit to joules per kilogram-kelvin, multiply by 4186.8; and to convert cubic feet per pound to cubic meters per kilogram, multiply by 0.0624. ∗Entrapolated to represent metastable equilibrium with undercooled liquid.

Example 12-4 Cooling and Dehumidification Find the cooling load per pound of dry air resulting from infiltration of room air at 80°F dry-bulb temperature and 67°F wet-bulb temperature into a cooler maintained at 30°F dry-bulb and 28°F wet-bulb temperatures, where moisture freezes on the coil, which is maintained at 20°F . Solution The path followed on a psychrometric chart is shown in Fig . 12-6d . Inlet enthalpy h1 = h′1 + D1 = 31 .62 - 0 .1 = 31 .52 Btu/lb dry air Exit enthalpy h2 = h′2 + D2 = 10 .1 + 0 .06 = 10 .16 Btu/lb dry air Inlet moisture H1 = 78 gr/lb dry air

Exit moisture H2 = 19 gr/lb dry air Moisture rejected ΔH = 59 gr/lb dry air Enthalpy of rejected moisture = -1 .26 Btu/lb dry air ( from small diagram of Fig . 12-2) Cooling load qr = 31 .52 - 10 .16 + 1 .26 = 22 .62 Btu/lb dry air Note that if the enthalpy deviations were ignored, the calculated cooling load would be about 5 percent low .

Example 12-5 Cooling Tower Determine water consumption and the amount of heat dissipated per 1000 ft3/min of entering air at 90°F dry-bulb temperature and 70°F wet-bulb temperature when the air leaves saturated at 110°F and the makeup water is at 75°F . Solution The path followed is shown in Fig . 12-6e . Exit moisture H2 = 416 gr/lb dry air Inlet moisture H1 = 78 gr/lb dry air Moisture added ΔH = 338 gr/lb dry air Enthalpy of added moisture hw = 2 .1 Btu/lb dry air ( from small diagram of Fig . 12-2)

FIG. 12-6a Diagram of psychrometric chart showing

the properties of moist air .

FIG. 12-6b Heating process .

PSYCHROMETRY

FIG. 12-6c

12-11

Spray or evaporative cooling.

FIG. 12-6f

Drying process with recirculation.

Enthalpy of room air h1 = 30.2 − 0.3 = 29.9 Btu/lb dry air Enthalpy of entering air h3 = 92.5 − 1.3 = 91.2 Btu/lb dry air Enthalpy of leaving air h4 = 92.5 − 0.55 = 91.95 Btu/lb dry air Quantity of air required is 100/(0.0518 − 0.0418) = 10,000 lb dry air/h. At the dryer inlet the specific volume is 17.1 ft3/lb dry air. Air volume is (10,000)(17.1)/60 = 2850 ft3/min. Fraction exhausted is FIG. 12-6d Cooling and dehumidifying process.

X 0 .0518 − 0 .0418 = = 0 .247 Wa 0 .0518 − 0 .0113 where X = quantity of fresh air and Wa = total airflow. Thus 75.3 percent of the air is recirculated. Load on the preheater is obtained from an enthalpy balance qa = 10,000(91.2) − 2470(29.9) − 7530(91.95) = 146,000 Btu/h

PSYCHROMETRIC CALCULATIONS

FIG. 12-6e Cooling tower.

If greater precision is desired, hw can be calculated as hw = (338/7000)(1)(75 − 32) = 2 .08 Btu/lb dry air Enthalpy of inlet air h1 = h′1 + D1 = 34 .1 − 0 .18 = 33 .92 Btu/lb dry air Enthalpy of exit air h2 = h′2 + D2 = 92 .34 + 0 = 92 .34 Btu/lb dry air Heat dissipated = h2 − h1 − hw = 92 .34 − 33 .92 − 2 .08 = 56 .34 Btu/lb dry air Specific volume of inlet air = 14.1 ft3/lb dry air (1000)(56 .34) Total heat dissipated = = 3990 Btu/min 14 .1

Example 12-6 Recirculating Dryer A dryer is removing 100 lb water/h from the material being dried. The air entering the dryer has a dry-bulb temperature of 180°F and a wet-bulb temperature of 110°F. The air leaves the dryer at 140°F. A portion of the air is recirculated after mixing with room air having a dry-bulb temperature of 75°F and a relative humidity of 60 percent. Determine the quantity of air required, recirculation rate, and load on the preheater if it is assumed that the system is adiabatic. Neglect the heat up of the feed and of the conveying equipment. Solution The path followed is shown in Fig. 12-6f. Humidity of room air H1 = 0.0113 lb/lb dry air Humidity of air entering dryer H3 = 0.0418 lb/lb dry air Humidity of air leaving dryer H4 = 0.0518 lb/lb dry air

Table 12-5 gives the steps required to perform the most common humidity calculations, using the formulas given earlier. Methods (i) to (iii) are used to find the humidity and dew point from temperature readings from a wet- and dry-bulb psychrometer. Method (iv) is used to find the absolute humidity and dew point from a relative humidity measurement at a given temperature. Methods (v) and (vi) give the adiabatic saturation and wet-bulb temperatures from absolute humidity (or relative humidity) at a given temperature. Method (vii) gives the absolute and relative humidity from a dew point measurement. Method (viii) allows the calculation of all the main parameters if the absolute humidity is known, e.g., from a mass balance on a process plant. Method (ix) converts the volumetric form of absolute humidity to the mass form (mixing ratio). Method (x) allows the dew point to be corrected for pressure. The basis is that the mole fraction y = p/P is the same for a given mixture composition at all values of total pressure P. In particular, the dew point measured in a compressed air duct can be converted to the dew point at atmospheric pressure, from which the humidity can be calculated. It is necessary to check that the temperature change associated with compression or expansion does not bring the dry-bulb temperature to a point where condensation can occur. Also, at these elevated pressures, it is strongly advisable to apply the enhancement factor (see British Standard BS1339 Part 1). Psychrometric Software and Tables As an alternative to using charts or individual calculations, lookup tables have been published for many years for common psychrometric conversions, e.g., to find relative humidity given the dry-bulb and wet-bulb temperatures. These were often very extensive. To give precise coverage of Twb in 1°C or 0.1°C steps, a complete table would be needed for each individual dry-bulb temperature. Software is available that will perform calculations of humidity parameters for any point value, and for plotting psychrometric charts. Moreover, British Standard BS 1339 Part 2 (2006) provides functions as macros that can be embedded into any Excel-compatible spreadsheet. Users can therefore generate their own tables for any desired combination of parameters as well as perform point calculations. Hence, the need for published lookup tables has been eliminated. However, this software, like the previous lookup tables, is only valid for the air-water system. For other vapor-gas systems, the equations given in previous sections must be used.

12-12

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

TABLE 12-5 Calculation Methods for Various Humidity Parameters Known

Required

i .

T, Twb

Y

ii .

T, Twb

Tdp, dυ

iii . iv .

T, Twb T, %RH

%RH (ψ) Y, dυ

v .

T, %RH (or T, Y)

Tas

vi .

T, %RH (or T, Y)

Twb

vii .

T, Tdp

Y, %RH

T, Y T, Yυ Tdp at P1 (elevated)

Tdp, dυ, %RH, Twb Y Tdp at P2 (ambient)

viii . ix . x .

Method Find saturation vapor pressure pwb at wet-bulb temperature Twb from Eq . (12-4) . Find actual vapor pressure p at dry-bulb temperature T from psychrometer equation (12-11) . Find mixing ratio Y by conversion from p (Table 12-1) . Find p if necessary by method (i) above . Find dew point Tdp from Eq . (12-4) by calculating the T corresponding to p [iteration required; Antoine equation (12-5) gives a first estimate] . Calculate volumetric humidity Yυ, using Eq . (12-1) . Use method (i) to find p . Find saturation vapor pressure ps at T from Eq . (12-4) . Now relative humidity %RH = 100p/ps . Find saturation vapor pressure ps at T from Eq . (12-4) . Actual vapor pressure p = ps(%RH/100) . Convert to Y (Table 12-1) . Find Yυ from Eq . (12-1) . Use method (iv) to find p and Y . Make an initial estimate of Tas, say, using a psychrometric chart . Calculate Yas from Eq . (12-6) . Find p from Table 12-1 and Tas from Antoine equation (12-5) . Repeat until iteration converges (e .g ., using spreadsheet) . Alternative method: Evaluate enthalpy Hest at these conditions and H at initial conditions . Find Has from Eq . (12-7) and compare with Hest . Make new estimate of Yas which would give Hest equal to Has . Find p from Table 12-1 and Tas from Antoine equation (12-5) . Reevaluate Has from Eq . (12-7) and iterate to refine value of Yas . Use method (iv) to find p and Y . Make an initial estimate of Twb, e .g ., using a psychrometric chart, or ( for air-water system) by estimating adiabatic saturation temperature Tas . Find pwb from psychrometer equation (12-11) . Calculate new value of Twb corresponding to pwb by reversing Eq . (12-4) or using the Antoine equation (12-5) . Repeat last two steps to solve iteratively for Twb (computer program is preferable method) . Find saturation vapor pressure at dew point Tdp from Eq . (12-4); this is the actual vapor pressure p . Find Y from Table 12-1 . Find saturation vapor pressure ps at dry-bulb temperature T from Eq . (12-4) . Now %RH = 100p/ps . Find p by conversion from Y (Table 12-1) . Then use method (ii), (iii), or (v) as appropriate . Find specific humidity YW from Eqs . (12-2) and (12-1) . Convert to absolute humidity Y using Y = YW/(1 − YW) . Find vapor pressure p1 at Tdp and P1 from Eq . (12-4) . Convert to vapor pressure p2 at new pressure P2 by the formula p2 = p1P2/P1 . Find new dew point Tdp from Eq . (12-4) by calculating the T corresponding to p2 [iteration required as in (ii)] .

Software may be effectively used to draw psychrometric charts or perform calculations . A wide variety of other psychrometric software may be found on the Internet, but quality varies considerably; the source and basis of the calculation methods should be carefully checked before using the results . In particular, most methods only apply for the air-water system at moderate temperatures (below 100°C) . For high-temperature dryer calculations, only software stated as suitable for this range should be used . Reliable sources include the following: 1 . The American Society of Agricultural Engineers (ASAE): http://www .asae .org . Psychrometric data in chart and equation form in both SI and USCS units . Charts for temperature ranges of −35 to 600°F in USCS units and −10 to 120°C in SI units . Equations and calculation procedures . Air-water system and Grosvenor (temperature-humidity) charts only . 2 . The American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE): http://www .ashrae .org . Psychrometric Analysis CD with energy calculations and creation of custom charts at virtually any altitude or pressure . Detailed scientific basis given in ASHRAE Handbook . Air-water system and Grosvenor charts only . 3 . Carrier Corporation, a United Technologies Company: http://www .training .carrier .com . PSYCH+, computerized psychrometric chart and instructional guide, including design of air-conditioning processes and/or cycles . Printed psychrometric charts also supplied . Air-water system and Grosvenor charts only . 4 . Linric Company: http://www .linric .com . PsycPro generates custom psychrometric charts in English (USCS) or metric (SI) units, based on ASHRAE formulas . Air-water system and Grosvenor charts only . 5 . Aspen Technology: http://www .aspentech .com . PSYCHIC, one of the Process Tools in the Aspen Engineering Suite, generates customized psychrometric charts . Mollier and Bowen enthalpy-humidity charts are produced in addition to Grosvenor . Any gas-vapor system can be handled as well as air-water; data supplied for common organic solvents . It can draw operating lines and spot points, as shown in Fig . 12-7 . 6 . British Standards Institution: http://www .bsigroup .com . British Standard BS 1339 Part 2 is a spreadsheet-based software program providing functions based on the latest internationally agreed standards . It calculates all key psychrometric parameters and can produce a wide range of psychrometric tables . Users can embed the functions in their own spreadsheets to do psychrometric calculations . Air-water system only (although BS 1339 Part 1 text gives full calculation methods for other gas-vapor systems) . SI (metric) units . It does not plot psychrometric charts . 7 . Akton Associates: http://www .aktonassoc .com . Akton provides digital versions of psychrometry charts .

PSYCHROMETRIC CALCULATIONS—WORKED EXAMPLES Example 12-7 Determination of Moist Air Properties An air-water mixture is found from the heat and mass balance to be at 60°C (333 K) and 0 .025 kg/kg (25 g/kg) absolute humidity . Calculate the other main parameters for the mixture . Take atmospheric pressure as 101,325 Pa . Method: Consult item (vi) in Table 12-5 for the calculation methodology . From the initial terminology section, specific humidity YW = 0 .02439 kg/kg, mole ratio z = 0 .0402 kmol/kmol, mole fraction y = 0 .03864 kmol/kmol .

From Table 12-1, vapor pressure p = 3915 Pa (0 .03915 bar) and volumetric humidity Yυ = 0 .02547 kg/m3 . Dew point is given by the temperature corresponding to p at saturation . From the reversed Antoine equation (12-5), Tdp = 3830/(23 .19 − ln 3915) + 44 .83 = 301 .58 K = 28 .43°C . Relative humidity is the ratio of actual vapor pressure to saturation vapor pressure at drybulb temperature . From the Antoine equation (12-5), ps = exp [23 .19 − 3830/(333 .15 − 44 .83)] = 20,053 Pa (new coefficients), or ps = exp [23 .1963 − 3816 .44/(333 .15 − 46 .13)] = 19,921 Pa (old coefficients) . From Sonntag equation (12-4), ps = 19,948 Pa; the difference from the Antoine is less than 0 .5 percent . Relative humidity = 100 × 3915/19,948 = 19 .6 percent . From a psychrometric chart, e .g ., Fig . 12-1, a humidity of 0 .025 kg/kg at T = 60°C lies very close to the adiabatic saturation line for 35°C . Hence a good first estimate for Tas and Twb will be 35°C . Refining the estimate of Twb by using the psychrometer equation and iterating gives pwb = 3915 + 6 .46 × 10−4 (1 .033)(101,325) (60 − 35) = 5605 Pa From the Antoine equation, Twb = 3830/(23 .19 − ln 5605) + 44 .83 = 307 .9 K = 34 .75°C Second iteration: pwb = 3915 + 6 .46 × 10−4(1 .033)(101,325)(60 − 34 .75) = 5622 Pa Twb = 307 .96 K = 34 .81°C To a sensible level of precision, Twb = 34 .8°C . From Table 12-1, Ywb = 5622 × 0 .622/(101,325 − 5622) = 0 .0365(4) kg/kg . Enthalpy of original hot air is approximately given by H = (CPg + CPυY) (T − T0) + λ0Y (1 + 1 .9 × 0 .025) × 60 + 2501 × 0 .025 = 62 .85 + 62 .5 = 125 .35 kJ/kg . A more accurate calculation can be obtained from steam tables; CPg = 1 .005 kJ/ (kg ⋅ K) over this range, Hυ at 60°C = 2608 .8 kJ/kg, H = 60 .3 + 65 .22 = 125 .52 kJ/kg . Calculation (v), method 1: If Tas = 34 .8, from Eq . (12-6), with Cs = 1 + 1 .9 × 0 .025 = 1 .048 kJ/ (kg ⋅ K), then λas = 2419 kJ/kg (steam tables), Yas = 0 .025 + 1 .048/2419 (60 − 34 .8) = 0 .0359(2) kg/kg . From Table 12-1, p = 5530 Pa . From the Antoine equation (12-5), Tas = 3830/(23 .19 − ln 5530) + 44 .83 = 307 .65 K = 34 .52°C . Repeat until iteration converges (e .g ., using spreadsheet) . Final value Tas = 34 .57°C, Yas = 0 .0360 kg/kg . Enthalpy check: From Eq . (12-7), Has − H = 4 .1868 × 34 .57 × (0 .036 − 0 .025) = 1 .59 kJ/kg . So Has = 127 .11 kJ/kg . Compare Has calculated from enthalpies; Hg at 34 .57°C = 2564 kJ/kg, Hest = 34 .90 + 92 .29 = 127 .19 kJ/kg . The iteration has converged successfully . Note that Tas is 0 .2°C lower than Twb and Yas is 0 .0005 kg/kg lower than Ywb, both negligible differences .

Example 12-8 Calculation of Humidity and Wet-Bulb Condition A dryer exhaust which can be taken as an air-water mixture at 70°C (343 .15 K) is measured to have a relative humidity of 25 percent . Calculate the humidity parameters and wet-bulb conditions for the mixture . Pressure is 1 bar (100,000 Pa) . Method: Consult item (v) in Table 12-5 for the calculation methodology . From the Antoine equation (12-5), using standard coefficients (which give a better fit in this temperature range), ps = exp[23 .1963 − 3816 .44/(343 .15 − 46 .13)] = 31,170 Pa . Actual vapor pressure p = 25 percent of 31,170 = 7792 Pa (0 .078 bar) . From Table 12-1, absolute humidity Y = 0 .05256 kg/kg and volumetric humidity Yυ = 0 .0492 kg/m3 . From the terminology section, mole fraction y = 0 .0779 kmol/kmol, mole ratio z = 0 .0845 kmol/kmol, specific humidity YW = 0 .04994 kg/kg . Dew point Tdp = 3816 .44/(23 .1963 − ln 7792) + 46 .13 = 314 .22 K = 41 .07°C

PSYCHROMETRY

12-13

Mollier Chart for Nitrogen/Acetone at 10 kPa 140

160

180

200

220

240

260

120 80

100 80

60

Enthalpy (kJ/kg)

40 40 20

20 0

0

− 20

Gas temperature (°C)

60

− 20

− 40 − 40 − 60 0

0.02

0.04

0.06

0.08

0.1 Gas humidity

0.12

0.14

0.16

Boiling Pt

Sat line

Adiabat sat

Triple Pt

Rel humid

Spot point

0.18

0.2

FIG. 12-7 Mollier psychrometric chart ( from PSYCHIC software program) showing determination of adiabatic saturation temperature plots of humidity

(abscissa) against enthalpy (lines sloping diagonally from top left to bottom right) . (Courtesy AspenTech.)

From the psychrometric chart, a humidity of 0 .0526 kg/kg at T = 70°C falls just below the adiabatic saturation line for 45°C . Estimate Tas and Twb as 45°C . Refining the estimate of Twb by using the psychrometer equation and iterating gives

From the Antoine equation (12-5), ln ps = C 0 −

pwb = 7792 + 6 .46 × 10−4 (1 .0425)(105)(70 − 45) = 9476 From the Antoine equation, Twb = 3816 .44/(23 .1963 − ln 9476) + 46 .13 = 317 .96 K = 44 .81°C Second iteration (taking Twb = 44 .8):

Since T = 60°C, ln ps = 6 .758, ps = 861 .0 mmHg . Hence ps = 1 .148 bar = 1 .148 × 105 Pa . The saturation vapor pressure is higher than atmospheric pressure; this means that acetone at 60°C must be above its normal boiling point . Check: Tbp for acetone = 56 .5°C . Vapor pressure p = yP = 0 .01191 × 10,000 = 119 .1 Pa (0 .001191 bar)—much lower than before because of the reduced total pressure . This is 0 .89 mmHg . Volumetric humidity Yυ = 0 .0025 kg/m3—again substantially lower than at 1 atm . Dew point is the temperature where ps equals p′ . From the reversed Antoine equation (12-5),

pwb = 9489Twb = 317 .99 K = 44 .84°C The iteration has converged .

Example 12-9 Calculation of Psychrometric Properties of Acetone/ Nitrogen Mixture A mixture of nitrogen N2 and acetone CH3COCH3 is found from the heat and mass balance to be at 60°C (333 K) and 0 .025 kg/kg (25 g/kg) absolute humidity (same conditions as in Example 12-7) . Calculate the other main parameters for the mixture . The system is under vacuum at 100 mbar (0 .1 bar, 10,000 Pa) . Additional data for acetone and nitrogen are obtained from The Properties of Gases and Liquids (Prausnitz et al .) . Molecular weight (molal mass) Mg for nitrogen = 28 .01 kg/kmol; for acetone Mυ = 58 .08 kg/kmol . Antoine coefficients for acetone are 16 .6513, 2940 .46, and 35 .93, with ps in mmHg and T in K . Specific heat capacity of nitrogen is approximately 1 .014 kJ/(kg ⋅ K) . Latent heat of acetone is 501 .1 kJ/kg at the boiling point . The psychrometric ratio for the nitrogen-acetone system is not given, but the diffusion coefficient D can be roughly evaluated as 1 .34 × 10−5, compared to 2 .20 × 10−5 for water in air . As the psychrometric ratio is linked to D2/3, it can be estimated as 0 .72, which is in line with tabulated values for similar organic solvents (e .g ., propanol) . Method: Consult item (vi) in Table 12-5 for the calculation methodology . From the terminology, specific humidity YW = 0 .02439 kg/kg, the same as in Example 12-7 . Mole ratio z = 0 .0121 kmol/kmol, mole fraction y = 0 .01191 kmol/kmol—lower than in Example 12-7 because molecular weights are different .

2940 .46 C1 = 16 .6513 − T − C2 T − 35 .93

T=

C1 + C2 C 0 − ln ps

so Tdp =

2940 + 35 .93 = 211 .27 K = −61 .88°C 16 .6513 − ln 0 .89

This very low dew point is due to the low boiling point of acetone and the low concentration . Relative humidity is the ratio of actual vapor pressure to saturation vapor pressure at dry-bulb temperature . So p = 119 .1 Pa, ps = 1 .148 × 105 Pa, RH = 0 .104 percent—again very low . A special psychrometric chart would need to be constructed for the acetone-nitrogen system to get first estimates (this can be done using PSYCHIC, as shown in Fig . 12-7) . A humidity of 0 .025 kg/kg at T = 60°C lies just below the adiabatic saturation line for −40°C . The wet-bulb temperature will not be the same as Tas for this system; since the psychrometric ratio β is less than 1, Twb should be significantly above Tas . However, let us assume no good first estimate is available and simply take Twb to be 0°C initially . When using the psychrometer equation, we will need to use Eq . (12-13) to obtain the value of the psychrometer coefficient . Using the tabulated values above, we obtain A = 0 .00135, about double the value for air-water . We must remember that the

12-14

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

estimate will be very rough because of the uncertainty in the value of β . Refining the estimate of Twb by using the psychrometer equation and iterating gives pwb = 119 .1 + 1 .35 × 10−3 (104) (60 − 0) = 932 .3 Pa = 7 .0 mmHg From the Antoine equation, Twb = 2940/(16 .6513 − ln 7) + 35 .93 = 235 .84 K = −37 .3°C Second iteration: pwb = 119 .1 + 1 .35 × 10−3 (104) (60 + 37 .3) = 1433 Pa = 10 .7 mmHg Twb = 241 .85 K = −31 .3°C Third iteration: pwb = 119 .1 + 1 .35 × 10−3 (104) (60 + 31 .3) = 1352 Pa = 10 .1 mmHg Twb = 241 .0 K = −32 .1°C The iteration has converged successfully, despite the poor initial guess . The wet-bulb temperature is −32°C; given the levels of error in the calculation, it will be meaningless to express this to any greater level of precision . In a similar way, the adiabatic saturation temperature can be calculated from Eq . (12-6) by taking the first guess as −40°C and assuming the humid heat to be 1 .05 kJ/(kg ⋅ K) including the vapor: Yas = Y +

Cs (T − Tas ) λ as

1 .05  (60 + 40) = 0 .235 kg/kg = 0 .025 +   501 .1  From Table 12-2, pas = 1018 Pa = 7 .63 mmHg From the Antoine equation, Tas = 237 .05 K = −36 .1°C Second iteration: Yas = 0 .025 + (1 .05/501 .1)(60 + 36 .1) = 0 .226 kg/kg pas = 984 Pa = 7 .38 mmHg From the Antoine equation, Tas = 236 .6 K = −36 .6°C This has converged . A more accurate figure could be obtained with more refined estimates for Cs and λwb .

MEASUREMENT OF HUMIDITY Hygrometers Electric hygrometers have been the fastest-growing form of humidity measurement in recent years and are now the most commonly

used sensors for process measurement . They measure the electrical resistance, capacitance, or impedance of a film of moisture-absorbing materials exposed to the gas . A wide variety of sensing elements are used . Normally, relative humidity is measured, with a corresponding temperature measurement and conversion to absolute humidity . Mechanical hygrometers utilizing materials such as human hair, wood fiber, and plastics have been used to measure humidity . These methods rely on a change in dimension with humidity . They are not suitable for process use . Other hygrometric techniques in process and laboratory use include electrolytic and piezoelectric hygrometers, infrared and mass spectroscopy, and vapor pressure measurement, e .g ., by a Pirani gauge . The gravimetric method is accepted as the most accurate humidity-measuring technique . In this method a known quantity of gas is passed over a moisture-absorbing chemical such as phosphorus pentoxide, and the increase in weight is determined . It is mainly used for calibrating standards and measurements of gases with SOx present . Dew Point Method The dew point of wet air is measured directly by observing the temperature at which moisture begins to form on an artificially cooled, polished surface . Optical dew point hygrometers employing this method are often used as a fundamental technique for determining humidity . Uncertainties in temperature measurement of the polished surface, gradients across the surface, and the appearance or disappearance of fog have been much reduced in modern instruments . Automatic mirror cooling, e .g ., Peltier thermoelectric, is more accurate and reliable than older methods using evaporation of a low-boiling solvent such as ether, or external coolants (e .g ., vaporization of solid carbon dioxide or liquid air, or water cooling) . Contamination effects have also been reduced or compensated for, but regular recalibration is still required, at least once a year . Wet-Bulb/Dry-Bulb Method In the past, probably the most commonly used method for determining the humidity of a gas stream was the measurement of wet- and dry-bulb temperatures . The wet-bulb temperature is measured by contacting the air with a thermometer whose bulb is covered by a wick saturated with water . If the process is adiabatic, the thermometer bulb attains the wet-bulb temperature . When the wet- and drybulb temperatures are known, the humidity is readily obtained from charts such as Figs . 12-1 through 12-4 . To obtain reliable information, care must be exercised to ensure that the wet-bulb thermometer remains wet and that radiation to the bulb is minimized . The latter is accomplished by making the relative velocity between wick and gas stream high [a velocity of 4 .6 m/s (15 ft/s) is usually adequate for commonly used thermometers] or by the use of radiation shielding . In the Assmann psychrometer, the air is drawn past the bulbs by a motor-driven fan . Making sure that the wick remains wet is a mechanical problem, and the method used depends to a large extent on the particular arrangement . Again, as with the dew point method, errors associated with the measurement of temperature can cause difficulty . For measurement of atmospheric humidities, the sling or whirling psychrometer was widely used in the past to give a quick and cheap, but inaccurate, estimate . A wet- and dry-bulb thermometer is mounted in a sling which is whirled manually to give the desired gas velocity across the bulb . In addition to the mercury-in-glass thermometer, other temperaturesensing elements may be used for psychrometers . These include resistance thermometers, thermocouples, bimetal thermometers, and thermistors .

EVAPORATIVE COOLING General References: ASHRAE is the American Society of Heating, Refrigeration and Air Conditioning Engineers: www .ashrae .org; ASHRAE Handbook of Fundamentals, “Climatic Design Information,” chap . 14, ASHRAE, Atlanta, Ga ., 2013 . Cooling Technology Institute: www .cti .org . ASHRAE and CTI are both professional organizations and both websites contain technical resources and contacts for engineers .

INTRODUCTION Evaporative cooling, using recirculated cooling water systems, is the method most widely used throughout the process industries for employing water to remove process waste heat, rejecting that waste heat into the environment . Maintenance considerations (water-side fouling control), through control of makeup water quality and control of cooling water chemistry, form one reason for this preference . Environmental considerations—by minimizing consumption of potable water, minimizing the generation and release of contaminated cooling water, and controlling the release into the

environment of chemicals from leaking heat exchangers—form the second major reason . Local ambient climatic conditions, particularly the maximum summer wet-bulb temperature, determine the design of the evaporative equipment . Typically, the wet-bulb temperature used for design is the 0 .4 percent value, as listed in the ASHRAE Handbook of Fundamentals, equivalent to 35-h exceedance per year on average . The first subsection below presents the classic cooling tower (CT), the evaporative cooling technology most widely used today . The second subsection presents the wet surface air cooler (WSAC), a more recent technology, combining within one piece of equipment the functions of cooling tower, circulated cooling water system, and heat exchange tube bundle . The most common application for WSACs is in the direct cooling of process streams . However, the closed-circuit cooling tower, employing WSACs for cooling the circulated cooling water (replacing the CT), is an important alternative WSAC application, presented at the end of this section .

EVAPORATIVE COOLING 180

12-15

A h′ (Hot water temperature)

Enthalpy, kJ/kg of dry air

160 h (Air out)

140

u

Eq

120 h′ (Cold water temperature)

100

riu ilib

m

e lin D

B

iing

at per

O

h (Air in)

80

Twet bulb, in

60 20

25

line

C Twater, in 30

Twet bulb, out 35

Twater, out 40

45

Temperature, °C FIG. 12-8

Cooling-tower process heat balance and solution to Example 12-10 .

To minimize the total annualized costs for evaporative cooling is a complex engineering task in itself, separate from classic process design . The evaluation and the selection of the best option for process cooling impact many aspects of how the overall project will be optimally designed (utilities supply, reaction and separations design, pinch analyses, 3D process layout, plot plan, etc .) . Therefore, evaluation and selection of the evaporative cooling technology system should be performed at the start of the project design cycle, during conceptual engineering (Sec . 9, Process Economics, Value Improving Practices), when the potential to influence project costs is at a maximum value (Sec . 9, VIP Fig . 9-26). The relative savings achievable for selection of the optimum heat rejection technology option can frequently exceed 25 percent, for the installed cost for the technology alone . PRINCIPLES The processes of cooling water are among the oldest known . Usually water is cooled by exposing its surface to air . Some of the processes are slow, such as the cooling of water on the surface of a pond; others are comparatively fast, such as the spraying of water into air . These processes all involve the exposure of water surface to air in varying degrees . The heat-transfer process involves (1) latent heat transfer owing to vaporization of a small portion of the water and (2) sensible heat transfer owing to the difference in temperatures of water and air . Approximately 80 percent of this heat transfer is due to latent heat and 20 percent to sensible heat . COOLING TOWERS General References: Hensley, Cooling Tower Fundamentals, 2d ed ., Marley Cooling Technologies,∗ Bridgewater, N .J ., 1998 . McAdams, Heat Transmission, 3d ed ., McGraw-Hill, New York, 1954, pp . 356–365 . Extensive information can be found online at the following websites: www .cti .org; www .ashrae .org; www .marleyct .com; www .spxcooling .com .

Process Description A cooling tower is a simultaneous heat- and mass-transfer device that cools a hot process water stream directly by evaporation into ambient air . The water is pumped up to the top of the tower and sprayed into flowing ambient air . The tower contains a packing (called fill ) to increase the surface area of contact of the water with the air as it falls to the cool water collection basin . The fill is commonly made from wood slats or PVC . Theoretical possible heat removal per unit mass of air circulated in a cooling tower depends on the temperature and moisture content of air . An indication of the moisture content of the air is its wet-bulb temperature . Ideally, then, the wet-bulb temperature is the lowest theoretical temperature to which the water can be cooled . Practically, the cold water temperature approaches but does not equal the air wet-bulb temperature in a cooling tower; this is so because it is impossible to contact all the ∗The contributions of Ken Mortensen and coworkers of Marley Cooling Technologies, Overland Park, Kansas, toward the review and update of this subsection are gratefully acknowledged .

water with fresh air as the water drops through the wetted fill surface to the basin . The magnitude of the approach to the wet-bulb temperature is dependent on the tower design . Important factors are air-to-water contact time, amount of fill surface, and breakup of water into droplets . In actual practice, cooling towers are seldom designed for approaches closer than 2 .8°C (5°F) . Cooling Tower Theory The most generally accepted theory of the cooling tower heat-transfer process is that developed by Merkel [Merkel, Z. Ver. Dtsch. Ing. Forsch., no . 275 (1925)] . The theory is developed using the same approach as the HTU-NTU model for mass or heat transfer in packed columns . Mass and energy balances are constructed within a differential vertical increment and then integrated over the height of the tower . The Merkel equation combines the mass- and heat-transfer processes to arrive at one driving force—enthalpy to capture the simultaneous heat- and masstransfer processes in one equation . Both the Chilton-Colburn analogy and the fact that the Lewis number is near unity (see Psychrometry subsection) for air-water systems are used to derive the equation; this treatment is only valid for air-water systems . See Wankat, Equilibrium Staged Separations, Elsevier, 1988, pp . 674–688 for a lucid and detailed description of this equation and a worked example . In the integrated form, the Merkel equation is given by T1 C dT Ka V L =∫ T2 h ′ − h L

(12-14)

where K = mass-transfer coefficient, kg water/(m2 ⋅ s); a = contact area, m2/m3 tower volume; V = active cooling volume, m3/m2 of plan area; L = water rate, kg/(m2 ⋅ s); CL = heat capacity of water, J/(kg ⋅ °C); h′= enthalpy of saturated air at water temperature, J/kg; h = enthalpy of airstream, J/kg; and T1 and T2 = entering and leaving water temperatures, °C . The right-hand side of Eq . (12-14) is entirely in terms of air and water properties and is independent of tower dimensions . The left-hand side is the “tower characteristic,” KaV/L, which can be determined by integration . To predict tower performance, it is necessary to know the required tower characteristics for fixed ambient and water conditions . Figure 12-8 illustrates water and air relationships and the driving potential which exist in a counterflow tower, where air flows parallel but opposite in direction to water flow . An understanding of this diagram is important in visualizing the cooling tower process and evaluating the integral in the Merkel equation . Figure 12-8 is an enthalpy-temperature diagram, containing two lines: an equilibrium line and an operating line . The equilibrium line is shown by AB . This line represents the enthalpy of saturated water vapor . It can be plotted using the definition of humid enthalpy in the Psychrometry subsection . h ′ = (C P , g + C P , y ⋅Y )(T − T0 ) + λ 0Y

(12-15)

If we choose a reference temperature of 0°C, then λ0 = 2501 kJ/kg . The absolute humidity at saturation is found first by calculating the vapor

12-16

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

pressure (at T ) using Eq . (12-5) and then by using the following relationship from Table 12-1: Y=

0 .622 ⋅ p P− p

(12-16)

The operating line describes the enthalpy of the air moving through the tower and is given by line CD . The highest temperature is that of the water entering (point D), and the lowest is that of the water leaving (point C ) . This difference is called the range . The difference between the wet-bulb temperature of the air entering and the temperature of the water exiting is called the approach . The operating line is given by L h − hwet bulb, air in =  ⋅C p , water  ⋅ (T − Twater , out ) G 

(12-17)

The enthalpy of the wet-bulb temperature is on the equilibrium line, and it is found by using the same procedure as outlined above . Mechanical draft cooling towers normally are designed for L/G ratios ranging from 0 .75 to 1 .50; accordingly, the values of KaV/L vary from 0 .50 to 2 .50 . The tower characteristic contains the kinetic information in the design, which is affected by the nature of the fill and the velocity of the air . A useful discussion on optimization of cooling towers is found in Picardo, J . R ., Energy Conversion and Management 57: 167–172 (2012) . Some practical guidelines on the height and cross-sectional area are given below . Example 12-10 Calculation of Mass-Transfer Coefficient Group Determine the theoretically required KaV/L value for a cooling duty from 41°C inlet water, 29 .4°C outlet water, 25°C ambient wet-bulb temperature, and an L/G ratio of 1 .2 . We first evaluate the equilibrium and operating lines over the temperature range of interest . These are plotted as Fig . 12-8 . The enthalpy h of the air at the wet-bulb temperature equals 74 .75 kJ/kg, using Eqs . (12-5), (12-15), and (12-16) . Numerical integration of the Merkel equation using a spreadsheet gives KaV/L = 2 .32 . Cooling Tower Equipment The airflow in a cooling tower is driven by fans or by natural convection . When fans are used, it is called a mechanical draft tower . Two types are in use today, the forced-draft and the induceddraft towers . In the forced-draft tower, the fan is mounted at the base, and air is forced in at the bottom and discharged at low velocity through the top . This arrangement has the advantage of locating the fan and drive outside the tower, where it is convenient for inspection, maintenance, and repairs . Since the equipment is out of the hot, humid top area of the tower, the fan is not subjected to corrosive conditions . However, because of the low exitair velocity, the forced-draft tower is subjected to excessive recirculation of the humid exhaust vapors back into the air intakes . Since the wet-bulb temperature of the exhaust air is considerably higher than the wet-bulb temperature of the ambient air, there is a decrease in performance evidenced by an increase in cold (leaving) water temperature . The induced-draft tower is the most common type used in the United States . It is further classified into counterflow and cross-flow design, depending on the relative flow directions of water and air . Thermodynamically, the counterflow arrangement is more efficient, since the coldest water contacts the coldest air, thus obtaining maximum enthalpy potential . The greater the cooling ranges and the more difficult the approaches, the more distinct are the advantages of the counterflow type . The cross-flow tower manufacturer may effectively reduce the tower characteristic at very low approaches by increasing the air quantity to give a lower L/G ratio . The increase in airflow is not necessarily achieved by increasing the air velocity, but primarily by lengthening the tower to increase the airflow cross-sectional area . It appears then that the cross-flow fill can be made progressively longer in the direction perpendicular to the airflow and shorter in the direction of the airflow until it almost loses its inherent potential-difference disadvantage . However, as this is done, fan power consumption increases . Ultimately, the economic choice between counterflow and cross-flow is determined by the effectiveness of the fill, design conditions, water quality, and costs of tower manufacture . Performance of a given type of cooling tower is governed by the ratio of the weights of air to water and the time of contact between water and air . In commercial practice, the variation in the ratio of air to water is first obtained by keeping the air velocity constant at about 1148 m/(min ⋅ m2) of active tower area [350 ft/(min ⋅ ft2 of active tower area)] and varying the water concentration, L/(min ⋅ m2 of ground area) [gal/(min ⋅ ft2 of tower area)] . As a secondary operation, air velocity is varied to make the tower accommodate the cooling requirement . The time of contact between water and air is governed largely by the time required for the water to discharge from the nozzles and fall through the tower to the basin . The time of contact is therefore obtained in a given type of unit by varying the height of the tower . Should the time of contact be

insufficient, no amount of increase in the ratio of air to water will produce the desired cooling . It is therefore necessary to maintain a certain minimum height of cooling tower . When a wide approach of 8 to 11°C (15 to 20°F) to the wet-bulb temperature and a 13 .9 to 19 .4°C (25 to 35°F) cooling range are required, a relatively low cooling tower will suffice . A tower in which the water travels 4 .6 to 6 .1 m (15 to 20 ft) from the distributing system to the basin is sufficient . When a moderate approach and a cooling range of 13 .9 to 19 .4°C (25 to 35°F) are required, a tower in which the water travels 7 .6 to 9 .1 m (25 to 30 ft) is adequate . Where a close approach of 4 .4°C (8°F) with a 13 .9 to 19 .4°C (25 to 35°F) cooling range is required, a tower is required in which the water travels from 10 .7 to 12 .2 m (35 to 40 ft) . It is usually not economical to design a cooling tower with an approach of less than 2 .8°C (5°F) . The cooling performance of any tower containing a given depth of fill varies with the water concentration . It has been found that maximum contact and performance are obtained with a tower having a water concentration of 80 to 200 L/(min ⋅ m2 of ground area) [2 to 5 gal/(min ⋅ ft2 of ground area)] . Thus the problem of calculating the size of a cooling tower becomes one of determining the proper concentration of water required to obtain the desired results . Once the necessary water concentration has been established, the tower area can be calculated by dividing the liters per minute circulated by the water concentration in liters per minute per square meter . The required tower size then is a function of the following: 1 . Cooling range (hot water temperature minus cold water temperature) 2 . Approach to wet-bulb temperature (cold water temperature minus wet-bulb temperature) 3 . Quantity of water to be cooled 4 . Wet-bulb temperature 5 . Air velocity through the cell 6 . Tower height These considerations in combination with the Markel equation can help engineers with basic conceptual designs that can be used in conjunction with vendors for process design . Cooling Tower Operation: Water Makeup It is the open nature of evaporative cooling systems, bringing in external air and water continuously, that determines the unique water problems these systems exhibit . Cooling towers (1) concentrate solids by the mechanisms described above and (2) wash air . The result is a buildup of dissolved solids, suspended contaminants, organics, bacteria, and their food sources in the circulating cooling water . These unique evaporative water system problems must be specifically addressed to maintain cooling equipment in good working order . Makeup requirements for a cooling tower consist of the sum of evaporation loss, drift loss, and blowdown . Therefore, Wm = We + Wd + Wb

(12-18)

where Wm = makeup water, We = evaporation loss, Wd = drift loss, and Wb = blowdown (consistent units: m3/h or gal/min) . Evaporation loss can be estimated by We = 0 .00085Wc(T1 − T2)

(12-19)

where Wc = circulating water flow, m3/h or gal/min, at tower inlet and T1 − T2 = inlet water temperature minus outlet water temperature, °F . The 0 .00085 evaporation constant is a good rule-of-thumb value . The actual evaporation rate will vary by season and climate . Drift loss can be estimated by Wd = 0 .0002Wc

(12-20)

Drift is entrained water in the tower discharge vapors . Drift loss is a function of the drift eliminator design and is typically less than 0 .02 percent of the water supplied to the tower given the new developments in eliminator design . Blowdown discards a portion of the concentrated circulating water due to the evaporation process in order to lower the system solids concentration . The amount of blowdown can be calculated according to the number of cycles of concentration required to limit scale formation . The cycles of concentration are the ratio of dissolved solids in the recirculating water to dissolved solids in the makeup water . Since chlorides remain soluble on concentration, cycles of concentration are best expressed as the ratio of the chloride contents of the circulating and makeup waters . Thus, the blowdown quantities required are determined from Cycles of concentration =

or

Wb =

We + Wb + Wd Wb + Wd

We − (cycles − 1) Wd cycles − 1

(12-21)

(12-22)

EVAPORATIVE COOLING

12-17

TABLE 12-6 Blowdown (Percent) Range, °F 10 15 20 25 30

2X

3X

4X

5X

6X

0 .83 1 .26 1 .68 2 .11 2 .53

0 .41 0 .62 0 .83 1 .04 1 .26

0 .26 0 .41 0 .55 0 .69 0 .83

0 .19 0 .30 0 .41 0 .51 0 .62

0 .15 0 .24 0 .32 0 .41 0 .49

Cycles of concentration involved with cooling tower operation normally range from 3 to 5 cycles . For water qualities where operating water concentrations must be below 3 to control scaling, blowdown quantities will be large . The addition of acid or scale-inhibiting chemicals can limit scale formation at higher cycle levels and will allow substantially reduced water usage for blowdown . The blowdown equation (12-22) translates to calculated percentages of the cooling system circulating water flow exiting to drain, as listed in Table 12-6 . The blowdown percentage is based on the cycles targeted and the cooling range . The range is the difference between the system hot water and cold water temperatures . Example 12-11 Calculation of Makeup Water Determine the amount of makeup required for a cooling tower with the following conditions:

FIG. 12-9 Parallel-path cooling-tower arrangement for plume abatement .

(Marley Co.) Inlet water flow, m3/h (gal/min) Inlet water temperature, °C (°F) Outlet water temperature, °C (°F) Drift loss, percent Concentration cycles

2270 (10,000) 37 .77 (100) 29 .44 (85) 0 .02 5

Evaporation loss [using Eq . (12-19)]: We, m3/h = 0 .00085 × 2270 × (37 .77 − 29 .44) × (1 .8°F/°C) = 28 .9 We, gal/min = 127 .5 Drift loss Wd, m3/h = 2270 × 0 .0002 = 0 .45 Wd, gal/min = 2 Blowdown Wb, m3/h = 6 .8 Wb, gal/min = 29 .9 Makeup Wm, m3/h = 28 .9 + 0 .45 + 6 .8 = 36 .2 Wm, gal/min = 159 .4

Fans and Pumps The fan and pump power requirements are important considerations in system design since they impact cost and performance . The power requirement of the fan depends on the configuration and the pressure drop/air velocity characteristics of the fill . The power requirement and pressure rating on the pump depend on the tower height and how the incoming water is distributed over the fill . Fogging and Plume Abatement A phenomenon that occurs in cooling tower operation is fogging, which produces a highly visible plume and possible icing hazards . Fogging results from mixing warm, highly saturated tower discharge air with cooler ambient air that lacks the capacity to absorb all the moisture as vapor . While in the past visible plumes have not been considered undesirable, properly locating towers to minimize possible sources of complaints has now received the necessary attention . In some instances, high fan stacks have been used to reduce ground fog . Although tall stacks minimize the ground effects of plumes, they can do nothing about water vapor saturation or visibility (which can be a safety matter) . The persistence of plumes is much greater in periods of low ambient temperatures . Special care must be taken regarding the placement of cooling towers relative to other buildings to ensure a fresh air supply . Environmental aspects have caused public awareness and concern over any visible plume, although many laypersons misconstrue cooling tower discharge as harmful . This has resulted in a new development for plume abatement known as a wet-dry cooling tower configuration . Reducing the relative humidity or moisture content of the tower discharge stream will

reduce the frequency of plume formation . Figure 12-9 shows a “parallel path” arrangement that has been demonstrated to be technically sound but at substantially increased tower investment . Ambient air travels in parallel streams through the top dry-surface section and the evaporative section . Both sections benefit thermally by receiving cooler ambient air with the wet and dry airstreams mixing after leaving their respective sections . Water flow is arranged in series, flowing first to the dry coil section and then to the evaporation fill section . A “series path” airflow arrangement, in which dry coil sections can be located before or after the air traverses the evaporative section, also can be used . However, series-path airflow has the disadvantage of water impingement, which could result in coil scaling and restricted airflow . Natural Draft Towers, Cooling Ponds, and Spray Ponds Natural draft towers are primarily suited to very large cooling water quantities, and the reinforced concrete structures used are as large as 80 m (260 ft) in diameter and 105 m (340 ft) high . When large ground areas are available, large cooling ponds offer a satisfactory method of removing heat from water . A pond may be constructed at a relatively small investment by pushing up earth in an earth dike 2 to 3 m (6 to 9 ft) high . Spray ponds provide an arrangement for lowering the temperature of water by evaporative cooling and in so doing greatly reduce the cooling area required in comparison with a cooling pond . Natural draft towers, cooling ponds, and spray ponds are infrequently used in new construction today in the chemical processing industry . Additional information may be found in the 7th edition of Perry’s Handbook . WET SURFACE AIR COOLERS (WSACs) General References: Kals, “Wet Surface Aircoolers,” Chem. Engg. July 1971; Kals, “Wet Surface Aircoolers: Characteristics and Usefulness,” AIChE-ASME Heat Transfer Conference, Denver, CO ., August 6–9, 1972; Elliott and Kals, “Air Cooled Condensers,” Power, January 1990; Kals, “Air Cooled Heat Exchangers: Conventional and Unconventional,” Hydrocarbon Processing, August 1994; Hutton, “Properly Apply Closed Circuit Evaporative Cooling,” Chem. Engg. Progress, October 1996; Hutton, “Improved Plant Performance through Evaporative Steam Condensing,” ASME 1998 International Joint Power Conference, Baltimore, Md ., August 23–26, 1998; http://www .niagarablower .com/; http://www .baltimoreaircoil .com .

Principles Rejection of waste process heat through a cooling tower (CT) requires transferring the heat in two devices in series, using two different methods of heat transfer . This requires two temperature driving forces in series: first, sensible heat transfer from the process stream across the heat exchanger (HX) into the cooling water, and, second, sensible and latent heat transfer from the cooling water to atmosphere across the CT . Rejecting process heat with a wet surface air cooler transfers the waste heat in a single device by using a single-unit operation . The single required temperature driving force is lower because the WSAC does not require the use of cooling water sensible heat to transfer heat from the process stream to the atmosphere . A WSAC tube cross section (Fig . 12-10) shows the characteristic external tube surface having a continuous flowing film of evaporating water, which cascades through the WSAC tube bundle .

12-18

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-10 WSAC tube cross section . Using a small T, heat flows

from (A) the process stream, through (B) the tube, through (C) the flowing film of evaporating water, into (D) flowing ambient air .

Consequently, process streams can be economically cooled to temperatures much closer to the ambient wet-bulb temperature, as low as to within 2 .2°C (4°F), depending on the process requirements and economics for the specific application . Wet Surface Air Cooler Basics The theory and principles for the design of WSACs are a combination of those known for evaporative cooling tower design and for HX design . However, the design practices for engineering WSAC equipment remain a largely proprietary, technical art, and the details are not presented here . Any evaluation of the specifics and economics for a particular application requires direct consultation with a reputable vendor . Because ambient air is contacted with evaporating water within a WSAC, from a distance a WSAC has a similar appearance to a CT (Fig . 12-11) . Economically optimal plot plan locations for WSACs can vary: integrated into, or with, the process structure, remote to it, in a pipe rack, etc . In the WSAC the evaporative cooling occurs on the wetted surface of the tube bundle . The wetting of the tube bundle is performed by recirculating water the short vertical distance from the WSAC collection basin, through the spray nozzles, and onto the top of the bundle (Fig . 12-12) . The tube bundle is completely deluged with this cascading flow of water . Using water application rates between 12 and 24 (m3/h)/m2 (5 and 10 gpm/ft2), the tubes have a continuous, flowing external water film, minimizing the potential for water-side biological fouling, sediment deposition, etc . Process inlet temperatures are limited to a maximum of about 85°C (185°F), to prevent external water-side mineral scaling . However, higher process inlet temperatures can be accepted by incorporating bundles of dry, air-cooled finned tubing within the WSAC unit, to reduce the temperature of the process

FIG. 12-11

Overhead view of a single-cell WSAC .

FIG. 12-12 Nozzles spraying onto wetted tube bundle in a WSAC unit .

stream to an acceptable level before it enters the wetted evaporative tube bundles . The WSAC combines within one piece of equipment the functions of cooling tower, circulated cooling water system, and water-cooled HX . In the basic WSAC configuration (Fig . 12-13), ambient air is drawn in and down through the tube bundle . This airflow is cocurrent with the evaporating water flow, recirculated from the WSAC collection basin sump to be sprayed over the tube bundles . This downward cocurrent flow pattern minimizes the generation of water mist (drift) . At the bottom of the WSAC, the air changes direction through 180°, disengaging entrained fine water droplets . Drift eliminators can be added to meet very low drift requirements . Because heat is extracted from the tube surfaces by water latent heat (and not sensible heat), only about 75 percent as much circulating water is required in comparison to an equivalent CT-cooling water heat exchange application . The differential head of the circulation water pump is relatively small, since dynamic losses are modest (short vertical pipe and a low ΔP spray nozzle) and the hydraulic head is small, only about 6 m (20 ft) from the basin to the elevation of the spray header . Combined, the pumping energy demand is about 35 percent that for an equivalent CT application . The capital cost for this complete water system is also relatively small . The pumps and motors are smaller, the piping has a smaller diameter and is much shorter, and the

FIG. 12-13 Basic WSAC configuration .

EVAPORATIVE COOLING required piping structural support is almost negligible, compared to an equivalent CT application . WSAC fan horsepower is typically about 25 percent less than that for an equivalent CT . A WSAC is inherently less sensitive to water-side fouling . This is so because the deluge rate prevents the adhesion of waterborne material which can cause fouling within a HX . A WSAC can accept relatively contaminated makeup water, such as CT blowdown, treated sewage plant effluent, etc . WSACs can endure more cycles of concentration without fouling than can a CT application . This higher practical operating concentration reduces the relative volume for the evaporative cooling blowdown, and therefore it also reduces the relative volume of required makeup water . For facilities designed for zero liquid discharge, the higher practical WSAC blowdown concentration reduces the size and the operating costs for the downstream water treatment system . Since a hot process stream provides the unit with a heat source, a WSAC has intrinsic freeze protection while operating . Common WSAC Applications and Configurations Employment of a WSAC can reduce process system operating costs that are not specific to the WSAC unit itself . A common WSAC application is condensation of compressed gas (Fig . 12-14) . A compressed gas can be condensed in a WSAC at a lower pressure, by condensing at a temperature closer to the ambient wetbulb temperature, typically 5 .5°C (10°F) above the wet-bulb temperature . This reduced condensation pressure reduces costs, by reducing the gas compressor motor operating horsepower . Consequently, WSACs are widely applied for condensing refrigerant gases, for HVAC, process chillers, ice makers, gas-turbine inlet air cooling, chillers, etc . WSACs are also used directly to condense lower-molecular-weight hydrocarbon streams, such as ethane, ethylene, propylene, and LPG . A related WSAC application is the cooling of compressed gases (CO2, N2, methane, LNG, etc .), which directly reduces gas compressor operating costs (inlet and interstage cooling) and indirectly reduces downstream condensing costs (after cooling the compressed gas to reduce the downstream refrigeration load) . For combined-cycle electric power generation, employment of a WSAC increases steam turbine efficiency . Steam turbine exhaust can be condensed at a lower pressure (higher vacuum) by condensing at a temperature closer to the ambient wet-bulb temperature, typically 15°C (27°F) above the wetbulb temperature . This reduced condensation pressure results in a lower turbine discharge pressure, increasing electricity generation by increasing output shaft power (Fig . 12-15) . Due to standard WSAC configurations, a second cost advantage is gained at the turbine itself . The steam turbine can be placed at grade, rather than being mounted on an elevated platform, by venting horizontally into the WSAC, rather than venting downward to condensers located below the platform elevation, as is common for conventional water-cooled vacuum steam condensers . A WSAC can eliminate chilled water use, for process cooling applications with required temperatures close to and just above the ambient wet-bulb temperature, typically about 3 .0 to 5 .5°C (5 to 10°F) above the wet-bulb temperature . This WSAC application can eliminate both chiller capital and operating costs . In such an application, either the necessary process temperature is below the practical CT water supply temperature, or they are so close to it that the use of CT water is uneconomical (a low-HX log-mean temperature difference) . WSACs can be designed to simultaneously cool several process streams in parallel separate tube bundles within a single cell of a WSAC (Fig . 12-16) . Often one of the streams is closed-circuit cooling water to be

FIG. 12-15 WSAC configuration with electricity generation .

A lower steam condensing pressure increases the turbine horsepower extracted .

used for remote cooling applications . These might be applications not compatible with a WSAC (rotating seals, bearings, cooling jackets, internal reactor cooling coils, etc .) or merely numerous, small process streams in small HXs . WSAC for Closed-Circuit Cooling Systems A closed-circuit cooling system as defined by the Cooling Technology Institute (CTI) (www .cti .org) employs a closed loop of circulated fluid (typically water) remotely as a cooling medium . By definition, this medium is cooled by water evaporation involving no direct fluid contact between the air and the enclosed circulated cooling medium . Applied in this manner, a WSAC can be used as the evaporative device to cool the circulated cooling medium, used remotely to cool process streams . This configuration completely isolates the cooling water (and the hot process streams) from the environment (Fig . 12-17) . The closed circuit permits complete control of the cooling water chemistry, which permits minimizing the cost for water-side materials of construction and eliminating water-side fouling of, and fouling heat-transfer resistance in, the heat exchangers (or jackets, reactor coils, etc .) . Elimination of water-side fouling is particularly helpful for high-temperature cooling applications, especially where heat recovery may otherwise be impractical (quench oils, low-density polyethylene reactor cooling, etc .) . Closed-circuit cooling minimizes circulation pumping horsepower, which must overcome only dynamic pumping losses . This results through recovery of the returning circulated cooling water hydraulic head . A closed-circuit system can be designed for operation at elevated pressures, to guarantee that any process heat-transfer leak will be into the process . Such high-pressure operation is economical, since the system overpressure is not lost during return flow to the circulation pump .

FIG. 12-14 WSAC configuration for condensing a compressed gas .

A lower condensing pressure reduces compressor operating horsepower .

12-19

FIG. 12-16

WSAC configuration with parallel streams .

12-20

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING AIR-COOLED FINNED TUBES WARM AIR OUT HOT LIQUID IN

AIR IN SPRAY WATER TC

FIG. 12-17 WSAC configuration with no direct fluid contact .

COLD LIQUID OUT WATER BYPASS

Closed-circuit cooling splits the water chemistry needs into two isolated systems: the evaporating section, exposed to the environment, and the circulated cooling section, isolated from the environment . Typically, this split reduces total water chemistry costs and water-related operations and maintenance problems . However, the split permits the effective use of a low-quality or contaminated makeup water for evaporative cooling, or a water source having severe seasonal quality problems, such as high sediment loadings . If highly saline water is used for the evaporative cooling, a reduced flow of makeup saline water would need to be supplied to the WSAC . This reduction results from using latent cooling rather than sensible cooling to reject the waste heat . This consequence reduces the substantial capital investment required for the saline water supply and return systems (canal structures) and pump stations, and the saline supply pumping horsepower . (When saline water is used as the evaporative medium, special attention is paid to materials of construction and spray water chemical treatment due to the aggravated corrosion and scaling tendencies of this water .) Water Conservation Applications—“Wet-Dry” Cooling A modified and hybridized form of a WSAC can be used to provide what is called wet-dry cooling for water conservation applications (Fig . 12-18) . A hybridized combination of air-cooled dry finned tubes, standard wetted bare tubes, and wet deck surface area permits the WSAC to operate without water in cold weather, reducing water consumption by about 75 percent of the total for an equivalent CT application . Under design conditions of maximum summer wet-bulb temperature, the unit operates with spray water deluging the wetted tube bundle . The exiting water then flows down into and through the wet deck surface, where the water is cooled adiabatically to about the wet-bulb temperature and then to the sump . As the wet-bulb temperature drops, the process load is shifted from the wetted tubes to the dry finned tubes . By bypassing the process stream around the wetted tubes, cooling water evaporation (consumption) is proportionally reduced . When the wet-bulb temperature drops to the switch point, the process bypassing has reached 100 percent . This switch point wet-bulb temperature is at or above 5°C (41°F) . As the ambient temperature drops further, adiabatic evaporative cooling continues to be used, to lower the dry-bulb temperature to below the switch point temperature . This guarantees that the entire cooling load can be cooled in the dry finned tube bundle .

M AR

W

R

AI

EVAPORATIVE WETTED TUBES

MIST ELIMINATORS AIR WATER IN

AR W

M

R

AIR INLET LOUVERS

SPRAY PUMP

AI

WET DECK SURFACE

FIG. 12-18 As seasonal ambient temperatures drop, the “wet-dry” configuration for a WSAC progressively shifts the cooling load from evaporative to convective cooling .

The use of water is discontinued after ambient dry-bulb temperatures fall below the switch point temperature, since the entire process load can be cooled using only cold fresh ambient air . By using this three-step load-shifting practice, total wet-dry cooling water consumption is about 25 percent of that consumption total experienced with an equivalent CT application . Wet-dry cooling permits significant reduction of water consumption, which is useful where makeup water supplies are limited or where water treatment costs for blowdown are high . Because a WSAC (unlike a CT) has a heat source (the hot process stream), wet-dry cooling avoids various coldweather-related CT problems . Fogging and persistent plume formation can be minimized or eliminated during colder weather . Freezing and icing problems can be eliminated by designing a wet-dry system for water-free operation during freezing weather, typically below 5°C (41°F) . In the arctic, or regions of extreme cold, elimination of freezing fog conditions is realized by not evaporating any water during freezing weather .

SOLIDS-DRYING FUNDAMENTALS General References: Cook and DuMont, Process Drying Practice, McGraw-Hill, New York, 1991 . Drying Technology—An International Journal, Taylor and Francis, New York . Hall, Dictionary of Drying, Marcel Dekker, New York, 1979 . Keey, Introduction to Industrial Drying Operations, Pergamon, New York, 1978 . Keey, Drying of Loose and Particulate Materials, Hemisphere, New York, 1992 . Masters, Spray Drying Handbook, Wiley, New York, 1990 . Mujumdar, Handbook of Industrial Drying, Marcel Dekker, New York, 1987 . Strumillo and Kudra, Drying: Principles, Application and Design, Gordon and Breach, New York, 1986 . van’t Land, Industrial Drying Equipment, Marcel Dekker, New York, 1991 . Tsotsas and Mujumdar, eds ., Modern Drying Technology (vols . 1 to 6), Wiley, New York, 2011 . Aspen Process Manual (Internet knowledge base), Aspen Technology, Boston, 2000 onward .

INTRODUCTION Drying is the process by which volatile materials, usually water, are evaporated from a material to yield a solid product . Drying is a heat- and masstransfer process . Heat is necessary to evaporate water . The latent heat of vaporization of water is about 2500 J/g, which means that the drying process requires a significant amount of energy . Simultaneously, the evaporating material must leave the drying material by diffusion and/or convection .

SOLIDS-DRYING FUNDAMENTALS Heat transfer and mass transfer are not the only concerns when one is designing or operating a dryer . The product quality (color, particle density, hardness, texture, flavor, etc .) is also very strongly dependent on the drying conditions and the physical and chemical transformations occurring in the dryer . Understanding and designing a drying process involves measurement and/or calculation of the following: 1 . Mass and energy balances 2 . Thermodynamics 3 . Mass- and heat-transfer rates 4 . Product quality considerations The subsection below explains how these factors are measured and calculated and how the information is used in engineering practice .

12-21

FIG. 12-19 Relationship between wet-weight and dry-weight

bases .

TERMINOLOGY Generally accepted terminology and definitions are given alphabetically in the following paragraphs . Absolute humidity is the mass ratio of water vapor (or other solvent mass) to dry air . Activity is the ratio of the fugacity of a component in a system relative to the standard-state fugacity . In a drying system, it is the ratio of the vapor pressure of a solvent (e .g ., water) in a mixture to the pure solvent vapor pressure at the same temperature . Boiling occurs when the vapor pressure of a component in a liquid exceeds the ambient total pressure . Bound moisture in a solid is that liquid which exerts a vapor pressure less than that of the pure liquid at the given temperature . Liquid may become bound by retention in small capillaries, by solution in cell or fiber walls, by homogeneous solution throughout the solid, by chemical or physical adsorption on solid surfaces, and by hydration of solids . Capillary flow is the flow of liquid through the interstices and over the surface of a solid, caused by liquid-solid molecular attraction . Constant-rate period (unhindered) is that drying period during which the rate of water removal per unit of drying surface is constant, assuming the driving force is also constant . Convection is heat or mass transport by bulk flow . Critical moisture content is the average moisture content when the constantrate period ends, assuming the driving force is also constant . Diffusion is the molecular process by which molecules, moving randomly due to thermal energy, migrate from regions of high chemical potential (usually concentration) to regions of lower chemical potential . Dry basis expresses the moisture content of wet solid as kilograms of water per kilogram of bone-dry solid . Equilibrium moisture content is the limiting moisture to which a given material can be dried under specific conditions of air temperature and humidity . Evaporation is the transformation of material from a liquid state to a vapor state . Falling-rate period (hindered drying) is a drying period during which the instantaneous drying rate continually decreases . Free moisture content is that liquid which is removable at a given temperature and humidity . It may include bound and unbound moisture . Hygroscopic material is material that may contain bound moisture . Initial moisture distribution refers to the moisture distribution throughout a solid at the start of drying . Latent heat of vaporization is the specific enthalpy change associated with evaporation . Moisture content of a solid is usually expressed as moisture quantity per unit weight of the dry or wet solid . Moisture gradient refers to the distribution of water in a solid at a given moment in the drying process . Nonhygroscopic material is material that can contain no bound moisture . Permeability is the resistance of a material to bulk or convective, pressuredriven flow of a fluid through it . Relative humidity is the partial pressure of water vapor divided by the vapor pressure of pure water at a given temperature . In other words, the relative humidity describes how close the air is to saturation . Sensible heat is the energy required to increase the temperature of a material without changing the phase . Unaccomplished moisture change is the ratio of the free moisture present at any time to that initially present . Unbound moisture in a hygroscopic material is that moisture in excess of the equilibrium moisture content corresponding to saturation humidity . All water in a nonhygroscopic material is unbound water . Vapor pressure is the partial pressure of a substance in the gas phase that is in equilibrium with a liquid or solid phase of the pure component . Wet basis expresses the moisture in a material as a percentage of the weight of the wet solid . Use of a dry-weight basis is recommended since

the percentage change of moisture is constant for all moisture levels . When the wet-weight basis is used to express moisture content, a 2 or 3 percent change at high moisture contents (above 70 percent) actually represents a 15 to 20 percent change in evaporative load . See Fig . 12-19 for the relationship between the dry- and wet-weight bases . THERMODYNAMICS The thermodynamic driving force for evaporation is the difference in chemical potential or water activity between the drying material and the gas phase . Although drying of water is discussed in this subsection, the same concepts apply analogously for solvent drying . For a pure water drop, the driving force for drying is the difference between the vapor pressure of water and the partial pressure of water in the gas phase . The rate of drying is proportional to this driving force; please see the discussion on drying kinetics later in this section .

(

sat Rate ∝ ppure − pw , air

)

(12-23)

The activity of water in the gas phase is defined as the ratio of the partial pressure of water to the vapor pressure of pure water, which is also related to the definition of relative humidity . awvapor =

pw %RH = sat ppure 100

(12-24)

The activity of water in a mixture or solid is defined as the ratio of the vapor pressure of water in the mixture to that of a reference, usually the vapor pressure of pure water . In solids drying or drying of solutions, the vapor pressure (or water activity) is lower than that for pure water . Therefore, the water activity value equals 1 for pure water and is less than 1 when binding is occurring . This is caused by thermodynamic interactions between the water and the drying material . In many standard drying references, this is called bound water. awsolid =

sat pmixture sat ppure

(12-25)

When a solid sample is placed into a humid environment, water will transfer from the solid to the air or vice versa until equilibrium is established . At thermodynamic equilibrium, the water activity is equal in both phases: awvapor = awsolid = aw

(12-26)

Sorption isotherms quantify how tightly water is bound to a solid . This is a result of chemical interactions, such as hydrogen bonding, between the solid and the water . The goal of obtaining a sorption isotherm for a given solid is to measure the equilibrium relationship between the percentage of water in the sample and the vapor pressure of the mixture . The sorption isotherm describes how dry a product can get if contacted with humid air for an infinite amount of time . An example of a sorption isotherm is shown in Fig . 12-20 . In the sample isotherm, a feed material dried with 50 percent relative humidity air (aw = 0 .5) will approach a moisture content of 10 percent on a dry basis . Likewise, a material kept in a sealed container will create a headspace humidity according to the isotherm; a 7 percent moisture sample in the example below will create a 20 percent relative humidity (aw = 0 .2) headspace in a sample jar or package . Strictly speaking, the equilibrium moisture content of the sample in a given environment should be independent of the initial condition of

% Water, Wet Basis

12-22 20 18 16 14 12 10 8 6 4 2 0

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING TABLE 12-7 Maintenance of Constant Humidity Saturated salt solution Lithium bromide Lithium chloride Potassium acetate Sodium iodide Sodium bromide Sodium chloride Potassium chloride 0

10

20

30

40

50

60

70

80

% Relative humidity at 25°C 6 .37 11 .30 22 .51 38 .17 57 .57 75 .29 84 .34

LiBr LiCl KC2H3O2 NaI NaBr NaCl KCl

90

% Relative Humidity FIG. 12-20 Example of a sorption isotherm (coffee at 22°C) .

the sample . However, in some cases the sorption isotherm of an initially wet sample (sometimes called a desorption isotherm) is different from that of an identical, but initially dry sample . This is called hysteresis and can be caused by irreversible changes in the sample during wetting or drying, micropore geometry in the sample, and other factors . Paper products are notorious for isotherm hysteresis . Most materials show little or no hysteresis . Sorption isotherms cannot generally be predicted from theory . They need to be measured experimentally . The simplest method of measuring a sorption isotherm is to generate a series of controlled-humidity environments by using saturated salt solutions, allow a solid sample to equilibrate in each environment, and then analyze the solid for moisture content . The basic apparatus is shown in Fig . 12-21, and a table of salts is shown in Table 12-7 . It is important to keep each chamber sealed and to be sure that crystals are visible in the salt solution to ensure that the liquid is saturated . Additionally, the solid should be ground into a powder to facilitate mass transfer . Equilibration can take 2 to 3 weeks . Successive moisture measurements should be used to ensure that the sample has equilibrated, i .e ., achieved a steady value . Care must be taken when measuring the moisture content of a sample; this is described later in this section . Another common method of measuring a sorption isotherm is to use a dynamic vapor sorption device . This machine measures the weight change of a sample when exposed to humidity-controlled air . A series of humidity points are programmed into the unit, and it automatically delivers the proper humidity to the sample and monitors the weight . When the weight is stable, an equilibrium point is noted and the air humidity is changed to reflect the next setting in the series . When one is using this device, it is critical to measure and record the starting moisture of the sample, since the results are often reported as a percentage of change rather than a percentage of moisture . There are several advantages to the dynamic vapor sorption device . First, any humidity value can be dialed in, whereas salt solutions are not available for every humidity value and some are quite toxic . Second, since the weight is monitored as a function of time, it is clear when equilibrium is reached; however, this can be a slow process, so care must be taken to ensure equilibrium is actually achieved . The dynamic devices also give the sorption/ desorption rates, although these can easily be misused (see the drying kinetics subsection later) . The salt solution method, however, is significantly less expensive to buy and maintain . Samples created in salt solution chambers can also be qualitatively assessed for physical characteristics such as stickiness, flowability, or deliquescence . An excellent reference on all aspects of sorption isotherms is that by Bell and Labuza, Moisture Sorption, 2d ed ., American Association of Cereal Chemists, St . Paul, Minnesota, 2000 .

MECHANISMS OF MOISTURE TRANSPORT WITHIN SOLIDS Drying requires moisture to travel to the surface of a material . There are several mechanisms by which this can occur: 1 . Diffusion of moisture through solids . Diffusion is a molecular process, brought about by random wanderings of individual molecules . If all the water molecules in a material are free to migrate, they tend to diffuse from a region of high moisture concentration to one of lower moisture concentration, thereby reducing the moisture gradient and equalizing the concentration of moisture . 2 . Convection of moisture within a liquid or slurry . If a flowable solution is drying into a solid, then liquid motion within the material brings wetter material to the surface . 3 . Evaporation of moisture within a solid and gas transport out of the solid by diffusion and/or convection. Evaporation can occur within a solid if it is boiling or porous . Subsequently vapor must move out of the sample . 4 . Capillary flow of moisture in porous media . The reduction of liquid pressure within small pores due to surface tension forces causes liquid to flow in porous media by capillary action . DRYING KINETICS This subsection discusses the rate of drying . The kinetics of drying dictate the size of industrial drying equipment, which directly affects the capital and operating costs of a process involving drying . The rate of drying can also influence the quality of a dried product since other simultaneous phenomena, such as heat transfer, shrinkage, microstructure development, and chemical reactions, are often affected by the moisture and temperature history of the material . The most classical drying kinetics problem is that of a pure water drop drying in air, as shown in Example 12-12 . Example 12-12 Drying of a Pure Water Drop See Marshall, Atomization & Spray Drying, 1986 . Calculate the time to dry a drop of water, given the air temperature and relative humidity as a function of drop size . Solution Assume that the drop is drying at the wet-bulb temperature . Begin with an energy balance [Eq . (12-27)] Mass flux =

h (Tair − Tdrop ) ∆H vap

(12-27)

Next, a mass balance is performed on the drop . The change in mass equals the flux times the surface area . ρ dVdroplet dt

= − A × mass flux

(12-28)

Evaluating the area and volume for a sphere gives ρ ⋅ 4πR2

dR = −4πR2 × mass flux dt

(12-29)

Combining Eqs . (12-28) and (12-29) and simplifying give ρ

dR − h (Tair − Tdrop ) = dt ∆H vap

(12-30)

A standard correlation for heat transfer to a sphere is given by Ranz and Marshall, “Evaporation from Drops,” Chem. Eng. Prog. 48(3): 141–146 and 48(4): 173–180 (1952), as Nu =

h(2R ) = 2 + 0 .6 Re 0 .5 Pr 0 .33 kair

(12-31)

For small drop sizes or for stagnant conditions, the Nusselt number has a limiting value of 2 . Nu = FIG. 12-21 Sorption isotherm apparatus . A saturated salt solution is in the

bottom of the sealed chamber; samples sit on a tray in the headspace .

h=

h(2 R ) =2 kair

(12-32)

kair R

(12-33)

SOLIDS-DRYING FUNDAMENTALS

12-23

10

Drop Lifetime, s

1

0.1

20% Humidity 60% Humidity 80% Humidity 95% Humidity

0.01

0.001

0.0001 1

10

100

Initial Drop Diameter, lm Drying time of pure water drops as function of relative humidity at 25°C .

Insertion into Eq . (12-30) gives (12-34)

Integration yields R02 R 2 kair (Tair − Tdrop ) ⋅ t − = 2 2 ρ∆H vap

(12-35)

where R0 = initial drop radius, m . Now the total lifetime of a drop can be calculated from Eq . (12-35) by setting R = 0: t=

ρ∆ H vap R02 2 kair (Tair − Tdrop )

(12-36)

The effects of drop size and air temperature are readily apparent from Eq . (12-36) . The temperature of the drop is the wet-bulb temperature and can be obtained from a psychrometric chart, as described in the previous subsection . Sample results are plotted in Fig . 12-22 .

The above solution for drying of a pure water drop cannot be used to predict the drying rates of drops containing solids . Drops containing solids will not shrink uniformly and will develop internal concentration gradients ( falling-rate period) in most cases . Drying Curves and Periods of Drying The most basic and essential kinetic information on drying of solid materials is a drying curve . A drying curve describes the drying kinetics and how they change during drying . The drying curve is affected by the material properties, size or thickness of the drying material, and drying conditions . In this subsection, the general characteristics of drying curves and their uses are described . Experimental techniques to obtain drying curves are discussed in the Experimental Methods subsection . Several representations of a typical drying curve are shown in Fig . 12-23 . The top plot, Fig . 12-23a, is the moisture content (dry basis) as a function of time . The middle plot, Fig . 12-23b, is the drying rate as a function of time, the derivative of the top plot . The bottom plot, Fig . 12-23c, is the drying rate as affected by the average moisture content of the drying material . Since the material loses moisture as time passes, the progression of time in this bottom plot is from right to left . Some salient features of the drying curve show the different periods of drying . These are common periods, but not all occur in every drying process . The first period of drying is called the induction period . This period occurs when material is being heated early in drying . The second period of drying is called the constant-rate period . During this period, the surface remains wet enough to maintain the vapor pressure of water on the surface . Once the surface dries sufficiently, the drying rate decreases and the fallingrate period occurs . This period can also be referred to as hindered drying. Figure 12-23 shows the transition between constant- and falling-rate periods of drying occurring at the critical point . The critical point refers to the average moisture content of a material at this transition . This is a useful concept, but the critical point can depend on drying conditions . The subsections below show examples of drying curves and the phenomena that give rise to different common types .

Dry-basis moisture content

dR kair (Tair − Tdrop ) = ρ ∆H vap dt

Time (a) Drying rate, kg moisture/(kg dry material·time)

R

Introduction to Internal and External Mass-Transfer Control— Drying of a Slab The concepts in drying kinetics are best illustrated with a simple example—air drying of a slab . Consider a thick slab of homogeneous wet material, as shown in Fig . 12-24 . In this particular example, the slab is dried on an insulating surface under constant conditions . The heat for drying is carried to the surface with hot air, and air carries water vapor

Drying rate, kg moisture/(kg dry material·time)

FIG. 12-22

Constant-rate period

Falling-rate period

Induction period Critical point Time (b) Hindered drying, falling-rate period for constant external conditions

Unhindered drying, constantrate period for constant external conditions

Induction period

Time Critical point Dry-basis moisture content (c)

FIG. 12-23 Several common representations of a typical drying curve .

12-24

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING Hot air

z Winitial FIG. 12-24

0

Drying of a slab .

Dry-basis moisture

from the surface . At the same time, a moisture gradient forms within the slab, with a dry surface and a wet interior . The curved line is the representation of the gradient . At the bottom of the slab (z = 0), the material is wet and the moisture content is drier at the surface . The following processes must occur to dry the slab: 1 . Heat transfer from the air to the surface of the slab 2 . Mass transfer of water vapor from the surface of the slab to the bulk air 3 . Mass transfer of moisture from the interior of the slab to the surface of the slab Depending on the drying conditions, thickness, and physical properties of the slab, any of the above steps can be rate-limiting . Figure 12-25 shows two examples of rate-limiting cases . Example 12-14 shows how to compute these from physical property data and how the same material can exhibit different drying curves . The top example shows the situation of external rate control . In this situation, the heat transfer to the surface and/or the mass transfer from the surface to the vapor phase is slower than mass transfer to the surface from the bulk of the drying material . In this limiting case, the moisture gradient in the material is minimal, and the rate of drying will be constant as long as the average moisture content remains high enough to maintain a high water activity (see the subsection on thermodynamics for a discussion of the relationship between moisture content and water vapor pressure) . External rate control leads to the observation of a constant-rate period drying curve . The bottom example shows the opposite situation: internal rate control . In the case of heating from the top, internal control refers to a slow rate of mass transfer from the bulk of the material to the surface of the material . Diffusion, convection, and capillary action (in the case of porous media) are possible mechanisms for mass transfer of moisture to the surface of the slab . In the internal rate control situation, moisture is removed from the surface by the air faster than moisture is transported to the surface . This regime is caused by relatively thick layers or high values of the mass- and heat-transfer coefficients in the air . Internal rate control leads to the observation of a falling-rate period drying curve . Generally speaking, drying curves show both behaviors . When drying begins, the surface is often wet enough to maintain a constant-rate period and is therefore externally controlled . But as the material dries, the masstransfer rate of moisture to the surface often slows, causing the rate to

decrease since the lower moisture content on the surface causes a lower water vapor pressure . However, some materials begin dry enough that there is no observable constant-rate period . Note that falling-rate periods do sometimes occur when drying is externally controlled . The drying rate depends on the water activity at the surface of the material, and the rate, by itself, is not a measure of an internal moisture gradient . The observation of falling-rate periods with external rate control is more likely during drying of powder, where moisture can be tightly bound but the distance for diffusion to the drying surface is small . Concept of a Characteristic Drying Rate Curve In 1958, van Meel observed that the drying rate curves, during the falling-rate period, for a specific material often show the same shape (Fig . 12-26), so that a single characteristic drying curve can be drawn for the material being dried . Strictly speaking, the concept should only apply to materials of the same specific size (surface area to material ratio) and thickness, but Keey (1992) shows evidence that it applies over a somewhat wider range with reasonable accuracy . In the absence of experimental data, a linear falling-rate curve is often a reasonable first guess for the form of the characteristic function (good approximation for milk powder, fair for ion-exchange resin and silica gel) . At each volume-averaged free moisture content, it is assumed that there is a corresponding specific drying rate relative to the unhindered drying rate in the first drying period that is independent of the external drying conditions . Volume-averaged means averaging over the volume (distance cubed for a sphere) rather than just the distance . The relative drying rate is defined as f=

N Nm

(12-37)

where N is the drying rate, Nm is the rate in the constant-rate period, and the characteristic moisture content becomes Φ=

X − Xe X cr − X e

(12-38)

where X is the volume-averaged moisture content, Xcr is the moisture content at the critical point, and Xe is that at equilibrium . Thus, the drying curve is normalized to pass through the point (1, 1) at the critical point of transition in drying behavior and the point (0, 0) at equilibrium . This representation leads to a simple lumped-parameter expression for the drying rate in the falling-rate period, namely, N = fNm = f [kφm(YW − YG)]

(12-39)

Here k is the external mass-transfer coefficient, φm is the humidity-potential coefficient (corrects for the humidity not being a strictly true representation of the driving force; close to unity most of the time), YW is the humidity above a fully wetted surface, and YG is the bulk-gas humidity . Equation (12-39) has been used extensively as the basis for understanding the behavior of industrial drying plants owing to its simplicity and the separation of the parameters

1

z Time

winitial

0

Relative drying rate f = N/Nm

Dry-basis moisture

Characteristic drying curve for material f = fn(Φ)

0

z Time

winitial

0 0

FIG. 12-25 Drying curves and corresponding moisture gradients for situations involving external heat- and mass-transfer control and internal mass-transfer control .

1 Characteristic moisture content Φ = (X – Xe)/(Xcr – Xe)

FIG. 12-26 Characteristic drying curve .

SOLIDS-DRYING FUNDAMENTALS that influence the drying process: the material itself f, the design of the dryer k, and the process conditions φm(YW − YG)f . Example 12-13 Characteristic Drying Curve Application Suppose (with nonhygroscopic solids, Xe = 0 kg/kg) that we have a linear falling-rate curve, with a maximum drying rate Nm of 0 .5 kg moisture/(kg dry solids ⋅ s) from an initial moisture content of 1 kg moisture/kg dry solids . If the drying conditions around the sample are constant, what is the time required to dry the material to a moisture content of 0 .2 kg moisture/kg dry solids? The linear falling-rate drying curve is given by this relationship: N =−

dX kg 1 = X ⋅ 0 .5 dt kg s

(12-40)

from theory alone, or obtained from physical property databanks; practical measurements are required . Because of this, experimental work is almost always necessary to design a dryer accurately, and scale-up calculations are more reliable than design based only on thermodynamic data . The experiments are used to verify the theoretical model and find the difficult-to-measure parameters; the full-scale dryer can then be modeled more realistically . Heat and Mass Balance The heat and mass balance on a generic continuous dryer is shown schematically in Fig . 12-27 . In this case, mass flows and moisture contents are given on a dry basis . The mass balance is usually performed on the principal solvent and gives the evaporation rate E (kg/s) . In a contact or vacuum dryer, this is approximately equal to the exhaust vapor flow, apart from any noncondensibles . In a convective dryer, this gives the increased outlet humidity of the exhaust . For a continuous dryer at steady-state operating conditions,

where N = the drying rate, kg/(kg ∙ s) and X = average dry basis moisture content . Rearranging and integrating Eq . (12-40) gives 0 .2

∫ 1

dX 0 .2 kg 1 = ln   = −0 .5 ⋅ ⋅t  1  X kg s

(12-41)

t = 3 .21 s The characteristic drying curve, however, is clearly a gross approximation . A common drying curve will be found only if the volume-averaged moisture content reflects the moistness of the surface in some fixed way . An additional worked example using a linear falling-rate drying curve is in the Continuous Agitated Dryer subsection . For example, in the drying of impermeable timbers, for which the surface moisture content reaches equilibrium quickly, there is unlikely to be any significant connection between the volume-averaged and the surface moisture contents, so the concept is unlikely to apply . While the concept might not be expected to apply to the same material with different thickness, Pang finds that it applies for different thicknesses in the drying of softwood timber (Keey, 1992), and its applicability appears to be wider than the theory might suggest . A paper by Kemp and Oakley (2002) explains that many of the errors in the assumptions in this method often cancel out, meaning that the concept has wide applicability .

12-25

E = F(XI - XO) = G(YO - YI)

(12-42)

This assumes that the dry gas flow G and dry solids flow F do not change between dryer inlet and outlet . Mass balances can also be performed on the overall gas and solids flows to allow for features such as air leaks and solids entrainment in the exhaust gas stream . In a design calculation (including scale-up), the required solids flow rate, inlet moisture content XI, and outlet moisture XO are normally specified, and the evaporation rate and outlet gas flow are calculated . In a performance calculation, this is normally reversed; the evaporation rate under new operating conditions is found, and the new solids throughput or outlet moisture content is back-calculated . For a batch dryer with a dry mass m of solids, a mass balance only gives a snapshot at one point during the drying cycle and an instantaneous drying rate, given by − dX  = G (YO - YI ) E = m   dt 

(12-43)

The heat balance on a continuous dryer takes the generic form DRYER MODELING, DESIGN, AND SCALE-UP General Principles Models and calculations on dryers can be categorized in terms of (1) the level of complexity used and (2) the purpose or type of calculation (design, or scale-up) . A fully structured approach to dryer modeling can be developed from these principles, as described below and in greater detail by Kemp and Oakley (2002) . In this section, we cover the principles and refer the reader to specific examples relevant for each type of dryer in the Drying Equipment subsection . Levels of Dryer Modeling Modeling can be carried out at four different levels, depending on the amount of data available and the level of detail and precision required in the answer . Level 1 . Heat and mass balances . These balances give information on the material and energy flows to and from the dryer, but do not address the kinetics or required size of the equipment . Level 2 . Scoping. Approximate or scoping calculations give rough sizes and throughputs (mass flow rates) for dryers, using simple data and making some simplifying assumptions . Either heat-transfer control or first-order drying kinetics is assumed . Level 3 . Scaling. Scaling calculations give overall dimensions and performance figures for dryers by scaling up drying curves from smallscale or pilot-plant experiments . Level 4 . Detailed. Rigorous or detailed methods aim to track the temperature and drying history of the solids and find local conditions inside the dryer . Naturally, these methods use more complex modeling techniques with many more parameters and require many more input data . Types of Dryer Calculations The user may wish to design a new dryer, dry a different formulation, or improve the performance of an existing dryer . Three types of calculations are possible: • Design of a new dryer to perform a given duty, using information from the process flowsheet and physical properties databanks • Performance calculations for an existing dryer at a new set of operating conditions or to dry a different material • Scale-up from laboratory-scale or pilot-plant experiments to a full-scale dryer Solids drying is very difficult to model reliably, particularly in the fallingrate period which usually has the main effect on determining the overall drying time . Falling-rate drying kinetics depend strongly on the internal moisture transport within a solid . This is highly dependent on the internal structure, which in turn varies with the upstream process, the solids formation step, and often between individual batches . Hence, many key drying parameters within solids (e .g ., diffusion coefficients) cannot be predicted

GIGI + FISI + Qin = GIGO + FISO + Qwl

(12-44)

Here I is the enthalpy (kJ/kg dry material) of the solids or gas plus their associated moisture . Enthalpy of the gas includes the latent heat term for the vapor . Expanding the enthalpy terms gives G(CsITGI + λYI) + F(CPS + XICPL)TSI + Qin = G(CSOTGO + λYO) + F(CPS + XOCPL)TSO + Qwl

(12-45)

Here Cs is the humid heat CPG + YCPY . In convective dryers, the left-hand side is dominated by the sensible heat of the hot inlet gas GCsITGI; in contact dryers, the heat input from the jacket Qin is dominant . In both cases, the largest single term on the right-hand side is the latent heat of the vapor GλYO . Other terms are normally below 10 percent . This shows why the operating line of a convective dryer on a psychrometric chart is roughly parallel to a constantenthalpy line. The corresponding equation for a batch dryer is GIGI + Qin = GIGO + m

dI s + Qwl dt

(12-46)

Further information on heat and mass balances, including practical advice on industrial dryers, is given later in this section . Worked examples are shown in the continuous band and tunnel dryer, pneumatic conveying dryer, and spray dryer subsections .

Heat losses Qwl Dry gas G,YI,TGI, IGI

Wet gas Dryer

G,YO,TGO, IGO

Wet solids F, XI,TSI, ISI

Dry solids F, XO,TSO, ISO Indirect heating Qin (conduction, radiation, RF/MW)

FIG. 12-27

Heat and material flows around a continuous dryer .

12-26

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

Scoping Design Calculations In scoping calculations, some approximate dryer dimensions and drying times are obtained based mainly on a heat and mass balance, without measuring a drying curve or other experimental drying data . They allow the cross-sectional area of convective dryers and the volume of batch dryers to be estimated quite accurately, but are less effective for other calculations and can yield overoptimistic results . Some examples of scoping calculations are shown later in the batch agitated dryer, spray drying, drum dryer, and sheet dryer subsections . Scaling Models These models use experimental data from drying kinetics tests in a laboratory, pilot-plant or full-scale dryer, and are thus more accurate and reliable than methods based only on estimated drying kinetics . They treat the dryer as a complete unit, with drying rates and air velocities averaged over the dryer volume, except that, if desired, the dryer can be subdivided into a small number of sections . These methods are used for layer dryers (tray, oven, horizontal-flow band, and vertical-flow plate types) and for a simple estimate of fluidized-bed dryer performance . For batch dryers, they can be used for scale-up by refining the scoping design calculation . The basic principle is to take an experimental drying curve and perform two transformations: (1) from test operating conditions to full-scale operating conditions and (2) from test dimensions to full-scale dryer dimensions . If the operating conditions of the test (e .g ., temperature, gas velocity, agitation rate) are the same as those for the full-scale plant, then the first correction is not required . Scaling models are the main design method traditionally used by dryer manufacturers . Pilot-plant test results are scaled to a new set of conditions on a dryer with greater airflow or surface area by empirical rules, generally based on the external driving forces (temperature, vapor pressure, or humidity driving forces) . By implication, therefore, a characteristic drying curve concept is again being used, scaling the external heat and mass transfer and assuming that the internal mass transfer changes in proportion . A good example is the set of rules described under Fluidized-Bed Dryers, which include the effects of temperature, gas velocity, and bed depth on drying time in the initial test and the full-scale dryer . A worked example is shown in the fluidized-bed drying subsection . Specific Drying Rate Concept An intuitive, useful method for scale-up of layer dryers from experimental data has been developed and reported by C . Moyers [Drying Technol. 12(1 & 2): 393–417 (1994)] . The method defines a specific drying rate (SDR) as SDR =  

mS ρs z = Ac (1 + X 1 )τ

(12-47)

where rs is the bulk density of the dry solids, z is the layer thickness, X1 is the initial moisture content, t is the drying time, and Ac is the surface area of contact . The method assumes that the SDR is constant between scales . The article presents practical examples using laboratory data for continuous rotating shelf dryers, plate dryers, and continuous paddle dryers . Detailed or Rigorous Models These models aim to predict local conditions within the dryer and the transient condition of the particles and gas in terms of temperature, moisture content, velocity, etc . Naturally, they require many more input data on the dryer equipment and material properties as well as computational tools (hardware and software) to solve the equations . There are many published models of this type in the academic literature . They give the possibility of more-detailed results, but the potential cumulative errors are also greater . Two types are discussed here: incremental models and computational fluid dynamics (CFD) models . Incremental Model The one-dimensional incremental model is a key analysis tool for several types of dryers . A set of simultaneous equations is solved at a given location (Fig . 12-28), and the simulation moves along the dryer axis in a series of steps or increments, hence the name . A spreadsheet or other computer program is needed, and any number (sometimes thousands) of increments may be used . Examples of incremental models are shown later in the pneumatic conveying drying, sheet drying, and electromagnetic drying subsections .

dQwl Gas

G, Y, TG, UG

Solids

F, X, TS, US z

dz

FIG. 12-28 Principle of the incremental model .

Increments may be stated in terms of time (dt), length (dz), or moisture content (dX ) . A set of six simultaneous equations is then solved, and ancillary calculations are also required, e .g ., to give local values of gas and solids properties . The generic set of equations ( for a time increment ∆t) is as follows: QP = hPGAP(TG − TS)

(12-48)

− dX = function (X, Y, TP, TG, hPG, AP) dt

(12-49)

Heat transfer to particle: Mass transfer from particle:

Mass balance on moisture:

G ∆Y = −F ∆X = F

Heat balance on particle:

∆TS =

− dX ∆t dt

QP ∆t − λ ev mP ∆X mP (C PS + C PL X )

(12-50)

(12-51)

Heat balance for increment: −∆TG =

F (C PS + C PL X ) ∆TS + G (λ 0 + C PY TG ) ∆Y + ∆QWl G (C PG + C PY Y )

(12-52)

∆z = US ∆t

(12-53)

Particle transport:

The mass and heat balance equations are the same for any type of dryer, but the particle transport equation is completely different, and the heat- and mass-transfer correlations are also somewhat different as they depend on the environment of the particle in the gas (i .e ., single isolated particles, agglomerates, clusters, layers, fluidized beds, or packed beds) . The mass-transfer rate from the particle is regulated by the drying kinetics and is thus obviously material-dependent (at least in falling-rate drying) . The model is effective and appropriate for dryers where both solids and gas are approximately in axial plug flow, such as pneumatic conveying and cascading rotary dryers . However, it runs into difficulties where there is recirculation or radial flow . The incremental model is also useful for measuring variations in local conditions such as temperature, solids moisture content, and humidity along the axis of a dryer (e .g ., plug-flow fluidized bed), through a vertical layer (e .g ., tray or band dryers), or during a batch drying cycle (using time increments, not length) . Any fundamental mathematical model of drying contains mass and energy balances, constitutive equations for mass- and heat-transfer rates, and physical properties . Table 12-8 shows the differential mass balance equations that can be used for common geometries and solved as incremental models . Note there are two sets of differential mass balances— one including shrinkage and one not including shrinkage . When moisture leaves a drying material, the material can either shrink, or develop porosity, or both . The equations in Table 12-8 are insufficient on their own . Some algebraic relationships are needed to formulate a complete problem, as illustrated in Example 12-14 . Equations for the mass- and heat-transfer coefficients are also needed for the boundary conditions presented in Table 12-8 . These require the physical properties of the air, the object geometry, and the Reynolds number . Analytical solutions exist for the equations on the left-hand side of Table 12-8 in the special case of a constant diffusion coefficient . These can be found in Crank, J ., Mathematics of Diffusion, 2d ed ., Oxford University Press, Oxford, UK, 1975 . However, the values of the water-solid diffusion coefficient often vary 1 to 3 orders of magnitude with the local moisture content, and so use of these analytical solutions is not recommended . Some data and some theories are available in the literature on the variation of a moisture (or solvent)/solid diffusion coefficient with moisture level; see, e .g ., Zielinski, J . M ., and Duda, J . L ., AIChE Journal 38(3): 405–413 (1992) . Example 12-14 shows the solution for a problem using numerical modeling . This example shows some of the important qualitative characteristics of drying . Example 12-14 Air Drying of a Thin Layer of Paste Simulate the drying kinetics of 100 µm of paste initially containing 50 percent moisture (wet-basis) with dry air at 60°C, 0 percent relative humidity air at velocities of 0 .1, 1 .0, or 10 m/s . The diffusion coefficient of water in the material depends on the local moisture content . The length of the layer in the airflow direction is 2 .54 cm (Fig . 12-29) .

SOLIDS-DRYING FUNDAMENTALS

12-27

TABLE 12-8 Mass-Balance Equations for Drying Modeling When Diffusion Is Mass-Transfer Mechanism of Moisture Transport Case

Mass balance without shrinkage

Mass balance with shrinkage

At top surface, −$(w )

∂Cw P bulk − Pwsurface = kp w ∂ z top surface P − Pwsurface

∂Cw =0 ∂ z bottom surface

At bottom surface,

At surface, −$(w )

At center,

P bulk − Pwsurface ∂Cw = kp w ∂rsurface P − Pwsurface

∂Cw =0 ∂rcenter

At surface, −$(w )

At center,

At surface, −$(w )r

At center,

∂Cw =0 ∂rcenter

∂u =0 ∂ ssurface

At surface, −$(w )r 2

At center,

∂s = rρ s ∂z

P bulk − Pwsurface ∂uCw = kp w ∂ ssurface P − Pwsurface

∂u  ∂u ∂  4 ρs $(w )  = ∂t ∂ s  ∂s 

P bulk − Pwsurface ∂Cw = kp w ∂rsurface P − Pwsurface

∂u P bulk − Pwsurface = kp w ∂ s top surface P − Pwsurface

∂u =0 ∂ s bottom surface

∂u ∂  2 ∂u  = ρs $(w )  ∂t ∂ s  ∂s 

∂C  ∂Cw 1 ∂  2 r $(w ) w  = ∂r  ∂t r 2 ∂r 

Spherical geometry

At top surface, −$(w )

At bottom surface,

∂C  ∂Cw 1 ∂  r $(w ) w  = ∂r  ∂t r ∂r 

Cylindrical geometry

∂s = ρs ∂z

∂u ∂  ∂u  = $(w )  ∂t ∂ s  ∂s 

∂C  ∂Cw ∂  = $(w ) w  ∂z  ∂t ∂ z 

Slab geometry

∂s = r 2ρ s ∂z

P bulk − Pwsurface ∂u = kp w ∂ ssurface P − Pwsurface

∂u =0 ∂ s bottom surface

The variable µ is the dry-basis moisture content. The equations that include shrinkage are taken from Van der Lijn, doctoral thesis, Wageningen (1976).

Physical Property Data

Sorption isotherm data fit well to the following equation: 5

4

%RH  %RH  %RH  − 6 .21  + 4 .74  w = 3 .10   100   100   100 

Mass- and heat-transfer coefficients are given by

3

Nu =

hL = 0 .664 Re0 .5 Pr0 .333 kair

(12-58)

Sh =

kc L = 0 .664 Re0 .5 Sc0 .333 Dair/water

(12-59)

(12-54)

2

%RH  %RH  −1 .70  + 0 .378   100   100  Solid density = 1150 kg/m

3

kp = kc ⋅ ρair

Heat of vaporization = 2450 J/g Solid heat capacity = 2 .5 J/(g ⋅ K) Water heat capacity = 4 .184 J/(g ⋅ K)

The Reynolds number uses the length of the layer L in the airflow direction: Re =

Solution The full numerical model needs to include shrinkage since the material is 50 percent water initially and the thickness will decrease from 100 to 46 .5 mm during drying . Assuming the layer is viscous enough to resist convection in the liquid, diffusion is the dominant liquid-phase transport mechanism . Table 12-8 gives the mass balance equation: ∂u ∂  ∂u  = $( u )  ∂t ∂ s  ∂s 

∂s =  ρs ∂z

 p bulk − pwsurface  ∂u −$( u )  = k p  w ∂s  P − pwsurface 

(12-55)

∂u =0 ∂ s top surface

(12-56)

C p , air µ air kair

= 0 .70

Sc =

µ air = 0 .73 ρair Dair/water

(12-62)

1 w 1−w = + ο density of wet material (assumes volume additivity) ρ ρwο ρs concentration of water

(12-63) (12-64) (12-65)

%RH Pw ,surface = definition of relative humidity 100 Pw ,sat The Antoine equation for vapor pressure of water is

= [ h ⋅(Tair − Tlayer ) − F ⋅∆H vap ]⋅ A

Air

100 µm layer 2.54 cm FIG. 12-29

Pr =

ρs = (1 − w)ρ concentration of solids

The temperature is assumed to be uniform through the thickness of the layer .

dt

(12-61)

where V = air velocity . The Prandtl and Schmidt numbers, Pr and Sc, respectively, for air are given by

Cw = w ⋅ ρ

At bottom surface,

dTlayer

VLρair µ air

The following algebraic equations are also needed:

At top surface,

(C p ,solids + C p ,water ⋅wavg ,dry-basis ) ⋅ msolids ⋅

(12-60)

Drying of a thin layer of paste.

(12-57)

ln( Pw , sat ) = 23 .1963 −

3816 .44 (T + 273 .15) − 46 .13

(12-66)

Equation (12-67) is the dependence of diffusion coefficient on moisture content for maltodextrin from Raderer, M ., et al ., Chemical Engineering Journal 86: 185–191 (2002) . For dry-basis moisture contents of 1, 0 .5, and 0 .25, the values of 𝒟 are 1 .88 × 10−10, 6.28 × 10−11, and 1.11 × 10−11 m2/s, respectively. 35 .8 + 215 ⋅ u  $(u ) = exp  −  1 + 10 .2 ⋅ u 

(12-67)

Result: The results of simulations for air velocities of 0.1, 1.0, and 10 m/s are shown in Fig. 12-30. The top plot shows the average moisture content of the layer as a function of time, the middle plot shows the drying rate as a function of time, and the bottom plot shows the moisture gradient in each layer after 60 s of drying.

12-28

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-30

Simulation results for thin-layer drying example .

These results illustrate the relationships between the external air conditions, drying rate, and moisture gradient . In each case, drying begins in a constant-rate period and then moves to a falling-rate period . The drying rates in the constant-rate period are controlled by the air velocity, which affects the external heat- and mass-transfer coefficients [Eqs . (12-58) and (12-59)] . The surface dries, reaching a critical moisture content, and the falling-rate period begins in each case . In the falling-rate period, the rate-limiting step is internal diffusion so the rate becomes independent of air velocity . The plot of the internal moisture gradient at 60 s (bottom plot) illustrates that the falling-rate period has begun for the 10 m/s case, but not yet for the 1 .0 and 0 .1 m/s cases . The equation set in this example was solved by using a differential algebraic equation solver called gPROMS from Process Systems Enterprises (www .pse .com) . It can also be solved with other software and programming languages such as FORTRAN . Example 12-14 is too complicated to be done on a spreadsheet .

Computational Fluid Dynamics CFD provides a very detailed and accurate model of the gas phase, including three-dimensional effects and swirl . Where localized flow patterns have a major effect on the overall performance of a dryer and the particle history, CFD can yield immense improvements in modeling and in the understanding of physical phenomena . Conversely, where the system is well mixed or drying is dominated by

falling-rate kinetics and local conditions are unimportant, CFD modeling will give little or no advantage over conventional methods, but will incur a vastly greater cost in computing time . CFD has been extensively applied in recent years to spray dryers (Langrish and Fletcher, 2001), but it has also been useful for other local three-dimensional swirling flows, e .g ., around the feed point of pneumatic conveying dryers (Kemp et al ., 1991), and for other cases where airflows affect drying significantly, e .g ., local overdrying and warping in timber stacks (Langrish, 1999) . See Jamaleddine, T ., and Ray, M ., Drying Technology 28: 120–154 (2010), for a comprehensive review on how CFD has been used for a wide variety of drying problems . CFD software packages specialize in their treatment of the turbulence and other details of airflows . However, the differential equations that describe transport within the solid material in the dryer are usually greatly simplified into algebraic relationships so they can be called as user-defined functions within the solver . Usually, one cannot simultaneously employ a detailed treatment of the equipment and the product at the same time . The engineer must decide which level of detail will enable the designs or business decisions .

SOLIDS-DRYING FUNDAMENTALS TABLE 12-9 Sample Techniques for Various Dryer Types Dryer type

Sampling method

Fluid bed dryer Sheet dryer

Sampling cup (see Fig . 12-31) Collect at end of dryer . Increase speed to change the drying time . Record initial moisture and mass of tray with time . Decrease residence time with higher flow rate and sample at exit . Residence time of product is difficult to determine and change . Special probes have been developed to sample partially dried powder in different places within the dryer (ref . Langrish) .

Tray dryer Indirect dryer Spray dryer

EXPERIMENTAL METHODS Lab-, pilot-, and plant-scale experiments all play important roles in drying research . Lab-scale experiments are often necessary to study product characteristics and physical properties; pilot-scale experiments are often used in proof-of-concept process tests and to generate larger quantities of sample material; and plant-scale experiments are often needed to diagnose processing problems and to start or change a full-scale process . Quite often, however, plant data are difficult to obtain since plants are not generally designed to facilitate experimental measurements . Measurement of Drying Curves Measuring and using experimental drying curves can be difficult . Typically, this is a three-step process . The first step is to collect samples at different times of drying, the second step is to analyze each sample for moisture, and the third step is to interpret the data to make process decisions . Solid sample collection techniques depend on the type of dryer . Since a drying curve is the moisture content as a function of time, it must be possible to obtain material before the drying process is complete . There are several important considerations when sampling material for a drying curve: 1 . The sampling process needs to be fast relative to the drying process . Drying occurring during or after sampling can produce misleading results . Samples must be sealed prior to analysis . Plastic bags do not provide a sufficient seal . 2 . In heterogeneous samples, the sample must be large enough to accurately represent the composition of the mixture . Table 12-9 outlines some sampling techniques for various dryer types . Moisture measurement techniques are critical to the successful collection and interpretation of drying data . The key message of this subsection is that the moisture value almost certainly depends on the measurement technique and that it is essential to have a consistent technique when measuring moisture . Table 12-10 compares and contrasts some different techniques for moisture measurement . The most common method is gravimetric (“loss on drying”) . A sample is weighed in a sample pan or tray and placed into an oven or heater at some high temperature for a given length of time . The sample is weighed again after drying . The difference in weight is then assumed to be due to the complete evaporation of water from the sample . The sample size, temperature, and drying time are all important factors . A very large or thick sample may not dry completely in the given time; a very small sample may not accurately represent the composition of a heterogeneous sample . A low temperature

TABLE 12-10

12-29

can fail to completely dry the sample, and a temperature that is too high can burn the sample, causing an artificially high loss of mass . Usually solid samples are collected as described, but in some experiments, it is more convenient to measure the change in humidity of the air due to drying . This technique requires a good mass balance of the system and is more common in lab-scale equipment than pilot- or plant-scale equipment . Performing a Mass and Energy Balance on a Large Industrial Dryer Measuring a mass and energy balance on a large dryer is often necessary to understand how well the system is operating and how much additional capacity may be available . This exercise can also be used to detect and debug gross problems, such as leaks and product buildup . There are four steps to this process . 1 . Draw a sketch of the overall process including all the flows of mass into and out of the system . Look for places where air can leak into or out of the system . There is no substitute for physically walking around the equipment to get this information . 2 . Decide on the envelope for the mass and energy balance . Some dryer systems have hot-air recycle loops and/or combustion or steam heating systems . It is not always necessary to include these to understand the dryer operation . 3 . Decide on places to measure airflows and temperatures and to take feed and product samples . Drying systems and other process equipment are frequently not equipped for such measurements; the system may need minor modification, such as the installation of ports into pipes for pitot tubes or humidity probes . These ports must not leak when a probe is in place . 4 . Take the appropriate measurements and calculate the mass and energy balances . In continuous operations, these measurements should be taken when the process is at a steady-state condition; data from different locations should be coordinated to be collected within a narrow time window . Care should be taken to seal samples effectively and analyze them quickly, ideally during the course of the experiment . The measurements are inlet and outlet temperatures, humidities, and flow rates of the air inlets and outlets as well as the moisture and temperature of the feed and dry solids . The following are methods for each of the measurements: Airflow Rate This is often the most difficult to measure . Fan curves are frequently available for blowers but are not always reliable . A small pitot tube can be used (see Sec . 22, Waste Management, in this text) to measure the local velocity . The best location for use of a pitot tube is in a straight section of pipe . Measurements at multiple positions in the cross section of the pipe or duct are advisable, particularly in laminar flow or near elbows and other flow disruptions . Air Temperature A simple thermocouple can be used in most cases, but in some cases special care must be taken to ensure that wet or sticky material does not build up on the thermocouple . A wet thermocouple will yield a low temperature from evaporative cooling . Air Humidity Humidity probes need to be calibrated before use, and the absolute humidity needs (or both the relative humidity and temperature need) to be recorded . If the probe temperature is below the dew point of the air in the process, then condensation on the probe will occur until the probe heats . Feed and Exit Solids Rate These are generally known, particularly for a unit in production . Liquids can be measured by using a bucket and stopwatch . Solids can be measured in a variety of ways .

Moisture Determination Techniques

Method

Principle

Advantages

Disadvantages

Gravimetric (loss on drying)

Water evaporates when sample is held at a high temperature . Difference in mass is recorded .

Simple technique . No extensive calibration methods are needed . Lab equipment is commonly available .

Method is slow . Measurement time is several minutes to overnight (depending on material and accuracy) . Generally not suitable for process control . Does not differentiate between water and other volatile substances .

IR/NIR

Absorption of infrared radiation by water is measured . Absorption of RF or microwave energy is measured . The equilibrium relative humidity headspace above sample in a closed chamber is measured . Sorption isotherm is used to determine moisture .

Fast method . Suitable for very thin layers or small particles . Fast method . Suitable for large particles . Relatively quick method . Useful particularly if a final moisture specification is in terms of water activity (to retard microorganism growth) .

Only surface moisture is detected . Extensive calibration is needed . Extensive calibration is needed .

Chemical titration that is water-specific . Material can be either added directly to a solvent or heated in an oven, with the headspace purged and bubbled through solvent .

Specific to water only and very precise . Units can be purchased with an autosampler . Measurement takes only a few minutes .

RF/microwave Equilibrium relative humidity (ERH)

Karl Fischer titration

May give misleading results since the surface of the material will equilibrate with the air . Large particles with moisture gradients can give falsely low readings . Measurement of relative humidity can be imprecise . Equipment is expensive and requires solvents . Minimal calibration required . Sample size is small, which may pose a problem for heterogeneous mixtures .

12-30

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-31 Variety of tools used to measure mass and energy balances on dryers .

DRYING OF NONAQUEOUS SOLVENTS Practical Considerations Removal of nonaqueous solvents from a material presents several practical challenges . First, solvents are often flammable and require drying either in an inert environment, such as superheated steam or nitrogen, or in a gas phase comprised solely of solvent vapor . The latter will occur in indirect or vacuum drying equipment . Second, the solvent vapor must be collected in an environmentally acceptable manner . An additional practical consideration is the remaining solvent content that is acceptable in the final product . Failure to remove all the solvent can lead to problems such as toxicity of the final solid or can cause the headspace of packages, such as drums, to accumulate solvent vapor . Physical Properties The physical properties that are important in solvent drying are the same as those for an aqueous system . The vapor pressure of a solvent is the most important property since it provides the thermodynamic driving force for drying . Acetone (BP 57°C), for example, can be removed from a solid at atmospheric pressure readily by boiling, but glycerol (BP 200°C) will dry only very slowly . Like water, a solvent may become bound to the solid and have a lower vapor pressure . This effect should be considered when one is designing a solvent-drying process . Diffusion of nonaqueous solvents through a material can be slow . The diffusion coefficient is directly related to the size of the diffusing molecule, so molecules larger than water typically have diffusion coefficients that have a much lower value . This phenomenon is known as selective diffusion. Large diffusing molecules can become kinetically trapped in the solid matrix . Solvents with a lower molecular weight will often evaporate from a material faster than a solvent with a higher molecular weight, even if the vapor pressure of the larger molecule is higher . Some encapsulation methods rely on selective diffusion; an example is instant coffee production using spray drying, where volatile flavor and aroma components are retained in particles more than water, even though they are more volatile than water, as shown in Fig . 12-32 . PRODUCT QUALITY CONSIDERATIONS Overview The drying operation usually has a very strong influence on final product quality and product performance measures . And the final product quality strongly influences the value of the product . Generally, a specific particle or unit size, a specific density, a specific color, and a specific target moisture are desired . Naturally every product is somewhat different, but these are usually the first things we need to get right .

Target Moisture This seems obvious, but it’s very important to determine the right moisture target before we address other drying basics . Does biological activity determine the target, flowability of the powder, shelf life, etc .? Sometimes a very small (1 to 2 percent) change in the target moisture will have a profound impact on the size of dryer required . This is especially true for difficult-to-dry products with flat falling-rate drying characteristics . Therefore, spend the time necessary to get clear on what really determines the moisture target . And as noted earlier in this subsection, care should be taken to define a moisture measurement method since results are often sensitive to the method . Particle Size Generally a customer or consumer wants a very specific particle size—and the narrower the distribution, the better . No one wants lumps or dust . The problem is that some attrition and sometimes agglomeration occur during the drying operation . We may start out with the right particle size, but we must be sure the dryer we’ve selected will not adversely affect particle size to the extent that it becomes a problem . Some dryers will

100

10−1 Dacetone/Dwater

Feed and Exit Solids Moisture Content These need to be measured by using an appropriate technique, as described above . Use the same method for both the feed and exit solids . Don’t rely on formula sheets for feed moisture information . Figure 12-31 shows some common tools used in these measurements .

10−2

Coffee extract

10−3

10−4

0

20

40 60 Water, wt %

80

100

FIG. 12-32 The ratio of the diffusion coefficients of acetone to water in instant coffee as a function of moisture content (taken from Thijssen et al ., De Ingenieur, JRG, 80, Nr . 47 (1968)] . Acetone has a much higher vapor pressure than water, but is selectively retained in coffee during drying .

SOLIDS-DRYING FUNDAMENTALS treat particles more gently than others . Particle size is also important from a segregation standpoint . See Sec . 18, Liquid-Solid Operations and Equipment . Fine particles can also increase the risk of fire or explosion . Density Customers and consumers are generally very interested in getting the product density they have specified or expect . If the product is a consumer product and is going into a box, then the density needs to be correct to fill the box to the appropriate level . If density is important, then product shrinkage during drying can be an important harmful transformation to consider . This is particularly important for biological products for which shrinkage can be very high . This is why freeze drying can be the preferred dryer for many of these materials . Solubility Many dried products are rewet either during use by the consumer or by a customer during subsequent processing . Shrinkage can again be a very harmful transformation . Often shrinkage is a virtually irreversible transformation that creates an unacceptable product morphology . Case hardening is a phenomenon that occurs when the outside of the particle or product initially shrinks to form a very hard and dense skin that does not easily rewet . A common cause is capillary collapse, discussed along with shrinkage below . Flowability If we’re considering particles, powders, and other products that are intended to flow, then this is a very important consideration . These materials need to easily flow from bins, from hoppers, and out of boxes for consumer products . Powder flowability is a measurable characteristic using rotational shear cells (Peschl, Freeman) or translational shear cells (Jenike) in which the powder is consolidated under various normal loads; then the shear force is measured, enabling a complete yield locus curve to be constructed . This can be done at various powder moistures to create a curve of flowability versus moisture content . Some minimal value is necessary to ensure free flow . Additional information on these devices and this measure can be found in Sec . 21, Solids Processing and Particle Technology . Color Product color is usually a very important product quality attribute, and a change in color can be caused by several different transformations . Transformations Affecting Product Quality Drying, as with any other unit operation, has both productive and harmful transformations that occur . The primary productive transformation is water removal of course, but there are many harmful transformations that can occur and adversely affect product quality . The most common of these harmful transformations includes product shrinkage; attrition or agglomeration; loss of flavor, aroma, and nutritional value; browning reactions; discoloration; stickiness; and flowability problems . These issues were discussed briefly above, but are worth a more in-depth review . Shrinkage Shrinkage is a particularly important transformation with several possible mechanisms to consider . It’s usually especially problematic with food and other biological materials, but is a very broadly occurring phenomenon . Shrinkage generally affects solubility, wettability, texture and morphology, and absorbency . It can be observed when drying lumber when it induces stress cracking and during the drying of coffee beans prior to roasting . Tissue, towel, and other paper products undergo some shrinkage during drying . And many chemical products shrink as water evaporates, creating voids and capillaries prone to collapse as additional water evaporates . As we consider capillary collapse, there are several mechanisms worth mentioning . Surface tension . The capillary suction created by a receding liquid meniscus can be extremely high . Plasticization . An evaporating solvent which is also a plasticizer of polymer solute product will lead to greater levels of collapse and shrinkage . Electric charge effects . The van der Waals and electrostatic forces can also be a strong driver of collapse and shrinkage . Surface Tension These effects are very common and worthy of a few more comments . Capillary suction created by a receding liquid meniscus can create very high pressures for collapse . The quantitative expression for the pressure differential across a liquid-fluid interface was first derived by Laplace in 1806 . The meniscus, which reflects the differential, is affected by the surface tension of the fluid . Higher surface tensions create greater forces for collapse . These strong capillary suction pressures can easily collapse a pore . We can reduce these suction pressures by using low-surface-tension fluids or by adding surfactants, in the case of water, which will also significantly reduce surface tension ( from 72 to 30 dyn/cm) . The collapse can also be reduced with some dryer types . Freeze drying and heat pump drying can substantially reduce collapse, but the capital cost of these dryers is sometimes prohibitive . At the other extreme, dryers that rapidly flash off the moisture can reduce collapse . This mechanism can also be affected by particle size such that the drying is primarily boundary-layercontrolled . When the particle size becomes sufficiently small, moisture can diffuse to the surface at a rate sufficient to keep the surface wetted . This has been observed in a gel-forming food material when the particle size reached 150 to 200 µm (Genskow, “Considerations in Drying Consumer Products,” Proceedings International Drying Symposium, Versailles, France, 1988) .

12-31

Biochemical Degradation Biochemical degradation is another harmful transformation that occurs with most biological products . There are four key reactions to consider: lipid oxidation, Maillard browning, protein denaturation, and various enzyme reactions . These reactions are both heat- and moisture-dependent such that control of temperature and moisture profiles can be very important during drying . Lipid oxidation Lipid oxidation is normally observed as a product discoloration and can be exacerbated with excessive levels of bleach . It is catalyzed by metal ions, enzymes, and pigments . Acidic compounds can be used to complex the metal ions . Synthetic antioxidants such as butylated hydroxytoluene (BHT) and butylated hydroxyanisole (BHA) can be added to the product, but are limited and coming under increased scrutiny due to toxicology concerns . It may be preferable to use natural antioxidants such as lecithin or vitamin E or to dry under vacuum or in an inert (nitrogen, steam) atmosphere . Protein denaturation Normally protein denaturation is observed as an increase in viscosity and a decrease in wettability . It is temperaturesensitive, generally occurring between 40 and 80°C . A common drying process scheme is to dry thermally and under wet-bulb drying conditions without overheating and then vacuum, heat-pump, or freeze-dry to the target moisture . Enzyme reactions Enzymatic browning is caused by the enzyme polyphenol oxidase which causes phenols to oxidize to orthoquinones . The enzyme is active between pH 5 and 7 . A viable process scheme again is to dry under vacuum or in an inert (nitrogen, steam) atmosphere . Maillard browning reaction This nonenzymatic reaction is observed as a product discoloration, which in some products creates an attractive coloration . The reaction is temperature-sensitive, and normally the rate passes through a maximum and then falls as the product becomes drier . The reaction can be minimized by minimizing the drying temperature, reducing the pH to acidic, or adding an inhibitor such as sulfur dioxide or metabisulfate . A viable process scheme again is to dry thermally and under wet-bulb drying conditions without overheating and then vacuum, heat-pump, or freeze-dry to the target moisture . Some of the above reactions can be minimized by reducing the particle size and using a monodisperse particle size distribution . The small particle size will better enable wet-bulb drying, and the monodisperse size will reduce overheating of the smallest particles . Stickiness, Lumping, and Caking These are not characteristics we generally want in our products . They generally connote poor product quality, but can be a desirable transformation if we are trying to enlarge particle size through agglomeration . Stickiness, lumping, and caking are phenomena that are dependent on product moisture and product temperature . The most general description of this phenomenon is created by measuring the cohesion (particle to particle) of powders, as described below . A related measure is adhesion—particle-to-wall interactions . Finally, the sticky point is a special case for materials that undergo glass transitions . The sticky point can be determined by using a method developed by Lazar and later by Downton [Downton, Flores-Luna, and King, “Mechanism of Stickiness in Hygroscopic, Amorphous Powders,” I&EC Fundamentals 21: 447 (1982)] . In the simplest method, a sample of the product, at a specific moisture, is placed in a closed tube which is suspended in a water bath . A small stirrer is used to monitor the torque needed to “stir” the product . The water bath temperature is slowly increased until the torque increases . This torque increase indicates a sticky point temperature for that specific moisture . The test is repeated with other product moistures until the entire stickiness curve is determined . A typical curve is shown in Fig . 12-33 . As noted, a sticky point mechanism is a glass transition—the transition when a material changes from the glassy state to the rubbery liquid state . Glass transitions are well documented in food science (Levine and Slade) . Roos and Karel [“Plasticizing Effect of Water on Thermal Behavior and Crystallization of Amorphous Food Models,” J . Food Sci . 56(1): 38–43 (1991)] have demonstrated that for these types of products, the glass transition temperature follows the sticky point curve within about 2°C . This makes it straightforward to measure the stickiness curve by using a differential scanning calorimeter (DSC) . Somewhat surprisingly, even materials that are not undergoing glass transitions exhibit this behavior, as demonstrated with the detergent stickiness curve above . Lumping and caking can be measured by using the rotational shear cells (Peschl, Freeman) or translational shear cells (Jenike) noted above for measuring flowability . The powder is consolidated under various normal loads, and then the shear force is measured, enabling a complete yield locus curve to be constructed . This can be done at various powder moistures to create a curve of cake strength versus moisture content . Slurries and dry solids are free-flowing, and there is a cohesion/adhesion peak at an intermediate moisture content, typically when voids between particles are largely full of liquid . A variety of other test methods for handling properties and flowability are available .

12-32

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING Suzuki et al ., “Mass Transfer from a Discontinuous Source,” Proc. PACHEC ’72, Kyoto, Japan, 3: 267–276 (1972) . Thijssen and Coumans, “Short-cut Calculation of Non-isothermal Drying Rates of Shrinking and Non-shrinking Particles Containing an Expanding Gas Phase,” Proc. 4th Int. Drying Symp., IDS ’84, Kyoto, Japan, 1: 22–30 (1984) . Thijssen and Rulkens, “Retention of Aromas in Drying Food Liquids,” De Ingenieur, JRG, 80(47) (1968) . Van der Lijn, “Simulation of Heat and Mass Transfer in Spray Drying,” doctoral thesis, Wageningen, 1976 . Van Meel, “Adiabatic Convection Batch Drying with Recirculation of Air,” Chem. Eng. Sci. 9: 36–44 (1958) . Viollez and Suarez, “Drying of Shrinking Bodies,” AIChE J. 31: 1566–1568 (1985) . Waananan, Litchfield, and Okos, “Classification of Drying Models for Porous Solids,” Drying Technol. 11(1): 1–40 (1993) .

20

% Moisture

Sticky Region

10

Nonsticky Region SOLIDS-DRYING EQUIPMENT—GENERAL ASPECTS 0 80

90

100

110

120

130

Temp. (°C) FIG. 12-33 Detergent stickiness curve .

Product quality was addressed quite comprehensively by Evangelos Tsotsas at the 2d Nordic Drying Conference [Tsotsas, “Product Quality in Drying—Luck, Trial, Experience, or Science?” 2d Nordic Drying Conference, Copenhagen, Denmark, 2003] . Tsotsas notes that 31 percent of the papers at the 12th International Drying Symposium refer to product quality . The top five were color (12 percent), absence of chemical degradation (10 percent), absence of mechanical damage (9 percent), bulk density (8 percent), and mechanical properties (7 percent) . All these properties are reasonably straightforward to measure . They are physical properties, and we are familiar with them for the most part . However, down the list at a rank of 20 with only 2 percent of the papers dealing with it, we have sensory properties . This is the dilemma—sensory properties should rank very high, but they don’t because we lack the tools to measure them effectively . For the most part, these quality measures are subjective rather than objective, and frequently they require direct testing with consumers to determine the efficacy of a particular product attribute . So the issue is really a lack of physical measurement tools that directly assess the performance measures important to the consumer of the product . The lack of objective performance measures and unknown mechanistic equations also makes mathematical modeling very difficult for addressing quality problems . The good news is that there has been a shift from the macro to the meso and now to the micro scale in drying science . We have some very powerful analytical tools to help us understand the transformations that are occurring at the meso scale and micro scale . ADDITIONAL READINGS Keey, Drying of Loose and Particulate Materials, Hemisphere, New York, 1992 . Keey, Langrish, and Walker, Kiln Drying of Lumber, Springer-Verlag, Heidelberg, 2000 . Keey and Suzuki, “On the Characteristic Drying Curve,” Int. J. Heat Mass Transfer 17: 1455–1464 (1974) . Kemp and Oakley, “Modeling of Particulate Drying in Theory and Practice,” Drying Technol. 20(9): 1699–1750 (2002) . Kock et al ., “Design, Numerical Simulation and Experimental Testing of a Modified Probe for Measuring Temperatures and Humidities in Two-Phase Flow,” Chem. Eng. J. 76(1): 49–60 (2000) . Liou and Bruin, “An Approximate Method for the Nonlinear Diffusion Problem with a Power Relation between the Diffusion Coefficient and Concentration . 1 . Computation of Desorption Times,” Int. J. Heat Mass Transfer 25: 1209–1220 (1982a) . Liou and Bruin, “An Approximate Method for the Nonlinear Diffusion Problem with a Power Relation between the Diffusion Coefficient and Concentration . 2 . Computation of the Concentration Profile,” Int. J. Heat Mass Transfer 25: 1221–1229 (1982b) . Marshall, “Atomization and Spray Drying,” AIChE Symposium Series, no . 2, p . 89 (1986) . Oliver and Clarke, “Some Experiments in Packed-Bed Drying,” Proc. Inst. Mech. Engrs . 187: 515–521 (1973) . Perré and Turner, “The Use of Macroscopic Equations to Simulate Heat and Mass Transfer in Porous Media,” in Turner and Mujumdar, eds ., Mathematical Modeling and Numerical Techniques in Drying Technology, Marcel Dekker, New York, 1996, pp . 83–156 . Ranz and Marshall, “Evaporation from Drops,” Chem. Eng. Prog. 48(3): 141–146 and 48(4): 173–180 (1952) . Schlünder, “On the Mechanism of the Constant Drying Rate Period and Its Relevance to Diffusion Controlled Catalytic Gas Phase Reactions,” Chem. Eng. Sci. 43: 2685–2688 (1988) . Schoeber and Thijssen, “A Short-cut Method for the Calculation of Drying Rates for Slabs with Concentration-Dependent Diffusion Coefficient,” AIChE. Symposium Series 73(163): 12–24 (1975) . Sherwood, “The Drying of Solids,” Ind. And Eng. Chem. 21(1): 12–16 (1929) .

General References: Cook and DuMont, Process Drying Practice, McGraw-Hill, New York, 1991 . Drying Technology—An International Journal, Taylor and Francis, New York, 1982 onward . Hall, Dictionary of Drying, Marcel Dekker, New York, 1979 . Keey, Introduction to Industrial Drying Operations, Pergamon, New York, 1978 . Mujumdar, ed ., Handbook of Industrial Drying, Marcel Dekker, New York, 1995 . Van’t Land, Industrial Drying Equipment, Marcel Dekker, New York, 1991 . Tsotsas and Mujumdar, eds ., Modern Drying Technology (vols . 1–6), Wiley, 2011 . Aspen Process Manual (Internet knowledge base), Aspen Technology, Boston, 2000 onward . Nonhebel and Moss, Drying of Solids in the Chemical Industry, CRC Press, Cleveland, Ohio, 1971 .

CLASSIFICATION AND SELECTION OF DRYERS Drying equipment may be classified in several ways . Effective classification is vital in selection of the most appropriate dryer for the task and in understanding the key principles on which it operates . The main drying-process attributes are as follows: 1 . Form of feed and product—particulate (solid or liquid feed), sheet, slab 2 . Mode of operation—batch or continuous 3 . Mode of heat transfer—convective (direct), conductive (indirect), radiative, or dielectric 4 . Condition of solids—static bed, moving bed, fluidized or dispersed 5 . Gas-solids contacting—parallel flow, perpendicular flow, or throughcirculation 6 . Gas flow pattern—cross-flow, cocurrent, or countercurrent Other important features of the drying system are the type of carrier gas (air, inert gas, or superheated steam/solvent), use of gas or solids recycle, type of heating (indirect or direct-fired), and operating pressure (atmospheric or vacuum) . However, in the selection of a group of dryers for preliminary consideration in a given drying problem, the most important factor is often category 1, the form, handling characteristics, and physical properties of the wet material . Table 12-11 shows the major categories of drying equipment, organized by feed type . This section compares these types in general terms . Each dryer type listed in Table 12-11 is discussed in greater detail in the Drying Equipment subsection . Description of Dryer Classification and Selection Criteria 1 . Form of Feed and Product Dryers are specifically designed for particular feed and product forms; dryers handling films, sheets, slabs, and bulky artifacts form a clear subset . Most dryers are for particulate products, but the feed may range from a solution or slurry ( free-flowing liquid) through a sticky paste to wet filter cakes, powders, or granules (again relatively freeflowing) . The ability to successfully mechanically handle the feed and product is a key factor in dryer selection (see Table 12-11) . The drying kinetics also depend strongly on solids properties, particularly particle size and porosity . The surface area/volume ratio and the internal pore structure control the extent to which an operation is diffusion-limited, i .e ., diffusion into and out of the pores of a given solids particle, not through the voids among separate particles . 2 . Mode of Operation Batch dryers are typically used for low throughputs (under 50 kg/h), for long drying times, or where the overall process is predominantly batch . Continuous dryers dominate for high throughputs, high evaporation rates, and where the rest of the process is continuous . Dryers that are inherently continuous can be operated in semibatch mode (e .g ., small-scale spray dryers) and vice versa . 3 . Mode of Heat Transfer Direct (convective) dryers These are the general operating characteristics of direct dryers . a. Direct contacting of hot gases with the solids is employed for solids heating and vapor removal . Note, in some cases, hot exhaust gas from combustion containing CO and CO2 should not contact the product and this exhaust gas heats fresh air that contacts the product using a separate heat exchanger; these are still considered “direct” dryers .

TABLE 12-11 Classification of Commercial Dryers Based on Feed Materials Handled Type of dryer

Liquids Slurries Pastes and sludges Free-flowing Pumpable suspen- Examples: filter-press True and colloidal 100-mesh (150-µm) or less . cakes, sedimentation solutions; emulRelatively free-flowing in sions . Examples: sludges, centrifuged sions . Examples: wet state . Dusty when dry . pigment slurries, solids, starch, detergents soap and deterinorganic salt Examples: centrifuged gents, calcium solutions, extracts, precipitates carbonate, benmilk, blood, waste liquors, rubber latex tonite, clay slip, lead concentrates Not applicable Not applicable Suitable only if material can Not applicable be preformed . Suited to batch operation .

Batch tray dryers Material is loaded onto a static tray and dried without agitation . Includes vacuum drying . Continuous tray and grav- Not applicable ity dryers Material dries on trays and moves between successive trays by gravity . Continuous band and Not applicable tunnel dryers Material is loaded on a continuous band or belt and is dried by convection, conduction, or radiant heat . Batch agitated and rotating Atmospheric or dryers vacuum . Suitable for Batch dryer where material small batches . Easily is moved to enhance mass- cleaned . Solvents and heat-transfer rates can be recovered . Material agitated while dried . Continuous agitated and Applicable with rotating dryers dry-product Material is mechanically recirculation . agitated or turned over during drying .

Fluidized- and spoutedbed dryers Particulate material is suspended/fluidized and simultaneously dried by upward-moving air . Pneumatic conveying dryers Particulate material is suspended in hot air (or superheated steam) and conveyed .

Not applicable

Suitable for small-scale and See comments under Pastes large-scale production . and Sludges . Vertical turbo-tray applicable

Granular, crystalline, or fibrous solids Larger than 100-mesh (150 µm) . Examples: rayon staple, salt crystals, sand, ores, potato strips, synthetic rubber

Large solids, special Continuous forms and shapes sheets Discontinuous sheets Examples: paper, Examples: veneer, Examples: pottery, wallboard, impregnated brick, rayon cakes, photographic shotgun shells, hats, fabrics, cloth, prints, leather, cellophane, painted objects, foam rubber sheets plastic sheets rayon skeins, lumber, pet food, croutons

Usually not suited for Primarily useful for materials smaller than small objects . 30-mesh (0 .5 mm) . Suited to small capacities .

Not applicable

Not applicable

Suitable for large particles Not suitable for large Not applicable (>500 µm) or small discrete or fragile objects . objects .

Not applicable

Usually not suited for Suited to a wide materials smaller than variety of shapes 30-mesh (0 .5 mm) . Material and forms . Can does not tumble or mix . be used to convey materials through heated zones . Suitable for small batches . Not applicable Easily cleaned . Material is agitated during drying, causing some degradation and/or balling up .

Not applicable

Special designs are required . Suited to veneers .

Not applicable

Not applicable

Not applicable

Not applicable

Not applicable

Not applicable

Not applicable

Not applicable

Only crystal filter Suitable for materials that dryer or centrifuge can be preformed . Will dryer may be handle large capacities suitable .

Not applicable

See comments under Liquids .

See comments under Liquids .

See comments under Liquids .

Applicable with dry-product recirculation .

Suitable only if product does not stick to walls and does not dust . Recirculation of product may prevent sticking . Generally requires recirculation of dry product . Little dusting occurs .

Applicable only as fluid-bed granulator with inert bed or dry-solids recirculator .

See comments under Liquids .

See comments under Liquids .

See comments under Slurries .

Can be used only if Usually requires recirculaproduct is recircu- tion of dry product to lated (backmixed) make suitable feed . Well to make feed suitsuited to high capacities . able for handling . Disintegration usually required .

Suitable for most materials and Suitable for most materials, Not applicable especially for high especially for high capacities, provided dusting is not capacities . Dusting or crystal abrasion will limit too severe . Chief advantage is low dust loss . Well suited its use . Low dust loss . Material must not stick or to most materials and capacities, particularly those be temperature-sensitive . requiring drying at steam temperature Fluidized bed suitable, if not Fluidized bed suitable for Only applicable for crystals, granules, and very spouted beds if too dusty . Internal coils can objects are supplement heating, short fibers . Suitable for especially for fine powders . high capacities . Suitable for conveyable in gas Suitable for high capacities . spouted beds for granules stream . over 800 µm . Suitable for materials that Suitable for materials Not applicable are easily suspended in a gas conveyable in a gas stream . stream and lose moisture Well suited to high readily . Well suited to high capacities . Only surface capacities . moisture usually removed . Product may suffer physical degradation .

12-33

12-34

TABLE 12-11 Classification of Commercial Dryers Based on Feed Materials Handled (Continued ) Type of dryer Spray dryers A liquid or slurry feed is atomized/sprayed, and the resulting droplets dry into particles .

Liquids Slurries Suited for large See comments capacities . Product under Liquids . is usually powdery, Pressure-nozzle spherical, and atomizers subject free-flowing . High to erosion . temperatures can sometimes be used with heat-sensitive materials . Products generally have low bulk density . See comments Drum and thin-film dryers Single, double, or Liquid or paste feed is twin . Atmospheric under Liquids . distributed on the outside or vacuum operaTwin-drum dryers of a hot, slowly rotating tion . Product flaky are widely used . drum . and usually dusty . Maintenance costs may be high . Sheet dryers Not applicable Not applicable Discrete or continuous solid sheets are dried by blowing air or steam through them or over them . Heat can be added by multiple methods . Freeze dryers Expensive . Usually See comments Air is removed from the used only for highunder Liquids . value products such system . Energy must be as pharmaceuticals; supplied via conduction products which are or radiation . heat-sensitive and readily oxidized . Electromagnetic drying Can be used in See comments (infrared, radiofrequency, combination with under Liquids . microwave) other dryers such as Batch or continuous drum . operation . Electromagnetic Infrared: only for thin energy added to material . films . Microwave/ radio-frequency: expensive, specialty applications .

Granular, crystalline, or fibrous solids Not applicable

Large solids, special Continuous forms and shapes sheets Not applicable Not applicable

Discontinuous sheets Not applicable

Not applicable

Not applicable

Not applicable

Not applicable

Not applicable

Not applicable

Not applicable

Not applicable

Not applicable

See description See description for for applications . applications . Items Web can be being dried need controlled with to be positioned or tension . held in place .

See comments under Liquids .

See comments under Liquids . Expensive . Usually used See comments under Applicable in spe- See comments under cial cases such on pharmaceuticals and Granular Solids . Granular Solids . as emulsionrelated products which cannot be dried successfully by coated films . other means . Applicable to fine chemicals .

See comments under Liquids .

Infrared: only for thin layers Radiofrequency/microwave

Pastes and sludges Requires special pumping equipment to feed the atomizer . See comments under Liquids .

Free-flowing Not applicable unless feed is pumpable .

Can be used only when paste or sludge can be made to flow . See comments under Liquids .

Primarily suited to drying surface moisture . Not suited for thick layers .

Especially suited for drying and baking paint and enamels .

Infrared . Useful See comments under for laboratory Continuous Sheets . work or in conjunction with other methods . Radiofrequency/ microwave: successful for foam rubber .

SOLIDS-DRYING FUNDAMENTALS b. Drying temperatures may range up to 750°C, the limiting temperature for most common structural metals . At higher temperatures, radiation becomes an important heat-transfer mechanism . c. At gas temperatures below the boiling point, the vapor content of gas influences the rate of drying and the final moisture content of the solid . With gas temperatures above the boiling point throughout, the vapor content of the gas has only a slight retarding effect on the drying rate and final moisture content . Thus, superheated vapors of the liquid being removed (e .g ., steam) can be used for drying . d. For low-temperature drying, dehumidification of the drying air may be required when atmospheric humidities are excessively high . e. Efficiency increases with an increase in the inlet gas temperature for a constant exhaust temperature . f. Because large amounts of gas are required to supply all the heat for drying, dust recovery or volatile organic compound (VOC) equipment may be very large and expensive, especially when drying very small particles . Indirect (contact or conductive) dryers These differ from direct dryers with respect to heat transfer and vapor removal: a. Heat is transferred to the wet material by conduction through a solid retaining wall, usually metallic . b. Surface temperatures may range from below freezing in the case of freeze dryers to above 500°C in the case of indirect dryers heated by combustion products . c. Indirect dryers are suited to drying under reduced pressures and inert atmospheres, to permit the recovery of solvents and to prevent the occurrence of explosive mixtures or the oxidation of easily decomposed materials . d. Indirect dryers using condensing fluids as the heating medium are generally economical from the standpoint of heat consumption, since they furnish heat only in accordance with the demand made by the material being dried . e. Dust recovery and dusty or hazardous materials can be handled more satisfactorily in indirect dryers than in direct dryers . Electromagnetic (Infrared, Radiofrequency, Microwave) These dryers use energy in the form of electromagnetic radiation . a. Infrared dryers depend on the transfer of radiant energy to evaporate moisture . The radiant energy is supplied electrically by infrared lamps, by electric resistance elements, or by incandescent refractories heated by gas . The last method has the added advantage of convection heating . Infrared heating is not widely used in the chemical industries for the removal of moisture . Its principal use is in baking or drying paint films (curing) and in heating thin layers of materials . It is sometimes used to give supplementary heating on the initial rolls of paper machines (cylinder dryers) . b. Dielectric dryers (radiofrequency or microwave) have not yet found a wide field of application, but are increasingly used . Their fundamental characteristic of generating heat within the solid indicates potentialities for drying massive geometric objects such as wood, sponge-rubber shapes, and ceramics, and for reduced moisture gradients in layers of solids . Power costs are generally much higher than the fuel costs of conventional methods; a small amount of dielectric heating (2 to 5 percent) may be combined with thermal heating to maximize the benefit at minimum operating cost . The high capital costs of these dryers must be balanced against product quality and process improvements . See more in the Drying Equipment part of this subsection . 4. Condition of Solids In solids-gas contacting equipment, the solids bed can exist in any of the following four conditions: Static This is a dense bed of solids in which each particle rests upon another at essentially the settled bulk density of the solids phase . Specifically, there is no relative motion among solids particles (Fig . 12-34) . Moving This is a slightly expanded bed of solids in which the particles are separated only enough to flow one over another . Usually the flow is downward under the force of gravity (Fig . 12-35), but upward motion by mechanical lifting or agitation may also occur within the process vessel (Fig . 12-36) . In some cases, lifting of the solids is accomplished in separate equipment, and solids flow in the presence of the gas phase is downward only . The latter is a moving bed as usually defined in the petroleum industry . In this definition, solids motion is achieved by either mechanical agitation or gravity force. Fluidized This is an expanded condition in which the solids particles are supported by drag forces caused by the gas phase passing through the interstices among the particles at some critical velocity . The superficial gas velocity upward is less than the terminal settling velocity of the solids particles; the gas velocity is not sufficient to entrain and convey continuously all the solids . Specifically, the solids phase and the gas phase are intermixed and together behave as a boiling fluid (Fig . 12-37) .

FIG. 12-34 Solids bed in static condition (tray dryer) .

12-35

FIG. 12-35 Horizontal moving bed .

Dispersed or dilute This is a fully expanded condition in which the solids particles are so widely separated that they exert essentially no influence upon one another . Specifically, the solids phase is so fully dispersed in the gas that the density of the suspension is essentially that of the gas phase alone (Fig . 12-38) . Commonly, this situation exists when the gas velocity at all points in the system exceeds the terminal settling velocity of the solids and the particles can be lifted and continuously conveyed by the gas; however, this is not always true . Cascading rotary dryers, countercurrent-flow spray dryers, and gravity settling chambers are three exceptions in which the gas velocity is insufficient to entrain the solids completely . Cascading (direct) rotary dryers with lifters illustrate all four types of flow in a single dryer . Particles sitting in the lifters ( flights) are a static bed . When they are in the rolling bed at the bottom of the dryer, or rolling off the top of the lifters, they form a moving bed . They form a falling curtain which is initially dense ( fluidized) but then spreads out and becomes dispersed . Dryers where the solid forms the continuous phase (static and moving beds) are called layer dryers, while those where the gas forms the continuous phase ( fluidized and dispersed solids) are classified as dispersion dryers. Gasparticle heat and mass transfer is much faster in dispersion dryers, and so these are often favored where high drying rates, short drying times, or high solids throughput is required . Layer dryers are very suitable for slow-drying materials requiring a long residence time . Because heat transfer and mass transfer in a gas-solids-contacting operation take place at the solids’ surfaces, maximum process efficiency can be expected with a maximum exposure of solids surface to the gas phase, together with thorough mixing of gas and solids . Both are important . Within any arrangement of particulate solids, gas is present in the voids among the particles and contacts all surfaces except at the points of particle contact . When the solids are fluidized or dispersed, the gas moves past them rapidly, and external heat- and mass-transfer rates are high . When the solids bed is in a static or slightly moving condition, however, gas within the voids is cut off from the main body of the gas phase and can easily become saturated, so that local drying rates fall to low or zero values . Some transfer of energy

FIG. 12-36

Moving solids bed in a rotary dryer with lifters .

12-36

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-39

FIG. 12-37 Fluidized solids

bed .

and mass may occur by diffusion, but it is usually insignificant . The problem can be much reduced by using through-circulation of gas instead of crosscirculation, or by agitating and mixing the solids . Solids Agitation and Mixing There are four alternatives: 1 . No agitation, e .g ., tray and band dryers . This is desirable for friable materials . However, drying rates can be extremely low, particularly for cross-circulation and vacuum drying . 2 . Mechanical agitation, e .g ., vertical pan and paddle dryers . This improves mixing and drying rates, but may give attrition depending on agitator speed; and solids may stick to the agitator . These are illustrated in Fig . 12-39 . 3 . Vessel rotation, e .g ., double-cone and rotary dryers . Mixing and heat transfer are better than for static dryers but may be less than for mechanical agitation . Formation of balls and lumps may be a problem . 4 . Airborne mixing, e .g ., fluidized beds and flash and spray dryers . Generally there is excellent mixing and mass transfer, but feed must be dispersible and entrainment and gas cleaning are higher . Solids transport In continuous dryers, the solids must be moved through the dryer . These are the main methods of doing this: 1 . Gravity flow (usually vertical), e .g ., turbo-tray, plate and moving-bed dryers, and rotary dryers (due to the slope) 2 . Mechanical conveying (usually horizontal), e .g ., band, tunnel, and paddle dryers 3 . Airborne transport, e .g ., fluidized beds and flash and spray dryers 4 . Vibration Solids flow pattern For most continuous dryers, the solids are basically in plug flow; backmixing is low for nonagitated dryers but can be extensive for mechanical, rotary, or airborne agitation . Exceptions are well-mixed fluidized beds, fluid-bed granulators, and spouted beds (well-mixed) and spray and spray/fluidized-bed units (complex flow patterns) . 5 . Gas-Solids Contacting Where there is a significant gas flow, it may contact a bed of solids in the following ways: a. Parallel flow or cross-circulation. The direction of gas flow is parallel to the surface of the solids phase . Contacting is primarily at the interface between phases, with possibly some penetration of gas into the voids among the solids near the surface . The solids bed is usually in a static condition (Fig . 12-40) .

FIG. 12-38 Solids in a dilute condition near the top of a spray dryer .

Paddle dryer .

b. Perpendicular flow or impingement. The direction of gas flow is normal to the phase interface . The gas impinges on the solids bed . Again the solids bed is usually in a static condition (Fig . 12-41) . This most commonly occurs when the solids are a continuous sheet, film, or slab . c. Through circulation. The gas penetrates and flows through interstices among the solids, circulating more or less freely around the individual particles (Fig . 12-42) . This may occur when solids are in static, moving, fluidized, or dilute conditions . 6 . Gas Flow Pattern in Dryer Where there is a significant gas flow, it may be in cross-flow, cocurrent, or countercurrent flow compared with the direction of solids movement . a. Cocurrent gas flow. The gas phase and solids particles both flow in the same direction (Fig . 12-43) . b. Countercurrent gas flow. The direction of gas flow is exactly opposite to the direction of solids movement . c. Cross-flow of gas. The direction of gas flow is at a right angle to that of solids movement, across the solids bed (Fig . 12-44) . The difference between these is shown most clearly in the gas and solids temperature profiles along the dryer . For cross-flow dryers, all solids particles are exposed to the same gas temperature, and the solids temperature approaches the gas temperature near the end of drying (Fig . 12-45) . In cocurrent dryers, the gas temperature falls throughout the dryer, and the final solids temperature is much lower than that for the cross-flow dryer (Fig . 12-46) . Hence cocurrent dryers are very suitable for drying heatsensitive materials, although it is possible to get a solids temperature peak inside the dryer . Conversely, countercurrent dryers give the most even temperature gradient throughout the dryer, but the exiting solids come into contact with the hottest, driest gas (Fig . 12-47) . These can be used to heat-treat the solids or to give low final moisture content (minimizing the local equilibrium moisture content) but are obviously unsuitable for thermally sensitive solids . SELECTION OF DRYING EQUIPMENT Dryer Selection Considerations Dryer selection is a challenging task . These are some important considerations: • Batch dryers are almost invariably used for mean throughputs below 50 kg/h, and continuous dryers are generally used above 1 ton/h; in the intervening range, either may be suitable . • Liquid or slurry feeds, large objects, or continuous sheets and films require completely different equipment from particulate feeds . • Particles and powders below 1 mm are effectively dried in dispersion or contact dryers, but most through-circulation units are unsuitable . Conversely, for particles of several millimeters or above, through-circulation dryers, rotary dryers, and spouted beds are very suitable . • Through-circulation and dispersion convective dryers (including fluidized-bed, rotary, and pneumatic types) and agitated or rotary contact dryers generally give better drying rates than nonagitated crosscirculated or contact tray dryers . • Nonagitated dryers (including through-circulation) may be preferable for fragile particles where it is desired to avoid attrition .

FIG. 12-40 Parallel gas flow over a static bed of solids .

SOLIDS-DRYING FUNDAMENTALS

FIG. 12-41 Circulating gas impinging on a large solid object in perpendicular flow, in a roller-conveyor dryer .

FIG. 12-42

Gas passing through a bed of preformed solids, in through-circulation on a perforated-band dryer .

FIG. 12-43

Cocurrent gas-solids flow in a vertical-lift dilute-phase pneumatic con-

veyor dryer .

• For organic solvents or solids which are highly flammable, are toxic, or decompose easily, contact dryers are often preferable to convective dryers, as containment is better and environmental emissions are easier to control . If a convective dryer is used, a closed-cycle system using an inert carrier gas (e .g ., nitrogen) is often required . • Cocurrent, vacuum, and freeze dryers can be particularly suitable for heatsensitive materials . A detailed methodology for dryer selection, including the use of a rulebased expert system, has been described by Kemp [Drying Technol . 13(5–7): 1563–1578 (1995) and 17(7 and 8): 1667–1680 (1999)] . A simpler step-by-step procedure is given here . 1 . Initial selection of dryers. Select those dryers which appear best suited to handling the wet material and the dry product, which fit into the continuity of the process as a whole, and which will produce a product of the desired physical properties . This preliminary selection can be made with the aid of Table 12-11, which classifies the various types of dryers on the basis of the materials handled . 2 . Initial comparison of dryers. The dryers so selected should be evaluated approximately from available cost and performance data . From this evaluation, those dryers that appear to be uneconomical or unsuitable from the standpoint of performance should be eliminated from further consideration . 3 . Drying tests. Drying tests should be conducted in those dryers still under consideration . These tests will determine the optimum operating conditions and the product characteristics and will form the basis for firm quotations from equipment vendors . 4 . Final selection of dryer. From the results of the drying tests and quotations, the final selection of the most suitable dryer can be made . These are the important factors to consider in the preliminary selection of a dryer: 1 . Properties of the material being handled a. Physical characteristics when wet (stickiness, cohesiveness, adhesiveness, flowability) b. Physical characteristics when dry c. Corrosiveness d. Toxicity e. Flammability f. Particle size g. Abrasiveness 2 . Drying characteristics of the material a. Type of moisture (bound, unbound, or both) b. Initial moisture content (maximum and range) c. Final moisture content (maximum and range) d. Permissible drying temperature e. Probable drying time for different dryers f. Level of nonwater volatiles 3 . Flow of material to and from the dryer a. Quantity to be handled per hour (or batch size and frequency) b. Continuous or batch operation c. Process prior to drying d. Process subsequent to drying

Cross-flow of gas and solids in a fluid-bed or band dryer .

150

Temperature, °C

FIG 12-44

100 Falling-rate (hindered) drying

Constant-rate (unhindered) drying

Induction period 50

Solids temperature Gas inlet temperature 0

0

5

10

15 Time

20

25

30

FIG. 12-45 Temperature profiles along a continuous plug-flow dryer for cross-flow of gas and solids .

(Aspen Technology Inc.)

12-37

12-38

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

150

Temperature, °C

Gas inlet temperature Solids temperature 100 Hindered drying

Unhindered drying 50 Solids peak temperature

0

1

0

4

3

2 Time

FIG. 12-46 Temperature profiles along a continuous plug-flow dryer for cocurrent flow of gas and

solids . (Aspen Technology Inc.)

4 . Product quality a. Shrinkage b. Contamination c. Uniformity of final moisture content d. Decomposition of product e. Overdrying f. Particle size distribution (if applicable) g. Product temperature h. Bulk density 5 . Recovery and environmental considerations a. Dust recovery b. Solvent recovery 6 . Facilities available at site of proposed installation a. Space b. Flow rate, temperature, humidity, and cleanliness of air c. Available fuels d. Available electric power e. Permissible noise, vibration, dust, or heat losses f. Source of wet feed g. Exhaust-gas outlets/permissible VOC discharge levels

Following preliminary selection of suitable types of dryers, a rough evaluation of the size and cost should be made to eliminate those which are obviously uneconomical . Information for this evaluation can be obtained from material presented under discussion of the various dryer types . When data are inadequate, usually preliminary cost and performance data can be obtained from the equipment manufacturer . In comparing dryer performance, the factors in the preceding list which affect dryer performance should be properly weighed . DRYER DESCRIPTIONS Batch Tray Dryers Examples and Synonyms Direct heat tray dryer, batch throughcirculation dryer, vacuum shelf dryer, through-circulation drying room, vacuum oven, vacuum-shelf dryer . Description A tray or compartment dryer is an enclosed, insulated housing in which solids are placed upon tiers of trays in the case of particulate solids or stacked in piles or upon shelves in the case of large objects . Heat transfer may be direct from gas to solids by circulation of large volumes of hot gas or indirect by use of heated shelves, radiator coils,

150

Temperature, °C

Hindered drying 100 Unhindered drying 50 Gas temperature Solids temperature

I Induction 0

0

1

2 Time

3

4

FIG. 12-47 Temperature profiles along a continuous plug-flow dryer for countercurrent flow of gas and solids . (Aspen Technology Inc.)

SOLIDS-DRYING FUNDAMENTALS or refractory walls inside the housing . In indirect-heat units, excepting vacuum-shelf equipment, circulation of a small quantity of gas is usually necessary to sweep moisture vapor from the compartment and prevent gas saturation and condensation . Compartment units are employed for the heating and drying of lumber, ceramics, sheet materials (supported on poles), painted and metal objects, and all forms of particulate solids . Field of Application Because of the high labor requirements usually associated with loading or unloading the compartments, batch compartment equipment is rarely economical except in the following situations: 1 . A long heating cycle is necessary because the size of the solid objects or permissible heating temperature requires a long holdup for internal diffusion of heat or moisture . This case may apply when the cycle will exceed 12 to 24 h . 2 . The production of several different products requires strict batch identity and thorough cleaning of equipment between batches . This is a situation existing in many small, multiproduct plants, e .g ., for pharmaceuticals or specialty chemicals . 3 . The quantity of material to be processed does not justify investment in more expensive, continuous equipment . This case would apply in many pharmaceutical drying operations . Further, because of the nature of solids-gas contacting, which is usually by parallel flow and rarely by through-circulation, heat transfer and mass transfer are comparatively inefficient . For this reason, use of tray and compartment equipment is restricted primarily to ordinary drying and heat-treating operations . Auxiliary Equipment If noxious gases, fumes, or dust is given off during the operation, dust or fume recovery equipment will be necessary in the exhaust gas system . Condensers are employed for the recovery of valuable solvents from dryers . To minimize heat losses, thorough insulation of the compartment with brick or other insulating compounds is necessary . Vacuum-shelf dryers require auxiliary stream jets or other vacuumproducing devices, intercondensers for vapor removal, and occasionally wet scrubbers or (heated) bag-type dust collectors . Uniform depth of loading in dryers and furnaces handling particulate solids is essential to consistent operation, minimum heating cycles, or control of final moisture . After a tray has been loaded, the bed should be leveled to a uniform depth . Special preform devices, noodle extruders, pelletizers, etc ., are employed occasionally for preparing pastes and filter cakes so that screen bottom trays can be used and the advantages of through-circulation approached . Control of tray and compartment equipment is usually maintained by control of the circulating air temperature (and humidity) and rarely by the solids temperature . On vacuum units, control of the absolute pressure and heating-medium temperature is utilized . In direct dryers, cycle controllers are frequently employed to vary the air temperature or velocity across the solids during the cycle; e .g ., high air temperatures may be employed during a constant-rate drying period while the solids surface remains close to the air wet-bulb temperature . During the falling-rate periods, this temperature may be reduced to prevent case hardening or other degrading effects caused by overheating the solids surfaces . In addition, higher air velocities may be employed during early drying stages to improve heat transfer; however, after surface drying has been completed, this velocity may need to be reduced to prevent dusting . Two-speed circulating fans are employed commonly for this purpose . Direct-Heat Tray Dryers Satisfactory operation of tray-type dryers depends on maintaining a constant temperature and a uniform air velocity over all the material being dried . Circulation of air at velocities of 1 to 10 m/s is desirable to improve the surface heat-transfer coefficient and to eliminate stagnant air pockets . Proper airflow in tray dryers depends on sufficient fan capacity, on the design of ductwork to modify sudden changes in direction, and on properly placed baffles . Nonuniform airflow is one of the most serious problems in the operation of tray dryers. Tray dryers may be of the tray-truck or the stationary-tray type . In the former, the trays are loaded on trucks which are pushed into the dryer; in the latter, the trays are loaded directly into stationary racks within the dryer . Trays may be square or rectangular, with 0 .5 to 1 m2 per tray, and may be fabricated from any material compatible with corrosion and temperature conditions . When the trays are stacked in the truck, there should be a clearance of not less than 4 cm between the material in one tray and the bottom of the tray immediately above . When material characteristics and handling permit, the trays should have screen bottoms for additional drying area . Metal trays are preferable to nonmetallic trays, since they conduct heat more readily . Tray loadings range usually from 1 to 10 cm deep . Steam is the usual heating medium, and a standard heater arrangement consists of a main heater before the circulating fan . When steam is not available or the drying load is small, electric heat can be used . For temperatures above 450 K, products of combustion can be used, or indirect-fired air heaters .

12-39

Air is circulated by propeller or centrifugal fans; the fan is usually mounted within or directly above the dryer . Total pressure drop through the trays, heaters, and ductwork is usually in the range of 2 .5 to 5 cm of water . Air recirculation is generally on the order of 80 to 95 percent except during the initial drying stage of rapid evaporation . Fresh air is drawn in by the circulating fan, frequently through dust filters . In most installations, air is exhausted by a separate small exhaust fan with a damper to control air recirculation rates . Prediction of heat- and mass-transfer coefficients in direct heat tray dryers In convection phenomena, heat-transfer coefficients depend on the geometry of the system, the gas velocity past the evaporating surface, and the physical properties of the drying gas . In estimating drying rates, the use of heattransfer coefficients is preferred because they are usually more reliable than mass-transfer coefficients . In calculating mass-transfer coefficients from drying experiments, the partial pressure at the surface is usually inferred from the measured or calculated temperature of the evaporating surface . Small errors in temperature have negligible effect on the heat-transfer coefficient but introduce relatively large errors in the partial pressure and hence in the mass-transfer coefficient . For many cases in drying, the heat-transfer coefficient is proportional to Ugn, where Ug is an appropriate local gas velocity . For flow parallel to plane plates, the exponent n has been reported to range from 0 .35 to 0 .8 . The differences in exponent have been attributed to differences in flow pattern in the space above the evaporating surface, particularly whether it is laminar or turbulent, and whether the length is sufficient to allow fully developed flow . In the absence of applicable specific data, the heat-transfer coefficient for the parallel-flow case can be taken, for estimating purposes, as h=

8 .8 J 0 .8 Dc0 .2

(12-68)

where h is the heat-transfer coefficient, W/(m2 ⋅ K); J is the gas mass flux, kg/ (m2 ⋅ s); and Dc is a characteristic dimension of the system . The experimental data have been weighted in favor of an exponent of 0 .8 in conformity with the usual Colburn j factor, and average values of the properties of air at 370 K have been incorporated . Typical values are in the range 10 to 50 W/(m2 ⋅ K) . Experimental data for drying from flat surfaces have been correlated by using the equivalent diameter of the flow channel or the length of the evaporating surface as the characteristic length dimension in the Reynolds number . However, the validity of one versus the other has not been established . The proper equivalent diameter probably depends at least on the geometry of the system, the roughness of the surface, and the flow conditions upstream of the evaporating surface . For airflow impinging normally to the surface from slots and nozzles, the heat-transfer coefficient can be obtained from the wellknown Martin correlation: Martin, “Heat and Mass Transfer Between Impinging Gas Jets and Solid Surfaces,” Advances in Heat Transfer, vol . 13, Academic Press, 1977, pp . 1–66 . This correlation uses relevant geometric properties such as the diameter of the holes, the spacing between the slots/nozzles, and the distance between the slots/nozzles and the sheet . See Example 12-23 for calculation of the heat-transfer coefficient from an array of jets . Most efficient performance is obtained with plates having open areas equal to 2 to 3 percent of the total heat-transfer area . The plate should be located at a distance equal to four to six hole (or equivalent) diameters from the heat-transfer surface . As with many drying calculations, the most reliable design method is to perform experimental tests and to scale up . By measuring performance on a single tray with similar layer depth, air velocity, and temperature, the specific drying rate (SDR) concept as described in the Solids Drying Fundamentals subsection can be applied to give the total area and number of trays required for the full-scale dryer . Performance data for direct heat tray dryers A standard two-truck dryer is illustrated in Fig . 12-48 . Adjustable baffles or a perforated distribution plate is normally employed to develop 0 .3 to 1 .3 cm of water pressure drop at the wall through which air enters the truck enclosure . This will enhance the uniformity of air distribution, from top to bottom, among the trays . Performance data on some typical tray and compartment dryers are tabulated in Table 12-12 . These indicate that an overall rate of evaporation of 0 .0025 to 0 .025 kg water/(s⋅m2) of tray area may be expected from tray and tray-truck dryers . The thermal efficiency of this type of dryer will vary from 20 to 50 percent, depending on the drying temperature used and the humidity of the exhaust air . In drying to very low moisture contents under temperature restrictions, the thermal efficiency may be on the order of 10 percent . Maintenance will run from 3 to 5 percent of the installed cost per year . Batch Through-Circulation Dryers These may be either of shallow bed or deep bed type . In the first type of batch through-circulation dryer, heated air passes through a stationary permeable bed of the wet material placed on removable screen-bottom trays suitably supported in the dryer . This type is similar to a standard tray dryer except that hot air passes through the wet solid

12-40

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING TABLE 12-13 Performance Data for Batch Through-Circulation Dryers* Kind of material Capacity, kg product/h Number of trays Tray spacing, cm Tray size, cm Depth of loading, cm Physical form of product

FIG. 12-48 Double-truck tray dryer . (A) Air inlet duct . (B) Air exhaust

duct with damper . (C ) Adjustable-pitch fan, 1 to 15 hp . (D) Fan motor . (E) Fin heaters . (F ) Plenum chamber . (G ) Adjustable air blast nozzles . (H ) Trucks and trays .

instead of across it. The pressure drop through the bed of material can be estimated using the Ergun equation [Ergun, S ., “Fluid Flow through Packed Columns,” Chem. Eng. Progress 48 (1952)] and does not usually exceed about 2 cm of water . In the second type, deep perforated-bottom trays are placed on top of plenum chambers in a closed-circuit hot air circulating system . In some food-drying plants, the material is placed in finishing bins with perforated bottoms; heated air passes up through the material and is removed from the top of the bin, reheated, and recirculated . The latter types involve a pressure drop through the bed of material of 1 to 8 cm of water at relatively low air rates . Table 12-13 gives performance data on three applications of batch through-circulation dryers . Batch through-circulation dryers are restricted in application to granular materials (particle size typically 1 mm or greater) that permit free flow-through circulation of air . Drying times are usually much shorter than in parallel-flow tray dryers . Design methods are included in the subsection Continuous Through-Circulation Dryers . Vacuum-Shelf Dryers Vacuum-shelf dryers are indirectly heated batch dryers consisting of a vacuum-tight chamber usually constructed of cast iron or steel plate; heated, supporting shelves within the chamber; a vacuum source; and usually a condenser . One or two doors are provided, depending on the size of the chamber . The doors are sealed with resilient gaskets of rubber or similar material . Hollow shelves of flat steel plate are fastened permanently inside the vacuum chamber and are connected in parallel to inlet and outlet headers . The heating medium, entering through one header and passing through the hollow shelves to the exit header, is generally steam, ranging in pressure from 700 kPa gauge to subatmospheric pressure for low-temperature operations . Low temperatures can be provided by circulating hot water, and high temperatures can be obtained by circulating hot oil or other heat-transfer liquids . Some small dryers employ electrically heated shelves . The material to be dried is placed in pans or trays on the heated shelves . The trays are generally of metal to ensure good heat transfer between the shelf and the tray . Vacuum-shelf dryers may vary in size from 1 to 24 shelves, the largest chambers having overall dimensions of 6 m wide, 3 m long, and 2 .5 m high .

TABLE 12-12

Granular polymer 122 16 43 91 .4 × 104 7 .0 Crumbs

Initial moisture content, % 11 .1 dry basis Final moisture content, % 0 .1 dry basis Air temperature, °C 88 Air velocity, superficial, 1 .0 m/s Tray loading, kg product/m2 16 .1 Drying time, h 2 .0 Overall drying rate, kg water 0 .89 evaporated/(h⋅m2) Steam consumption, kg/kg 4 .0 water evaporated Installed power, kW 7 .5 ∗Courtesy of Wolverine Proctor & Schwartz, Inc .

Vegetable

Vegetable seeds

42 .5 24 43 91 .4 × 104 6 0 .6-cm diced cubes 669 .0

27 .7 24 43 85 × 98 4 Washed seeds 100 .0

5 .0

9 .9

77 dry-bulb 0 .6 to 1 .0

36 1 .0

5 .2 8 .5 11 .86

6 .7 5 .5 1 .14

2 .42

6 .8

19

19

Vacuum is applied to the chamber, and vapor is removed through a large pipe which is connected to the chamber in such a manner that if the vacuum is broken suddenly, the in-rushing air will not greatly disturb the bed of material being dried . This line leads to a condenser where moisture or solvent that has been vaporized is condensed . The noncondensible exhaust gas goes to the vacuum source, which may be a wet or dry vacuum pump or a steam-jet ejector . Vacuum-shelf dryers are used extensively for drying pharmaceuticals, temperature-sensitive or easily oxidizable materials, and materials so valuable that labor cost is insignificant . They are particularly useful for handling small batches of materials wet with toxic or valuable solvents . Recovery of the solvent is easily accomplished without danger of passing through an explosive range . Dusty materials may be dried with negligible dust loss . Hygroscopic materials may be completely dried at temperatures below that required in atmospheric dryers . The equipment is employed also for freeze-drying processes, for metallizing-furnace operations, and for the manufacture of semiconductor parts in controlled atmospheres . All these latter processes demand much lower operating pressures than do ordinary drying operations . Design methods for vacuum-shelf dryers Heat is transferred to the wet material by conduction through the shelf and bottom of the tray and by radiation from the shelf above . The critical moisture content will not be necessarily the same as for atmospheric tray drying, as the heat-transfer mechanisms are different . During the constant-rate period, moisture is rapidly removed . Often 50 percent of the moisture will evaporate in the first hour of a 6- to 8-h cycle . The drying time has been found to be proportional to between the first and second powers of the depth of loading . Vacuum-shelf dryers operate in the range of 1 to 25 mmHg pressure . For size-estimating purposes, a heattransfer coefficient of 20 J/(m2 ⋅ s ⋅ K) may be used . The area employed in this case should be the shelf area in direct contact with the trays . For the same

Manufacturer’s Performance Data for Tray and Tray-Truck Dryers* Material

Type of dryer Capacity, kg product/h Number of trays Tray spacing, cm Tray size, cm Depth of loading, cm Initial moisture, % bone-dry basis Final moisture, % bone-dry basis Air temperature, °C Loading, kg product/m2 Drying time, h Air velocity, m/s Drying, kg water evaporated/(h⋅m2) Steam consumption, kg/kg water evaporated Total installed power, kW ∗Courtesy of Wolverine Proctor & Schwartz, Inc .

Color 2-truck 11 .2 80 10 60 × 75 × 4 2 .5 to 5 207 4 .5 85–74 10 .0 33 1 .0 0 .59 2 .5 1 .5

Chrome yellow 16-tray dryer 16 .1 16 10 65 × 100 × 2 .2 3 46 0 .25 100 33 .7 21 2 .3 65 3 .0 0 .75

Toluidine red 16-tray 1 .9 16 10 65 × 100 × 2 3 .5 220 0 .1 50 7 .8 41 2 .3 0 .41 — 0 .75

Half-finished Titone 3-truck 56 .7 180 7 .5 60 × 70 × 3 .8 3 223 25 95 14 .9 20 3 .0 1 .17 2 .75 2 .25

Color 2-truck 4 .8 120 9 60 × 70 × 2 .5 116 0 .5 99 9 .28 96 2 .5 0 .11 1 .5

SOLIDS-DRYING FUNDAMENTALS TABLE 12-14

12-41

Standard Vacuum-Shelf Dryers* Price/m2 (1995)

Shelf area, m2

Floor space, m2

Weight average, kg

Pump capacity, m3/s

Pump motor, kW

Condenser area, m2

Carbon steel

304 stainless steel

0 .4–1 .1 1 .1–2 .2 2 .2–5 .0 5 .0–6 .7 6 .7–14 .9 16 .7–21 .1

4 .5 4 .5 4 .6 5 .0 6 .4 6 .9

540 680 1130 1630 3900 5220

0 .024 0 .024 0 .038 0 .038 0 .071 0 .071

1 .12 1 .12 1 .49 1 .49 2 .24 2 .24

1 1 4 4 9 9

$110 75 45 36 27 22

$170 110 65 65 45 36

∗Stokes Vacuum, Inc .

reason, the shelves should be kept free from scale and rust . Air vents should be installed on steam-heated shelves to vent noncondensible gases . The heating medium should not be applied to the shelves until after the air has been evacuated from the chamber, to reduce the possibility of the material’s overheating or boiling at the start of drying . Case hardening ( formation of hard external layer) can sometimes be avoided by retarding the rate of drying in the early part of the cycle . Some performance data for vacuum-shelf dryers are given in Table 12-14 . The thermal efficiency of a vacuum-shelf dryer is usually on the order of 60 to 80 percent . Table 12-15 gives operating data for one organic and two inorganic compounds . Continuous Tray and Gravity Dryers Examples and Synonyms Turbo-tray dryer, plate dryer, moving-bed dryer, gravity dryer . Description Continuous tray dryers are equivalent to batch tray dryers, but with the solids moving between trays by a combination of mechanical movement and gravity . Gravity (moving-bed) dryers are normally throughcirculation convective dryers with no internal trays where the solids gradually descend by gravity . In all these types, the net movement of solids is vertically downward . Turbo-Tray Dryers The turbo-tray dryer (also known as rotating tray, rotating shelf, or Wyssmont Turbo-Dryer) is a continuous dryer consisting of a stack of rotating annular shelves in the center of which turbo-type fans revolve to circulate the air over the shelves . Wet material enters through the roof, falling onto the top shelf as it rotates beneath the feed opening . After completing one rotation, the material is wiped by a stationary wiper through radial slots onto the shelf below, where it is spread into a uniform pile by a stationary leveler . The action is repeated on each shelf, with transfers occurring once in each revolution . From the last shelf, material is discharged through the bottom of the dryer (Fig . 12-49) . The rate at which each fan circulates air can be varied by changing the pitch of the fan blades . In final drying stages, in which diffusion controls or the product is light and powdery, the circulation rate is considerably lower than in the initial stage, in which high evaporation rates prevail . In the majority of applications, air flows through the dryer upward in counterflow to the material . In special cases, required drying conditions dictate that airflow be cocurrent or both countercurrent and cocurrent with the exhaust leaving at some level between solids inlet and discharge . A separate cold-air-supply fan is provided if the product is to be cooled before being discharged . By virtue of its vertical construction, the turbo-type tray dryer has a stack effect, the resulting draft being frequently sufficient to operate the dryer with natural draft . Pressure at all points within the dryer is maintained close to atmospheric . Most of the roof area is used as a breeching, lowering the exhaust velocity to settle dust back into the dryer . Heaters can be located in the space between the trays and the dryer housing, where they are not in direct contact with the product, and thermal efficiencies up to 3500 kJ/kg (1500 Btu/lb) of water evaporated can be obtained by TABLE 12-15

reheating the air within the dryer . For materials which have a tendency to foul internal heating surfaces, an external heating system is employed . The turbo-tray dryer can handle materials from thick slurries [1 million N ⋅ s/m2 (100,000 cP) and over] to fine powders . Filter-press cakes are granulated before feeding . Thixotropic materials are fed directly from a rotary filter by scoring the cake as it leaves the drum . Pastes can be extruded onto the top shelf and subjected to a hot blast of air to make them firm and freeflowing after one rotation . The turbo-tray dryer is manufactured in sizes from package units 2 m in height and 1 .5 m in diameter to large outdoor installations 20 m in height and 11 m in diameter . Tray areas range from 1 m2 up to about 2000 m2 . The number of shelves in a tray rotor varies according to space available and the minimum rate of transfer required, from as few as 12 shelves to as many as 58 in the largest units . Standard construction permits operating temperatures up to 615 K, and high-temperature heaters permit operation at temperatures up to 925 K .

Performance Data for Vacuum-Shelf Dryers

Material

Sulfur black

Calcium carbonate

Calcium phosphate

Loading, kg dry material/m2 Steam pressure, kPa gauge Vacuum, mmHg Initial moisture content, % (wet basis) Final moisture content, % (wet basis) Drying time, h Evaporation rate, kg/(s ⋅ m2)

25

17

33

410

410

205

685–710 50

685–710 50 .3

685–710 30 .6

1

1 .15

4 .3

8 8 .9 × 10−4

7 7 .9 × 10−4

6 6 .6 × 10−4 FIG. 12-49

Turbo-Dryer . (Wyssmont Company, Inc.)

12-42

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-50 Turbo-Dryer in closed circuit for continuous drying

with solvent recovery . (Wyssmont Company, Inc.)

Design methods for turbo-tray dryers The heat- and mass-transfer mechanisms are similar to those in batch tray dryers, except that constant turning over and mixing of the solids significantly improve drying rates . Design usually must be based on previous installations or pilot tests by the manufacturer; apparent heat-transfer coefficients are typically 30 to 60 J/(m2 ⋅ s ⋅ K) for dry solids and 60 to 120 J/(m2 ⋅ s ⋅ K) for wet solids . Turbo-tray dryers have been employed successfully for the drying and cooling of calcium hypochlorite, urea crystals, calcium chloride flakes, and sodium chloride crystals . The Wyssmont “closed-circuit” system, as shown in Fig . 12-50, consists of the turbo-tray dryer with or without internal heaters, recirculation fan, condenser with receiver and mist eliminators, and reheater . Feed and discharge are through a sealed wet feeder and lock, respectively . This method is used for continuous drying without leakage of fumes, vapors, or dust to the atmosphere . A unified approach for scaling up dryers, such as turbo-tray, plate, conveyor, or any other dryer type that forms a defined layer of solids next to a heating source, is the SDR method described by Moyers [Drying Technol. 12(1 & 2): 393–417 (1994)] . Performance and cost data for turbo-tray dryers Performance data for four applications of closed-circuit drying are included in Table 12-16 . Operating, labor, and maintenance costs compare favorably with those of direct heat rotating equipment . Plate Dryers The plate dryer is an indirectly heated, fully continuous dryer available for three modes of operation: atmospheric, gastight, or full vacuum . The dryer is of vertical design, with horizontal, heated plates mounted inside the housing . The plates are heated by hot water, steam, or thermal oil, with operating temperatures up to 320°C possible . The product enters at the top and is conveyed through the dryer by a product transport system consisting of a central-rotating shaft with arms and plows . (See dryer schematic, Fig . 12-51 .) The thin product layer [approximately 12- mm (0 .5-in) depth] on the surface of the plates, coupled with frequent product turnover by the conveying system, results in short retention times

TABLE 12-16

FIG. 12-51 Indirect heat continuous plate dryer for atmospheric, gastight, or full-vacuum operation . (Krauss Maffei.)

(approximately 5 to 40 min), true plug flow of the material, and uniform drying . The vapors are removed from the dryer by a small amount of heated purge gas or by vacuum . The material of construction of the plates and housing is normally stainless steel, with special metallurgies also available . The drive unit is located at the bottom of the dryer and supports the centralrotating shaft . Typical speed of the dryer is 1 to 7 rpm . The plate dryer may vary in size from 5 to 35 vertically stacked plates with a heat-exchange area between 3 .8 and 175 m2 . Depending upon the loosebulk density of the material and the overall retention time, the plate dryer can process up to 5000 kg/h of wet product . The plate dryer is limited in its scope of applications only in the consistency of the feed material (the products must be friable, be free-flowing, and not undergo phase changes) and drying temperatures up to 320°C . Applications include specialty chemicals, pharmaceuticals, foods, polymers, pigments, etc . Initial moisture or volatile level can be as high as 65 percent, and the unit is often used as a final dryer to take materials to a bone-dry state, if necessary . The plate dryer can also be used for heat treatment, removal of waters of hydration (bound moisture), solvent removal, and a product cooler . The atmospheric plate dryer is a dust-tight system . The dryer housing is an octagonal, panel construction, with operating pressure in the range of ±0 .5 kPa gauge . An exhaust air fan draws the purge air through the housing for removal of the vapors from the drying process . The purge air velocity through the dryer is in the range of 0 .1 to 0 .15 m/s, resulting in minimal

Turbo-Dryer Performance Data in Wyssmont Closed-Circuit Operations*

Material dried Dried product, kg/h Volatiles composition Feed volatiles, % wet basis Product volatiles, % wet basis Evaporation rate, kg/h Type of heating system Heating medium Drying medium Heat consumption, J/kg Power, dryer, kW Power, recirculation fan, kW Materials of construction Dryer height, m Dryer diameter, m Recovery system Condenser cooling medium Location Approximate cost of dryer (2004) Dryer assembly ∗Courtesy of Wyssmont Company, Inc .

Antioxidant 500 Methanol and water 10 0 .5 53 External Steam Inert gas 0 .56 × 106 1 .8 5 .6 Stainless-steel interior 4 .4 2 .9 Shell-and-tube condenser Brine Outdoor $300,000 Packaged unit

Water-soluble polymer 85 Xylene and water 20 4 .8 16 External Steam Inert gas 2 .2 × 106 0 .75 5 .6 Stainless-steel interior 3 .2 1 .8 Shell-and-tube condenser Chilled water Indoor $175,000 Packaged unit

Antibiotic filter cake 2400 Alcohol and water 30 3 .5 910 External Steam Inert gas 1 .42 × 106 12 .4 37 .5 Stainless-steel interior 7 .6 6 .0 Direct-contact condenser Tower water Indoor $600,000 Field-erected unit

Petroleum coke 227 Methanol 30 0 .2 302 External Steam Inert gas 1 .74 × 106 6 .4 15 Carbon steel 6 .5 4 .5 Shell-and-tube condenser Chilled water Indoor $300,000 Field-erected unit

SOLIDS-DRYING FUNDAMENTALS Drying Curve Product “N”

35%

TTB…atmospheric plate dryer, vented VTT…vacuum plate dryer, P = 6.7 KPA Dryer type

Moisture content

1

Plate Drying temp. time

1…TTB 90°C 76 min 2…TTB 110°C 60 min

2

3…TTB 127°C 50 min 4…VTT 90°C 40 min

3

5…TTB 150°C 37 min 4 5 0

0 Time

90 min 5

4

3

2

1

FIG. 12-52 Plate dryer drying curves demonstrating impact of ele-

vated temperature and/or operation under vacuum . (Krauss Maffei.)

dusting and small dust filters for the exhaust air . The air temperature is normally equal to the plate temperature . The gastight plate dryer, together with the components of the gas recirculation system, forms a closed system . The dryer housing is semicylindrical and is rated for a nominal pressure of 5 kPa gauge . The flow rate of the recirculating purge gas must be sufficient to absorb the vapors generated from the drying process . The gas temperature must be adjusted according to the specific product characteristics and the type of volatile . After condensation of the volatiles, the purge gas (typically nitrogen) is recirculated back to the dryer via a blower and heat exchanger . Solvents such as methanol, toluene, and acetone are normally evaporated and recovered in the gastight system . The vacuum plate dryer is provided as part of a closed system . The vacuum dryer has a cylindrical housing and is rated for full-vacuum operation (typical pressure range of 3 to 27 kPa absolute) . The exhaust vapor is evacuated by a vacuum pump and is passed through a condenser for solvent recovery . There is no purge gas system required for operation under vacuum . Of special note in the vacuum-drying system are the vacuum feed and discharge locks, which allow for continuous operation of the plate dryer under full vacuum . Comparison Data—Plate Dryers Comparative studies have been done on products under both atmospheric and vacuum drying conditions . See Fig . 12-52 . These curves demonstrate (1) the improvement in drying

TABLE 12-17

∗Krauss Maffei

achieved with elevated temperature and (2) the impact to the drying process obtained with vacuum operation . Note that curve 4 at 90°C, pressure at 6 .7 kPa absolute, is comparable to the atmospheric curve at 150°C . Also the comparative atmospheric curve at 90°C requires 90 percent more drying time than the vacuum condition . The dramatic improvement with the use of vacuum is important to note for heat-sensitive materials . The above drying curves have been generated via testing on a plate dryer simulator . The test unit duplicates the physical setup of the production dryer; therefore, linear scale-up from the test data can be made to the fullscale dryer . Because of the thin product layer on each plate, drying in the unit closely follows the normal type of drying curve in which the constantrate period (steady evolution of moisture or volatiles) is followed by the falling-rate period of the drying process . This results in higher heat-transfer coefficients and specific drying capacities on the upper plates of the dryer compared to the lower plates . The average specific drying capacity for the plate dryer is in the range of 2 to 20 kg/(m2 ⋅ h) (based on final dry product) . Performance data for typical applications are shown in Table 12-17 . Gravity or Moving-Bed Dryers A body of solids in which the particles, consisting of granules, pellets, beads, or briquettes, flow downward by gravity at substantially their normal settled bulk density through a vessel in contact with gases is defined frequently as a moving-bed or tower dryer. Moving-bed equipment is frequently used for grain drying and plastic pellet drying, and it also finds application in blast furnaces, shaft furnaces, and petroleum refining . Gravity beds are also employed for the cooling and drying of extruded pellets and briquettes from size enlargement processes . A gravity dryer consists of a stationary vertical, usually cylindrical housing with openings for the introduction of solids (at the top) and removal of solids (at the bottom), as shown schematically in Fig . 12-53 . Gas flow is through the solids bed and may be cocurrent or countercurrent and, in some instances, cross-flow . By definition, the rate of gas flow upward must be less than that required for fluidization . Fields of Application One of the major advantages of the gravity-bed technique is that it lends itself well to true intimate countercurrent contacting of solids and gases . This provides for efficient heat transfer and mass transfer . Gravity-bed contacting also permits the use of the solid as a heattransfer medium, as in pebble heaters . Gravity vessels are applicable to coarse granular free-flowing solids which are comparatively dust-free . The solids must possess physical properties in size and surface characteristics so that they will not stick together, bridge, or segregate during passage through the vessel . The presence of significant quantities of fines or dust will close the passages among the larger particles through which the gas must penetrate, increasing pressure drop . Fines may also segregate near the sides of the bed or in other areas where gas velocities are low, ultimately completely sealing off these portions of the vessel . The high efficiency of gas-solids contacting in gravity beds is due to the uniform distribution of gas throughout the solids bed; hence choice of feed and its preparation are important factors to successful operation . Preforming techniques such as pelleting and briquetting are employed frequently for the preparation of suitable feed materials . Gravity vessels are suitable for low-, medium-, and high-temperature operation; in the last case, the housing will be lined completely with refractory brick . Dust recovery equipment is minimized in this type of operation

Plate Dryer Performance for Three Applications*

Product Volatiles Production rate, dry Inlet volatiles content Final volatiles content Evaporative rate Heating medium Drying temperature Dryer pressure Air velocity Drying time, min Heat consumption, kcal/kg dry product Power, dryer drive Material of construction Dryer height Dryer footprint Location Dryer assembly Power, exhaust fan Power, vacuum pump

12-43

Plastic additive Methanol 362 kg/hr 30% 0 .1% 155 kg/hr Hot water 70°C 11 kPa abs NA 24 350

Pigment Water 133 kg/hr 25% 0 .5% 44 kg/hr Steam 150°C Atmospheric 0 .1 m/sec 23 480

Foodstuff Water 2030 kg/hr 4% 0 .7% 70 kg/hr Hot water 90°C Atmospheric 0 .2 m/sec 48 100

3 kW SS 316L/316Ti 5m 2 .6 m diameter Outdoors Fully assembled NA 20 kW

1 .5 kW SS 316L/316Ti 2 .6 m 2 .2 m by 3 .0 m Indoors Fully assembled 2 .5 kW NA

7 .5 kW SS 316L/316Ti 8 .2 m 3 .5 m by 4 .5 m Indoors Fully assembled 15 kW NA

12-44

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-54

Section view of a continuous throughcirculation conveyor dryer. (Proctor & Schwartz, Inc.)

FIG. 12-53 Moving-bed gravity dryer.

since the bed actually performs as a dust collector itself, and dust in the bed will not, in a successful application, exist in large quantities . Other advantages of gravity beds include flexibility in gas and solids flow rates and capacities, variable retention times from minutes to several hours, space economy, ease of start-up and shutdown, the potentially large number of contacting stages, and ease of control by using the inlet and exit gas temperatures . Maintenance of a uniform rate of solids movement downward over the entire cross-section of the bed is one of the most critical operating problems encountered . For this reason, gravity beds are designed to be as high and narrow as practical . In a vessel of large cross-section, discharge through a conical bottom and center outlet will usually result in some degree of “ratholing” through the center of the bed . Flow through the center will be rapid while essentially stagnant pockets are left around the sides . To overcome this problem, multiple outlets may be provided in the center and around the periphery; table unloaders, rotating plows, wide moving grates, and multiple-screw unloaders are employed; insertion of inverted cone baffles in the lower section of the bed, spaced so that flushing at the center is retarded, is also a successful method for improving uniformity of solids movement . Continuous Band and Tunnel Dryers Examples and Synonyms Ceramic tunnel kilns, moving truck dryers, trolleys, atmospheric belt/band dryers, vibrating bed dryers, vacuum belt dryers, vibrating tray dryers, conveyor dryers, continuous-tunnel, beltconveyor, or screen-conveyor (band) dryers . Description Continuous-tunnel dryers are batch truck or tray compartments, operated in series . The solids to be processed are placed in trays or on trucks which move progressively through the tunnel in contact with hot gases . In high-temperature operations, radiation from walls and refractory lining may be significant also . Operation is semicontinuous; when the tunnel is filled, one truck is removed from the discharge end as each new truck is fed into the inlet end . Applications of tunnel equipment are essentially the same as those for batch tray and compartment units previously described, namely, practically all forms of particulate solids and large solid objects . Auxiliary equipment and the special design considerations discussed for batch trays and compartments apply also to tunnel equipment . For size-estimating purposes, tray and truck tunnels and furnaces can be treated in the same manner as discussed for batch equipment . Belt-conveyor and screen-conveyor (band) dryers are truly continuous in operation, carrying a layer of solids on an endless conveyor . Conveyor dryers are more suitable than (multiple) batch compartments for large-quantity production, usually giving investment and installation savings . Belt and screen conveyors which are truly continuous represent major labor savings over batch operations, but require additional investment for automatic feeding and unloading devices . Airflow can be totally cocurrent, countercurrent, or a combination of both . In addition, cross-flow designs are employed frequently, with the heating air flowing back and forth across the belts in series . Reheat coils may be installed after each cross-flow pass to maintain constant-temperature operation; large propeller-type circulating fans are installed at each stage,

and air may be introduced or exhausted at any desirable points . Conveyor dryers possess the maximum flexibility for any combination of airflow and temperature staging . Contact drying is also possible, usually under vacuum, with the bands resting on heating plates (vacuum band dryer) . Ceramic tunnel kilns handling large irregular-shaped objects must be equipped for precise control of temperature and humidity conditions to prevent cracking and condensation on the product . The internal mechanisms that cause cracking when drying clay and ceramics have been studied extensively . Information on ceramic tunnel kiln operation and design is reported fully in publications such as The American Ceramic Society Bulletin, Ceramic Industry, and Transactions of the British Ceramic Society. Continuous Through-Circulation Band Dryers Continuous throughcirculation dryers operate on the principle of blowing hot air through a permeable bed of wet material passing continuously through the dryer . Drying rates are high because of the large area of contact and short distance of travel for the internal moisture . The most widely used type is the horizontal conveyor dryer (also called perforated band or conveying-screen dryer), in which wet material is conveyed as a layer 2 to 15 cm deep (sometimes up to 1 m), on a horizontal mesh screen, belt, or perforated apron, while heated air is blown either upward or downward through the bed of material . This dryer consists usually of a number of individual sections, complete with fan and heating coils, arranged in series to form a housing or tunnel through which the conveying screen travels . As shown in the sectional view in Fig . 12-54, the air circulates through the wet material and is reheated before reentering the bed . It is not uncommon to circulate the hot gas upward in the wet end and downward in the dry end, as shown in Fig . 12-55 . A portion of the air is exhausted continuously by one or more exhaust fans, not shown in the sketch, which handle air from several sections . Since each section can be operated independently, extremely flexible operation is possible, with high temperatures usually at the wet end, followed by lower temperatures; in some cases, a unit with cooled or specially humidified air is employed for final conditioning . The maximum pressure drop that can be taken through the bed of solids without developing leaks or air bypassing is roughly 50 mm of water . Example 12-15 Mass and Energy Balance on a Dryer with Partially Recycled Air A continuous through-air dryer is producing 648 kg/h of a coarse granular product, as illustrated in Fig . 12-56 . The material enters the dryer at 40 percent moisture and exits at 10 percent moisture, on wet basis . The airflow rate is 4750 kg/h, and the ambient temperature and absolute humidity are 22°C and 0 .01 kg/kg, respectively . Measurements are being taken on the system to assess performance . To check the measurements against expected values, calculate the relative humidity and dew point of the exhaust air if 85 percent of the mass flow of air exiting the dryer is recycled . Neglect heat losses and sensible heating of the solids . Use the following physical properties: ΔHvap = 2257 kJ/kg; Cp,air = 1 .0 J/(g ⋅ K); Cp,water vapor = 1 .9 J/(g ⋅ K) We start by calculating the dry solids flow rate into the process, which equals 648(1 − 0.4) = 389 kg/h. The dry-basis moisture content of the feed and product are then calculated to be Xproduct = 0.111 g water/g dry material and Xfeed = 0.667 g water/g dry material. The relationship from the Solids Drying Fundamentals subsection was used: X = w/(1 − w), where X is the dry-basis moisture content and w is the wet-basis moisture content. The drying rate of the system equals the dry mass flow rate times the difference in the dry-basis moisture contents: Drying rate = m dry ( X feed − X product ) = 216 kg/h Now a series of steady-state mass balance equations can be written. Dry airflow rates (kg/h) are denoted by a, and water vapor flow rates (kg/h) are denoted by w. Subscripts refer to streams.

SOLIDS-DRYING FUNDAMENTALS Fresh air

Wet feed

Belt

12-45

Fans

Fresh air

Dry product

Fans

FIG. 12-55 Longitudinal view of a continuous through-circulation conveyor dryer with intermediate airflow reversal .

Air mass balances: a4 = a5 = a6 a4 = a1 + a2 a5 = a2 + a3

a2 = recycle ratio a5

Water vapor mass balances: w5 = w 4 + drying rate w 4 = w1 + w2 w5 = w2 + w3 w 4 = w6

w2 = recycle ratio w5

Energy balances: a4Cp4 (T4 − T5 ) = m ⋅ ∆H vap a4Cp4 (T4 − T6 ) = a6Cp6T6 = a1Cp1T1 + a2Cp2T2 T2 = T3 = T5 The equations above can be solved on a spreadsheet iteratively . The results of the calculation are shown in Table 12-18 . This type of calculation is very helpful to understanding performance of an industrial dryer . Once it is set up, different scenarios can be explored, such as changing the recycle rate . However, it is important to note that changing the conditions in the system can also affect the drying rate . For example, an increase of the recycle rate would increase the air velocity but also increase the humidity in the dryer . Using a drying kinetics model, such as the “characteristic curve” method (if that model is appropriate for the material), along with this model can help to optimize the system .

Through-circulation drying requires that the wet material be in a state of granular or pelleted subdivision so that hot air may be readily blown through it . Many materials meet this requirement without special preparation . Others require special and often elaborate pretreatment to render them suitable for through-circulation drying . The process of converting a wet solid to a form suitable for through-circulation of air is called preforming, and often the success or failure of this contacting method depends on the

preforming step . Fibrous, flaky, and coarse granular materials are usually amenable to drying without preforming . They can be loaded directly onto the conveying screen by suitable spreading feeders of the oscillating-belt or vibrating type or by spiked drums or belts feeding from bins . When materials must be preformed, several methods are available, depending on the physical state of the wet solid . 1 . Relatively dry materials such as centrifuge cakes can sometimes be granulated to give a suitably porous bed on the conveying screen . 2 . Pasty materials can often be preformed by extrusion to form spaghettilike pieces, about 6 mm in diameter and several centimeters long . 3 . Wet pastes that cannot be granulated or extruded may be predried and preformed on a steam-heated finned drum . Preforming on a finned drum may be desirable also in that some predrying is accomplished . 4 . Thixotropic filter cakes from rotary vacuum filters that cannot be preformed by any of the above methods can often be scored by knives on the filter, the scored cake discharging in pieces suitable for through-circulation drying . 5 . Material that shrinks markedly during drying is often reloaded during the drying cycle to 2 to 6 times the original loading depth . This is usually done after a degree of shrinkage which, by opening the bed, has destroyed the effectiveness of contact between the air and solids . 6 . In a few cases, powders have been pelleted or formed in briquettes to eliminate dustiness and permit drying by through-circulation . Table 12-19 gives a list of materials classified by preforming methods suitable for throughcirculation drying . Steam-heated air is the usual heat-transfer medium employed in these dryers, although combustion gases may also be used . Temperatures above 600 K are not usually feasible because of the problems of lubricating the conveyor, chain, and roller drives . Recirculation of air is in the range of 60 to 90 percent of the flow through the bed . Conveyors may be made of wiremesh screen or perforated-steel plate . The minimum practical screen opening size is about 30-mesh (0 .5 mm) . Multiple bands in series may be used . Vacuum band dryers utilize heating by conduction and are a continuous equivalent of vacuum tray (shelf) dryers, with the moving bands resting on heating plates . Drying is usually relatively slow, and it is common to find several bands stacked above one another, with material falling to the next band and flowing in opposite directions on each pass, to reduce dryer length and give some product turnover . Design Methods for Continuous Band Dryers A scoping calculation is a good starting point for designing a new system or for understanding an existing system . The required solids throughput F and the inlet and outlet moisture content XI and XO are known, as is the ambient humidity YI . If the inlet gas temperature TGI is chosen, the outlet gas conditions (temperature TGO and humidity YO) can be found, either by calculation or (more simply and quickly) by using the constant-enthalpy lines on a psychrometric chart .

TABLE 12-18 Results From Mass- and Energy-Balance Calculation for Dryer with Recycle

FIG. 12-56 Drying of a course granular material with partially recycled air .

Stream 1 2 3 4 5 6

Absolute humidity, kg/kg 0 .010 0 .051 0 .051 0 .045 0 .051 0 .045

Temperature, °C 22 .0 70 .5 70 .5 84 .7 70 .5 63 .8

% Relative humidity 57 .5 26 .2 26 .2 12 .7 26 .2 30 .7

Dew point, °C 13 .3 42 .4 42 .4 39 .8 42 .4 39 .8

12-46

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING TABLE 12-19 Methods of Preforming Some Materials for Through-Circulation Drying No preforming required Scored on filter Granulation Extrusion Finned drum Lithopone Calcium carbonate Starch Kaolin Cellulose acetate Zinc yellow White lead Aluminum hydrate Cryolite Silica gel Calcium carbonate Lithopone Lead arsenate Scoured wool Magnesium carbonate Titanium dioxide Cornstarch Sawdust Magnesium carbonate Cellulose acetate Rayon waste Dye intermediates Aluminum stearate Fluorspar Zinc stearate Tapioca Breakfast food Asbestos fiber Cotton linters Rayon staple

However, it may be necessary to allow for heat losses and sensible heating of solids, which typically reduce the useful enthalpy of the inlet gas by 10 to 20 percent . Also, if tightly bound moisture is being removed, the heat of wetting to break the bonds should be allowed for . The gas mass flow rate G can now be calculated, as it is the only unknown in the mass balance on the solvent [Eq . (12-69)] . For through-circulation and dispersion dryers, the cross-sectional area A is given by A=

G F ( X I − XO ) = ρGI U G ρGI U G (YO − X I )

(12-69)

The linear dimensions of a rectangular bed can then be calculated . The result is usually accurate to within 10 percent, and it can be further improved by better estimates of velocity and heat losses . The method gives no information about solids residence time or dryer length . A minimum drying time tmin can be calculated by evaluating the maximum (unhindered) drying rate Ncr, assuming gas-phase heat-transfer control and estimating a gas-to-solids heat-transfer coefficient . The simple Eq . (12-70) then applies: t min =

X I − XO N cr

(12-70)

Alternatively, it may be assumed that first-order falling-rate kinetics apply throughout the drying process, and one can scale the estimated drying time by using Eq . (12-70) . To correct from a calculated constant-rate (unhindered) drying time tCR to first-order falling-rate kinetics, the following equation is used, where X1 is the initial, X2 the final, and XE the equilibrium moisture content (all must be dry-basis): t FR X 1 − X E  X 1 − X E  = ln   t CR X 1 − X 2  X 2 − X E 

(12-71)

However, these crude methods can give serious underestimates of the required drying time, and it is much better to measure the drying time experimentally and apply scaling methods . Example 12-16 applies this method to a batch rotary dryer . A more detailed mathematical method of a through-circulation dryer has been developed by Thygeson [Am. Inst. Chem. Eng. J. 16(5): 749 (1970)] . Rigorous modeling is possible with a two-dimensional incremental model, with steps both horizontally along the belt and vertically through the layer; nonuniformity of the layer across the belt could also be allowed for, if desired . Heat-transfer coefficients are typically in the range of 100 to 200 W/(m2 ⋅ K), and the relationship hc = 12(rgUg/dp)0 .5 may be used for a first estimate, where rg is gas density (kg/m3); Ug, local gas velocity (m/s); and dp, particle diameter (m) . For 5-mm particles and air at 1 m/s, 80°C, and 1 kg/m3 [mass flux 1 kg/(m2 ⋅ s)] this gives hc = 170 W/(m2 ⋅ K) . In actual practice, design of a continuous through-circulation dryer is best based upon data taken in pilot-plant tests . Loading and distribution of solids on the screen are rarely as nearly uniform in commercial installations as in test dryers; 50 to 100 percent may be added to the test drying time for commercial design . Performance and Cost Data for Continuous Band and Tunnel Dryers Experimental performance data are given in Table 12-20 for numerous common materials . Performance data from several commercial throughcirculation conveyor dryers are given in Table 12-21 . Labor requirements vary depending on the time required for feed adjustments, inspection, etc . These dryers may consume as little as 1 .1 kg of steam/kg of water evaporated, but 1 .4 to 2 is a more common range . Thermal efficiency is a function of final moisture required and percent air recirculation .

Flaking on chilled drum Soap flakes

Briquetting and squeezing Soda ash Cornstarch Synthetic rubber

Conveying-screen dryers are fabricated with conveyor widths from 0 .3- to 4 .4-m sections 1 .6 to 2 .5 m long . Each section consists of a sheet-metal enclosure, insulated sidewalls and roof, heating coils, a circulating fan, inlet air distributor baffles, a fines catch pan under the conveyor, and a conveyor screen (Fig . 12-54) . Cabinet and auxiliary equipment fabrication is of aluminized steel or stainless-steel materials . Prices do not include temperature controllers, motor starters, preform equipment, or auxiliary feed and discharge conveyors . Table 12-22 gives approximate purchase costs for equipment with type 304 stainless-steel hinged conveyor screens and includes steam-coil heaters, fans, motors, and a variable-speed conveyor drive . Cabinet and auxiliary equipment fabrication is of aluminized steel or stainless-steel materials . Prices do not include temperature controllers, motor starters, preform equipment, or auxiliary feed and discharge conveyors . These may add $75,000 to $160,000 to the dryer purchase cost (2005 costs) . Batch Agitated and Rotating Dryers Examples and Synonyms Pan dryers, spherical and conical dryers, side-screw, Nauta, turbosphere, batch paddle, ploughshare . Description An agitated dryer is defined as one on which the housing enclosing the process is stationary while solids movement is accomplished by an internal mechanical agitator . A rotary dryer is one in which the outer housing rotates . Many forms are in use, including batch and continuous versions . The batch forms are almost invariably heated by conduction with operation under vacuum . Vacuum is used in conjunction with drying or other chemical operations when low solids temperatures must be maintained because heat will cause damage to the product or change its nature; when air combines with the product as it is heated, causing oxidation or an explosive condition; when solvent recovery is required; and when materials must be dried to extremely low moisture levels . Vertical agitated pan, spherical, and conical dryers are mechanically agitated; tumbler or doublecone dryers have a rotating shell . All these types are typically used for the drying of solvent or water-wet, free-flowing powders in small batch sizes of 1000 L or less, as frequently found in the pharmaceutical, specialty chemical, and fine chemicals industries . Corrosion resistance and cleanability are often important, and common materials of construction include SS 304 and 316 as well as Hastelloy . The batch nature of operation is of value in the pharmaceutical industry to maintain batch identification . In addition to pharmaceutical materials, the conical mixer dryer is used to dry polymers, additives, inorganic salts, and many other specialty chemicals . As the size increases, the ratio of jacket heat-transfer surface area to volume falls, extending drying times . For larger batches, horizontal agitated pan dryers are more common, but there is substantial overlap of operating ranges . Drying times may be reduced for all types by heating the internal agitator, but this increases complexity and cost . Mechanical versus rotary agitation Agitated dryers are applicable to processing solids that are relatively free-flowing and granular when discharged as product . Materials that are not free-flowing in their feed condition can be treated by recycle methods as described in the subsection Continuous Rotary Dryers . In general, agitated dryers have applications similar to those of rotating vessels . Their chief advantages compared with the latter are twofold: (1) Large-diameter rotary seals are not required at the solids and gas feed and exit points because the housing is stationary, and for this reason gas leakage problems are minimized . Rotary seals are required only at the points of entrance of the mechanical agitator shaft . (2) Use of a mechanical agitator for solids mixing introduces shear forces which are helpful for breaking up lumps and agglomerates . Balling and pelleting of sticky solids, an occasional occurrence in rotating vessels, can be prevented by special agitator design . The problems concerning dusting of fine particles in directheat units are identical to those discussed in subsection Continuous Rotary Dryers . Heated Agitators For all agitated dryers, in addition to the jacket heated area, heating the agitator with the same medium as the jacket (hot water,

SOLIDS-DRYING FUNDAMENTALS TABLE 12-20

12-47

Experimental Through-Circulation Drying Data for Miscellaneous Materials Moisture contents, kg/kg dry solid

Material Alumina hydrate Alumina hydrate Alumina hydrate Aluminum stearate Asbestos fiber Asbestos fiber Asbestos fiber Calcium carbonate Calcium carbonate Calcium carbonate Calcium carbonate Calcium stearate Calcium stearate Calcium stearate Cellulose acetate Cellulose acetate Cellulose acetate Cellulose acetate Clay Clay Cryolite Fluorspar Lead arsenate Lead arsenate Lead arsenate Lead arsenate Kaolin Kaolin Kaolin Kaolin Kaolin Lithopone ( finished) Lithopone (crude) Lithopone Magnesium carbonate Magnesium carbonate Mercuric oxide Silica gel Silica gel Silica gel Soda salt Starch (potato) Starch (potato) Starch (corn) Starch (corn) Starch (corn) Titanium dioxide Titanium dioxide White lead White lead Zinc stearate

Physical form Briquettes Scored filter cake Scored filter cake 0 .7-cm extrusions Flakes from squeeze rolls Flakes from squeeze rolls Flakes from squeeze rolls Preformed on finned drum Preformed on finned drum Extruded Extruded Extruded Extruded Extruded Granulated Granulated Granulated Granulated Granulated 1 .5-cm extrusions Granulated Pellets Granulated Granulated Extruded Extruded Formed on finned drum Formed on finned drum Extruded Extruded Extruded Extruded Extruded Extruded Extruded Formed on finned drum Extruded Granular Granular Granular Extruded Scored filter cake Scored filter cake Scored filter cake Scored filter cake Scored filter cake Extruded Extruded Formed on finned drum Extruded Extruded

Initial

Critical

0 .105 9 .60 5 .56 4 .20 0 .47 0 .46 0 .46 0 .85 0 .84 1 .69 1 .41 2 .74 2 .76 2 .52 1 .14 1 .09 1 .09 1 .10 0 .277 0 .28 0 .456 0 .13 1 .23 1 .25 1 .34 1 .31 0 .28 0 .297 0 .443 0 .36 0 .36 0 .35 0 .67 0 .72 2 .57 2 .23 0 .163 4 .51 4 .49 4 .50 0 .36 0 .866 0 .857 0 .776 0 .78 0 .76 1 .2 1 .07 0 .238 0 .49 4 .63

0 .06 4 .50 2 .25 2 .60 0 .11 0 .10 0 .075 0 .30 0 .35 0 .98 0 .45 0 .90 0 .90 1 .00 0 .40 0 .35 0 .30 0 .45 0 .175 0 .18 0 .25 0 .066 0 .45 0 .55 0 .64 0 .60 0 .17 0 .20 0 .20 0 .14 0 .21 0 .065 0 .26 0 .28 0 .87 1 .44 0 .07 1 .85 1 .50 1 .60 0 .24 0 .55 0 .42 0 .48 0 .56 0 .30 0 .60 0 .65 0 .07 0 .17 1 .50

steam, or thermal oil) will increase the heat-exchange area . This is usually accomplished via rotary joints . Obviously, heating the screw or agitator will mean shorter batch drying times, which yields higher productivity and better product quality owing to shorter exposure to the drying temperature, but capital and maintenance costs will be increased . In pan and conical dryers, the area is increased only modestly, by 15 to 30 percent; but in horizontal pan and paddle dryers, the opportunity is much greater and indeed the majority of the heat may be supplied through the agitator . Also the mechanical power input of the agitator can be a significant additional heat source, and microwave assistance has also been used in filter dryers and conical dryers to shorten drying times (and is feasible in other types) . Vacuum processing All these types of dryer usually operate under vacuum, especially when drying heat-sensitive materials or when removing flammable organic solvents rather than water . The heating medium is hot water, steam, or thermal oil, with most applications in the temperature range of 50 to 150°C and pressures in the range of 3 to 30 kPa absolute . The vapors generated during the drying process are evacuated by a vacuum pump and passed through a condenser for recovery of the solvent . A dust filter is normally mounted over the vapor discharge line as it leaves the dryer, thus allowing any entrapped dust to be pulsed back into the process area . Standard cloth-type dust filters are available, along with sintered metal filters . In vacuum processing and drying, a major objective is to create a large temperature-driving force between the jacket and the product .

Final 0 .00 1 .15 0 .42 0 .003 0 .008 0 .0 0 .0 0 .003 0 .0 0 .255 0 .05 0 .0026 0 .007 0 .0 0 .09 0 .0027 0 .0041 0 .004 0 .0 0 .0 0 .0026 0 .0 0 .043 0 .054 0 .024 0 .0006 0 .0009 0 .005 0 .008 0 .0033 0 .0037 0 .0004 0 .0007 0 .0013 0 .001 0 .0019 0 .004 0 .15 0 .215 0 .218 0 .008 0 .069 0 .082 0 .084 0 .098 0 .10 0 .10 0 .29 0 .001 0 .0 0 .005

Inlet-air temperature, K 453 333 333 350 410 410 410 410 410 410 410 350 350 350 400 400 400 400 375 375 380 425 405 405 405 405 375 375 375 400 400 408 400 400 415 418 365 400 340 325 410 400 400 345 380 345 425 425 355 365 360

Depth of bed, cm

Loading, kg product/m2

Air velocity, m/s × 101

6 .4 3 .8 7 .0 7 .6 7 .6 5 .1 3 .8 3 .8 8 .9 1 .3 1 .9 7 .6 5 .1 3 .8 1 .3 1 .9 2 .5 3 .8 7 .0 12 .7 5 .1 5 .1 5 .1 6 .4 5 .1 8 .4 7 .6 11 .4 7 .0 9 .6 19 .0 8 .2 7 .6 5 .7 7 .6 7 .6 3 .8 3 .8–0 .6 3 .8–0 .6 3 .8–0 .6 3 .8 7 .0 5 .1 7 .0 7 .0 1 .9 3 .0 8 .2 6 .4 3 .8 4 .4

60 .0 1 .6 4 .6 6 .5 13 .6 6 .3 4 .5 16 .0 25 .7 4 .9 5 .8 8 .8 5 .9 4 .4 1 .4 2 .7 4 .1 6 .1 46 .2 100 .0 34 .2 51 .4 18 .1 22 .0 18 .1 26 .9 44 .0 56 .3 45 .0 40 .6 80 .7 63 .6 41 .1 28 .9 11 .0 13 .2 66 .5 3 .2 3 .4 3 .5 22 .8 26 .3 17 .7 26 .4 27 .4 7 .7 6 .8 16 .0 76 .8 33 .8 4 .2

6 .0 11 .0 11 .0 13 .0 9 .0 9 .0 11 .0 11 .5 11 .7 14 .3 10 .2 5 .6 6 .0 10 .2 12 .7 8 .6 5 .6 5 .1 10 .2 10 .7 9 .1 11 .6 11 .6 10 .2 9 .4 9 .2 9 .2 12 .2 10 .16 15 .2 10 .6 10 .2 9 .1 11 .7 11 .4 8 .6 11 .2 8 .6 9 .1 9 .1 5 .1 10 .2 9 .4 7 .4 7 .6 6 .7 13 .7 8 .6 11 .2 10 .2 8 .6

Experimental drying time, s × 10−2 18 .0 90 .0 108 .0 36 .0 5 .6 3 .6 2 .7 12 .0 18 .0 9 .0 12 .0 57 .0 42 .0 24 .0 1 .8 7 .2 10 .8 18 .0 19 .2 43 .8 24 .0 7 .8 18 .0 24 .0 36 .0 42 .0 21 .0 15 .0 18 .0 12 .0 30 .0 18 .0 51 .0 18 .0 17 .4 24 .0 24 .0 15 .0 63 .0 66 .0 51 .0 27 .0 15 .0 54 .0 24 .0 15 .0 6 .3 6 .0 30 .0 27 .0 36 .0

To accomplish this purpose at fairly low jacket temperatures, it is necessary to reduce the internal process pressure so that the liquid being removed will boil at a lower vapor pressure . It is not always economical, however, to reduce the internal pressure to extremely low levels because of the large vapor volumes thereby created . It is necessary to compromise on operating pressure, considering leakage, condensation problems, and the size of the vapor lines and pumping system . Very few vacuum dryers operate below 5 mmHg pressure on a commercial scale . Air in-leakage through gasket surfaces will be in the range of 0 .2 kg/(h ⋅ lin m of gasketed surface) under these conditions . To keep vapor partial pressure and solids temperature low without pulling excessively high vacuum, a nitrogen bleed may be introduced, particularly in the later stages of drying . The vapor and solids surface temperatures then fall below the vapor boiling point, toward the wet-bulb temperature . Vertical Agitated Dryers This classification includes vertical pan dryers, filter dryers, and spherical and conical dryers . Vertical pan dryer The basic vertical pan dryer consists of a short, squat vertical cylinder (Fig . 12-57 and Table 12-23) with an outer heating jacket and an internal rotating agitator, again with the axis vertical, which mixes the solid and sweeps the base of the pan . Heat is supplied by circulation of hot water, steam, or thermal fluid through the jacket; it may also be used for cooling at the end of the batch cycle, using cooling water or refrigerant . The agitator is usually a plain set of solid blades, but may be a ribbon-type screw or internally heated blades . Product is discharged from a door at the lower

12-48

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

TABLE 12-21

Performance Data for Continuous Through-Circulation Dryer* Kind of material Inorganic pigment

Capacity, kg dry product/h Approximate dryer area, m Depth of loading, cm Air temperature, °C Loading, kg product/m2 Type of conveyor, mm

712 2

Preforming method or feed Type and size of preformed particle, mm Initial moisture content, % bone-dry basis Final moisture content, % bone-dry basis Drying time, min Drying rate, kg water evaporated/(h ⋅ m2) Air velocity (superficial), m/s Heat source per kg water evaporated, steam kg/kg gas (m3/kg) Installed power, kW

22 .11 3 120 18.8 1.59 by 6.35 slots Rolling extruder 6.35-diameter extrusions 120

Cornstarch 4536 66 .42 4 115 to 140 27.3 1.19 by 4.76 slots Filtered and scored Scored filter cake 85.2

Fiber staple 1724 Stage A, Stage B, 57 .04 35 .12

Charcoal briquettes 5443

Gelatin 295

Inorganic chemical 862

130 to 100    100 3.5 3.3 2.57-diameter holes, perforated plate Fiber feed

52 .02 16 135 to 120 182.0 8.5 × 8.5 mesh screen Pressed

104 .05 5 32 to 52 9.1 4.23 × 4.23 mesh screen Extrusion

Rolling extruder

Cut fiber

64 × 51 × 25

110

37.3

2-diameter extrusions 300

6.35-diameter extrusions 111.2

9

5.3

11.1

1.0

105 22.95

192 9.91

70 31.25

1.12 Waste heat

1.27 Steam 2.83

1.27 Gas 0.13

179.0

41.03

0.5

13.6

35 38.39

24 42.97

11 17.09

1.27 Gas 0.11

1.12 Steam 2.0

0.66 Steam 1.73

29.8

119.3

194.0

82.06

30 .19 4 121 to 82 33 1.59 × 6.35 slot

∗Courtesy of Wolverine Proctor & Schwartz, Inc.

side of the wall . Sticky materials may adhere to the agitator or be difficult to discharge . Filter dryer The basic Nutsche filter dryer is like a vertical pan dryer, but with the bottom heated plate replaced by a filter plate (see also Sec . 18, Liquid-Solid Operations and Equipment) . Hence, a slurry can be fed in and filtered, and the wet cake dried in situ . These units are especially popular in the pharmaceutical industry, as containment is good and a difficult wetsolids transfer operation is eliminated by carrying out both filtration and drying in the same vessel . Drying times tend to be longer than for vertical pan dryers, as the bottom plate is no longer heated . Some types (e .g ., Mitchell Thermovac, Krauss-Maffei TNT) invert the unit between the filtration and drying stages to avoid this problem . These are popular in the pharmaceutical and specialty chemicals industries as two operations are performed in the same piece of equipment without intermediate solids transfer, and containment is good . Spherical dryer Sometimes called the turbosphere, this is another agitated dryer with a vertical axis mixing shaft, but rotation is typically faster than in the vertical pan unit, giving improved mixing and heat transfer . The dryer chamber is spherical, with solids discharge through a door or valve near the bottom . Conical mixer dryer This is a vertically oriented conical vessel with an internally mounted rotating screw . Figure 12-58 shows a schematic of a typical conical mixer dryer . The screw rotates about its own axis (speeds up to 100 rpm) and around the interior of the vessel (speeds up to 0 .4 rpm) . Because it rotates around the full circumference of the vessel, the screw provides a self-cleaning effect for the heated vessel walls, as well as effective agitation; it may also be internally heated . Either top-drive (via an internal rotating arm) or bottom-drive (via a universal joint) may be used; the former is more common . The screw is cantilevered in the vessel and requires no additional support (even in vessel sizes up to 20-m3 operating volume) . Cleaning of the dryer is facilitated with clean-in-place (CIP) systems that can be used for cleaning, and/or the vessel can be completely flooded with water or solvents . The dryer makes maximum use of the product-heated areas— the filling volume of the vessel (up to the knuckle of the dished head) is the usable product loading . In some applications, microwaves have been used to provide additional energy input and shorten drying times .

TABLE 12-22 Length 7.5 m 15 m 22.5 m 30 m

Conveyor-Screen-Dryer Costs* 2.4-m-wide conveyor $8600/m2 $6700/m2 $6200/m2 $5900/m2

∗National Drying Machinery Company, 1996.

3.0-m-wide conveyor $7110/m2 $5600/m2 $5150/m2 $4950/m2

Horizontal Pan Dryer This dryer consists of a stationary cylindrical shell, mounted horizontally, in which a set of agitator blades mounted on a revolving central shaft stir the solids being treated . These dryers tend to be used for larger batches than vertical agitated or batch rotating dryers . Heat is supplied by circulation of hot water, steam, or other heat-transfer fluids through the jacket surrounding the shell and, in larger units, through the hollow central shaft . The agitator can take many different forms, including simple paddles, ploughshare-type blades, a single discontinuous spiral, or a double continuous spiral . The outer blades are set as closely as possible to the wall without touching, usually leaving a gap of 0 .3 to 0 .6 cm . Modern units occasionally employ spring-loaded shell scrapers mounted on the blades . The dryer is charged through a port at the top and emptied through one or more discharge nozzles at the bottom . Vacuum is applied and maintained by any of the conventional methods, i .e ., steam jets, vacuum pumps, etc . A similar type, the batch indirect rotary dryer, consists of a rotating horizontal cylindrical shell, suitably jacketed . Vacuum is applied to this unit through hollow trunnions with suitable packing glands . Rotary glands must be used also for admitting and removing the heating medium from the jacket . The inside of the shell may have lifting bars, welded longitudinally, to assist agitation of the solids . Continuous rotation is needed while emptying the solids, and a circular dust hood is frequently necessary to enclose the discharge-nozzle turning circle and prevent serious dust losses to the atmosphere during unloading . A typical horizontal pan vacuum dryer is illustrated in Fig . 12-59 . Tumbler or Double-Cone Dryers These are rotating batch vacuum dryers, as shown in Fig . 12-60 . Some types are an offset cylinder, but a double-cone shape is more common . They are very common in the pharmaceutical and fine chemicals industries . The gentle rotation can give less attrition than in some mechanically agitated dryers; on the other hand, formation of lumps and balls is more likely . The sloping walls of the cones permit more rapid emptying of solids when the dryer is in a stationary position, compared to a horizontal cylinder, which requires continuous rotation during emptying to convey product to the discharge nozzles . Several new designs of the doublecone type employ internal tubes or plate coils to provide additional heating surface . On all rotating dryers, the vapor outlet tube is stationary; it enters the shell through a rotating gland and is fitted with an elbow and an upward extension so that the vapor inlet, usually protected by a felt dust filter, will be near the top of the shell at all times . Design, Scale-Up, and Performance Like all batch dryers, agitated and rotating dryers are primarily sized to physically contain the required batch volume . Note that the nominal capacity of most dryers is significantly lower than their total internal volume, because of the headspace needed for mechanical drives, inlet ports, suction lines, dust filters, etc . Care must be taken to determine whether a stated percentage fill is based on nominal capacity or geometric volume . Vacuum dryers are usually filled to 50 to 65 percent of their total shell volume .

SOLIDS-DRYING FUNDAMENTALS

FIG. 12-57 Vertical pan dryer . (Buflovak Inc.)

FIG. 12-58

Bottom-drive conical mixer dryer . (Krauss Maffei.)

TABLE 12-23 I .D, ft 3 4 5 6 8 10

Dimensions of Vertical Pan Dryers (Buflovak Inc.)

Product depth, ft 0 .75 1 1 1 1 1 .5

Working volume, ft3 5 .3 12 .6 19 .6 28 .3 50 .3 117 .8

USG 40 94 147 212 377 884

Jacketed height, ft 1 .0 2 .0 2 .0 2 .0 2 .0 3 .0

Jacketed area, ft2 Cylinder wall Bottom 9 7 25 13 31 20 38 28 50 50 94 79

Total 16 38 51 66 101 173

Discharge door, in 5 8 6 8 8 9 8 9 8 9 12 12

12-49

12-50

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-59 A typical horizontal pan vacuum dryer . (Blaw-Knox Food & Chemical Equipment, Inc.)

The standard scoping calculation methods for batch conduction drying apply . The rate of heat transfer from the heating medium through the dryer wall to the solids can be expressed by the usual formula Q = hA ΔTm

(12-72)

where Q = heat flux, J/s (Btu/h); h = overall heat-transfer coefficient, J/(m2 ⋅ s ⋅ K) [Btu/(h ⋅ ft2 jacket area ⋅ °F)]; A = total jacket area, m2 ( ft2); and ΔTm = log-mean temperature driving force from heating medium to the solids, K (°F) . The overall heat-transfer rate is almost entirely dependent upon the film coefficient between the inner jacket wall and the solids, which depends on the dryer type and agitation rate and, to a large extent, on the solids characteristics . Overall heat-transfer coefficients may range from 30 to 200 J/(m2 ⋅ s ⋅ K), based upon total area if the dryer walls are kept reasonably clean . Heat-transfer coefficients as low as 5 or 10 J/(m2 ⋅ s ⋅ K) may be encountered if caking on the walls occurs . For estimating purposes without tests, a reasonable coefficient for ordinary drying, and without taking the product to absolute dryness, may be assumed as h = 50 J/(m2 ⋅ s ⋅ K) for mechanically agitated dryers (although higher figures have been quoted for conical and spherical dryers) and 35 J/(m2 ⋅ s ⋅ K) for rotating units . The true heat-transfer coefficient is usually higher, but this conservative assumption makes some allowance for the slowing down of drying during the falling-rate period . However, if at all possible, it is always preferable to do pilot-plant tests to establish the drying time of the actual material . Drying trials are conducted in small pilot dryers (50- to 100-L batch units) to determine material handling and drying retention times . Variables such as drying temperature, vacuum level, and screw speed are analyzed during the test trials . Scale-up to larger units is done based upon the area/volume ratio of the pilot unit versus the production dryer . In most applications, the overall drying time in the production models is in the range of 2 to 24 h . Agitator or rotation speeds range from 3 to 8 rpm . Faster speeds yield a slight improvement in heat transfer but consume more power and in some cases, particularly in rotating units, can cause more “balling up” and other stickiness-related problems .

FIG. 12-60 Rotating (double-cone) vacuum dryer . (Stokes Vacuum, Inc.)

In all these dryers, the surface area tends to be proportional to the square of the diameter D2, and the volume to diameter cubed D3 . Hence the area/volume ratio falls as the diameter increases, and drying times increase . It can be shown that the ratio of drying times in the production and pilot-plant dryers is proportional to the cube root of the ratio of batch volumes . However, if the agitator of the production unit is heated, the drying time increase can be reduced or reversed . Table 12-24 gives basic geometric relationships for agitated and rotating batch dryers, which can be used for approximate size estimation or (with great caution) for extrapolating drying times obtained from one dryer type to another . Note that these do not allow for nominal capacity or partial solids fill . For the paddle (horizontal pan) dryer with heated agitator, R is the ratio of the heat transferred through the agitator to that through the walls, which is proportional to the factor hA for each case . In the absence of experimental data, the following method may be used for scoping calculations . For constant-rate drying, the drying time tCR can be calculated from m (X − X final )λ ev tCR = s initial (12-73) hws ∆Tm As where Xinitial = initial dry-basis moisture content; Xfinal = final dry-basis moisture content; λev = latent heat of vaporization; As = surface area; ΔTm = log-mean temperature difference . To correct from a calculated constant-rate (unhindered) drying time tCR to first-order falling-rate kinetics, the following equation is used, where X1 is the initial, X2 the final, and XE the equilibrium moisture content (all must be dry-basis): t FR X 1 − X E  X 1 − X E  = ln   t CR X 1 − X 2  X 2 − X E 

(12-74)

Note that tFR ≥ tCR. Likewise, to convert to a two-stage drying process with constant-rate drying down to Xcr and first-order falling-rate drying beyond, the equation is t 2 S X 1 − X cr X cr − X E  X cr − X E  ln  = +  tCR X 1 − X 2 X 1 − X 2  X2 − X E 

(12-75)

SOLIDS-DRYING FUNDAMENTALS TABLE 12-24

Calculation of Key Dimensions for Various Batch Contact Dryers (Fig. 12-61 Shows the Geometries)

Dryer type

Volume as f (D)

Typical L/D

Diameter as f (V )

Surface area as f (D) 1/2

 πD 2  L    + 1  2  D 

Ratio A/V 1/2

2 A 6 L  = 1 +    V D D 

Tumbler/double-cone

V=

πD  L    12  D 

1 .5

 12V  D =   π( L/D ) 

Vertical pan

V=

πD 3  L    4 D

0 .5

 4V  D =   π( L/D ) 

 L 1 A = πD 2  +  D 4

A 4 D = 1 +  V D  4L 

Spherical

V=

πD 3  L    6 D

1

 6V  D =   π( L/D ) 

L A = πD 2   D

A 6 = V D

Filter dryer

V=

πD 3  L    4 D

0 .5

 4V  D =   π( L/D ) 

L A = πD 2   D

A 4 = V D

Conical agitated

V=

πD 3  L    12  D 

1 .5

 12V  D =   π( L/D ) 

A=

V=

πD 3  L    4 D

1/3

Paddle (horizontal agitated)

5

 4V  D =   π( L/D ) 

L A = πD 2   D

A 4 = V D

V=

πD 3  L    4 D

1/3

Paddle, heated agitator

5

 4V  D =   π( L/D ) 

L A = πD 2   (1 + R ) D

A 4 = (1 + R ) V D

3

1/3

tCR =

1/3

1/3

1/3

ms ( X O − X I )λ ev 5000(0 .3 − 0 .05)(2400) = 0 .05(154 As ) hws ∆Tws As

(12-76)

This gives tCR as 389,610/As s or 108 .23/As h . Values for As and calculated times for the various dryer types are given in Table 12-25 . For falling-rate drying throughout, time tFR is given by Eq . (12-77); the multiplying factor for drying time is 1 .2 ln 6 = 2 .15 for all dryer types . t FR  X 1 − X E   X 1 − X E  0 .3 0 .3 ln ln = = tCR  X 1 − X 2   X 2 − X E  0 .25 0 .05

(12-77)

If the material showed a critical moisture content, the calculation could be split into two sections for constant-rate and falling-rate drying . Likewise, the experimental

Double-con (tumbler) dryer

Vertical pan, filter dryers

D

Conical (Nauta) dryer

L

L

Spherical (turbosphere) dryer

FIG. 12-61

Horizontal pan (paddle) dryer

D

D

D

D

L

2

A= 1/3

Example 12-16 Calculations for Batch Dryer For a 10-m3 batch of material containing 5000 kg of dry solids and 30 percent moisture (dry basis), estimate the size of vacuum dryers required to contain the batch at 50 percent volumetric fill . Jacket temperature is 200°C, applied pressure is 100 mbar (0 .1 bar), and the solvent is water (take latent heat as 2400 kJ/kg) . Assuming the heat-transfer coefficient based on the total surface area to be 50 W/(m2 ⋅ K) for all types, calculate the time to dry to 5 percent for (a) unhindered (constant-rate) drying throughout, (b) first-order falling-rate (hindered) drying throughout, (c) the case where experiment shows the actual drying time for a conical dryer to be 12 .5 h and other cases are scaled accordingly . Take R = 5 with the heated agitator . Assume the material is nonhygroscopic (equilibrium moisture content XE = 0) . Solution The dryer volume V must be 20 m3, and the diameter is calculated from column 4 of Table 12-24, assuming the default L/D ratios . Table 12-25 gives the results . Water at 100 mbar boils at 46°C so take ΔT as 200 - 46 = 154°C . Then Q is found from Eq . (12-72) . For constant-rate drying throughout, drying time tCR = evaporation rate/heat input rate and was given by

D

12-51

Heated agitator

D

L

Basic geometries for batch dryer calculations .

L

1/2

πD 2  L  1    +  2  D  4  2

1/2

2 A 6  1D  = 1 +    V D 4 L  

drying time texpt for the conical dryer is 12 .5 h which is a factor of 3 .94 greater than the constant-rate drying time . A very rough estimate of drying times for the other dryer types has been made by applying the same scaling factor (3 .94) to their constant-rate drying times . Two major sources of error are possible: (1) The drying kinetics could differ between dryers; and (2) if the estimated heat-transfer coefficient for either the base case or the new dryer type is in error, then the scaling factor will be wrong . All drying times have been shown in hours, as this is more convenient than seconds . The paddle with heated agitator has the shortest drying time, and the filter dryer the longest (because the bottom plate is unheated) . Other types are fairly comparable . The spherical dryer would usually have a higher heat-transfer coefficient and shorter drying time than shown . An excellent model for a variety of agitated vacuum dryers has been developed and validated against experimental data . See Schlünder, E . and Mollekopf, N ., “Vacuum Contact Drying of Free Flowing Mechanically Agitated Particulate Material,” Chemical Engineering and Processing: Process Intensification 18(2): 93–111 (March–April 1984) .

Performance Data for Batch Vacuum Rotary Dryers Typical performance data for horizontal pan vacuum dryers are given in Table 12-26 . Size and cost data for rotary agitator units are given in Table 12-27 . Data for double-cone rotating units are shown in Table 12-28 . Continuous Agitated and Rotary Dryers Examples and Synonyms Disk, Porcupine, Nara, Solidaire, Forberg, steam tube, paddle dryers, continuous rotary dryers, rotary kiln, steam-tube dryer, rotary calciner, Roto-Louvre dryer . Continuous Agitated Dryers: Description Continuous agitated dryers, often known as paddle or horizontal agitated dryers, consist of one or more horizontally mounted shells with internal mechanical agitators, which may take many different forms . They are a continuous equivalent of the horizontal pan dryer and are similar in construction, but usually of larger dimensions . They have many similarities to continuous indirect rotary dryers and are sometimes classified as rotary dryers, but this is a misnomer because the outer shell does not rotate, although in some types there is an inner shell which does . Frequently, the internal agitator is heated, and a wide variety of designs exist . Often two intermeshing agitators are used . There are important variants with high-speed agitator rotation and supplementary convective heating by hot air . The basic differences are in the type of agitator, with the two key factors being the heat-transfer area and solids handling/stickiness characteristics . Unfortunately, the types giving the highest specific surface area (multiple tubes and coils) are often also the ones most susceptible to fouling and blockage and most difficult to clean . Figure 12-62 illustrates a number of different agitator types . Paddle Dryers Product trials are conducted in small pilot dryers (8- to 60-L batch or continuous units) to determine material handling and process retention times . Variables such as drying temperature, pressure level, and shaft speed are analyzed during the test trials . For initial design purposes, the heat-transfer coefficient for paddle dryers is typically in the range of 10 W/(m2 ⋅ K) (light, free-flowing powders) up to 150 W/(m2 ⋅ K) (dilute slurries) . However, it is preferable to scale up from the test results, fitting the data to estimate the heat-transfer coefficient and scaling up on the basis of total area of heat-transfer surfaces, including heated agitators . Typical length/ diameter ratios are between 5 and 8, similar to rotary dryers and greater than some batch horizontal pan dryers .

12-52

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

TABLE 12-25

Comparative Dimensions and Drying Times for Various Batch Contact Dryers h, kW/(m2 ⋅ K)

Dryer type Tumbler/double-cone Vertical pan Spherical Filter dryer Conical agitated Paddle (horizontal agitated) Paddle, heated agitator

TABLE 12-26

0 .05 0 .05 0 .05 0 .05 0 .05 0 .05 0 .05

L/D

D, m

L, m

A, m2

tCR, h

tFR, h

texpt, h

1 .5 0 .5 1 0 .5 1 .5 5 5

3 .71 3 .71 3 .37 3 .71 3 .71 1 .72 1 .72

5 .56 1 .85 3 .37 1 .85 5 .56 8 .60 8 .60

38 .91 32 .37 35 .63 21 .58 34 .12 46 .50 278 .99

2 .78 3 .34 3 .04 5 .01 3 .17 2 .33 0 .39

5 .98 7 .19 6 .54 10 .77 6 .82 5 .01 0 .83

11 .0 13 .2 12 .0 19 .8 12 .5 9 .2 1 .52

Performance Data of Vacuum Rotary Dryer*

Material

Diameter × length, m

Initial moisture, % dry basis

Batch Steam pressure, Pa × 103

Final Agitator speed, r/min

dry weight, kg

moisture, % dry basis

Pa × 103

1 .5 × 9 .1 1 .5 × 9 .1 1 .5 × 9 .1 0 .9 × 3 .0

87 .5 45–48 50 50

97 103 207 345

5 .25 4 4 6

610 3630 3180 450

6 12 1 2

90–91 88–91 91 95

Cellulose acetate Starch Sulfur black Fuller’s earth/mineral spirit ∗Stokes Vacuum, Inc .

TABLE 12-27 Diameter, m

Evaporation, kg/(h⋅m2)

7 4 .75 6 8

Standard Rotary Vacuum Dryer*

Length, m

Heating surface, m2

Working capacity, m3†

TABLE 12-28

Purchase price (1995)

Agitator speed, r/min

0.46 0.49 0.836 0.028 0.61 1.8 3.72 0.283 0.91 3.0 10.2 0.991 0.91 4.6 15.3 1.42 1.2 6.1 29.2 3.57 1.5 7.6 48.1 6.94 1.5 9.1 57.7 8.33 ∗Stokes Vacuum, Inc. Prices include shell, 50-lb/in2-gauge condensers. † Loading with product level on or around the agitator shaft.

Working capacity, m3

Time, h

Drive, kW

7½ 7½ 6 6 6 6 6

1.12 1.12 3.73 3.73 7.46 18.7 22.4

Weight, kg 540 1680 3860 5530 11,340 15,880 19,050

Carbon steel $ 43,000 105,000 145,000 180,000 270,000 305,000 330,000

Stainless steel (304) $ 53,000 130,000 180,000 205,000 380,000 440,000 465,000

jacket, agitator, drive, and motor; auxiliary dust collectors,

Standard (Double-Cone) Rotating Vacuum Dryer*

Total volume, m3

Heating surface, m2

Purchase cost (1995) Drive, kW

Floor space, m2

Weight, kg

Carbon steel

Stainless steel

0 .085 0 .130 1 .11 .373 2 .60 730 $ 32,400 $ 38,000 0 .283 0 .436 2 .79 .560 2 .97 910 37,800 43,000 0 .708 1 .09 5 .30 1 .49 5 .57 1810 50,400 57,000 1 .42 2 .18 8 .45 3 .73 7 .15 2040 97,200 106,000 2 .83 4 .36 13 .9 7 .46 13 .9 3860 198,000 216,000 4 .25 6 .51 17 .5 11 .2 14 .9 5440 225,000 243,000 ∗38 .7 7 .08 10 .5 11 .2 15 .8 9070 324,000 351,000 ∗46 .7 9 .20 13 .9 11 .2 20 .4 9980 358,000 387,000 ∗ 11 .3 16 .0 56 .0 11 .2 26 .0 10,890 378,000 441,000 ∗Stokes Vacuum, Inc . Price includes dryer, 15-lb/in2 jacket, drive with motor, internal filter, and trunnion supports for concrete or steel foundations. Horsepower is established on 65 percent volume loading of material with a bulk density of 50 lb/ft3. Models of 250 ft3, 325 ft3, and 400 ft3 have extended surface area.

(a)

(b)

(c)

(d)

FIG. 12-62 Typical agitator designs for paddle (horizontal agitated) dryers . (a) Simple unheated agitator . (b) Heated cut-flight agitator . (c) Multicoil

unit . (d ) Tube bundle .

1 .5 7 .3 4 .4 5 .4

SOLIDS-DRYING FUNDAMENTALS Feed

12-53

Cuneiform Hollow Heaters

Exhaust Gas

Purge Air

Purge Air Rotating Shaft (carrying heat medium)

Dried Product

Heating Jacket

Cuneiform Hollow Heater

FIG. 12-63 Nara twin-shaft paddle dryer .

The most common problem with paddle dryers (and with their closely related cousins, steam-tube and indirect rotary dryers) is the buildup of sticky deposits on the surface of the agitator or outer jacket . This leads, first, to reduced heat-transfer coefficients and slower drying and, second, to blockages and stalling of the rotor . Also thermal decomposition and loss of product quality can result . The problem is usually most acute at the feed end of the dryer, where the material is wettest and stickiest . A wide variety of different agitator designs have been devised to try to reduce stickiness problems and enhance cleanability while providing a high heat-transfer area . Many designs incorporate a high-torque drive combined with rugged shaft construction to prevent rotor stall during processing, and stationary mixing elements are installed in the process housing which continually clean the heat-exchange surfaces of the rotor to minimize any crust buildup and ensure an optimum heat-transfer coefficient at all times . Another alternative is to use two parallel intermeshing shafts, as in the Nara paddle dryer (Fig . 12-63) . Suitably designed continuous paddle and batch horizontal pan dryers can handle a wide range of product consistencies (dilute slurries, pastes, friable powders) and can be used for processes such as reactions, mixing, drying, cooling, melting, sublimation, distilling, and vaporizing . Continuous Rotary Dryers: Description A rotary dryer consists of a cylinder that rotates on suitable bearings and that is usually slightly inclined to the horizontal . The cylinder length may range from 4 to more than 10 times the diameter, which may vary from less than 0 .3 to more than 3 m . Solids fed into one end of the drum are carried through it by gravity, with rolling, bouncing and sliding, and drag caused by the airflow either retarding or enhancing the movement, depending on whether the dryer is cocurrent or countercurrent . It is possible to classify rotary dryers into direct-fired, where heat is transferred to the solids by direct exchange between the gas and the solids, and indirect, where the heating medium is separated from physical contact with the solids by a metal wall or tube . Many rotary dryers contain flights or lifters, which are attached to the inside of the drum and which cascade the solids through the gas as the drum rotates . For handling large quantities of granular solids, a cascading rotary dryer is often the equipment of choice . If the material is not naturally free-flowing, recycling of a portion of the final dry product may be used to precondition the feed, either in an external mixer or directly inside the drum . Hanging link chains and/or scrapper chains are also used for sticky feed materials . Their operating characteristics when performing heat- and mass-transfer operations make them suitable for the accomplishment of drying, chemical reactions, solvent recovery, thermal decompositions, mixing, sintering, and agglomeration of solids . The specific types included are the following: Direct cascading rotary dryer (cooler). This is usually a bare metal cylinder but with internal flights (shelves) which lift the material and drop it through the airflow . It is suitable for low- and medium-temperature operations, the operating temperature being limited primarily by the strength characteristics of the metal employed in fabrication . Direct rotary dryer (cooler). As above but without internal flights . Direct rotary kiln. This is a metal cylinder lined on the interior with insulating block and/or refractory brick . It is suitable for high-temperature operations .

Indirect steam-tube dryer. This is a bare metal cylinder provided with one or more rows of metal tubes installed longitudinally in the shell . It is suitable for operation up to available steam temperatures or in processes requiring water cooling of the tubes . Indirect rotary calciner. This is a bare metal cylinder surrounded on the outside by a fired or electrically heated furnace . It is suitable for operation at medium temperatures up to the maximum that can be tolerated by the metal wall of the cylinder, usually 650 to 700 K for carbon steel and 800 to 1025 K for stainless steel . Direct Roto-Louvre dryer. This is one of the more important special types, differing from the direct rotary unit in that true through-circulation of gas through the solids bed is provided . Like the direct rotary, it is suitable for low- and medium-temperature operation . Direct heat rotary dryer. The direct heat units are generally the simplest and most economical in operation and construction, when the solids and gas can be permitted to be in contact . The required gas flow rate can be obtained from a heat and mass balance . The bed cross-sectional area is found from a scoping design calculation (a typical gas velocity is 3 m/s for cocurrent and 2 m/s for countercurrent units) . Length is normally between 5 and 10 times the drum diameter (an L/D value of 8 can be used for initial estimation) or can be calculated by using an incremental model (see Example 12-17) . A typical schematic diagram of a rotary dryer is shown in Fig . 12-64, while Fig . 12-65 shows typical lifting flight designs . Residence Time, Standard Configuration The residence time in a rotary dryer τ represents the average time that particles are present in the equipment, so it must match the required drying time . The calculation of the residence time of material in the dryer is complex since the holdup depends on the design of the flights and material properties, such as the angle of repose . The flow of the material in the equipment to calculate the residence times has been the subject of a number of historical papers, including those by Sullivan et al . (U .S . Bureau of Mines Tech . Paper 384), Friedman and Marshall equation [Chem. Eng. Progr . 45(8): 482 (1949)], Saeman and Mitchell [Chem. Eng. Progr . 50(9): 467 (1954)], and Schofield and Glikin [Trans. IChemE 40: 183 (1962)] . The most complete analysis of particle motion in rotary dryers is given by Matchett and Baker [ J. Sep. Proc. Technol . 8: 11 (1987)] . They considered both the airborne phase (particles falling through air) and the dense phase (particles in the flights or the rolling bed at the bottom) . Typically, particles spend 90 to 95 percent of the time in the dense phase, but the majority of the drying takes place in the airborne phase . In the direction parallel to the dryer axis, most particle movement occurs through four mechanisms: by gravity and air drag in the airborne phase, and by bouncing, sliding, and rolling in the dense phase . The combined particle velocity in the airborne phase is UP1, which is the sum of the gravitational and air drag components for cocurrent dryers and the difference between them for countercurrent dryers . The dense-phase velocity, arising from bouncing, sliding, and rolling, is denoted UP2 . Papadakis et al . [Dry. Tech. 12(1&2): 259–277 (1994)] rearranged the Matchett and Baker model from its original “parallel” form into a more

12-54

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

(a)

(b) FIG. 12-64 Component arrangement (a) and elevation (b) of countercurrent direct-heat rotary dryer . (Air Preheater Company, Raymond & Bartlett Snow Products.)

computationally convenient “series” form . The sum of the calculated residence times in the airborne and dense phases, tG and tS, respectively, is the total solids residence time . The dryer length is simply the sum of the distances traveled in the two phases . τ = τG + τS

(12-78)

L = τGUP1 + τSUP2

(12-79)

For airborne phase motion, the velocity is affected by gravity and air drag . U P 1 = U PO1 + U Pd1

(12-80)

The velocity U PO1 due to the gravitational component is most conveniently expressed as U PO1 =

gD De tan α K fall = D cos α 2

gD tan α K K 2

(12-81)

where Kfall is a parameter that allows for particles falling from a number of positions, with different times of flight and lifting times, and is generally between 0 .7 and 1; and the effective diameter (internal diameter between lips of flights) is De . The contribution of air drag on the velocity of falling can be calculated using Eqs . (12-82) and (12-83) . The value is positive for concurrent airflow and negative for countercurrent airflow . For Reynolds numbers up to 220, U G ,super dP ρ g where Re = , µg U Pd1 = 7 .45 × 10 −4 Re2 .2

µU G super t a∗ ρ P d P2

(12-82)

Above this Reynolds number, the following equation was recommended by Matchett and Baker (1987):

FIG. 12-65 Typical lifting flight designs .

U Pd1 = 125

µU G super t a∗ ρ P d P2

(12-83)

SOLIDS-DRYING FUNDAMENTALS The variable t a* is the average time of flight of a particle in the airborne phase when the dryer is at the “design loaded,” i .e ., if the powder fills and does not overflow the flights; see Fig . 12-65 . If the dryer has more powder than this (overloaded), then the flights will not be able to carry all of it up as far and so the time of flight will be lower . The average time of flight of the particles can be estimated from 2D  t f =   g cos α 

U P 2 = a ⋅ N ⋅ D ⋅ tan α

(12-85)

Other workers suggested that, in underloaded and design-loaded dryers, bouncing was a significant transport mechanism, whereas for overloaded dryers, rolling was important . Bouncing mechanisms can depend on the airborne phase velocity UP1, since this affects the angle at which the particles hit the bottom of the dryer and the distance they move forward . Rolling mechanisms would be expected to depend on the depth of the bottom bed, and hence on the difference between the actual holdup and the designloaded holdup . As an example of the typical numbers involved, Matchett and Baker [ J. Sep. Proc. Technol . 9: 5 (1988)] used their correlations to assess the data of Saeman and Mitchell for an industrial rotary dryer with D = 1 .83 m and L = 10 .67 m, with a slope of 4°, 0 .067 m/m . For a typical run with UG = 0 .98 m/s and N = 0 .08 r/s, they calculated that UP1° = 0 .140 m/s, UP1d = −0.023 m/s, UP1 = 0.117 m/s, and UP2 = −0.02 m/s. The dryer modeled was countercurrent and therefore had a greater slope and lower gas velocity than those of a cocurrent unit; for the latter, UP1° would be lower and UP1d positive and larger. The ratio τS/τG is approximately 12 in this case, so that the distance traveled in dense-phase motion would be about twice that in the airborne phase. Kemp and Oakley [Dry. Tech. 20(9): 1699 (2002)] showed that the ratio τG/τS can be found by comparing the average time of flight from the top of the dryer to the bottom tf to the average time required for the particles to be lifted by the flights td. They derived the following equation: τ S t d K fl = = N τG t f

g D

(12-86)

Here all the unknowns have been rolled into a single dimensionless parameter Kfl, given by θ π 2 sin θ

D De

(12-87)

Here De is the effective diameter (internal diameter between lips of flights), and the solids are carried in the flights for an angle 2θ, on average, before falling. Kemp and Oakley concluded that Kfl can be taken to be 0.4 to a first (and good) approximation. For overloaded dryers with a large rolling bed, Kfl will increase. The form of Eq. (12-86) is very convenient for design purposes since it does not require De, which is unknown until a decision has been made on the type and geometry of the flights. The model of Matchett and Baker has been shown by Kemp (Proc. IDS 2004, B, 790) to be similar in form to that proposed by Saeman and Mitchell: t=

Author(s)

1 .1 L     1 ND  tan α ⋅ ( K K /K fl 2 + a ) + (1/K fl ) ⋅ U Pd1  gD  

Q = Uυa ⋅ Vdryer ⋅ ∆Tm

(12-89)

Here Q is the overall rate of heat transfer between the gas and the solids (W), Vdryer is the dryer volume (m3), and ∆Tm is an average temperature driving

0 0.16 0.37 0.46–0.60 0.67 0.80

force (K). When one is calculating the average temperature driving force, it is important to distinguish between the case of heat transfer with dry particles, where the change in the particle temperature is proportional to the change in the gas temperature, and the case of drying particles, where the particle temperature does not change so significantly. Where the particles are dry, the average temperature difference is the logarithmic mean of the temperature differences between the gas and the solids at the inlet and outlet of the dryer. The volumetric heat-transfer coefficient itself consists of a heat-transfer coefficient Uυ, based on the effective area of contact between the gas and the solids, and the ratio a of this area to the dryer volume. Thus, this procedure eliminates the need to specify where most of the heat transfer occurs (e.g., to material in the air, on the flights, or in the rolling bed). Empirical correlations are of the form U ua =

K ′U Gn super

(12-90)

D

where K¢ depends on the solids properties, the flight geometry, the rotational speed, and the dryer holdup. In Eq. (12-90), a is the surface area per unit volume of the powder. Table 12-29 gives the values of n chosen by various authors, and Table 12-30 gives references and conditions for a few published studies. The most accepted value for the exponent n is 0.67; however, this is not universally true. This is not surprising considering the complicated particle flow mechanics in the equipment. Experimental data on the materials used are preferred. An alternative procedure is the use of a conventional film heat-transfer coefficient hf [W/(m2 ⋅ K)] Q = hf ⋅ As ⋅ ∆T

(12-91)

Here Q is the local heat-transfer rate (W), As is the total surface area of all the particles (m2), and ∆T is the temperature difference between the gas and the solids (K). The method has the advantages that hf can be determined by relatively simple tests (or calculated from appropriate correlations in the literature), variations in operating conditions can be allowed for, and analogies between heat and mass transfer allow the film coefficients for these processes to be related. However, the area for heat transfer must be estimated under the complex conditions of gas-solids interaction present in particle cascades. Schofield and Glikin (1962) estimated this area to be the surface area of particles per unit mass 6/(rP dP), multiplied by the fraction of solids in the drum that are cascading through the gas at any moment, which was estimated as the fraction of time spent by particles cascading through the gas: tf 6 AS = (12-92) ρP d P t f + td Schofield and Glikin estimated the heat-transfer coefficient by using the correlation given by McAdams (1954), which correlates data for gas-toparticle heat transfer in air to about 20 percent over a range of Reynolds numbers (ReP, defined in the previous subsection) between 17 and 70,000: Nu P = 0 .33 ⋅ Re1/2 P

(12-88)

In Eq. (12-88), K K /( K fl 2) will typically be on the order of unity, and reported values of a are in the range of 1 to 4. The airborne gravity component is usually smaller than the dense-phase motion but is not negligible. Heat- and Mass-Transfer Estimates Many rotary dryer studies have correlated heat- and mass-transfer data in terms of an overall volumetric heat-transfer coefficient Uυa [W/(m3 ⋅ K)], defined by

Exponent n

Saeman and Mitchell (1954) Friedman and Marshall (1949) Aiken and Polsak (1982) Miller et al. (1942) McCormick (1962) Myklestad (1963)

(12-84)

Here, since we are designing the dryer, t f = t a∗ . Bouncing, rolling, and sliding are not so easily analyzed theoretically . Matchett and Baker (cited above) suggested that the dense-phase velocity could be characterized in terms of a dimensionless dense-phase velocity number a, using Eq . (12-85) . Values of a are in the range of 1 to 4 .

K fl =

TABLE 12-29 Values of the Index n in Correlations for the Volumetric HeatTransfer Coefficient (after Baker, 1983)

1/2

K fall

12-55

(12-93)

TABLE 12-30 Summary of the Predictions Using the Correlations for the Volumetric Heat-Transfer Coefficients of Various Authors (after Baker, 1983) Uυa, W/(m3 ⋅ K) Author(s) Miller et al. (1942) Commercial data Pilot-scale data Friedman and Marshall (1949) Saeman and Mitchell (1954) Myklestad (1963)

UGsuper1 = 1 m/s 248 82 67 495–1155 423

UGsuper1 = 3 m/s 516 184 138 1032–2410 1019

12-56

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

Here the particle Nusselt number is NuP, where NuP = hf dP/kG, and kG is the thermal conductivity of the gas [W/(m ⋅ K)] . They stated that the heat-transfer rates predicted by this procedure were much larger than those measured on an industrial cooler, which is probably due to the particles on the inside of the cascades not experiencing the full gas velocity . Kamke and Wilson (1986) used a similar approach to model the drying of wood chips, but used the Ranz-Marshall (1952) equation to predict the heat-transfer coefficient: 1/3 Nu = 2 + 0 .6 ⋅ Re1/2 P ⋅ PrG

(12-94)

where PrG is the Prandtl number of the gas . Drying Time Estimates Sometimes, virtually all the drying takes place in the airborne phase . Under such circumstances, the airborne-phase residence time τG and the drying time are virtually the same, and the required drying time can be estimated from equivalent times in drying kinetics experiments, e .g ., using a thin-layer test (Langrish, D .Phil . thesis, 1988) .

The essential idea is to calculate the average gas humidity Y at each average moisture content X . A differential mass balance on the air at any position in the bed is

Solution Application of concept of characteristic drying curve: A linear falling rate curve implies the following equation for the drying kinetics [see Solids Drying Fundamentals subsection, Eqs . (12-29) and (12-30)]:

where f is the drying rate relative to the initial drying rate f=

N (12-37) N initial

Since the material begins drying in the falling-rate period, the critical moisture content can be taken as the initial moisture content . The equilibrium moisture content is zero since the material is not hygroscopic . Φ=

X − X eq

Y − 0 .1 F =1= 0 .5 − X G

(12-98)

Y = 0 .6 − X

(12-99)

YO = 0.6 − 0.15 = 0.45 kg/kg

(12-100)

From the Mollier chart: Twb = 79°C

X cr − X eq

(12-95)

Application of mass balances (theory): A mass balance around the inlet and any section of the dryer is shown in Fig . 12-66 .

Ys∗ = 0.48 kg/kg

For the whole dryer, Y = 0 .275 kg/kg The mass balance information is important, but not the entire answer to the question. Now the residence time can be calculated from the kinetics. Application of concept of characteristic drying curve to estimating drying rates in practice (theory): The overall (required) change in moisture content is divided into a number of intervals of size ∆X, and the problem is solved using a spreadsheet; note that ∆X is difference in the dry-basis moisture content, not distance. The sizes of the intervals need not be the same and should be finer where the fastest moisture content change occurs. For the sake of simplicity, this example will use intervals of uniform size. Then the application of the concept of a characteristic drying curve gives the following outcomes: dX f ⋅ k ⋅φ A p ∗ = drying rate = (Ys − Y ) dt ρ p Vp

Ap

=

particle surface area 6 = particle volume φ p ⋅d p

GAS DRYER SOLIDS XI (kg/kg) TSI (°C) F (kg/s) FIG. 12-66

Y (kg/kg) TG (°C) X (kg/kg) Control volume

TS (°C)

Mass balance around a typical section of a cocurrent dryer.

(12-102)

where dparticle = Sauter-mean particle diameter for mixture (volume-surface diameter), m fp = particle shape factor, unity for spheres (dimensionless) k = mass-transfer coefficient, kg/(m2 ⋅ s), obtained from heat-transfer coefficient (often easier to obtain) using the Chilton-Colburn analogy k ⋅φ =

YI (kg/kg) TGI (°C) G (kg/s)

(12-101)

where f = relative drying rate in interval (dimensionless) Y = average humidity in interval, kg/kg f = humidity potential coefficient, close to unity ρp = density of dry solids, kg/m3 Ys∗ = humidity at saturation, from the adiabatic saturation contour on Mollier chart (Fig. 12-67)

Vp

X = 0 .5

(12-97)

Application of mass balances: Plugging in the numbers gives the relationship between absolute humidity and moisture in the solids at any position.

− f = Φ assumption of linear drying kinetics

(12-96)

where Y = gas humidity, kg moisture/kg dry gas X = solids moisture content, kg moisture/kg dry solids WG = flow rate of dry gas, kg dry gas/s WS = flow rate of dry solids, kg dry solids/s

Example 12-17 Sizing of a Cascading Rotary Dryer

The average gas velocity passing through a cocurrent, adiabatic, cascading rotary dryer is 4 m/s . The particles moving through the dryer have an average diameter of 5 mm (Sauter mean diameter), a solids density of 600 kg/m3, and a shape factor of 0 .75 . The particles enter with a moisture content of 0 .50 kg/kg (dry basis) and leave with a moisture content of 0 .15 kg/kg (dry basis) . The drying rate may be assumed to decrease linearly with average moisture content, with no unhindered (constant-rate) drying period . In addition, let us assume that the solids are nonhygroscopic (so that the equilibrium moisture content is zero; hygroscopic means that the equilibrium moisture content is nonzero) . The inlet humidity is 0 .10 kg/kg (dry basis) due to the use of a direct-fired burner, and the ratio of the flow rates of dry solids to dry gas is unity (F/G = 1) . The gas temperature at the inlet to the dryer is 800°C, and the gas may be assumed to behave as a pure water vapor/air mixture . Suppose that this dryer has a slope α of 4° and a diameter D of 1 .5 m, operating at a rotational speed N of 0 .04 r/s . What residence time is required to dry the solid material to the target moisture content? How long does the dryer need to be? Data: U = 4 m/s Xl = 0 .50 kg/kg F/G = 1 XO = 0 .15 kg/kg TGI = 800°C dparticle = 0 .005 m 3 ρP = 600 kg/m Xcr = 0 .50 kg/kg YI = 0 .10 kg/kg αP = 0 .75 Xe = 0 .0 kg/kg

F ⋅ dX = −G ⋅ dy dY F Y − Y I − = = dX G X I − X

β h C PY

(12-103)

where b = psychrometric ratio, close to unity for air/water vapor system CPY = humid heat capacity = CPG + YCP = 1050 + 0.275 × 2000 = 1600 J/(kg ⋅ K) CPG = specific heat capacity of dry gas (air) = 1050 J/(kg ⋅ K) CPV = specific heat capacity of water vapor = 2000 J/(kg ⋅ K) λG h = heat-transfer coefficient, W/(m2 ⋅ K) = ⋅ Nu p d particle lG = thermal conductivity of gas = 0.02 W/(m ⋅ K) NuP = particle Nusselt number = 2 + 0.6 ReP0.5 Pr0.33 Pr = Prandtl number for air = 0.7 U ⋅ d particle ReP = particle Reynolds number = v

SOLIDS-DRYING FUNDAMENTALS

12-57

FIG. 12-67 Enthalpy humidity chart used to generate the results in Table 12-31 plots humidity (abscissa) versus enthalpy (lines sloping diagonally

from top left to bottom right) .

U = relative velocity between gas and particles; in cascading rotary dryers, this is almost constant throughout the dryer and close to the superficial gas velocity UG super (equals 4 m/s in this example) n = kinematic viscosity of gas at average TG in dryer = 15 × 10-6 m2/s We might do a more accurate calculation by finding the gas properties at the conditions for each interval . Application of concept of characteristic drying curve to estimating drying rates in practice U ⋅ d p 4 ⋅ 0 .005 0 .02 From the relationships above, Re p = = = 1333; Nu p = 21 .5 ; h = ⋅ 21 .5 = n 15 × 10 -6 0 .005 86

W 86 kg A p 6 = 0 .054  2   ;  = = 1600 m −1 . ;k = m2 ⋅ K 1600 m ⋅ s V p 0.75 ⋅ 0.005 Plugging into Eq . (12-98) gives 0 . 0 .054 ⋅ 1600 dX (0 .48 − Y ) = 0 .14 ⋅ f ⋅ (0 .48 − Y ) = f 600 dt

(12-104)

As stated prior to this example, most of the drying in a cascading rotary dryer occurs while the particles are falling through the air . In this example, we will assume that is when all the drying occurs . We will also assume that while a particle is falling, the temperature can be calculated using a quasi-steady-state approximation . This means that we equate the heat transfer to the particle by convection to the evaporative cooling caused by drying, and we neglect the energy accumulation term . h(TG − TS ) = f ⋅ N w ⋅ ∆H vap

(12-105)

where Nw is the maximum (unhindered) drying rate . For completely unhindered drying, f = 1 and T S (the temperature of the solid) equals the wet-bulb temperature T W . Plugging those into Eq . (12-105) and taking the ratio give T −T f = G S TG − TW

Now that the relationships are defined, we can perform the incremental calculation using a spreadsheet . This is shown in Table 12-31 . We begin with column 2, where we set the increments of dry-basis moisture X from the inlet to the exit of the dryer (which are known from the problem statement) . The number of increments used is arbitrary; a higher number will give a more precise solution . Column 3 is the average of X in each increment of column 1 . Column 4 is the gas-phase composition Y, as calculated from Eq . (12-98) . Column 5 is the gas temperature, which is obtained from the Mollier diagram in Fig . 12-68 . Mollier diagrams are explained in the Psychrometry subsection . The gas temperature cools due to the evaporation of water; the line on the diagram is an adiabatic saturation line . The first point to mark on the diagram, indicated by a star, is the inlet air condition (absolute humidity = 0 .1 g/g and 800°C) . The wet-bulb temperature of this air is 78°C, obtained by following the adiabatic saturation line to the saturation curve at the bottom and reading the temperature . If calculations are preferred to using the diagram, Eq . (12-6) may be used for the gas temperature and the procedure described in Table 12-5vi can be used to calculate the wet-bulb temperature . The values of f in column 6 are calculated from the average solids moisture content, Eq . (12-94); the temperature of the solids in column 7 is calculated from Eq . (12-103); and the drying rate is calculated from Eq . (12-103) . The required drying time for the increment of DX in column 2 is calculated using the drying rate in column 10 (rightmost column) . The drying times for all increments add to 50 .82 s . The value of 50 .82 s is the time required for the particles when they are falling through the air . However, most of the residence time of the particles in the dryer is spent slowly rotating on the flights in a dense phase . The next steps in this analysis are to estimate the ratio of the time falling in the airborne phase to that of the time in dense phase and then the time in the dense phase per unit length of the dryer . To estimate the time of the particles in the dense phase, we can use Eq . (12-87) .

(12-106)

τ S t d K fl = = τG t f N

g 0 .4 9 .81 m/s 2 = = 25 .6 D 0 .04 s −1 1 .5 m

t S = 25 .6 ⋅ 50 .8 = 1300 s The total required residence time is therefore τ S + τG = τ = 1350 .8 s .

(12-107)

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

TABLE 12-31

Variation in Process Conditions for the Example of a Cocurrent Cascading Rotary Dryer     X, kg/kg Y, kg/kg TG, °C Twb, °C f =Φ TS, °C

Interval

Xj, kg/kg

1 2 3 4 5 6 7 8 out

0 .500 0 .456 0 .412 0 .369 0 .325 0 .281 0 .238 0 .194 0 .150

0 .478 0 .434 0 .391 0 .347 0 .303 0 .259 0 .216 0 .172

0 .122 0 .166 0 .209 0 .253 0 .297 0 .341 0 .384 0 .428

720 630 530 430 340 250 200 130

µ ⋅U G ,super t a∗ ρ p d p2

 2D  t a∗ = t f =   g cos α 

0 .956 0 .869 0 .781 0 .694 0 .606 0 .519 0 .431 0 .344

107 151 177 186 181 161 147 112

 dX/dt, kg/(kg ⋅ s)

Δtp, s

0 .04656 0 .03683 0 .02820 0 .02067 0 .01424 0 .00892 0 .00470 0 .00158

0 .94 1 .19 1 .55 2 .12 3 .07 4 .91 9 .32 27 .73

Total required gas-phase residence time (s) = 50.82 s (summation of last column)

The length of dryer per second of residence time can be estimated by using Eq . (12-89) . First we need to calculate the particle velocity due to air drag while falling . Since Rep = 1300, we use Eqs . (12-83) and (12-84) .

U Pd1 = 125 ⋅

79 .0 78 .5 78 .5 78 .0 78 .0 78 .0 78 .0 78 .0

= 125 ⋅

1/2

kg 4 m ⋅ ⋅ 0.554 s m ⋅s s = 0.332 m/s  600 kg  ( 0.005 m )2 3  m 

1 .8   ×  10 −5

2 ⋅1.5  K fall =   9.81cos 4° 

1/2

(1.0) = 0.554 s

We can apply Eq . (12-88), using KK/(Kfl 2 ) ≈ 1, Kfl ≈ 0 .4, Kfall ≈ 1, and take a to equal 2 .5 (within the range of 1 to 4) . 1 .1 τ = L (0 .04 s −1 )(1.5 m)   tan 4°⋅ (1 + 2.5) +   1 × 1 ⋅ 0.332 m/s  m   0.4 9.81 2 ⋅1.5 m   s = 30 s/m Since = 1300 s, L = 1350 .2/30 = 45 m . The dryer length/diameter ratio is therefore 45 m/1 .5 m = 30, which is significantly larger than the recommended ratio of between 5:1 and 10:1 . The remedy would then be to use a larger dryer diameter and repeat these calculations . The larger dryer diameter would decrease the gas velocity, slowing the particle velocity along the drum, increasing the residence time per unit length, and hence decreasing the required drum length, to give a more normal length/diameter ratio .

Performance and Cost Data for Direct Heat Rotary Dryers Table 12-32 gives estimating-price data for direct rotary dryers employing steam-heated air . Higher-temperature operations requiring combustion chambers and fuel

800

0.600

Solids Temperature (left)

700

0.500

Air Temperature (left)

600 Temperature, °C

burners will cost more . The total installed cost of rotary dryers including instrumentation, auxiliaries, allocated building space, etc ., will run from 150 to 300 percent of the purchase cost . Simple erection costs average 10 to 20 percent of the purchase cost . Operating costs will include 5 to 10 percent of one worker’s time, plus power and fuel required . Yearly maintenance costs will range from 5 to 10 percent of total installed costs . Total power for fans, dryer drive, and feed and product conveyors will be in the range of 0 .5D2 to 1 .0D2 . Thermal efficiency of a high-temperature direct heat rotary dryer will range from 55 to 75 percent and, with steam-heated air, from 30 to 55 percent . Table 12-32 gives some performance data for some cocurrent rotary dryers . A representative list of materials dried in direct heat rotary dryers is given in Table 12-33 . Indirect Heat Rotary Steam-Tube Dryers Probably the most common type of indirect heat rotary dryer is the steam-tube dryer (Fig . 12-69) . Steam-heated tubes running the full length of the cylinder are fastened symmetrically in one, two, or three concentric rows inside the cylinder and rotate with it . Tubes may be simple pipe with condensate draining by gravity into the discharge manifold or bayonet type . Bayonet-type tubes are also employed when units are used as water-tube coolers . When one is handling sticky materials, one row of tubes is preferred . These are occasionally shielded at the feed end of the dryer to prevent buildup of solids behind them . Lifting flights are usually inserted behind the tubes to promote solids agitation . Wet feed enters the dryer through a chute or screw feeder . The product discharges through peripheral openings in the shell in ordinary dryers . These openings also serve to admit purge air to sweep moisture or other evolved gases from the shell . In practically all cases, gas flow is countercurrent to solids flow . To retain a deep bed of material within the dryer, normally a 10 to 20 percent fill level, the discharge openings are supplied with removable chutes extending radially into the dryer . These, on removal, permit complete emptying of the dryer . Steam is admitted to the tubes through a revolving steam joint into the steam side of the manifold . Condensate is removed continuously, by gravity through the steam joint to a condensate receiver and by means of lifters in the condensate side of the manifold . By employing simple tubes, noncondensibles are continuously vented at the other ends of the tubes through

0.400

Moisture Content (right)

500 400

0.300

300

0.200

200 0.100

100 0

0.000 0

0.2

0.4

0.6

0.8

1

Fractional Residence Time FIG. 12-68

Typical variation of process conditions through a cocurrent cascading rotary dryer .

Moisture Content, kg/kg

12-58

SOLIDS-DRYING FUNDAMENTALS TABLE 12-32

Warm-Air Direct-Heat Cocurrent Rotary Dryers: Typical Performance Data*

1 .219 × 7 .62 1 .372 × 7 .621 1 .524 × 9 .144 1 .839 × 10 .668 Dryer size, m × m Evaporation, kg/h 136 .1 181 .4 226 .8 317 .5 Work, 108 J/h 3 .61 4 .60 5 .70 8 .23 2 Steam, kg/h at kg/m gauge 317 .5 408 .2 521 .6 725 .7 Discharge, kg/h 408 522 685 953 Exhaust velocity, m/min 70 70 70 70 3 Exhaust volume, m /min 63 .7 80 .7 100 .5 144 .4 Exhaust fan, kW 3 .7 3 .7 5 .6 7 .5 Dryer drive, kW 2 .2 5 .6 5 .6 7 .5 Shipping weight, kg 7700 10,900 14,500 19,100 Price, FOB Chicago $158,000 $168,466 $173,066 $204,400 ∗Courtesy of Swenson Process Equipment Inc . note: Material: heat-sensitive solid Maximum solids temperature: 65°C Feed conditions: 25 percent moisture, 27°C Product conditions: 0.5 percent moisture, 65°C Inlet-air temperature: 165°C Exit-air temperature: 71°C Assumed pressure drop in system: 200 mm System includes finned air heaters, transition piece, dryer, drive, product collector, duct, and fan. Prices are for carbon steel construction and include entire dryer system (November, 1994). For 304 stainless-steel fabrication, multiply the prices given by 1.5.

Sarco-type vent valves mounted on an auxiliary manifold ring, also revolving with the cylinder . Vapors ( from drying) are removed at the feed end of the dryer to the atmosphere through a natural-draft stack and settling chamber or wet scrubber . When employed in simple drying operations with 3 .5 × 105 to 10 × 105 Pa steam, draft is controlled by a damper to admit only sufficient outside air to sweep moisture from the cylinder, discharging the air at 340 to 365 K and 80 to 90 percent saturation . In this way, shell gas velocities and dusting are minimized . When used for solvent recovery or other processes requiring a sealed system, sweep gas is recirculated through a scrubber-gas cooler and blower . Steam-tube dryers are used for the continuous drying, heating, or cooling of granular or powdery solids which cannot be exposed to ordinary atmospheric or combustion gases . They are especially suitable for fine, dusty particles because of the low gas velocities required for purging of the cylinder . Tube sticking is avoided or reduced by employing recycle, shell knockers, etc ., as previously described; tube scaling by sticky solids is one of the major hazards to efficient operation . The dryers are suitable for drying, solvent recovery, and chemical reactions . Steam-tube units have found effective employment in soda ash production, replacing more expensive indirect heat rotary calciners .

TABLE 12-33 Dryers*

12-59

Representative Materials Dried in Direct-Heat Rotary Moisture content, % (wet basis)

Material dried

Initial

Final

High-temperature: Sand 10 0 .5 Stone 6 0 .5 Fluorspar 6 0 .5 Sodium chloride 3 0 .04 (vacuum salt) Sodium sulfate 6 0 .1 Ilmenite ore 6 0 .2 Medium-temperature: Copperas 7 1 (moles) Ammonium sulfate 3 0 .10 Cellulose acetate 60 0 .5 Sodium chloride 25 0 .06 (grainer salt) Cast-iron borings 6 0 .5 Styrene 5 0 .1 Low-temperature: Oxalic acid 5 0 .2 Vinyl resins 30 1 Ammonium nitrate prills 4 0 .25 Urea prills 2 0 .2 Urea crystals 3 0 .1 ∗Taken from Chem. Eng., June 19, 1967, p . 190, Table III .

Heat efficiency % 61 65 59 70–80 60 60–65 55 50–60 51 35 50–60 45 29 50–55 30–35 20–30 50–55

2 .134 × 12 .192 408 .2 1 .12 997 .9 1270 70 196 .8 11 .2 14 .9 35,800 $241,066

2 .438 × 13 .716 544 .3 1 .46 131 .5 1633 70 257 .7 18 .6 18 .6 39,900 $298,933

3 .048 × 16 .767 861 .8 2 .28 2041 2586 70 399 .3 22 .4 37 .3 59,900 $393,333

Design methods for indirect heat rotary steam-tube dryers Heat-transfer coefficients in steam-tube dryers range from 30 to 85 W/(m2 ⋅ K) . Coefficients will increase with increasing steam temperature because of increased heat transfer by radiation . In units carrying saturated steam at 420 to 450 K, the heat flux will range from 6300 W/m2 for difficult-to-dry and organic solids to 1890 to 3790 W/m2 for finely divided inorganic materials . The effect of steam pressure on heat-transfer rates up to 8 .6 × 105 Pa is illustrated in Fig . 12-70 . Performance and cost data for indirect heat rotary steam-tube dryers Table 12-34 contains data for a number of standard sizes of steam-tube dryers . Prices tabulated are for ordinary carbon-steel construction . Installed costs will run from 150 to 300 percent of the purchase cost . The thermal efficiency of steam-tube units will range from 70 to 90 percent, if a well-insulated cylinder is assumed . This does not allow for boiler efficiency, however, and is therefore not directly comparable with direct heat units such as the direct heat rotary dryer or indirect heat calciner . Operating costs for these dryers include 5 to 10 percent of one person’s time . Maintenance will average 5 to 10 percent of the total installed cost per year . Table 12-35 outlines typical performance data from three drying applications in steam-tube dryers . Indirect Rotary Calciners and Kilns These large-scale rotary processors are used for very high temperature operations . Operation is similar to that of rotary dryers . For additional information, refer to Perry’s 7th Edition, pages 12-56 to 12-58 . Indirect Heat Calciners Indirect heat rotary calciners, either batch or continuous, are employed for heat treating and drying at higher temperatures than can be obtained in steam-heated rotating equipment . They generally require a minimum flow of gas to purge the cylinder, to reduce dusting, and are suitable for gas-sealed operation with oxidizing, inert, or reducing atmospheres . Indirect calciners are widely utilized, and some examples of specific applications are as follows: 1 . Activating charcoal 2 . Reducing mineral high oxides to low oxides 3 . Drying and devolatilizing contaminated soils and sludges 4 . Calcination of alumina oxide–based catalysts 5 . Drying and removal of sulfur from cobalt, copper, and nickel 6 . Reduction of metal oxides in a hydrogen atmosphere 7 . Oxidizing and “burning off ” of organic impurities 8 . Calcination of ferrites This unit consists essentially of a cylindrical retort, rotating within a stationary insulation-lined furnace . The latter is arranged so that fuel combustion occurs within the annular ring between the retort and the furnace . To prevent sliding of solids over the smooth interior of the shell, agitating flights running longitudinally along the inside wall are frequently provided . These normally do not shower the solids as in a direct heat vessel, but merely prevent sliding so that the bed will turn over and constantly expose new surface for heat and mass transfer . To prevent scaling of the shell interior by sticky solids, cylinder scraper and knocker arrangements are occasionally employed . For example, a scraper chain is fairly common practice in soda ash calciners, while knockers are frequently utilized on metallic oxide calciners .

12-60

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-69 Steam-tube rotary dryer .

In general, the temperature range of operation for indirect heat calciners can vary over a wide range, from 475 K at the low end to approximately 1475 K at the high end . All types of carbon steel, stainless, and alloy construction are used, depending upon the temperature, process, and corrosion requirements . Design methods for calciners In indirect heat calciners, heat transfer is primarily by radiation from the cylinder wall to the solids bed . The thermal efficiency ranges from 30 to 65 percent . By utilization of the furnace exhaust gases for preheated combustion air, steam production, or heat for other process steps, the thermal efficiency can be increased considerably . The limiting factors in heat transmission lie in the conductivity and radiation constants of the shell metal and solids bed . If the characteristics of these are known, equipment may be accurately sized by employing the Stefan-Boltzmann radiation equation . Apparent heat-transfer coefficients will range from 17 W/(m2 ⋅ K) in low-temperature operations to 85 W/(m2 ⋅ K) in high-temperature processes . Cost data for calciners Power, operating, and maintenance costs are similar to those previously outlined for direct and indirect heat rotary dryers . Estimating purchase costs for preassembled and frame-mounted rotary calciners with carbon-steel and type 316 stainless-steel cylinders are given in Table 12-36 together with size, weight, and motor requirements . Sale price includes the cylinder, ordinary angle seals, furnace, drive, feed conveyor, burners, and controls . Installed cost may be estimated, not including

FIG. 12-70 Effect of steam pressure on the heat-transfer rate in steam-tube dryers .

building or foundation costs, at up to 50 percent of the purchase cost . A layout of a typical continuous calciner with an extended cooler section is illustrated in Fig . 12-71 . Direct Heat Roto-Louvre Dryer One of the more important special types of rotating equipment is the Roto-Louvre dryer . As illustrated in Fig . 12-72, hot air (or cooling air) is blown through louvres in a double-wall rotating cylinder and up through the bed of solids . The latter moves continuously through the cylinder as it rotates . Constant turnover of the bed ensures uniform gas contacting for heat and mass transfer . The annular gas passage behind the louvres is partitioned so that contacting air enters the cylinder only beneath the solids bed . The number of louvres covered at any one time is roughly 30 percent . Because air circulates through the bed, fillage levels of 13 to 15 percent or greater are employed . Roto-Louvre dryers range in size from 0 .8 to 3 .6 m in diameter and from 2 .5 to 11 m long . The largest unit is reported capable of evaporating 5500 kg/h of water . Hot gases from 400 to 865 K may be employed . Because gas flow is through the bed of solids, high pressure drop, from 7 to 50 cm of water, may be encountered within the shell . For this reason, both a pressure inlet fan and an exhaust fan are provided in most applications to maintain the static pressure within the equipment as close as possible to atmospheric . Roto-Louvre dryers are suitable for processing coarse granular solids which do not offer high resistance to airflow, do not require intimate gas contacting, and do not contain significant quantities of dust . Heat transfer and mass transfer from the gas to the surface of the solids are extremely efficient; hence the equipment size required for a given duty is frequently less than that required when an ordinary direct heat rotary vessel with lifting flights is used . Purchase price savings are partially balanced, however, by the more complex construction of the Roto-Louvre unit . A Roto-Louvre dryer will have a capacity roughly 1 .5 times that of a singleshell rotary dryer of the same size under equivalent operating conditions . Because of the cross-flow method of heat exchange, the average temperature is not a simple function of inlet and outlet temperatures . Three applications of Roto-Louvre dryers are outlined in Table 12-37 . Installation, operating, power, and maintenance costs will be similar to those experienced with ordinary direct heat rotary dryers . Thermal efficiency will range from 30 to 70 percent . Additional Readings Aiken and Polsak, “A Model for Rotary Dryer Computation,” in Mujumdar, ed ., Drying ’82, Hemisphere, New York, 1982, pp . 32–35 . Baker, “Cascading Rotary Dryers,” chap . 1 in Mujumdar, ed ., Advances in Drying, vol . 2, Hemisphere, New York, 1983, pp . 1–51 . Friedman and Mahall, “Studies in Rotary Drying . Part 1 . Holdup and Dusting . Part 2 . Heat and Mass Transfer,” Chem. Eng. Progr. 45: 482–493, 573–588 (1949) . Hirosue and Shinohara, “Volumetric Heat Transfer Coefficient and Pressure Drop in Rotary Dryers and Coolers,” 1st Int. Symp. on Drying 8 (1978) . Kamke and Wilson, “Computer Simulation of a Rotary Dryer . Part 1 . Retention Time . Part 2 . Heat and Mass Transfer,” AIChE J . 32: 263–275 (1986) .

SOLIDS-DRYING FUNDAMENTALS TABLE 12-34

12-61

Standard Steam-Tube Dryers*

Size, diameter × length, m

Tubes No . OD (mm)

m2 of free area

No . OD (mm)

Dryer speed, r/min

Motor size, hp

0 .965 × 4 .572 14 (114) 21 .4 6 2 .2 0 .965 × 6 .096 14 (114) 29 .3 6 2 .2 0 .965 × 7 .620 14 (114) 36 .7 6 3 .7 0 .965 × 9 .144 14 (114) 44 .6 6 3 .7 0 .965 × 10 .668 14 (114) 52 .0 6 3 .7 1 .372 × 6 .096 18 (114) 18 (63 .5) 58 .1 4 .4 3 .7 1 .372 × 7 .620 18 (114) 18 (63 .5) 73 .4 4 .4 3 .7 1 .372 × 9 .144 18 (114) 18 (63 .5) 88 .7 5 5 .6 1 .372 × 10 .668 18 (114) 18 (63 .5) 104 5 5 .6 1 .372 × 12 .192 18 (114) 18 (63 .5) 119 5 5 .6 1 .372 × 13 .716 18 (114) 18 (63 .5) 135 5 .5 7 .5 1 .829 × 7 .62 27 (114) 27 (76 .2) 118 4 5 .6 1 .829 × 9 .144 27 (114) 27 (76 .2) 143 4 5 .6 1 .829 × 10 .668 27 (114) 27 (76 .2) 167 4 7 .5 1 .829 × 12 .192 27 (114) 27 (76 .2) 192 4 7 .5 1 .829 × 13 .716 27 (114) 27 (76 .2) 217 4 11 .2 1 .829 × 15 .240 27 (114) 27 (76 .2) 242 4 11 .2 1 .829 × 16 .764 27 (114) 27 (76 .2) 266 4 14 .9 1 .829 × 18 .288 27 (114) 27 (76 .2) 291 4 14 .9 2 .438 × 12 .192 90 (114) 394 3 11 .2 2 .438 × 15 .240 90 (114) 492 3 14 .9 2 .438 × 18 .288 90 (114) 590 3 14 .9 2 .438 × 21 .336 90 (114) 689 3 22 .4 2 .438 × 24 .387 90 (114) 786 3 29 .8 *Courtesy of Swenson Process Inc . (prices from November, 1994) . Carbon steel fabrication; multiply by 1 .75 for 304 stainless steel .

Shipping weight, kg

Estimated price

5,500 5,900 6,500 6,900 7,500 10,200 11,100 12,100 13,100 14,200 15,000 19,300 20,600 22,100 23,800 25,700 27,500 29,300 30,700 49,900 56,300 63,500 69,900 75,300

$152,400 165,100 175,260 184,150 196,850 203,200 215,900 228,600 243,840 260,350 273,050 241,300 254,000 266,700 278,400 292,100 304,800 317,500 330,200 546,100 647,700 736,600 838,200 927,100

TABLE 12-35 Steam-Tube Dryer Performance Data Class 1

Class 2

Class of materials handled

High-moisture organic, distillers’ grains, brewers’ grains, citrus pulp

Description of class

Wet feed is granular and damp but not sticky or muddy and dries to granular meal 233

Pigment filter cakes, blanc fixe, barium carbonate, precipitated chalk Wet feed is pasty, muddy, or sloppy; product is mostly hard pellets 100

Normal moisture content of wet feed, % dry basis Normal moisture content of product, % dry basis Normal temperature of wet feed, K Normal temperature of product, K Evaporation per product, kg Heat load per lb product, kJ Steam pressure normally used, kPa gauge Heating surface required per kg product, m2 Steam consumption per kg product, kg

Class 3 Finely divided inorganic solids, water-ground mica, water-ground silica, flotation concentrates Wet feed is crumbly and friable; product is powder with very few lumps 54

11

0.15

0.5

310–320 350–355 2 2250 860 0.34

280–290 380–410 1 1190 860 0.4

280–290 365–375 0.53 625 860

3.33

1.72

0.072 0.85

TABLE 12-36 Indirect-Heat Rotary Calciners: Sizes and Purchase Costs* Diameter, ft

Overall cylinder length

Heated cylinder length

Cylinder drive motor hp

4 5 6 7

40 ft 45 ft 50 ft 60 ft

30 ft 35 ft 40 ft 50 ft

7.5 10 20 30

Approximate Shipping weight, lb 50,000 60,000 75,000 90,000

Approximate sale price in carbon steel construction† $275,000 375,000 475,000 550,000

Approximate sale price in No. 316 stainless construction $325,000 425,000 550,000 675,000

*Courtesy of ABB Raymone (Bartlett-SnowTM). † Prices for November, 1994.

Bellows seal

Feeder

Cylinder drive FIG. 12-71

Burners

Gas-fired rotary calciner with integral cooler. (Air Preheater Company, Raymond & Bartlett Snow Products.)

12-62

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-72

FMC Link-Belt Roto-Louvre dryer .

Kemp, “Comparison of Particle Motion Correlations for Cascading Rotary Dryers,” Drying 2004—Proceedings of the 14th International Drying Symposium (IDS 2004), São Paulo, Brazil, Aug . 22–25, 2004, vol . B ., pp . 790–797 . Kemp and Oakley, “Modeling of Particulate Drying in Theory and Practice,” Drying Technol. 20(9): 1699–1750 (2002) . Langrish, “The Mathematical Modeling of Cascading Rotary Dryers,” DPhil thesis, University of Oxford, 1988 . Matchett and Baker, “Particle Residence Times in Cascading Rotary Dryers . Part 1— Derivation of the Two-Stream Model,” J. Separ. Proc. Technol. 8: 11–17 (1987) . Matchett and Baker, “Particle Residence Times in Cascading Rotary Dryers . Part 2— Application of the Two-Stream Model to Experimental and Industrial Data,” J. Separ. Proc. Technol. 9: 5 (1988) . McCormick, “Gas Velocity Effects on Heat Transfer in Direct Heat Rotary Dryers,” Chem. Eng. Progr. 58: 57–61 (1962) . Miller, Smith, and Schuette, “Factors Influencing the Operation of Rotary Dryers . Part 2 . The Rotary Dryer as a Heat Exchanger,” Trans. AIChE 38: 841–864 (1942) . Myklestad, “Heat and Mass Transfer in Rotary Dryers,” Chem. Eng. Progr. Symp. Series 59: 129–137 (1963) . Papadakis et al ., “Scale-up of Rotary Dryers,” Drying Technol. 12(1&2): 259–278 (1994) . Ranz and Marshall, “Evaporation from Drops, Part 1,” Chem. Eng. Progr. 48: 123–142, 251–257 (1952) . Saeman and Mitchell, “Analysis of Rotary Dryer Performance,” Chem. Eng. Progr. 50(9): 467–475 (1954) . Schofield and Glikin, “Rotary Dryers and Coolers for Granular Fertilisers,” Trans. IChemE 40: 183–190 (1962) . Sullivan, Maier, and Ralston, “Passage of Solid Particles through Rotary Cylindrical Kilns,” U .S . Bureau of Mines Tech . Paper, 384, 44 (1927) .

Fluidized-Bed and Spouted-Bed Dryers Examples and synonyms Fluid beds, fluidized beds, spouted beds, vibrating fluidized beds, vibro-fluidized bed . Description A fluidized bed is a deep layer of particles supported by both a distributor plate (containing numerous small holes) and the fluidizing gas . The bed has many properties of a liquid; the particles seek their own level, assume the shape of the vessel they are in, and exhibit buoyancy effects . The basic principles of fluidized-bed technology are thoroughly described in Sec . 17, Gas-Solid Operations and Equipment . The technology has several advantages . These include no moving parts, rapid heat and mass transfer

between gas and particles, rapid heat transfer between the gas/particle bed and immersed objects, intense mixing, and continuous or batch operation . These advantages allow fluidized beds to be used as both dryers and coolers . As described in Sec . 17, the process parameter of the highest importance is the fluidizing gas velocity in the fluidized bed, also referred to as the superficial gas velocity . This velocity is of nominal character since the flow field will be disturbed and distorted by the presence of the solid phase and the turbulent fluctuations created by the gas/solid interaction . Proper design and operation of a fluidized-bed dryer requires consideration of fluidization and drying characteristics of a material, the fluidization velocity, the particle size distribution, the design of the gas distributor plate, the operating conditions, and the mode of operation . Fluidization characteristics have been investigated by Geldart, resulting in the well-known Geldart diagram (Fig . 12-73) . The Geldart diagram shows that particulate material can be handled successfully in a fluidized bed only if it is not too fine or too coarse with a mean particle size between 20 mm and 10 mm . Fluidized beds are best suited for flowable particles that are regular in shape and not too sticky . Needle- or leaflike shaped particles should be considered as nonfluidizable . The total drying time needed to reach the final moisture and the heat sensitivity of the material is an important parameter for design of an industrial plant . Small batch fluidized-bed tests can measure a drying curve as shown in Fig . 12-74 . Figure 12-74a shows two drying curves for the same material . The curves differ based on the bed loading . The drying curves clearly show that the moisture is rapidly evaporating while the material is maintained at a low temperature . This particular material does not have a constant-rate period, evidenced by the decline in drying rate and rise of temperature with time . This is indicative of the drying of the surface of the particles; as they dry, the driving force for evaporation decreases . A moisture sorption isotherm, described in the Solids Drying Fundamentals subsection, is how this decrease can be quantified . The falling rate, by itself, does not mean that the rate is limited by internal mass transfer within each particle . Additional drying curves can be measured to determine whether the drying rate of a material is internally or externally limited . Internally limited materials are slow to dry with moisture that is tightly bound and unable to move to the evaporating surface of the individual particles quickly enough; changes in superficial velocity and bed depth do not influence drying . Externally limited materials are influenced by the external drying conditions at which they are dried including both drying temperature and superficial gas velocity . The drying curve data presented in Fig . 12-74a were normalized as shown in Fig . 12-74b . This suggests externally limited drying behavior . In this particular material, the rate is falling due to the dryness of the particles but not due to slow moisture transport through each particle . Rate-limiting steps in drying processes are described further in the Solids-Drying Fundamentals subsection; specifically, see Fig . 12-25 . See Table 12-38 to learn how to increase the throughput by using the air velocity or bed depth, depending on whether the drying rate is controlled externally or internally . For production, increasing gas velocity is beneficial for externally limited materials, giving reduced drying time and either a higher throughput or a smaller bed area, but gives no real benefit for internally limited materials; likewise, increasing bed depth is beneficial for internally limited materials, giving either a higher throughput or enabling use of a smaller bed area with the same drying time but not for externally limited materials . However, using unnecessarily high gas velocity or an unnecessarily deep bed can increase the pressure drop, operating costs, elutriation, attrition, and backmixing .

TABLE 12-37 Manufacturer’s Performance Data for FMC Link-Belt Roto-Louvre Dryer* Material dried

Ammonium sulfate

Foundry sand

Metallurgical coke

Dryer diameter 2 ft 7 in 6 ft 4 in 10 ft 3 in Dryer length 10 ft 24 ft 30 ft Moisture in feed, % wet 2 .0 6 .0 18 .0 basis Moisture in product, % wet 0 .1 0 .5 0 .5 basis Production rate, lb/h 2500 32,000 38,000 Evaporation rate, lb/h 50 2130 8110 Type of fuel Steam Gas Oil 3 115 gal/h Fuel consumption 255 lb/h 4630 ft /h Calorific value of fuel 837 Btu/lb 1000 Btu/ft3 150,000 Btu/gal Efficiency, Btu, supplied 4370 2170 2135 per lb evaporation Total power required, hp 4 41 78 *Courtesy of Material Handling Systems Division, FMC Corp . To convert British thermal units to kilojoules, multiply by 1 .06; to convert horsepower to kilowatts, multiply by 0 .746 .

FIG. 12-73 Geldart diagram .

SOLIDS-DRYING FUNDAMENTALS

12-63

(a)

Moisture Content, 1.0-kg batch Moisture Content, 1.5-kg batch Bed Temperature, 1.0-kg batch Bed Temperature, 1.5-kg batch

(b)

Moisture Content, 1.0-kg batch Moisture Content, 1.5-kg batch Bed Temperature, 1.0-kg batch Bed Temperature, 1.5-kg batch

FIG. 12-74 Drying curve of organic material .

The fluidization velocity is of major importance, as indicated in the introduction . Each material will have individual requirements for the gas velocity and pressure drop to provide good fluidization . An investigation of the relationship between fluidization velocity and bed pressure drop for a given material is called a fluidization curve . An example is shown in Fig . 12-75 . The results are illustrative and intended to give a clear picture of the relationship . The minimum fluidization velocity can be estimated from the Wen and Yu correlation [AIChE J. 12(3): 610–612 (1966)] given in Sec . 19 .

At a superficial velocity below the value required for minimum fluidization, the pressure drop over the bed will increase proportionally with the velocity . Above a critical velocity, the pressure drop corresponds to the weight of the fluidized mass of material . This is referred to as the minimum fluidization; the bed is said to be in an incipiently fluidized state . A further increase in the superficial velocity will result in little or no increase in the pressure drop . The particle layer now behaves as a liquid, and the bed volume expands considerably . At even higher gas velocities the motion will be

12-64

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

TABLE 12-38 Drying

Comparison of Internally and Externally Limited

Batch

Air velocity Bed depth Air velocity Bed depth

Internally limited drying

Continuous

2X air velocity ≈ no change in drying time 2X bed depth ≈ no change in drying time 2X air velocity ≈ no change in production rate 2X bed depth ≈ production rate increases

FIG. 12-76

Traditional perforated plate for fluid-bed application .

Externally limited drying Batch Continuous

Air velocity Bed depth Air velocity Bed depth

2X air velocity ≈ 1/2 drying time 2X bed depth ≈ 2X drying time 2X air velocity ≈ 2X production rate 2X bed depth ≈ no change in production rate

stronger, and the excess gas flow will tend to appear as bubbles . In this state the particle layer will undergo vigorous mixing, while still appearing as a dense layer of fluidlike material or a boiling liquid . A further increase in the superficial velocity will result in the solid phase being entrained by the gas flow and will appear as lean phase pneumatic transport . Accordingly, the pressure drop falls to zero . Figure 17-4 provides examples of these fluidization regimes . However, as a general recommendation, a value between the critical value and the value where the pressure drop falls off will be right . A first choice could be a factor of 2 to 5 times the minimum fluidization velocity . The fluidizing velocity value that will serve a drying task best cannot be derived exactly from the diagram and must be verified through experimentation . There are additional consequences to using a high air velocity in fluidized beds such as particle elutriation and attrition . Given a particle size distribution in the bed, the finer particles will have a lower terminal velocity and will be selectively carried out of the bed, i .e ., elutriated . See Geldart et al ., “Entrainment of FCC from Fluidized Beds—a New Correlation for Elutriation ∗ Rate Constant K i∞ ,” Powder Technol . 95: 240–247 (1998), for more information on this transformation . The design of the gas distributor plate is important for several reasons . First, the plate serves as a manifold, distributing fluidization and drying gas evenly and preventing dead spots in the bed . This requires an even pattern of orifices in the plate and a sufficient pressure drop over the plate . As a general rule, the pressure drop across the gas distributor should equal at least one-half of the pressure drop across the powder bed with the following range (of pressure drops across the plate) of 500 to 2500 Pa . The estimation of the pressure drop in design situations may be difficult except for the case of the traditional perforated sheet with cylindrical holes perpendicular to the plane of the plate, as shown in Fig . 12-76 . For this type of plate, see McAllister et al ., “Perforated-Plate Performance,” Chem. Eng. Sci. 9: 25–35 (1958) . A calculation using this formula will show that a plate giving a required pressure drop of 1500 Pa and a typical fluidizing velocity of 0 .35 m/s will need an open area of roughly 1 percent . Provided by a plate of 1-mm thickness and 1-mm-diameter holes, this requires approximately 12,732 holes per square meter . However, this type of plate is being replaced in most fluid-bed applications because of its inherent disadvantages, which are caused by the manufacture of the plate, i .e ., punching holes of a smaller diameter than the

FIG. 12-77

Conidur plate for fluid-bed application . (Hein, Lehmann Trennund Fördertechnik GmbH.)

FIG. 12-78

Gill Plate for fluid-bed application . (GEA)

thickness of the plate itself . The result is that the plates are weak and are prone to sifting finer particles . The perpendicular flow pattern also means that the plate does not provide a transport capacity for lumps of powder along the plane of the plate . This transport capacity is provided by so-called gill-type plates of which there are two distinct categories . One category is the type where plates are punched in a very fine regular pattern, not only to provide holes or orifices but also to deform the plate so that each orifice acquires a shape suited for acceleration of the gas flow in magnitude and direction . An example of this type is shown in Fig . 12-77, representing the Conidur type of plate . The particular feature of Conidur sheets is the specific hole shape which creates a directional airflow to help in discharging the product and influences the retention time in the fluid bed . The special method of manufacturing Conidur sheets enables finishing of fine perforations in sheets with an initial thickness many times over the hole width . Perforations of only 100 mm in an initial sheet thickness of 0 .7 mm are possible . With holes this small 1 m2 of plate may comprise several hundred thousand individual orifices . The capacity of contributing to the transport of powder in the plane of the plate due to the horizontal component of the gas velocity is also the present for the second category of plates of the gill type . Figure 12-78 shows an example .

FIG. 12-75 Fluid-bed pressure drop versus fluidizing velocity . (revised, GEA)

SOLIDS-DRYING FUNDAMENTALS

FIG. 12-79

12-65

Non-sifting Gill Plate . (Patented by GEA)

In this type of plate, the holes or orifices are large, and the number of gills per square meter is just a few thousand . The gas flow through each of the gills has a strong component parallel to the plate, providing powder transport capacity as well as a cleaning effect . The gills are punched individually or in groups and can be oriented individually to provide a possibility of articulating the horizontal transport effect . In certain applications in the food and pharmaceutical industries, the nonsifting property of a fluid-bed plate is particularly appreciated . This property of a gill-type plate can be enhanced as illustrated in Fig . 12-79, where the hole after punching is additionally deformed so that the gill overlaps the orifice . The final type of fluid-bed plate mentioned here is the so bubble plate type . Illustrated in Fig . 12-80, in principle it is a gill-type plate . The orifice is cut out of the plate, and the bubble is subsequently pressed so that the orifice is oriented in a predominantly horizontal direction . A fluid-bed plate will typically have only 1600 holes per m2 . By this technology a combination of three key features is established . The plate is nonsifting, it has directional transport capacity that can be articulated through individual orientation of bubbles, and it is totally free of cracks that may compromise sanitary aspects of the installation . The operating conditions of a fluid bed are, to a high degree, dictated by the properties of the material to be dried . For most products, the temperature is of primary importance, since the fluidized state results in very high heat-transfer rates so that heat sensitivity may restrict temperature and thereby prolong process time . To achieve the most favorable combination of conditions to carry out a fluid-bed drying process, it is necessary to consider the different modes of fluid-bed drying available . Industrial Fluid-Bed Drying The first major distinction between fluid-bed types is the choice of mode: batch or continuous . Batch fluid beds may appear in several forms . The process chamber has a perforated plate or screen in the bottom and a drying gas outlet at the top, usually fitted with an internal filter . The drying gas enters the fluid bed through a plenum chamber below the perforated plate and leaves through the filter arrangement . The batch of material is enclosed in the process chamber for the duration of the process . Figure 12-81 shows a sketch of a typical batch fluid-bed dryer as used in the food and pharmaceutical industries . The process chamber is conical in order to create a freeboard velocity in the upper part of the chamber that is lower than the fluidizing velocity just above the plate . The enclosed product batch is prevented from escaping the process chamber and will therefore allow a freer choice of fluidizing velocity than is the case in a continuous fluid bed, as described later . Continuous fluid beds may be even more varied than batch fluid beds . The main distinction between continuous fluid beds will be according to the solids flow pattern in the dryer . The continuous fluid bed will have an inlet point for moist granular materials to be dried and an outlet for the dried material . If the moist material is immediately fluidizable, it can be introduced directly onto the plate and led through the bed in a plug-flow pattern that will enhance control of product residence time and temperature control . If the moist granular material is too sticky or cohesive due to surface moisture and requires a certain degree of drying before fluidization, it can be handled by a backmix fluid bed, to be described later . Continuous plug-flow beds are designed to lead the solids flow along a distinct path through the bed . Baffles will be arranged to prevent or limit solids mixing in the horizontal direction . Thereby the residence time distribution of the solids becomes narrow . The bed may be of cylindrical or rectangular shape . The temperature and moisture contents of the solids will vary along the path of solids through the bed and thereby enable the solids to come close to equilibrium with the drying gas . A typical plug-flow fluid bed is shown in Fig . 12-82 . Continuous plug-flow beds of stationary as well as vibrating type may benefit strongly from use of the gill-type fluid-bed plates with the capacity for controlling the movement of powder along the plate and around bends and corners created by baffles . Proper use of these means may make it possible to optimize the combination of fluidization velocity, bed layer height, and powder residence time .

FIG. 12-80 Bubble Plate . (Patented by GEA.)

FIG. 12-81 Batch-type fluid bed . (Aeromatic-Fielder .)

Continuous backmix beds are used in particular when the moist granular material needs a certain degree of drying before it can fluidize . By distributing the material over the surface of an operating fluid bed arranged for total solids mixing, also called backmix flow, it will be absorbed by the dryer material in the bed, and lumping as well as sticking to the chamber surfaces will be avoided . The distribution of the feed can be arranged in different ways, among which a rotary thrower is an obvious choice . A typical backmix fluid bed is shown in Fig . 12-83 . Backmix fluid beds can be of box-shaped design or cylindrical . The whole mass of material in the backmix fluid bed will be totally mixed, and all powder particles in the bed will experience the same air temperature regardless of their position on the drying curve illustrated in Fig . 12-74a. The residence time distribution becomes very wide, and part of the material may get a very long residence time while another part may get a very short time .

FIG. 12-82

Continuous plug-flow fluid bed . (GEA)

12-66

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-84 FIG. 12-83

Continuous backmix fluid bed . (GEA)

dryer that can produce 1000 kg . The new bed will operate at 150°C with Twb = 38°C and an air mass flux G2 = 0 .75 kg/(m2 ⋅ s) .

Continuous-contact fluid beds are common in the chemical industry as the solution to the problem arising from materials requiring low fluidizing air temperature due to heat sensitivity and high energy input to complete the drying operation . The main feature of the contact fluid bed is the presence of heating panels, which are plate or tube structures submerged in the fluidized-bed layer and heated internally by an energy source such as steam, water, or oil . The fluidized state of the bed provides very high heat-transfer rates between the fluidizing gas, the fluidized material, and any objects submerged in the bed . The result is that a very significant portion of the required energy input can be provided by the heating panels without risk of overheating the material . The fluidized state of the bed ensures that the material in the bed will flow with little restriction around the heating panels . Design and Scale-Up of Fluid Beds When fluid-bed technology can be applied to drying of granular products, significant advantages compared to other drying processes can be observed . Design variables such as fluidizing velocity, critical moisture content for fluidization, and residence time required for drying to the specified residual moisture must, however, be established by experimental or pilot test before design steps can be taken . Reliable and highly integrated fluid-bed systems of either batch or continuous type can be designed, but only by using a combination of such pilot tests and industrial experience . For scale-up based on an experimentally recorded batch drying curve, including performance mode calculations and altering operating conditions, Kemp and Oakley (2002) showed that the drying time for a given range of moisture content ΔX scales according to the following relationships: Externally limited ( fast drying material):

Z=

∆τ 2 (mB /A )2 G1 (TGI − Twb )1 = ∆τ1 (mB /A )1 G2 (TGI − Twb )2 (12-108)

Internally limited (slow drying material):

Z=

∆τ 2 (TGI − Twb )1 = ∆τ1 (TGI − Twb )2

Vibrating conveyor dryer . (Carrier Vibrating Equipment, Inc.)

(12-109)

Here 1 denotes experimental or original conditions and 2 denotes full-scale or new conditions; Z is the normalization factor; G is gas mass flux; mB/A is bed mass per unit area, proportional to bed depth z . This method can be used to scale a batch drying curve section by section . Almost always, one of these two simplified limiting cases applies, known as externally limited and internally limited normalization . For a typical pilot-plant experiment, the fluidization velocity and temperature driving forces are similar to those of the full-size bed, but the bed diameter or depth can be much less . Hence, for externally limited normalization, the mB/A term dominates; Z can be much greater than 1 . Example 12-18 Scaling a Batch Fluidized-Bed Dryer An experimental batch drying curve has been measured at 100°C, and the drying time was 30 min . The bed diameter was 0 .15 m with a bed mass of 1 .0 kg . Assume that temperature driving forces are proportional to T − Twb, with Twb = 30°C and that the air mass flux = 0 .55 kg/ (m2 ⋅ s) . Assuming a scaling normalization factor of 2 .5, calculate the bed area for a new

A=

(1000 kg) (0.55 kg/m 2 ⋅ s) (150° − 38°) = 9.03 m 2 (1 kg/0.017 m 2 ) (0.75 kg/m2 ⋅ s) (100° − 30°) (2.5)

More complicated mathematical models exist for design and scaling of fluid-bed dryers, namely, those described by Tsotsas et al ., “Experimental Investigation and Modelling of Continuous Fluidized Bed Drying under Steady-State and Dynamic Conditions,” Chem. Eng. Sci. 57: 5021–5038 (2002) .

Vibrating Fluidized-Bed Dryers Information on vibrating conveyors and their mechanical construction is given in Sec . 21, Solids Processing and Particle Technology . The vibrating conveyor dryer is a modified form of fluidized-bed equipment, in which fluidization is maintained by a combination of pneumatic and mechanical forces . The heating gas is introduced into a plenum beneath the conveying deck through ducts and flexible hose connections and passes up through a screen, perforated, or slotted conveying deck, through the fluidized bed of solids, and into an exhaust hood (Fig . 12-84) . If ambient air is employed for cooling, the sides of the plenum may be open and a simple exhaust system used; however, because the gas distribution plate may be designed for several inches of water pressure drop to ensure a uniform velocity distribution through the bed of solids, a combination pressure-blower exhaust-fan system is desirable to balance the pressure above the deck with the outside atmosphere and prevent gas in-leakage or blowing at the solids feed and exit points . Units are fabricated in widths from 0 .3 to 1 .5 m . Lengths are variable from 3 to 50 m; however, most commercial units will not exceed a length of 10 to 16 m per section . Power required for the vibrating drive will be approximately 0 .4 kW/m2 of deck . Capacity is primarily limited by the air velocity that can be used without excessive dust entrainment . Table 12-39 shows limiting air velocities suitable for various solids particles . Usually, the equipment is satisfactory for particles larger than 150 mm . When a stationary vessel is employed for fluidization, all solids being treated must be fluidized; nonfluidizable fractions fall to the bottom of the bed and may eventually block the gas distributor . The addition of mechanical vibration to a fluidized system offers the following advantages: 1 . Equipment can handle nonfluidizable solids fractions . 2 . Prescreening or sizing of the feed is less critical than in a stationary fluidized bed . 3 . Air channeling at the incipient fluidization velocity is reduced . TABLE 12-39 Estimating Maximum Superficial Air Velocities Through Vibrating-Conveyor Screens* Velocity, m/s Mesh size

2 .0 specific gravity

200 0.22 100 0.69 50 1.4 30 2.6 20 3.2 10 6.9 5 11.4 *Carrier Vibrating Equipment, Inc.

1.0 specific gravity 0.13 0.38 0.89 1.8 2.5 4.6 7.9

SOLIDS-DRYING FUNDAMENTALS 4 . Fluidization may be accomplished with lower pressures and gas velocities . 5 . Vibrating conveyor dryers are suitable for free-flowing solids containing mainly surface moisture . Retention is limited by conveying speeds which range from 0 .02 to 0 .12 m/s . Bed depth rarely exceeds 7 cm, although units are fabricated to carry 30- to 46-cm-deep beds; these also employ plate and pipe coils suspended in the bed to provide additional heat-transfer area . Vibrating dryers are not suitable for fibrous materials which mat or for sticky solids which may ball or adhere to the deck . For estimating purposes for direct heat drying applications, it can be assumed that the average exit gas temperature leaving the solids bed will approach the final solids discharge temperature on an ordinary unit carrying a 5- to 15-cm-deep bed . Calculation of the heat load and selection of an inlet air temperature and superficial velocity (Table 12-39) will then permit approximate sizing, provided an approximation of the minimum required retention time can be made . Vibrating conveyors employing direct contacting of solids with hot, humid air have also been used for the agglomeration of fine powders, chiefly for the preparation of agglomerated water-dispersible food products . Control of inlet air temperature and dew point permits the uniform addition of small quantities of liquids to solids by condensation on the cool incoming-particle surfaces . The wetting section of the conveyor is followed immediately by a warm-air drying section and particle screening . Spouted Beds The spouted-bed technique was developed primarily for solids too coarse to be handled in fluidized beds, typically classified as type D on the Geldart diagram . Although their applications overlap, the methods of gas-solids mixing are completely different . A schematic view of a spouted bed is given in Fig . 12-85 . Mixing and gas-solids contacting are achieved first in a fluid “spout,” flowing upward through the center of a loosely packed bed of solids . Particles are entrained by the fluid and conveyed to the top of the bed . They then flow downward in the surrounding annulus as in an ordinary gravity bed, countercurrently to gas flow . The mechanisms of gas flow and solids flow in spouted beds were first described by Mathur and Gishler [Am. Inst. Chem. Eng. J. 1(2): 157–164 (1955)] . Drying studies have been carried out by Cowan [Eng. J. 41: 5, 60–64 (1958)], and a theoretical equation for predicting the minimum fluid velocity necessary to initiate spouting was developed by Madonna and Lama [Am. Inst. Chem. Eng. J. 4(4): 497 (1958)] . Investigations to determine maximum spoutable depths and to develop theoretical relationships based on vessel geometry and operating variables have been carried out by Lefroy [Trans. Inst. Chem. Eng. 47(5): T120–128 (1969)] and Reddy [Can. J. Chem. Eng. 46(5): 329–334 (1968)] . Information on the scale-up of spouted beds is provided by Passos, Mujumdar, and Massarani [Drying Technol. 12(1–2): 351–391 (1994)] . Gas flow in a spouted bed is partially through the spout and partially through the annulus . About 30 percent of the gas entering the system immediately diffuses into the downward-flowing annulus . Near the top of the bed, the quantity in the annulus approaches 66 percent of the total gas flow; the gas flow through the annulus at any point in the bed equals that which would flow through a loosely packed solids bed under the same conditions of pressure drop . Solids flow in the annulus is both downward and slightly inward . As the fluid spout rises in the bed, it entrains more and more particles, losing velocity and gas into the annulus . The volume of solids displaced by the spout is roughly 6 percent of the total bed . On the basis of experimental studies, Mathur and Gishler derived an empirical correlation to describe the minimum fluid flow necessary for spouting, in 3- to 12-in-diameter columns: u=

D p  Do  D  D  c

c

1/3

 2 gL(rs - r f )    rf  

0 .5

(12-110)

FIG. 12-85 Schematic diagram of spouted bed . Schematic diagram of spouted bed . [Mathur and Gishler, Am. Inst. Chem. Eng. J. 1: 2, 15 (1955) .]

12-67

where u = superficial fluid velocity through the bed; Dp = particle diameter; Dc = column (or bed) diameter; Do = fluid inlet orifice diameter; L = bed height; rs = absolute solids density; rf = fluid density; and g = gravity acceleration . The inlet orifice diameter, air rate, bed diameter, and bed depth were all found to be critical and interdependent: 1 . In a given-diameter bed, deeper beds can be spouted as the gas inlet orifice size is decreased . 2 . Increasing bed diameter increases spoutable depth . 3 . As indicated by Eq . (12-110), the superficial fluid velocity required for spouting increases with bed depth and orifice diameter and decreases as the bed diameter is increased . Additional Reading Davidson and Harrison, Fluidized Particles, Cambridge University Press, Cambridge, UK, 1963 . Geldart, Powder Technol . 6: 201–205 (1972) . Geldart, Powder Technol . 7: 286–292 (1973) . Grace, “Fluidized-Bed Hydrodynamics,” chap . 8 .1 in Handbook of Multiphase Systems, McGraw-Hill, New York, 1982 . Gupta and Mujumdar, “Recent Developments in Fluidized Bed Drying,” chap . 5 in Mujumdar, ed ., Advances in Drying, vol . 2, Hemisphere, Washington, D .C ., 1983, p . 155 . Kemp and Oakley, “Modeling of Particulate Drying in Theory and Practice,” Drying Technol. 20(9): 1699–1750 (2002) . Kunii and Levenspiel, Fluidization Engineering, 2d ed ., Butterworth-Heinemann, Stoneham, Mass ., 1991 . McAllister et al ., “Perforated-Plate Performance,” Chem. Eng. Sci. 9: 25–35 (1958) . Poersch, Aufbereitungs-Technik 4: 205–218 (1983) . Richardson, “Incipient Fluidization and Particulate Systems,” chap . 2 in Davidson and Harrison, eds ., Fluidization, Academic Press, London, 1972 . Romankows, “Drying,” chap . 12 in Davidson and Harrison, eds ., Fluidization, Academic Press, London, 1972 . Vanacek, Drbohlar, and Markvard, Fluidized Bed Drying, Leonard Hill, London, 1965 .

Pneumatic Conveying Dryers Synonyms and Examples Flash dryer, spin flash dryer, ring dryer . Description Pneumatic conveyor dryers comprise a long tube or duct carrying a gas at high velocity, a fan to propel the gas, a suitable feeder for addition and dispersion of particulate solids in the gas stream, and a cyclone collector or other separation equipment for final recovery of solids from the gas . Pneumatic conveying dryers simultaneously dry and convey particles by using high-velocity hot air . The quantity and velocity of the gas phase are sufficient to lift and convey the solids against the forces of gravity and friction . These systems are sometimes incorrectly called flash dryers when in fact the moisture is not actually “flashed” off . (True flash dryers are sometimes used for soap drying to describe moisture removal when pressure is quickly reduced .) Pneumatic systems may be distinguished by two characteristics: 1 . Retention of a given solids particle in the system is on average very short, usually no more than a few seconds . This means that any process conducted in a pneumatic system cannot be internally controlled (diffusioncontrolled) . The solids particles must be so small that heat transfer and mass transfer from the interiors are essentially instantaneous . 2 . On an energy content basis, the system is balanced at all times; i .e ., there is sufficient energy in the gas (or solids) present in the system at any time to complete the work on all the solids (or gas) present at the same time . This is significant in that there is no lag in response to control changes or in starting up and shutting down the system; no partially processed residual solids or gas need be retained between runs . It is for these reasons that pneumatic equipment is especially suitable for processing heat-sensitive, easily oxidized, explosive, or flammable materials which cannot be exposed to process conditions for extended periods . The solids feeder may be of any type: Screw feeders, venturi sections, high-speed grinders, and dispersion mills are employed . For pneumatic conveyors, selection of the correct feeder to obtain thorough initial dispersion of solids in the gas is of major importance . For example, by employing an air-swept hammer mill in a drying operation, 65 to 95 percent of the total heat may be transferred within the mill itself if all the drying gas is passed through it . Fans may be of the induced-draft or the forced-draft type . The former is usually preferred because the system can then be operated under a slight negative pressure . Dust and hot gas will not be blown out through leaks in the equipment . Cyclone separators are preferred for low investment . If maximum recovery of dust or noxious fumes is required, the cyclone may be followed by a wet scrubber or bag collector . Pneumatic conveyors are suitable for materials which are granular and free-flowing when dispersed in the gas stream, so they do not stick on the conveyor walls or agglomerate . Sticky materials such as filter cakes may be dispersed and partially dried by an air-swept disintegrator in many cases . Otherwise, dry product may be recycled and mixed with fresh feed, and then the two dispersed are together in a disintegrator . Coarse material containing internal moisture may be subjected to fine grinding in a hammer mill .

12-68

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

The main requirement in all applications is that the operation be instantaneously completed; internal diffusion of moisture must not be limiting in drying operations, and particle sizes must be small enough that the thermal conductivity of the solids does not control during heating and cooling operations . Pneumatic conveyors are rarely suitable for abrasive solids . Pneumatic conveying can result in significant particle size reduction, particularly when crystalline or other friable materials are being handled . This may or may not be desirable but must be recognized if the system is selected . The action is similar to that of a fluid-energy grinder . Pneumatic conveyors may be single-stage or multistage . The former is employed for evaporation of small quantities of surface moisture . Multistage installations are used for difficult drying processes, e .g ., drying heat-sensitive products containing large quantities of moisture and drying materials initially containing internal as well as surface moisture . Typical single- and two-stage drying systems are illustrated in Figs . 12-86, 12-87, and 12-88 . Figure 12-86 illustrates the flow diagram of a single-stage dryer with a paddle mixer, a screw conveyor followed by a rotary disperser for introduction of the feed into the airstream at the throat of a venturi section . The drying takes place in the drying column after which the dry product is collected in a cyclone . A diverter introduces the option of recycling part of the product into the mixer in order to handle somewhat sticky products . The environmental requirements are met with a wet scrubber in the exhaust stream . Figure 12-87 illustrates a two-stage dryer where the initial feed material is dried in a flash dryer by using the spent drying air from the second stage . This semidried product is then introduced into the second-stage flash dryer for contact with the hottest air . This concept is in use in the pulp and paper industry . Its use is limited to materials that are dry enough on the surface after the first stage to avoid plugging of the first-stage cyclone . The main advantage of the two-stage concept is the heat economy which is improved considerably over that of the single-stage concept . Figure 12-88 is an elevation view of an actual single-stage dryer . It employs an integral coarse-fraction classifier to separate undried particles for recycle . Several typical products dried in pneumatic conveyors are described in Table 12-40 . Design methods for pneumatic conveyor dryers Depending upon the temperature sensitivity of the product, inlet air temperatures between 125 and 750°C are employed . With a heat-sensitive solid, a high initial moisture content should permit use of a high inlet air temperature . Evaporation of surface moisture takes place at essentially the wet-bulb air temperature . Until this has been completed, by which time the air will have cooled significantly, the surface-moisture film prevents the solids temperature from exceeding the wet-bulb temperature of the air . Pneumatic conveyors are used for solids having initial moisture contents ranging from 3 to 90 percent, wet basis . The air quantity required and solids-to-gas loading are fixed by

FIG. 12-87

WEATHER HOOD VENT STACK

CYCLONE

DUST COLLECTOR WITH DISCHARGE SCREW AND ROTARY AIRLOCK

DOUBLE FLAP VALVE AIR HEATER MILL FEED

CAGE MILL

SYSTEM FAN FIG. 12-86

Flow diagram of single-stage flash dryer . (Air Preheater Company, Raymond & Bartlett Snow Products .)

Flow diagram of countercurrent two-stage flash dryer . (GEA)

SOLIDS-DRYING FUNDAMENTALS

FIG. 12-88 Flow diagram of Strong Scott flash dryer with integral coarse-fraction classifier . (Bepex Corp.)

the moisture load, the inlet air temperature, and frequently the exit air humidity . See Example 12-19 for a calculation of the mass and energy balance of a pneumatic conveying dryer . The gas velocity in the conveying duct must be sufficient to convey the largest particle . This may be calculated accurately by methods given in Sec . 17, Gas-Solids Operations and Equipment . For estimating purposes, a velocity of 25 m/s, calculated at the exit air temperature, is frequently employed . The exit solids temperature will approach the exit gas dry-bulb temperature . Observation of operating conveyors indicates that the solids are rarely uniformly dispersed in the gas phase . With infrequent exceptions, the particles move in a streaklike pattern, following a streamline along the duct wall where the flow velocity is at a minimum . Complete or even partial diffusion in the gas phase is rarely experienced even with low-specific-gravity particles . Air velocities may approach 20 to 30 m/s . It is doubtful, however, that

even finer and lighter materials reach more than 80 percent of this speed, while heavier and larger fractions may travel at much slower rates [Fischer, Mech. Eng. 81(11): 67–69 (1959)] . Very little information and few operating data have been published on pneumatic conveyor dryers which would permit a true theoretical basis for design . Therefore, firm design always requires pilot tests . It is believed, however, that the significant velocity effect in a pneumatic conveyor is the difference in velocities between gas and solids, which is strongly linked to heat- and mass-transfer coefficients and is the reason why a major part of the total drying actually occurs in the feed input section . See Mills, D ., Pneumatic Conveying Design Guide, 3d ed ., Elsevier, Amsterdam, Netherlands, 2015 for comprehensive information on pneumatic conveying systems . For estimating purposes, the conveyor cross-section is fixed by the assumed air velocity and quantity . The standard scoping design method is used, obtaining the required gas flow rate from a heat and mass balance, and the duct cross-sectional area and diameter from the gas velocity (if unknown, a typical value is 20 m/s) . An incremental model may be used to predict drying conditions along the duct . However, several parameters are hard to obtain, and conditions change rapidly near the feed point . Hence, for reliable estimates of drying time and duct length, pilot-plant tests should always be used . A conveyor length larger than 50 duct diameters is rarely required . The length of the full-scale dryer should always be somewhat larger than required in pilot-plant tests, because wall effects are higher in small-diameter ducts . This gives greater relative velocity (and thus higher heat transfer) and lower particle velocity in the pilotplant dryer, both effects giving a shorter length than the full-scale dryer for a given amount of drying . If desired, the length difference on scale-up can be predicted by using the incremental model and the pilot-plant data to back-calculate the uncertain parameters; see Kemp, Drying Technol . 12(1&2): 279–297 (1994) and Kemp and Oakley (2002) . An alternative method of estimating dryer size very roughly is to estimate a volumetric heat-transfer coefficient [typical values are around 2000 J/(m3 ⋅ s ⋅ K)] and thus calculate dryer volume . Pressure drop in the system may be computed by methods described in Sec . 6, Fluid and Particle Dynamics . To prevent excessive leakage into or out of the system, which may have a total pressure drop of 2000 to 4000 Pa, rotary air locks or screw feeders are employed at the solids inlet and discharge . Ring Dryers The ring dryer is a development of flash, or pneumatic conveyor, drying technology, designed to increase the versatility of application of this technology and overcome many of its limitations . One of the great advantages of flash drying is the very short retention time, typically no more than a few seconds . However, in a conventional flash dryer, residence time is fixed, and this limits its application to materials in which the drying mechanism is not diffusion-controlled and where a range of moisture within the final product is acceptable . The ring dryer offers two advantages over the flash dryer . First, residence time is controlled by the use of an adjustable internal classifier that allows fine particles, which dry quickly, to leave while larger particles, which dry slowly, have an extended residence time within the system . Second, the combination of the classifier with an internal mill can allow simultaneous grinding and drying with control of product particle size and moisture . Available with a range of different feed systems to handle a variety of applications, the ring dryer provides wide versatility . The essential difference between a conventional flash dryer and the ring dryer is the manifold centrifugal classifier . The manifold provides classification of the product about to leave the dryer by using differential centrifugal force .

TABLE 12-40 Typical Products Dried in Pneumatic Conveyor Dryers (Barr-Rosin) Material Expandable polystyrene beads Coal fines Polycarbonate resin Potato starch Aspirin Melamine Com gluten meal Maize fiber Distillers dried grains (DDGs) Vital wheat gluten Casein Tricalcium phosphate Zeolite Orange peels Modified com starch Methylcellulose

Initial moisture, wet basis, % 3 23 25 42 22 20 60 60 65 70 50 30 45 82 40 45

12-69

Final moisture, wet basis, %

Plant configuration

0.1 1.0 10 20 0.1 0.05 10 18 10 7 10 0.5 20 10 10 25

Single-stage flash Single-stage flash Single-stage flash Single-stage flash Single-stage flash Single-stage flash Feed-type ring dryer Feed-type ring dryer Feed-type ring dryer Full-ring dryer Full-ring dryer Full-ring dryer Full-ring dryer Full-ring dryer P-type ring dryer P-type ring dryer

12-70

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

FIG. 12-89

Full manifold classifier for ring dryer . (Barr-Rosin.)

The manifold, as shown in Fig . 12-89, uses the centrifugal effect of an airstream passing around the curve to concentrate the product into a moving layer, with the dense material on the outside and the light material on the inside . This enables the adjustable splitter blades within the manifold classifier to segregate the denser, wetter material and return it for a further circuit of drying . Fine, dried material is allowed to leave the dryer with the exhaust air and to pass to the product collection system . This selective extension

FIG. 12-90

of residence time ensures a more evenly dried material than is possible from a conventional flash dryer . Many materials that have traditionally been regarded as difficult to dry can be processed to the required moisture content in a ring dryer . The recycle requirements of products in different applications can vary substantially depending upon the scale of operation, ease of drying, and finished-product specification . The location of reintroduction of undried material back into the drying medium has a significant impact upon the dryer performance and final-product characteristics . The full ring dryer is the most versatile configuration of the ring dryer . See Fig . 12-90 . It incorporates a multistage classifier which allows much higher recycle rates than the single-stage manifold . This configuration usually incorporates a disintegrator which provides adjustable amounts of product grinding depending upon the speed and manifold setting . For sensitive or fine materials, the disintegrator can be omitted . Alternative feed locations are available to suit the material sensitivity and the final-product requirements . The full ring configuration gives a very high degree of control of both residence time and particle size, and it is used for a wide variety of applications from small production rates of pharmaceutical and fine chemicals to large production rates of food products, bulk chemicals, and minerals . Other ring dryer configurations are available, including ones that have a cyclone within the loop to enable readdition of larger particles to remix or redispersion with the feed . An important element in optimizing the performance of a flash or ring dryer is the degree of dispersion at the feed point . Maximizing the product surface area in this region of highest evaporative driving force is a key objective in the design of this type of dryer . Ring dryers are fed using equipment similar to that of conventional flash dryers . Ring dryers with vertical configuration are normally fed by a flooded screw and a disperser which propels the wet feed into a high-velocity venturi, in which the bulk of the evaporation takes place . The full ring dryer normally employs an air-swept disperser or mill within the drying circuit to provide screenless grinding when required . Together with the manifold classifier this ensures a product with a uniform particle size . For liquid, slurry, or pasty feed materials, backmixing of the feed with a portion of the dry product will be carried out to produce a conditioned friable material . This further increases the versatility of the ring dryer, allowing it to handle sludge and slurry feeds with ease . The air velocity required and air/solids ratio are determined by the evaporative load, the air inlet temperature, and the exhaust air humidity . Too high an exhaust air humidity would prevent complete drying, so then a higher air inlet temperature and air/solids ratio would be required . The air velocity within the dryer must be sufficient to convey the largest particle, or agglomerate . The air/solids ratio must be high enough to convey both the product and backmix, together with internal recycle from the manifold . For estimating purposes, a velocity of 25 m/s, calculated at dryer exhaust conditions, is appropriate for both pneumatic conveyor and ring dryers .

Flow diagram of full manifold-type ring dryer . (Barr-Rosin.)

SOLIDS-DRYING FUNDAMENTALS

12-71

Example 12-19 Mass and Energy Balance for a Pneumatic Conveying Dryer Calculate the exit temperature and relative humidity of a pneumatic conveying system with an inlet air temperature, mass flow rate, and absolute humidity of 700°C, 9 kg/s, and 0 .01 g/g, respectively . The feed material has a flow rate of 6 .12 kg/s and wet-basis moisture content of 35 percent . Use the following physical properties: Cp,air = 1 .0 J/(g ⋅ K), Cp,dry solids = J/(g ⋅ K), Cp,liquid water = 4 .18 J/(g ⋅ K), Cp,water vapor = 2 .0 J/(g ⋅ K), and heat of vaporization of water (at 100°C) = 2257 J/g . Solution First, assume all the water in the feed evaporates . If all the water in the feed evaporates, then the mass flow of water vapor exiting the dryer will equal the water vapor entering the dryer (0 .01 ⋅ 9 kg/s) plus the water evaporated (0 .35 ⋅ 6 .12 kg/s), which equals 2 .24 kg/s . The dry air feed rate is (1 − 0.01) ⋅ 9 kg/s, so the absolute humidity in the exhaust is 2.24/[(1 − 0.01) ⋅ 9] = 0.239 kg water vapor/kg dry air. The energy balance can be calculated on a spreadsheet, by setting the sum of the enthalpy terms to zero and solving iteratively for Tout. The last three terms calculate the change of enthalpy of water entering as a liquid (within the solid) in the feed at one temperature and exiting as a vapor at a different temperature. Enthalpy is a state function, so we can choose any convenient calculation path. Since we have the heat of vaporization at 100°C, it is convenient to sum the energy terms for the heating of the liquid water to the evaporation temperature of 100°C, vaporize it at that temperature, then account for the enthalpy difference between water vaper at 100°C and the exit temperature. The solution for Tout is 87°C in this case.

Bag filter

Feed inlet

Feed tank

Product outlet Drying chamber

Feed dosing Gdry air C p , air (Tair in − Tout ) + Gwater vapor out  C p ,  water vapor (Tair in − Tout ) +   Fsolids in  C p , solids (Tsolids in − Tout ) +   Fliquid water out  C p , liquid water (Tsolids in − Tevap ) − Gevaporated   ⋅ ∆H vap  + Gevaporated  C p ,  water vapor (Tevap − Tout ) = 0

Heater

(9 .44)(1 .0 − 0 .01)(700 − 87) + (9 .44)(0 .01)(2 .0)(700 − 87) +  (3.98)(1.46)(21 − 87) +  (2.14)(4.18)(21 − 100) − (2.14)(2257)

FIG. 12-91 Agitated flash dryer with open cycle. (GEA)

+ (2.14)(2.0)(100 − 87) = 0 Air at a temperature of 87°C and an absolute humidity of 0.239 kg/kg has a relative humidity of 45 percent. The relative humidity is the ratio of the partial pressure to the vapor pressure of pure water at the exhaust temperature. Table 12-1 can be used to calculate the partial pressure of water and Eq. (12-5) to calculate the vapor pressure of pure water. An exhaust relative humidity of 45 percent may be too high for the product. To make this judgment, a moisture sorption isotherm is needed. If this product were to have an isotherm such as the one shown in Fig. 12-20, then the moisture of the product would be at least 8 percent exiting the dryer. To target a specific moisture content of the exiting material, the isotherm can be used to select a maximum exit relative humidity and the calculation above can be repeated. An isotherm equation could be included in the calculation algorithm, the assumption of complete evaporation can also be changed, and an estimate of heat losses to the environment can be included if more-exact calculations are needed.

Agitated Flash Dryers Agitated flash dryers produce fine powders from feeds with high solids contents, in the form of filter cakes, pastes, or thick, viscous liquids. Many continuous dryers are unable to dry highly viscous feeds. Spray dryers require a pumpable feed. Conventional flash dryers often require backmixing of dry product to the feed in order to fluidize. Other drying methods for viscous pastes and filter cakes are well known, such as contact, drum, band, and tray dryers. They all require long processing time, large floor space, high maintenance, and aftertreatment such as milling. The agitated flash dryer offers a number of process advantages, such as ability to dry pastes, sludges, and filter cakes to a homogeneous, fine powder in a single-unit operation; continuous operation; compact layout; effective heat- and mass-transfer short drying times; negligible heat loss and high thermal efficiency; and easy access and cleanability. The agitated flash dryer (Fig. 12-91) consists of four major components: feed system, drying chamber, heater, and exhaust air system. Wet feed enters the feed tank, which has a slow-rotating impeller to break up large particles. The level in the feed tank is maintained by a level controller. The feed is metered at a constant rate into the drying chamber via a screw conveyor mounted under the feed tank. If the feed is shear-thinning and can be pumped, the screw feeder can be replaced by a positive displacement pump. The drying chamber is the heart of the system consisting of three important components: air disperser, rotating disintegrator, and drying section. Hot, drying air enters the air disperser tangentially and is introduced into the drying chamber as a swirling airflow. The swirling airflow is established by a guide-vane arrangement. The rotating disintegrator is mounted at the base of the drying chamber. The feed, exposed to the hot, swirling airflow and the agitation of the rotating disintegrator, is broken up and dried. The fine, dry particles exit with the exhaust air and are collected in the bag filter. The speed of the rotating disintegrator controls the particle size. The outlet air temperature controls the product moisture content. The drying air is heated either directly or indirectly, depending upon the feed material, powder properties, and available fuel source. The heat

sensitivity of the product determines the drying air temperature. The highest possible value is used to optimize thermal efficiency. A bag filter is usually recommended for collecting the fine particles produced. The exhaust fan maintains a slight vacuum in the dryer, to prevent powder leakage into the surroundings. The appropriate process system is selected according to the feed and powder characteristics, available heating source, energy utilization, and operational health and safety requirements. Open systems use atmospheric air for drying. In cases where products pose a potential for dust explosion, plants are provided with pressure relief or suppression systems. For recycle systems, the drying system medium is recycled, and the evaporated solvent is recovered as condensate. There are two alternative designs. In the self-inertizing mode, oxygen content is held below 5 percent by combustion control at the heater. This is recommended for products with serious dust explosion hazards. In the inert mode, nitrogen is the drying gas. This is used when an organic solvent is evaporated or product oxidation during drying must be prevented. Design methods The size of the agitated flash dryer is based on the evaporation rate required. The operating temperatures are product-specific. Once established, they determine the airflow requirements. The drying chamber is designed based on air velocity (approximately 3 to 4 m/s) and residence time (product-specific). Spray Dryers Spray drying is a process for the transformation of a pumpable liquid feed into dried particulates in a single operation. The process comprises atomization of the feed followed by intense contact with hot air. The dry particulate product is formed while the spray droplets are still suspended in the hot drying air. The process is concluded by the separation and recovery of the product from the drying air. Industrial Applications Thousands of products are spray-dried. The most common products may include agrochemicals, catalysts, ceramics, chemicals, detergents, dyestuffs and pigments, foodstuffs, pharmaceuticals, and waste products. A few examples are shown in Table 12-41. For each of these product groups and any other product, successful drying depends on the proper selection of a plant concept and operational parameters, in particular inlet and outlet temperatures and the atomization method. The air temperatures are traditionally established through experiments and test work. The inlet temperatures reflect the heat sensitivity of the different products, and the outlet temperatures the willingness of the products to release moisture. The percentage of moisture in the feed is an indication of feed viscosity and other properties that influence the pumpability atomization behavior. A spray-drying plant comprises six process stages, as shown in Table 12-42. Preatomization Spray drying may require a number of operations prior to the drying process. These operations are meant to ensure optimal atomization processes for the given feedstock. Elements for preatomization include but are not limited to low- and/or high-pressure pumping, high-shear mixing and/or in-line milling, viscosity modifications, and preheating. These processes can be achieved by any number of unit operations or equipment.

12-72

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

TABLE 12-41 Some Products That Have Been Successfully Spray-Dried Air temperature, K In

Product

Out

Water in feed, %

Air/evap . ratio, kg/kg

Air/prod . ratio, kg/kg

Yeast

500

335

86

15 .4

96 .2

Zinc sulfate

600

380

55

12 .4

15 .2

Lignin

475

365

63

24 .3

41 .4

Aluminum hydroxide

590

325

93

9 .7

128 .4

Silica gel

590

350

95

10 .9

206 .5

Magnesium carbonate

590

320

92

9 .5

108 .7

Tannin extract

440

340

46

26 .4

22 .5

Coffee extract

420

355

70

40 .6

94 .8

Detergent

505

395

50

25 .4

25 .4

Manganese sulfate

590

415

50

16 .3

16 .3

Aluminum sulfate

415

350

70

40 .5

94 .4

Urea resin

535

355

60

14 .8

22 .1

Sodium sulfide

500

340

50

16 .5

16 .5

Pigment

515

335

73

14 .4

39

Atomization Stage Atomization creates very a large surface area which enables rapid evaporation from the droplets in the spray . For example, atomization of 1 L of water into a uniform spray of 100-mm droplets results in approximately 1 .9 × 109 individual particles with a combined surface area of 60 m2 . Atomization is the primary means to create the final particle attributes; the droplet size distribution from the nozzle directly affects the particle size distribution of the dry powder . Atomization fundamentals are discussed further in Sec . 14 of this text and in the Lefebvre and Lipp references at the end of this section . In this section, we focus on the most important elements of atomization for spray-drying applications . Choice of atomizer system The choice of atomizer system for a specific spray-drying operation depends upon 1 . The particle size distribution required in the final dried product 2 . The physical and chemical properties of the feed liquid (e .g ., rheology) 3 . The shape of the drying chamber In this subsection, we introduce and compare the three most common atomization methods for spray drying: rotary atomization, hydraulic nozzles (also called pressure nozzles), and two-fluid nozzles (also called pneumatic nozzles) . Table 12-43 shows a comparison of these three methods . Other specialized atomizers such as ultrasonic nozzles may be used; their use is severely limited based on high operating costs, low individual production rates, and inability to handle viscous feedstocks .

TABLE 12-42

Stages of Spray Drying

Process stages for spray drying

Methods

1 . Preatomization

Pumping In-line milling Viscosity modification Preheating

2 . Atomization

Rotary atomization Pressure nozzle atomization Two-fluid nozzle atomization

3 . Spray/hot air interaction

Cocurrent flow Countercurrent flow Mixed flow

4 . Evaporation

Drying Particle morphology

5 . Post-treatment

Fluid-bed dryer Sieve Cooling Agglomeration

6 . Recovery

Drying chamber Dry collector Wet collector

Rotary Atomizer The liquid feed is supplied to the atomizer by gravity or hydraulic pressure . A liquid distributor system leads the feed to the inner part of a rotating wheel . Since the wheel is mounted on a spindle supported by bearings in the atomizer structure, the liquid distributor is usually formed as an annular gap or a ring of holes of various shapes or orifices concentric with the spindle and wheel . The liquid is forced to follow the wheel either by friction or by contact with internal vanes in the wheel . Due to the high centrifugal forces acting on the liquid, it moves rapidly toward the rim of the wheel, where it is ejected as a film or a series of jets or ligaments (see Fig . 12-92) . By interaction with the surrounding air, the liquid breaks up to form a spray of droplets of varying size . The spray pattern is virtually horizontal with a spray angle said to be 180° . The mean droplet size of the spray depends strongly on the atomizer wheel speed and to a much lesser degree on the feed rate and the feed physical properties such as viscosity . More details about spray characteristics such as droplet size distribution are given below . As indicated earlier, the atomizer wheel speed is the important parameter influencing the spray droplet size and thus the particle size of the final product . Also important for the atomization process is the selection of a wheel capable of handling a specific liquid feed with characteristic properties such as abrasiveness, high viscosity/nonnewtonian behavior . A highly abrasive feedstock can quickly erode a wheel if proper materials are not used . The most common design of atomizer wheel has radial vanes . This wheel type is widely used in the chemical industry and is virtually blockage-free and simple to operate, even at very high speed . For high-capacity applications, the number and height of the vanes may be increased to maintain limited liquid-film thickness conditions on each vane . Wheels with radial vanes have one important drawback, i .e ., their capacity for pumping large amounts of air through the wheel . This so-called air pumping effect causes unwanted product aeration, resulting in powders of low bulk density for some sensitive spray-dried products . Unwanted air pumping effect and product aeration can be reduced through careful wheel design involving change of the shape of the vanes that may appear forward-curved, as seen in Fig . 12-93a . This wheel type is used widely in the dairy industry to produce powders of high bulk density . The powder bulk density may increase as much as 15 percent when a curved vane wheel is replacing a radial vane wheel of standard design . Another way of reducing the air pumping effect is to reduce the space between the vanes so that the liquid feed takes up a larger fraction of the available cross-sectional area . This feature is used with the so-called bushing wheels shown in Fig . 12-93b . This wheel combines two important design aspects . The air pumping effect is reduced by reducing the flow area to a number of circular orifices, each 5 to 10 mm in diameter . Table 12-44 gives the main operational parameters for three typical atomizers covering the wide range of capacity and size . The Niro F1000 atomizer is one of the largest rotary atomizers offered to industry today . It has a capacity up to 200 ton/h in one single atomizer . As indicated above, the atomizer wheel speed is the important parameter influencing the spray droplet size . The wheel speed U also determines the power consumption Ps of the atomizer; see Table 12-44 for calculations and estimates for various atomizers . The capacity limit of an atomizer is normally its maximum power rating . Since the atomizer wheel peripheral speed is proportional to the rotational speed, the maximum feed rate that can be handled by a rotary atomizer declines with the square of the rotational speed . The maximum feed rates indicated in Table 12-44 are therefore not available at the higher end of the speed ranges . The rotary atomizer has one distinct advantage over other means of atomization . The degree or fineness of atomization achieved at a given speed is only slightly affected by changes in the feed rate . In other words, the rotary atomizer has a large turndown capability . Hydraulic pressure nozzle In hydraulic pressure nozzles, the liquid is fed to the nozzle under pressure . In the nozzle orifice, the pressure energy is converted to kinetic energy . The internal parts of the nozzle are normally designed to apply a certain amount of swirl to the feed flow so that it issues from the orifice as a high-speed film in the form of a cone with a desired vertex angle (see Fig . 12-94) . This film disintegrates readily into droplets due to instabilities . The vertex or spray angle is normally on the order of 50° to 80°, a much narrower spray pattern than is seen with rotary atomizers . This means that spray drying chamber designs for pressure nozzle atomization differ substantially from designs used with rotary atomizers . The droplet size distribution produced by a pressure nozzle atomizer varies inversely with the pressure and to some degree with the feed rate and viscosity . The capacity of a pressure nozzle varies with the square root of the pressure . To obtain a certain droplet size, the pressure nozzle must operate very close to the design pressure and feed rate . This implies that the pressure nozzle has very little turndown capability .

SOLIDS-DRYING FUNDAMENTALS TABLE 12-43

12-73

Comparison of Rotary, Hydraulic, and Two-Fluid Atomizers

Atomizer Advantages

Rotary High feed rates Can tolerate abrasive materials Negligible blocking Low-pressure feed system Simple size adjustment Narrow size distribution Minimal agglomeration Large turndown

Disadvantages

Higher energy consumption than pressure nozzles

Hydraulic (Pressure) Simple construction Low cost Low energy consumption Spray characteristic can be changed by nozzle design Dryer chambers generally smaller than those for rotary      

Two-fluid Can atomize highly viscous materials Control of size, pattern, and capacity during operation Low-pressure feed system Dryer chambers generally smaller than those for rotary Can produce sprays of high homogeneity and small size      

Requires a large chamber diameter

Control of size, pattern, and capacity during operation not possible Swirl nozzles not suitable for suspensions due to phase separation Tendency to clog Wear can greatly affect nozzle performance Requires high-pressure pumps Low turndown

Cost considerations

Cost is in the capital investment of the atomizer wheel and motor

Cost is in the high-pressure pumping of the feed

Cost is in the requirements for large air compressors

Key considerations

Can be limited as the wheel periphery speed required for fine atomization puts the wheel under extreme tensile stress Due to high capacity of the atomizers, typically only one is required in most dryers

Suited for coarse atomization as pressures above 300 bar are not practical

Droplet size tends to vary inversely with the ratio of gas to liquid

Since capacity of an individual nozzle is limited, dryer may require multiple nozzles

The capacity is not linked to performance, so some turndown is possible Since capacity of an individual nozzle is limited, dryer may require multiple nozzles

Cannot tolerate highly viscous fluids

Higher cost than pressure nozzles Must be operated within design parameters for both liquid and air feeds        

Power consumption

5–11 kWh/ton

up to 3 kWh/ton

up to 25 kWh/ton

Typical droplet size

40–100 mm

50–250 mm

5–500 mm

Typical spray angle

180°

50°–80°

10°–60°

Hydraulic pressure nozzles cannot combine the capability for fine atomization with high feed capacity in one single unit . Many spray dryer applications, where pressure nozzles are applied, require multinozzle systems with the consequence that start-up, operational control, and shutdown procedures become more complicated . Two-fluid nozzle atomization In two-fluid nozzle atomizers, the liquid feed is fed to the nozzle under marginal or no pressure conditions . An additional flow of gas, normally air, is fed to the nozzle under pressure . Near the nozzle orifice, internally or externally, the two fluids ( feed and pressurized gas) are mixed and the pressure energy is converted to kinetic energy, as shown in Fig . 12-95 . The flow of feed disintegrates into droplets during the interaction with the high-speed gas flow which may have sonic velocity . The spray angle obtained with two-fluid nozzles is normally on the order of 10° to 60° . The spray pattern may be narrow and is related to the spread of a free jet of gas . Spray-drying chamber designs for two-fluid nozzle atomization are very specialized according to the application . The droplet size produced by a two-fluid nozzle atomizer varies inversely with the ratio of gas to liquid and with the pressure of the atomization gas . The capacity of a two-fluid nozzle is not linked to its atomization performance . Therefore, two-fluid nozzles can be attributed with some turndown capability . Two-fluid nozzles share with pressure nozzles the lack of high feed capacity combined with fine atomization in one single unit . Many spray dryer applications with two-fluid nozzle atomization have a very high

(a)

(b)

number of individual nozzles . The main advantage of two-fluid nozzles is the capability to achieve very fine atomization . Table 12-45 shows several relationships between liquid properties and spray qualities . In general, spray drying operation parameters are experience and pilotscale testing . Droplet size is critical for all spray-drying operations . When droplet size data are unavailable for a spray, the scientific literature contains numerous empirical relationships that can be used to make predictions of the droplet sizes in a spray . If any difference between the atomization means mentioned here were to be pointed out, it would be the tendency for two-fluid nozzles to have the wider particle size distribution and narrower pressure nozzles with rotary atomizers in between . Spray/Hot Air Contact Atomization is first and most important process stage in spray drying . The final result of the process does, however, depend to a very large degree on the second stage, the spray/hot air contact . This stage influences the quality of the product . In general terms, three possible forms can be defined . These are depicted in Fig . 12-96 as cocurrent, countercurrent, and mixed flow . Different drying chamber forms and different methods of hot air introduction accompany the different flow pattern forms and are selected according to • Required particle size in product specification • Required particle form • Temperature or heat sensitivity of the dried particle

(c)

FIG. 12-92 The regimes of droplet formation in rotary disk atomizer: (a) drop regime; (b) ligament regime; (c) sheet regime. (Reprinted with permission from Bayvel and Orzochowski, Liquid Atomization, Taylor and Francis, Washington D.C., 1993.)

12-74

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

TABLE 12-44

Operational Parameters of Rotary Atomizers (GEA)

Rotary atomizer design Atomizer type

 

F1.5X/FX1

F100

F160

Nominal power rating

kW

1.5

75

160

F1000 1100

Maximum feed rate

ton/h

0.3

20

30

140

Atomizer wheel diameter

mm

100

210

210/240 350

Minimum speed

rpm

10,000

7400

6000

5800

Maximum speed

rpm

30,000

18,200

18,600

11,500

Typical periphery velocity U

m/s

141

160

165

161

Typical specific power Ps (Ps = U 2/3600)

kWh/ton

5.52

7.11

7.56

7.20

Figure 12-96a shows a cocurrent cone-based tall form chamber with roof gas disperser . This chamber design is used primarily with pressure nozzle atomization to produce powders of large particle sizes with a minimum of agglomeration . The chamber can be equipped with an oversize cone section to maximize powder discharge from the chamber bottom . This type of dryer is often used for dyestuffs, baby foods, detergents, and instant coffee powder . Figure 12-96b shows a standard cocurrent cone-based chamber with roof gas disperser . The chamber can have either single- or two-point discharge and can be equipped with rotary or nozzle atomization . Fine or moderately coarse powders can be produced . This type of dryer finds application in dairy, food, chemical, pharmaceutical, agrochemical, and polymer industries . A version of Fig . 12-96b with a flat-based cocurrent chamber can be used with limited building height . Figure 12-96c shows a countercurrent flow chamber with pressure nozzle atomization . This design is in limited use because it cannot produce heatsensitive products . Detergent powder is the main application; see Huntington, D . L ., Drying Technol. 22(6): 1261–1287 (2004), for a large-scale example . Figure 12-96d shows a high-temperature chamber with the hot gas distributor arranged internally on the centerline of the chamber . The atomizer is rotary . Inlet temperature in the range of 600 to 1000°C can be utilized in the drying of non-heat-sensitive products in the chemical and mining industries . Kaolin and mineral flotation concentrates are typical examples . Figure 12-96e shows a mixed-flow chamber with pressure nozzle atomization arranged in fountain mode . This design is ideal for producing a coarse product in a limited-size low-cost drying chamber . This type of dryer is used extensively for ceramic products . Powder removal requires a sweeping suction device . One of few advantages is ease of access for manual cleaning . These are widely used in production of flavoring materials . The layouts in Fig . 12-96 can be augmented with an integrated fluid-bed chamber in the spray dryer . The final stage of the drying process is accomplished in a fluid bed located in the lower cone of the chamber . This type of operation allows lower outlet temperatures to be used, leading to fewer temperature effects on the powder and higher energy efficiency . Similarly, the layouts can be modified with an integrated belt chamber where product is sprayed onto a moving belt, which also acts as the air exhaust filter . It is highly suitable for slowly crystallizing and high-fat products . Previous operational difficulties derived from hygienic problems on the belt have been overcome, and the integrated belt dryer is now moving the limits of products that can be dried by spray drying . In general terms, selection of chamber design and flow pattern form follows these guidelines: • Use cocurrent spray drying for heat-sensitive products of fine as well as coarse particle size, where the final product temperature must be kept lower than the dryer outlet temperature .

(a)

(b)

Rotary atomizers: (a) forward-curved vane; (b) vaned and bushingtype rotary wheels. (GEA)

FIG. 12-93

Schematic view of a simplex swirl atomizer. (Reprinted with permission from Lefebvre, A.H., Atomization and Sprays, Taylor and Francis, Washington D.C., 1989.) FIG. 12-94

• Use countercurrent spray drying for products which are not heat-sensitive, but may require some degree of heat treatment to obtain a special characteristic, i .e ., porosity or bulk density . In this case the final powder temperature may be higher than the dryer outlet temperature . • Use mixed-flow spray drying when a coarse product is required and the product can withstand short time exposure to heat without adverse effects on dried product quality . • Dryers with rotary atomizers have a wider diameter to accommodate the spray pattern without wall buildup . Evaporation Stage Evaporation takes place from a moisture film that establishes on the droplet surface . The droplet surface temperature is kept low and close to the adiabatic saturation temperature of the drying air . As the temperature of the drying air drops off and the solids content of the droplet/particle increases, the evaporation rate is reduced . The drying chamber design must provide a sufficient residence time in suspended condition for the particle to enable completion of the moisture removal . During the evaporation stage, the atomized spray droplet size distribution may undergo changes as droplets shrink, expand, collapse, fracture, or agglomerate . The quality of a spray-dried product is often strongly dependent on its morphological characteristics . Attributes include particle size, density, ability to dissolve, fragility, retention of trace volatile components (aroma), etc . Typical morphological changes that may occur are outlined in Fig . 21-175 of Perry’s 8th ed . and in Fig . 12-97 [Walton and Mumford, “The Morphology of Spray-Dried Particles—The Effects of Process Variables upon the Morphology of Spray-dried Particles,” Trans IChemE 77(Part A): 442–460 (1999)] . See also numerous articles from C . J . King . These morphological transformations can be difficult to predict a priori and require experimentation to determine final particle properties . A number of experimental studies have been conducted on single droplets to better understand the mechanisms [Hecht, J . P ., and King, C . J ., Ind. Eng. Chem. Res. 39: 1766–1774 (2000)] . Post-treatment Manipulating powder properties including moisture content, particle size, density, morphology, and dispersibility can be done with a variety of unit operations . These include fluid-bed dryers and agglomerators, coaters, sieves, granulator, presses, etc . The treatment will depend on the final uses of the product dried . Post-treatment may take place prior to or after dry product recovery . Product Recovery Product recovery is the last stage of the spray-drying process . Two distinct systems are used: • In two-point discharge, primary discharge of a coarse powder fraction is achieved by gravity from the base of the drying chamber . The fine fraction is recovered by secondary equipment downstream of the chamber air exit . • In single-point discharge, total recovery of dry product is accomplished in the dryer separation equipment . Collection of powder from an airstream is a large subject area of its own . In spray drying, dry collection of powder in a nondestructive way is achieved by use of cyclones, filters with textile bags or metallic cartridges, and electrostatic precipitators or a combination thereof . With the current emphasis on environmental protection, many spray dryers are equipped with additional means to collect even the finest fraction . This collection is often destructive to the powder . Equipment in use includes wet scrubbers, bag or other kinds of filters, and in a few cases incinerators . Industrial Designs and Systems Thousands of different products are processed in spray dryers representing a wide range of feed and product properties as well as drying conditions . The flexibility of the spray-drying concept, which is the main reason for this wide application, is described by the following systems .

SOLIDS-DRYING FUNDAMENTALS

12-75

FIG. 12-95 Schematic view of two-fluid atomizers . (Spraying Systems Co .)

Plant Layouts All the above-mentioned chamber layouts can be used in open-cycle, partial-recycle, or closed-cycle layouts . The selection is based on the needs of operation, feed, drying gas, solvent and powder specification, and environmental considerations . An open-cycle layout is by far the most common in industrial spray drying . The open layout involves intake of drying air from the atmosphere and discharge of exhaust air to the atmosphere . Drying air can be supplemented by a waste heat source to reduce overall fuel consumption . The heater may be direct, i .e ., natural gas burner, or indirect by steam-heated heat exchanger or other heat recovery systems . An example of an open-cycle layout is shown in Fig . 12-98 . A closed-cycle layout is used for drying inflammable or toxic solvent feedstocks or gases . The closed-cycle layout ensures complete solvent recovery and prevents explosion and fire risks . The reason for the use of a solvent system is often to avoid oxidation/degradation of the dried product . Consequently closed-cycle plants are gastight installations operating with an inert drying medium, usually nitrogen . These plants operate at a slight gauge pressure to prevent inward leakage of air . Partial recycle is used in a plant type applied for products of moderate sensitivity toward oxygen . The atmospheric drying air is heated in a direct fuel-burning heater . Part of the exhaust air, depleted of its oxygen content by the combustion, is dried by using a condenser and recycled to the heater . This type of plant is also designated self-inertizing . As a consequence, the amount of drying air or gas required for drying one unit of feed or product varies considerably . A quick scoping estimate of the size of an industrial spray dryer can be made on this basis . The required evaporation rate or product rate can be multiplied by the relevant ratio to give the mass flow rate of the drying gas . The next step would be to calculate the size of a spray-drying chamber to allow the drying gas at outlet conditions for a given residence time . TABLE 12-45 Properties of Fluids and How They Influence Atomization (Spraying Systems) Increase with specific gravity

Increase in viscosity

Increase in fluid temperature

Increase in surface tension

Pattern quality

Negligible

Deteriorates

Improves

Negligible

Capacity

Decreases

—

—

No effect

Spray angle

Negligible

Decreases

Increases

Decreases

Drop size

Negligible

Increases

Decreases

Increases

Drop velocity

Decreases

Decreases

Increases

Negligible

Impact

Negligible

Decreases

Increases

Negligible

Wear

Negligible

Decreases

—

No effect

Example 12-20 Scoping Exercise for Size of Spray Dryer Estimate the size of a zinc sulfate spray dryer with cylindrical chamber with diameter D, height H equal to D, and a 60° conical bottom . The dryer has an evaporative capacity of 2 .0 ton/h and requires a drying gas flow rate of 8 .45 kg/s with a residence time of 25 s . The outlet gas density is 0 .89 kg/m3 . The dryer has a nominal geometric volume Vchamber (cylinder on top of cone) of Vchamber =

π 2  1 3  D ×H + ⋅ D = 1 .01 × D 3 4 3 2  

Based on the drying gas flow rate, outlet gas density, and residence time, the required chamber volume is Vchamber = (8 .45 kg/s)/(0 .89 kg/m3) × 25 s = 237 m3 The chamber size now becomes D=

3

237 = 6 .2 m 1 .01

The selection of the plant concept involves the dryer modes illustrated in Fig . 12-96 . For different products a range of plant concepts are available to secure successful drying at the lowest cost . These concepts are illustrated in Fig . 12-99 . Figure 12-99 shows a traditional spray dryer layout with a cone-based chamber and roof gas disperser . The chamber has two-point discharge and rotary atomization . The powder leaving the chamber bottom as well as the fines collected by the cyclone is conveyed pneumatically to a conveying cyclone from which the product discharges . A bag filter serves as the common air pollution control system . Figure 12-99 also shows closed-cycle spray dryer layout used to dry certain products with a nonaqueous solvent in an inert gas flow . The background for this may be product sensitivity to water and oxygen or severe explosion risk . Typical products can be tungsten carbide or pharmaceuticals . Figure 12-99 also shows an integrated fluid-bed chamber layout of the type used to produce agglomerated product . The drying process is accomplished in several stages, the first being a spray dryer with atomization . The second stage is an integrated static fluid bed located in the lower cone of the chamber . The final stages are completed in external fluid beds of the vibrating type . This type of operation allows lower outlet temperatures to be used, leading to fewer temperature effects on the powder and higher energy efficiency . The chamber has a mixed-flow concept with air entering and exiting at the top of the chamber . This chamber is ideal for heat-sensitive, sticky products . It can be used with pressure nozzle as well as rotary atomization . An important feature is the return of fine particles to the chamber to enhance the agglomeration effect . Many products have been made feasible for spray drying by the development of this concept, which was initially

12-76

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING Cocurrent

Countercurrent

Mixed

Air in Atomizer

Atomizer

Air in

Air in

Atomizer

Air in Atomizer Air in

Air in

Air in

(a)

(b)

= Air

(c)

= Product

(d)

(e)

(f)

= Fluid feed

FIG. 12-96 Different forms of spray/hot air contact . (revised, GEA)

200°C

No Particle Formation

1% w/w Semi Instant Skimmed Milk

Initial Droplet 15% w/w

Inflated Hollow Particle

Cycle Repeats 200°C

Skin Formation

70°C

Internal Bubble Nucleation

Collapse

Reinflation

Shriveled Particle

Saturated Surface Drying (potassium nitrate)

Blistered Particle Particle decreases in size and the skin thickens

Internal Bubble Nucleation

Shriveled Particle

Partially Inflated Hollow Particle

30% w/w Semi Instant Skimmed Milk

Solid Particle

Grossly Inflated Hollow Particle Partially Inflated Hollow Particle FIG. 12-97 Description of possible particle morphologies . (Reprinted with permission from Walton and Mumford, Trans IChemE, 77(Part A): 442–460, 1999.)

SOLIDS-DRYING FUNDAMENTALS

FIG. 12-98

Spray dryer with rotary atomizer and pneumatic powder conveying . (GEA)

FIG. 12-99 Spray dryer layout with multiple possible configurations .

12-77

12-78

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

aimed at the food and dairy industry . Recent applications have, however, included dyestuffs, agrochemicals, polymers, and detergents . Spray Dryer Modeling Modeling of spray dryers is a unique challenge due to the vast differences in the length scales [dryer (1 .0 to 10 m in diameter) compared to droplets (100 mm in diameter)], billions of particles, one or more sprays, and multiple, complex micro-scale transformations . Making measurements inside a spray dryer to develop and validate models is notoriously difficult . Computational fluid dynamics (CFD) can be used to examine the complex airflow patterns within many dryers and also to track particle trajectories . Other modeling techniques have examined the drying kinetics of various droplet types . Invariably, efforts to date have simplified either the air patterns in the dryer or the drop-drying dynamics . A recent notable effort to combine these scales is the EDECAD Project [Verdurmen et al ., “Agglomeration in Spray Drying Installations (The EDECAD Project): Stickiness Measurements and Simulation Results,” Drying Technol. 24: 721–726 (2006)] . Drynetics is a commercially available method to incorporate experimental single-drop drying into CFD software . Experiments can be conducted on individual droplets of a feed to determine their drying properties . The results are then transferred to the CFD software with the help of appropriate mathematical models, making it possible to simulate the drying process accurately . This modeling workflow is seen in Fig . 12-100 . Drying kinetics as well as morphology formation during drying of a single particle can be found experimentally by using an apparatus such as the drying kinetics analyzer (DKA) which is based on the principle of ultrasonic levitation . In an ultrasonic levitator a small particle may be held constant against gravity due to the forces of an ultrasonic field between the so-called transmitter and the so-called reflector . While the levitated particle is drying, it may be monitored with a camera to record the morphology development and by an infrared device to record the development in particle temperature . A levitator can be encapsulated in a drying chamber so that the drying gas temperature and humidity may be set arbitrarily . If the drying gas is injected through small holes in the reflector below the particle, as in the DKA, the relative velocity between the gas and droplets in a spray dryer may be simulated . Further, equipment such as the DKA may also be used to analyze the solidification of a melted particle (Coolnetics) which is relevant, e .g ., for congealing processes . Here a melt or a solid particle can be inserted into the ultrasonic field . If a solid particle is inserted, it may subsequently be melted, e .g ., using laser light or by infrared radiation . Example 12-21 Mass and Energy Balance on a Spray Dryer A pilot-scale spray dryer has a nominal evaporative rate of 1 .0 kg water/h . The dryer is typically operated with an inlet air temperature of 200°C . The dryer is operated with an inlet airflow of 26 .4 kg/h . The feedstock has a moisture content of 70 percent (wet basis) and is fed in to the dryer at 25°C . The powder exits the dryer at 6 percent moisture and the same temperature as the exiting air . The ambient air conditions are 22°C and 55 percent relative humidity . 1 . Calculate the relative humidity in the exhaust airstream . 2 . Calculate the exit air and product temperature . 3 . Estimate the increase in production if the moisture content of the feedstock is decreased from 70 to 65 percent . Solution The mass balance is given by the following equations:

The wet-basis moisture content of the incoming feedstock and outgoing powder are given by win  =   wout  =  

Fliquid water in  Fliquid water in  + Fbone dry solids in Fliquid water out  Fliquid water out  + Fbone dry solids out

The relationship between the total airflow and the absolute humidity is given by Gdry air  = Gair  

1 1 = 10 kg/h = 9.91 kg/h 1 +  0.009 1 +  Y

The absolute humidity of each air stream is given by Yin  = Yout =

Gwater vapor in  Gdry air in Gwater vapor out  Gdry air out

The mass flow rate of bone-dry solids into the dryer can be calculated from the evaporation rate and the incoming and exit moisture contents: Fevap = Fliquid water in  − Fliquid water out  Fevap =

w win    Fbone dry solids in  − out  Fbone dry solids out  1 − win  1 − wout

This can be simplified as follows: Fevaporated 1.0 kg / h =  = 0.44 kg / h w 0.7 0.06 win  − − out  1 − win   1 − wout  0.3 0.94 win  0.7  0.44 kg / h = 1.03 kg / h   Fsolids = = 0.3 1 − win  wout 0.06  0.44 kg / h = 0.03 kg / h   Fsolids = = 0.94 1 − wout 

Fsolids =

Fliquid water in  Fliquid water out 

Since the dryer heats ambient air, the absolute humidity can be determined from the psychrometric chart . The mass flow rate of dry air and water vapor can be calculated from the overall airflow rate and the absolute humidity of the incoming air:

Fbone dry solids in = Fbone dry solids out Fliquid water in  = Fliquid water out  + Fevaporated Gdry air in  = Gdry air out  Gwater vapor in  + Fevaporated = Gwater vapor out 

FIG. 12-100 Modeling work flow for spray-drying modeling, Drynetics . (GEA)

1 Yin = 26.16 kg/h ⋅ 0.009 = 0.24 kg/h 1 +  Yin = Gwater vapor in  + Fevap = 0.24 kg/h + 1.0 kg/h = 1.24 kg/h

Gwater vapor in  = Gair   Gwater vapor out 

Yout =

Gwater vapor out  Gdry air out 

=

1.24 kg/h = 0.047 26.16 kg/h

SOLIDS-DRYING FUNDAMENTALS Next an energy balance must be used to estimate the outgoing air and product temperature: H dry air in  +   H water vapor in  +   H bone dry solids in +   H liquid water in  =   H dry air out  +   H water vapor out  +   H bone dry solids out +   H liquid water out   

+ heat losses to surroundings

Heat losses to the surrounding environment can be difficult to calculate and can be neglected for a first approximation . This assumption is more valid for larger systems than smaller systems and is neglected in this example . The equation above was rearranged in terms of enthalpy differences: ∆H dry air  + ∆H water vapor  + ∆H solids + ∆H liquid water  + ∆H evap = 0 Since enthalpy is a state function, the path for determination must be stated . There are several paths that would yield equivalent results . For this example, it is assumed that the evaporation is occurring at the inlet temperature and that the water vapor is being heated from the inlet temperature to the outlet temperature . The terms of the equation can be evaluated by using ∆H dry air  = Gdry air C p , air (Tair in − Tair out ) ∆H water vapor  = Gwater vapor out  C p , water vapor (Tair in − Tair out ) ∆H solids  = Fsolids C p , solids (Tsolids in − Tsolids out ) ∆H liquid water  = Fliquid water out C p , liquid water (Tsolids in − Tsolids out ) ∆H evap  = −Gevaporated  ⋅∆H vap  + Gevap C p ,   water vapor (Tevap − Tout ) Since the powder and air exit the dryer at the same temperature, Tair out = Tsolids out = Tout , the relationships above can be rewritten as Gdry air C p , air (Tair in − Tout ) + Gwater vapor out C p ,  water vapor (Tair in − Tout ) + Fsolids in C p , solids (Tsolids in − Tout ) + Fliquid water out  C p , liquid water (Tsolids in − Tout ) − Gevap  ⋅ ∆H vap  + Gevap C p ,   water vapor (Tevap − Tout ) = 0 From the steam tables ∆Hvap at 25°C = 2442 kJ/kg, hl = 105 kJ/kg, and at 200°C (superheated, low pressure) hg = 2880 kJ/kg .

Drum and Thin-Film Dryers Synonyms and Examples Drum dryer, film drum dryer, thin-film dryer (note: this term is used by the paper industry for heated cylinder dryers— these are covered in Sheet Drying) . Description Drum (Film-Drum) Dryers A film of liquid or paste is spread onto the outer surface of a rotating, internally heated drum . Heat transfer occurs by conduction . At the end of the revolution the dry product is removed by a doctor’s knife . The material can be in the form of powder, flakes, or chips and typically is 100 to 300 mm thick . Drum dryers cannot handle feedstocks that do not adhere to metal, products that dry to a glazed film, or thermoplastics . The drum is heated normally by condensing steam or in vacuum drum dryers by hot water . Figure 12-101 shows three of the many possible forms . The dip feed system is the simplest and most common arrangement, but is not suitable for viscous or pasty materials . The nip feed system is usually employed on double-drum dryers, especially for viscous materials, but it cannot handle lumpy or abrasive solids . With nip feed systems, the fluid is exposed to the hot surface of the drum, possibly causing the liquid to boil . This may change the fluid rheology due to sudden evaporation and liquid heating or degrade the fluid . Lumpy or abrasive solids are usually applied by roller, and this is also effective for sticky and pasty materials . Spray and splash devices are used for feeding heat-sensitive, low-viscosity materials . Vacuum drum dryers are simply conventional units encased in a vacuum chamber with a suitable air lock for product discharge . Air impingement is also used as a secondary heat source on drum and can dryers, as shown in Fig . 12-102 . Impingement or other additional air can be used to purge saturated vapor away from the drums to aid in drying . In drum drying, the moist material covers a hot surface which supplies the heat required for the drying process . Let us consider a moist material lying on a hot flat plate of infinite extent . Figure 12-103 illustrates the temperature profile for the fall in temperature from TH in the heating fluid to TG in the surrounding air . It is assumed that the temperatures remain steady, unhindered drying takes place, and there is no air gap between the material being dried and the heating surface .

(26 .16 kg/h)(1 kJ/kg ⋅°C)(200°C − Tout ) + (1 .24 kg/h)(2 kJ/kg ⋅°C)(200°C − Tout )  kJ  + (0 .44 kg/h)  2 .5  (25°C − Tout )  kg ⋅°C  + (1 .03 kg/h)(4 .18 kJ/kg ⋅°C)(25°C − Tout ) − 1 .0 kg/h ⋅

2775 kJ   kg

+ (1.0 kg/h)(2.5 kJ/kg ⋅°C)(100°C − Tout ) = 0 Tout = 99.9°C With the absolute humidity defined and the outlet temperature calculated, the exit relative humidity was determined from the psychrometric chart as 7 .1 percent . Assuming the drying kinetics and the nominal evaporation rate remain the same with a decrease in the inlet moisture content (there may be a slight adjustment to the energy balance):

(a)

Fevap   w 0 .06  1.0 kg/h   Fout =  1 + out   = 0.47 kg/h =  1 +  0 .94  0.7 0.06  1 − wout   win  − wout  − 0.3 0.94 1 − win  1 − wout  Fevap   w 0.06  1.0 kg/h Fout =  1 + out     = 0.59 kg/h =  1 +  0.94  0.65 0.06  1 − wout   win  − wout  − 0.35 0.94 1 − win  1 − wout  This suggests the throughput can increase by 27 percent assuming the inlet moisture content can be decreased by 5 percent .

(b)

Additional Readings Bayvel and Orzechowski, Liquid Atomization, Taylor & Francis, New York, 1993 . Brask, A ., T . Ullum, A . Thybo, and S . K . Andersen, High-Temperature Ultrasonic Levitator for Investigating Drying Kinetics of Single Droplets. 6th International Conference on Multiphase Flow, Leipzig, Germany, 2007 . Geng Wang et al ., “An Experimental Investigation of Air-Assist Non-Swirl Atomizer Sprays,” Atomisation and Spray Technol. 3: 13–36 (1987) . Lefebvre, Atomization and Sprays, Hemisphere, New York, 1989 . Lipp, C ., Practical Spray Technology, Lake Innovation, LLC, Lake Jackson, Texas (2013) . Marshall, “Atomization and Spray Drying,” Chem. Eng. Prog. Mng. Series, 50(2) (1954) . Masters, Spray Drying in Practice, SprayDryConsult International ApS, Denmark, 2002 . Ullum, T ., J . Sloth, A . Brask, and M . Wahlberg, CFD Simulation of a Spray Dryer Using an Empirical Drying Model. 16th International Drying Symposium, Hyderabad, India, 2008, pp . 301, 308 . Walzel, P ., “Zerstäuben von Flüssigkeiten,” Chem.-Ing.-Tech. 62 (1990) Nr . 12, S . 983–994 . Nuzzo, M ., A . Millqvist-Fureby, J . Sloth, and B . Bergenstahl, “Surface Composition and Morphology of Particles Dried Individually and by Spray Drying,” Drying Technol . 33(6) (2015) .

12-79

(c) FIG. 12-101 Main types of drum dryers . (a) Dip; (b) nip; (c) roller .

12-80

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING conduction through the axial shaft to the bearing mounts . The use of Eq . (12-114) to estimate the maximum drying rate is illustrated in Example 12-22 . Example 12-22 Heat-Transfer Calculations on a Drum Dryer A single rotating drum of 1 .250-m diameter and 3 m wide is internally heated by saturated steam at 0 .27 MPa . As the drum rotates, a film of slurry 0 .05 mm thick is picked up and dried . The dry product is removed by a knife, as shown in Fig . 12-101a. About three-quarters of the drum’s surface is available for evaporating moisture . Estimate the maximum drying rate when the outside air temperature TG is 15°C and the surface temperature is 90°C; and compare the effectiveness of the unit with a dryer without end effects and in which all the surface could be used for drying . Data: Heat-transfer coefficient hC = 50 W/(m2 ⋅ K) Thickness of cylinder wall bB = 10 mm Thermal conductivity of wall λB = 40 W/(m ⋅ K) Thermal conductivity of slurry film λs = 0 .10 W/(m ⋅ K) Film transfer coefficient for condensing steam hH = 2 .5 kW/(m2 ⋅ K) Overall heat-transfer coefficient U: The thermal resistances are as follows: 1/2 .5 = 0 .40 m2 ⋅ K/kW

Steam side Wall Film side

0 .01/0 .04 = 0 .25 m2 ⋅ K/kW 5 .0 × 10−5/0 .1 × 10−3 = 0 .5 m2 ⋅ K/kW

∴ Overall resistance = 0 .40 + 0 .25 + 0 .5 = 1 .15 m2 ⋅ K/kW U = 1/1 .15 = 0 .870 kW/(m2 ⋅ K) Wall temperature TB : At 0 .27 MPa, the steam temperature is 130°C . If it is assumed that the temperature drops between the steam and the film surface are directionally proportional to the respective thermal resistances, it follows that

FIG. 12-102 Example of the use of air impingement in

drying as a secondary heat source on a double-drum dryer . (Sloan, C.E., et. al, Chem. Eng., 197, June 19, 1967 )

TH − TB 0 .40 + 0 .25 = = 0 .565 TH − TS 1 .15

The heat conducted through the wall and material is dissipated by evaporation of moisture and convection from the moist surface to the surrounding air . A heat balance yields U(TH - TS) = NW ΔHVS + hC(TS - TG)

(12-111)

where U is the overall heat-transfer coefficient . This coefficient is found from the reciprocal law of summing resistances in series: 1 1 bB bs = + + U hH λ B λ s

(12-112)

in which hH is the heat-transfer coefficient for convection inside the heating fluid . If condensing steam is used, this coefficient is very large normally and the corresponding resistance 1/hH is negligible . Rearrangement of Eq . (12-111) yields an expression for the maximum drying rate U (TH − TS ) − hC (TS − TG ) (12-113) ∆H VS Equation (12-113), as it stands, would give an overestimate of the maximum drying rate for the case of contact drying over heated rolls, when there are significant heat losses from the ends of the drum and only part of the drum’s surface can be used for drying . In the roller drying arrangements shown in Fig . 12-101, only a fraction a of the drum’s periphery is available from the point of pickup to the point where the solids are peeled off . Let qE be the heat loss per unit area from the ends . The ratio of the end areas to cylindrical surface, from a drum of diameter D and length L, is 2(1/4 ⋅ πD2)/πDL or D/2L . Equation (12-113) for the maximum drying rate under roller drying conditions thus becomes NW =

aU (TH − TS ) − hC (TS − TG ) − Dq E /2 L ∆H VS

∴ TB = TH − 0 .565(TH − TS) = 130 − 0 .565 (130 − 90) = 107 .4°C Heat losses from ends qE : For an emissivity ~1 and an air temperature of 15°C with a drum temperature of 107 .4°C, one finds [see Eq . (12-120)] qE = 798 W/(m2 ⋅ s) Maximum drying rate NW : From Eq . (12-114), NW =

aU (TH − TS ) − hC (TS − TG ) − Dq E /2 L ∆H VS

0 .75 × 0 .870(130 − 90) − 0 .05(90 − 15) − (1 .25 × 0 .798)/6 2382 = 0 .0093 kg/(m2 × s)

=

The ideal maximum rate is given by Eq . (12-113) for an endless surface: NN =

0 .870(130 − 90) − 0 .05(90 − 15) 2382 = 0 .0130 kg/(m 2 ⋅ s) =

Therefore the effectiveness of the dryer is 0 .0093/0 .0130 = 0 .714 . The predicted thermal efficiency η is

(12-114)

η= 1 −

The total evaporation from the drum is NWa(πDL) . Equation (12-114) could be refined further, as it neglects the effect caused by the small portion of the drum’s surface being covered by the slurry in the feed trough, as well as thermal

=1−

NW =

FIG. 12-103 Temperature profile in con-

ductive drying .

U (TH − TS ) − hC (TS − TG ) ∆H VS

hC (TS − TG ) + Dq E /2 L aU (TH − TS )

0 .05(90 − 15) + (1 .25 × 0 .798)/6 0 .75 × 0 .869(130 − 90) = 0 .850

These estimates may be compared with the range of values found in practice, as shown in Table 12-46 (Nonhebel and Moss, Drying of Solids in the Chemical Industry, Butterworths, London, 1971, p . 168) . The typical performance is somewhat less than the estimated maximum evaporative capacity, although values as high as 25 g/(m2 ⋅ s) have been reported . As the solids dry out, the thermal resistance of the film increases and the evaporation falls off accordingly . Heat losses through the bearing of the drum shaft have been neglected, but the effect of radiation is accounted for in the value of hC taken . In the case of drying organic pastes, the heat losses have been determined to be 2 .5 kW/m2 over the whole surface, compared with 1 .75 kW/m2 estimated here for the cylindrical surface . The inside surface of the drum has been assumed to be clean, and scale would reduce the heat transfer markedly . For constant hygrothermal conditions, the base temperature TB is directly proportional to the thickness of the material over the hot surface . When the wet-bulb

SOLIDS-DRYING FUNDAMENTALS TABLE 12-46

12-81

Drum Dryer Operating Information  

This estimate 2

Specific evaporation, g/(m ⋅ s)

9.3

Thermal efficiency

0.85

C

Typical range

D

7–11 0.4–0.7

temperature is high and the layer of material is thick enough, the temperature TB will reach the boiling point of the moisture . Under these conditions, a mixed vapor-air layer interposes between the material and the heating surface . This is known as the Leidenfrost effect, and the phenomenon causes a greatly increased thermal resistance to heat transfer to hinder drying .

Thin-Film Dryers Evaporation and drying take place in a single unit, normally a vertical chamber with a vertical rotating agitator which almost touches the internal surface . The feed is distributed in a thin layer over the heated inner wall and may go through liquid, slurry, paste, and wet solid forms before emerging at the bottom as a dry solid . These dryers are based on wiped-film or scraped-surface (Luwa-type) evaporators and can handle viscous materials and deal with the “cohesion peak” experienced by many materials at intermediate moisture contents . They also offer good containment . Disadvantages are complexity, limited throughput, and the need for careful maintenance . Continuous or semibatch operation is possible . A typical unit is illustrated in Fig . 12-104 . Sheet Dryers Synonyms and Examples Cylinder dryer, drum dryer (note: this term is used by the paper industry, not to be confused with the drum dryers for pastes in this text), stenter dryers, and tenter dryers . Description The construction of dryers where both the feed and the product are in the form of a sheet, web, or film is markedly different from that for dryers used in handling particulate materials . The main users are the paper and textile industries . Almost invariably the material is formed into a very long sheet (often hundreds or thousands of meters long) which is dried in a continuous process . The sheet is wound onto a bobbin at the exit from the dryer; this may be several meters in diameter and several meters wide . Alternatively, the sheet may be chopped into shorter sections . The heat-transfer calculations [Eqs . (12-114) through (12-115)] used in the Drum Drying subsection are directly applicable for sheet drying when a sheet is in contact with a roller . Cylinder Dryers and Paper Machines The most common type of dryer in papermaking is the cylinder dryer (Fig . 12-105), which is a contact dryer . The paper web is taken on a convoluted path during which it wraps around the surface of cylinders that are internally heated by steam or hot water . In papermaking, the sheet must be kept taut, and a large number of cylinders are used, with only short distances between them and additional small unheated rollers to maintain the tension . Normally, a continuous sheet of felt is also used to hold the paper onto the cylinders, and this also becomes damp and is dried on a separate cylinder .

B A

E

B

B

E

EE E

B

B

B

B

C

D

A: Paper B: Drying cylinders C: Felt D: Felt dryers E: Pockets

FIG. 12-105 Cylinder dryer (paper machine).

Most of the heating is conductive, through contact with the drums . However, infrared assistance is frequently used in the early stages of modern paper machines . This gets the paper sheet up to the wet-bulb temperature more rapidly, evaporates greater surface moisture, and enables reduction of the number of cylinders for a given throughput . Hot air jets (jet foil dryer) may also be used to supplement heating at the start of the machine . Infrared and dielectric heating may also be used in the later stages to assist the drying of the interior of the sheet . Although paper is the most common application, multicylinder dryers can also be used for polymer films and other sheet-type feeds . Convective dryers may be used as well in papermaking . In the Yankee dryer (Fig . 12-106), high-velocity hot airstreams impinging on the web surface give heating by cross-convection . The “Yankees” are barbs holding the web in place . Normally the cylinder is also internally heated, giving additional conduction heating of the lower bed surface . In the rotary through-dryer (Fig . 12-107), the drum surface is perforated and hot air passes from the outside to the center of the drum, so that it is a through-circulation convective dryer . Another approach to drying of sheets has been to suspend or “float” the web in a stream of hot gas, using the Coanda effect, as illustrated in Fig . 12-108 . Air is blown from both sides, and the web passes through as an almost flat sheet (with a slight “ripple”) . The drying time is reduced because the heat transfer from the impinging hot air jets is faster than that from stagnant hot air in a conventional oven . It is essential to control the tension of the web very accurately . The technique is particularly useful for drying coated paper, as the expensive surface coating can stick to cylinder dryers . Stenters (Tenters) and Textile Dryers These are the basic type of dryer used for sheets or webs in the textile industry . The sheet is held by its edges by clips (clip stenter) or pins (pin stenter), which not only suspend

Hood

Hot air nozzles Yankee

Hot air exhaust

Felt Web Web on felt FIG. 12-104 Continuous thin-film dryer.

FIG. 12-106

Doctor knife Yankee dryer.

12-82

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING Hot air inlet

Dry product

Wet product

FIG. 12-109

Stenter or tenter for textile drying .

where D = inside diameter of nozzle, m f =

Exhaust Carrier fabric FIG. 12-107

Rotary through-dryer .

the sheet but also keep it taut and regulate its width—a vital consideration in textile drying . Drying is by convection; hot air is introduced from one or both sides, passes over the surface of the sheet, and permeates through it . Infrared panels may also be used to supply additional heat . A schematic diagram of the unit is shown in Fig . 12-109 . A typical unit is 1 .4 m wide and handles 2 to 4 tons/h of material . Heavy-duty textiles with thick webs may need a long residence time, and the web can be led up and down in “festoons” to reduce dryer length . Substantial improvements in drying rates have been obtained with radiofrequency heating assistance . Air impingement dryers as in Fig . 12-108 may also be used for textiles . Example 12-23 Impinging Air Drying of Sheets Estimate the dryer length needed to dry a continuous thin polyethylene sheet moving at 0 .1 m/s using impinging air from a wet-basis moisture of 40 to 10 percent . Assume that moisture is evenly distributed on the top surface of the sheet and that the sheet nonhygroscopic (i .e ., there is no bound water) . Ambient air at 22°C and 50 percent relative humidity is heated to 120°C . The impinging air dryer has an array of jets that are 7 cm apart from one another, 1 cm in diameter, and 5 cm above the sheet . The air velocity through each jet is 10 m/s . Estimate the dryer size reductions possible if (a) the impinging air were predried, using a dessicant wheel, to 10 percent relative humidity, (b) the inlet moisture content was reduced to 35 percent, and (c) the air temperature was increased to 130°C . Physical properties: Pr = 0 .71; Dwater/air = 2 .7 × 10−5 m2/s; kinematic viscosity of air = 2 .2 × 10−5 m2/s; Sc = 0 .64 (= 2 .2/2 .7); kair = 0 .03 W/(m ⋅ K); ΔHvap = 2450 kJ/kg . Both belt and polyethylene sheet are 1 kg/m2 with a specific heat of 2 J/(g ⋅ K) and both enter the dryer at 22°C . Solution For this example, we will create an incremental calculation using a spreadsheet . We will make use of a well-known correlation for prediction of heat- and mass-transfer coefficients for air impinging on a surface from arrays of holes (jets) . This correlation uses relevant geometric properties such as the diameter of the holes, the distance between the holes, and the distance between the holes and the sheet [Martin, “Heat and Mass Transfer Between Impinging Gas Jets and Solid Surfaces,” Advances in Heat Transfer, vol . 13, Academic Press, Cambridge, Mass ., 1977, pp . 1–66] . 6 Sh Nu   H /D   = 0 .42 = 1 +  0 .42   Sc Pr   0 .6/ f  

×

f

−0 .05

(12-115)

1 − 2 .2 f × Re2/3 1 + 0 .2( H / D − 6) f

FIG. 12-108 Air flotation (impingement) dryer .

π  D 2 3  LD 

2

H = distance from nozzle to sheet, m LD = average distance between nozzles, m Nu = Nusselt number Pr = Prandtl number wD Re = Reynolds number = v Sc = Schmidt number Sh = Sherwood number w = velocity of air at nozzle exit, m/s ν = kinematic viscosity of air, m2/s The heat- and mass-transfer coefficients were then calculated from the definitions of the Nusselt and Sherwood numbers . Nu =

hD kth

where kth = thermal conductivity of air, W/(m ⋅ Κ) D = diameter of holes in air bars, m Sh =

km∗ D diff

where diff = diffusion coefficient of water vapor in air, m2/s . Plugging in the values of H = 5 cm, D = 1 cm, L = 7 cm, and the values of Pr, Sc, Dwater/air, and kair gives heat- and mass-transfer coefficients of 74 W/(m2 ⋅ K) and 0 .0705 m/s, respectively . Now we write an energy balance equation for the temperature of the sheet, which we assume to be a single value through the thickness of the sheet (it is the same as in Example 12-14): (C p ,solids + C p ,water ⋅ wavg,dry-basis ) ⋅

msheet dTsheet ⋅ = h ⋅ (Tair − Tsheet ) − F ⋅ ∆H vap A dt

(12-116)

We also write a mass balance: dmw 1 = kc ⋅ (Cwsurface − Cwbulk ) dt A

(12-117)

msheet ), the A heat- and mass-transfer coefficients (h and kc), heat of vaporization (ΔHvap), and the bulk water concentration in the air (Cwbulk ) are all constant . Values of the sheet temperature, the drying flux (F), the water concentration in the air immediately adjacent to the m sheet (Cwsurface ), and the mass loading of water ( water ) on the sheet all change with time . A We convert the time into distance from the dryer feed point by using the sheet velocity . The concentration of water vapor (also called the volumetric humidity) immediately adjacent to the wet sheet is calculated using equations from the psychrometry section . Specifically, Eq . (12-5) is used to calculate the vapor pressure of the water at the sheet temperature, and Table 12-1 is used to calculate the volumetric humidity from the vapor pressure and sheet temperature . The specific heat values (Cp,solids and Cp,water), the basis weight of the sheet (

SOLIDS-DRYING FUNDAMENTALS

FIG. 12-110

Simulation results for sheet drying example.

The two equations above were solved in stepwise explicit manner with a spreadsheet . Each row represents a small time step . The temperature from the previous time step was used to calculate all the changing quantities in the new time step . Results from this calculation are shown in Fig . 12-110 . For the base conditions, the results show that a dryer length of 23 .0 m is needed . In Table 12-47, the results for all the cases are shown . The results show us the relative sensitivity of the process to some typical methods to increase the drying rate and therefore reduce the dryer size . The biggest handle is the reduction of the initial moisture content . This is a nonlinear effect with wet-basis moisture content . In practice, this is often accomplished by a mechanical dewatering process upstream of thermal drying . The dry-basis moisture content is 0 .667 for the base case and 0 .35/0 .65 = 0 .538 . So a reduction from 40 percent to 35 percent on a wet basis equates to a drying load reduction of nearly 20 percent, (1 − 0.538/0.667) × 100 percent. The heat-transfer calculations [Eqs. (12-110) through (12-113)] used in the Drum Drying subsection are directly applicable for heating/drying of sheets in contact with rollers.

Freeze Dryers* In freeze drying (lyophilization), the feed material is frozen and ice sublimes directly to vapor. This gives gentle drying, preserves heat-sensitive materials, and preserves the solid structure without shrinkage and deformation. The process must operate at temperatures and vapor partial pressures below the triple point (0.006 bar and 0.01°C for water), normally by operating at high vacuum (vacuum freeze drying—see Fig. 12-111), although atmospheric freeze drying with highly dehumidified air is sometimes possible. Because of the low driving forces, freeze drying is generally an expensive option in both equipment and operating cost, with typical process times of hours or days. Applications Freeze drying is mainly used for high-value products where the gain in product quality justifies the high cost, particularly in the food, beverage, and pharmaceutical industries. The major advantages are as follows: • Preservation of original flavor, aroma, color, shape, and texture (or development of special food textures and flavor effects) TABLE 12-47 Sheets

• Retention of original distribution of soluble substances such as sugars, salts, and acids, which can migrate to the product surface in conventional drying • Negligible shrinkage, resulting in excellent and near-instantaneous rehydration characteristics • Negligible product loss • Minimal risk of cross-contamination Freeze drying is used for selected vegetables, fruits, meat, fish, and beverage products, such as instant coffee ( flavor and aroma retention), strawberries (color preservation), and chives (shape preservation). For pharmaceuticals, solutions of sterile products may be dried in glass vials, or blocks or slabs of material may be dried on trays. The freeze-drying process Industrial freeze drying is carried out in three steps: 1. Freezing of the feed material 2. Primary drying, i.e., sublimation drying of the main ice content, corresponding to the constant-rate period in conventional drying 3. Secondary drying, i.e., desorption drying of the internal or bound moisture or hydrates, corresponding to the falling-rate period in conventional drying Unlike many conventional processes, the primary drying period is usually the longest. The secondary drying period is relatively short and may run at a higher temperature. Freezing The freezing methods applied for solid products are all conventional freezing methods such as blast freezing, individual quick freezing (IQF), or similar. To ensure good stability of the final product during storage, a product temperature of −20 to −30°C should be achieved to ensure that more than 95 percent of the free water is frozen. Freezing may be performed within the dryer or externally. External freezing can debottleneck a dryer being used for repeated cycles, e.g., in the food industry where 2 to 3 batches may be run per day.

Results for Example 12-23: Impinging Air Drying of Cases 1

2

3

4

120

130

120

120

Relative humidity of air (before heating), percent

40

40

10

40

Initial wet-basis moisture content, percent

40

40

40

35

Dryer length needed, m

23

20.9

22

17.8

Air temperature, °C

12-83

∗Special thanks are due to Prof. A. Basseri, University of Turin, Italy, for his input to this subsection.

FIG. 12-111

Phase diagram for freeze drying.

12-84

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

The free water freezes to pure ice crystals, leaving the soluble substances as high concentrates or even crystallized . Solid products maintain their natural cell structure, as long as the ice crystals are small enough to avoid damaging the cells . For liquid feeds (with no cell structure) the product structure is formed by the freezing process as an intercrystalline matrix of the concentrated product around the ice crystals . Freezing rate is a key parameter; small ice crystals are obtained by quick freezing, while slow freezing gives larger ice crystals . The structure of the matrix can affect the freeze-drying performance as well as the appearance, mechanical strength, and solubility rate . Small ice crystals lead to light color (high surface reflection of light) and a good mechanical strength of the freeze-dried product, but give diffusion restrictions for vapor transport inside the product (particularly for solutions) and hence slower drying . Large ice crystals lead to the opposite results . An optimum may be achieved by initial fast freezing followed by annealing at a higher temperature, allowing crystal growth and a more porous structure and significantly reducing primary drying time, as shown in Table 12-48 . Thus the freezing method must be carefully adapted to the quality criteria of the finished product . Common methods include • Drum freezing, by which a thin slab of 1 .5 to 3 mm is frozen within 1 .5 to 3 min • Belt freezing, by which a slab of 6 to10 mm passing through different freezing zones is frozen during 10 to 20 min • Shelf freezing in situ in the dryer, particularly for pharmaceuticals • Foaming, used to influence the structure and mainly to control the density of the freeze-dried product Batch Freeze Dryers Freeze dryers are normally multishelf units with the product in trays or multiple glass vials . The main components are (1) the vacuum chamber, heating plates, and vapor traps, all built into the freeze dryer and (2) the external systems, such as the transport system for the product trays, the deicing system, and the support systems for supply of heat, vacuum, and refrigeration . In some units, the trays are carried in tray trolleys suspended in an overhead rail system for easy transport and quick loading and unloading, as illustrated in Fig . 12-112 . Heat transfer is by conduction from the shelf below and radiation from the shelves above and below . As driving forces are low, a large heating surface is desirable . The heating plates should be at uniform temperatures, not exceeding 2°C to 3°C across the dryer, so the distribution of the heating medium (usually silicone thermal oil) to the heating plates and the flow rate inside the plates are very important factors . If the product has been frozen externally, the operation vacuum should be reached quickly (within 10 min) to avoid the risk of product melting, and the heating plates are cooled to approximately 25°C . When the operating vacuum is achieved, the heating plate temperature is raised quickly to the desired operating temperature . Important features of a modern freeze-drying plant include a built-in vapor trap, allowing a large opening for vapor flow to the condenser, and a continuous deicing (CDI) system, reducing the ice layer on the condenser to a maximum of 6 to 8 mm . At 1 mbar pressure, the vapor flow rate is typically about 1 m3/(s × m2 of tray area) .

Tray carrier

Product tray Heating plates

Cycle Operating Conditions Low shelf temperatures give slower drying and increase the refrigeration load; about 75 percent of the energy costs relate to the refrigeration plant, and if the set temperature is 10°C lower than optimum, its energy consumption will increase by approximately 50 percent . However, although the product is kept cool by the sublimation, it must be kept below the temperature where product “collapse” or “meltback” occurs . This value can be measured at small scale with a freeze-drying microscope, and it can be chosen as an upper limit for the shelf temperature in primary drying . A control strategy is generally based on applied pressure and shelf temperature . In secondary drying, there is no danger of meltback, and higher shelf temperatures may be usable . Final moisture is typically 2 to 3 percent . Typical vacuum levels are 0 .4 to 1 .3 mbar absolute (40 to 130 Pa) for foods and 10 to 20 Pa for pharmaceuticals . Table 12-48 shows a typical cycle for a pharmaceutical product . Continuous Freeze Drying The utility requirements for batch freeze dryers vary considerably over the cycle . During sublimation drying, the requirements are 2 to 2 .5 times the average requirement, and the external systems must be designed accordingly . To overcome this peak load and to meet the market request for high unit capacities, continuous freeze dryer designs have been developed and implemented for coffee drying . These require vacuum locks for product both entering and leaving the dryer . As the tray stacks move through the freeze dryer, they can pass through different temperature zones to give a heating profile, selected so that overheating of dry surfaces is avoided . Design Methods The size of the freeze-drying plant is based on the batch size and average sublimation capacity required as well as on the product type and form . The evaporation temperature of the refrigeration plant depends on the required vacuum . At 1 mbar it will be −35 to −40°C depending on the vapor trap performance . Sample data are shown in Table 12-49 . There is extensive specialized literature on freeze drying, and hands-on courses are available, e .g ., from Biopharma . Electromagnetic Drying Methods Examples and Synonyms Infrared, radiofrequency, microwave, electromagnetic heating, dielectric heating Description Electromagnetic drying methods employ radiation (infrared, radiofrequency, and microwave) to produce heating . In the instances of radiofrequency and microwave heating, electromagnetic radiation is absorbed by dipolar liquids, such as water or liquids containing dissolved salts . In infrared heating, heat radiates from an extremely hot element . Generally, dielectric methods heat volumetrically and are suitable for thicker materials whereas infrared energy is considered a surface-heating method . Since these are heating methods, drying systems also need to enable moisture removal either by using air or heating the material above the boiling temperature . These heating methods are often used in conjunction with hot air . Dielectric Methods (Radiofrequency and Microwave) Schiffmann (1995) states that dielectric/radiofrequency heating operates in the range of 1 to 100 MHz, while microwave frequencies range from 300 MHz to 300 GHz . The electromagnetic spectrum shown in Fig . 12-113 illustrates the relative differences in wavelength and frequency between radio waves and microwaves . All electromagnetic waves are characterized by both wavelength and frequency . An example of a simplified electromagnetic wave is shown in Fig . 12-114 . An electromagnetic wave is a combination of an electric component E and a magnetic component H . Note that E and H are perpendicular to each other and both are perpendicular to the direction of travel . The devices used for generating microwaves are called magnetrons and klystrons whereas the devices used to generate dielectric frequencies are referred to as oscillators and triodes or tetrodes . Water molecules are dipolar (i .e ., they have an asymmetric charge center) and are normally randomly oriented . The rapidly changing polarity of a microwave or radiofrequency field attempts to pull these dipoles into alignment with the field . As the field changes polarity, the dipoles return to a

Sliding gate Vacuum plant Condenser under de-icing

TABLE 12-48 Example Pharmaceuticals Freeze-Drying Cycles, with and Without Annealing During Freezing

Active condenser

No annealing

Freezing Deicing chamber

FIG. 12-112

Cross-section of RAY batch freeze dryer . (GEA)

Primary drying

With annealing

Shelf temperature, °C

Time, h

Shelf temperature, °C

−40

6

−30, −5, −40

10 40

Time, h

0

55

0

Secondary drying

25

2

25

2

Total

—

63

—

52

SOLIDS-DRYING FUNDAMENTALS TABLE 12-49

12-85

Freeze Dryer Performance Date, Niro Ray and Conrad Types Typical sublimation capacity Tray area, m2

Flat tray, kg/h

Ribbed tray, kg/h

Electricity consumption, kWh/kg, sublimated

Steam consumption, kg/kg sublimated

68 91 114

68 91 114

100 136 170

1 .1 1 .1 1 .1

2 .2 2 .2 2 .2

240 320 400

240 320 400

360 480 600

1 .0 1 .0 1 .0

2 .0 2 .0 2 .0

RAY Batch Plant—1 mbar RAY 75 RAY 100 RAY 125∗ CONRAD Continuous Plant—1 mbar CONRAD 300 CONRAD 400 CONRAD 500∗ ∗Other sizes available .

random orientation before being pulled the other way . This buildup and decay of the field, and the resulting stress on the molecules, causes a conversion of electric field energy to stored potential energy, then to random kinetic or thermal energy . Hence dipolar molecules such as water absorb energy in these frequency ranges . The power developed per unit volume Pυ by this mechanism is Pυ = kE 2 f ε ′ tan δ = kE 2 f ε ′′

(12-118)

where k is a dielectric constant, depending on the units of measurement, E is the electric field strength (V/m3), f is the frequency, e′ is the relative dielectric constant or relative permeability, tan d is the loss tangent or dissipation factor, and e″ is the loss factor . The field strength and the frequency are dependent on the equipment, while the dielectric constant, dissipation factor, and loss factor are materialdependent . The electric field strength is also dependent on the location of the material within the microwave/radiofrequency cavity [Turner and Ferguson, “A Study of the Power Density Distribution Generated during the Combined Microwave and Convective Drying of Softwood,” Drying Technol. 12(5–7): 1411–1430 (1995)], which is one reason why domestic microwave ovens have rotating turntables (so that the food is exposed to a range of microwave intensities) . This mechanism is the major one for the generation of heat within materials by these electromagnetic fields . There is also a heating effect due to ionic conduction . The water inside a material may contain ions such as sodium, chloride, and hydroxyl; these ions are accelerated and decelerated by the changing electric field . The collisions that occur as a result of the rapid accelerations and decelerations lead to an increase in the random kinetic (thermal) energy of the material . This type of heating is not significantly dependent on either temperature or frequency . The power developed per unit volume Pυ from this mechanism is Pu = E 2 qnµ

(12-119)

where q is the amount of electric charge on each of the ions, n is the charge density (ions/m3), and m is the level of mobility of the ions . Schiffmann (1995) indicates that the dielectric constant of water is more than an order of magnitude higher than that of most underlying materials, and the overall dielectric constant of most materials is usually nearly proportional to moisture content up to the critical moisture content, often around 20 to 30 percent . Hence microwave and radiofrequency methods

preferentially heat and dry wetter areas in most materials, a process which tends to give more-uniform final moisture contents . The dielectric constant of air is very low compared with that of water, so lower density usually means lower heating rates . For water and other small molecules, the effect of increasing temperature is to decrease the heating rate slightly, hence leading to a self-limiting effect . Other effects ( frequency, conductivity, specific heat capacity, etc .) are discussed by Schiffmann (1995), but are less relevant because the range of available frequencies (which do not interfere with radio transmissions) is small (2 .45 GHz, 910 MHz) . Higher frequencies lead to lower penetration depths into a material than lower frequencies do . Sometimes the 2 .45-GHz frequency has a penetration depth as low as 2 .5 cm (1 in) . For in-depth heating (volumetric heating), radio frequencies with lower frequencies and longer wavelengths are often used . Note that not all frequencies are available to use in all geographies as designated by the International Telecommunication Union, as seen in Table 12-50 . Also note that microwave and radiofrequency generators are often used in conjunction with other dryer types to enhance drying rates, especially in thicker materials . Achieving uniform heating is challenging when using these electromagnetic heating methods . Infrared Methods Infrared (IR) radiation is commonly used in the dehydration of coated films and to even out the moisture content profiles in the drying of paper and boards . The mode of heating is essentially on the material surface, and IR sources are relatively inexpensive compared with dielectric sources . The heat flux obtainable from an IR source is given by

(

4 4 − Tdrying material q = F αε Tsource

(12-120)

where q = heat flux, W/m2; α = Stefan-Boltzmann constant = 5 .67 × 10−8 W/ (m2 ⋅ K4); ε = emissivity (0 to 1); F = view factor; and T = absolute temperature of the source or drying material . The emissivity is a property of the material . The limiting value is 1 (blackbody); shiny surfaces have a low value of emissivity . The view factor is a fractional value that depends on the geometric orientation of the source with respect to the heating object . It is very important to recognize the T 4 dependence on the heat flux . IR sources need to be very hot to give appreciable heat fluxes . Therefore, IR sources should not be used with flammable materials . Improperly designed IR systems can also overheat materials and equipment .

Wavelength, m

Frequency, MHz FIG. 12-113 Electromagnetic spectrum .

)

12-86

PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING TABLE 12-51 Results for Example 12-24: Sheet Drying with Convection and Infrared

y

Distance, m

E

H

EO

IR panel temperature, °C

23 .0

None

13 .4

300

6 .4

500

3 .0

700

x “see” and they need to be extremely hot . The panels must be shut off if the line stops, or else the material may be damaged or pose a fire risk . Infrared heating needs special considerations if the process is expected to create volatile or flammable materials .

HO

Additional Reading z

Schiffman, R, “Microwave and Dielectric Drying,” chap . 11 in Mujumdar, A ., Handbook of Industrial Drying, 2d ed., Marcel Dekker, New York, 1995, pp . 345–372 .

FIG. 12-114 Illustration of a simple EM wave . Here E and H represent the electrical and magnetic components of the wave, respectively . E0 and H0 show their respective amplitudes . (Reprinted with permission from Mujumdar, A.S., Handbook of Industrial Drying, 2nd ed., Marcel Dekker Inc., New York, 1995.)

Example 12-24 Sheet Drying with Convection and Infrared In the same sheet drying problem as in Example 12-23, the belt has been removed, and now the sheet to be dried will be suspended in air using tensioning rollers (see Fig . 12-104) . The same impinging air heat-transfer process occurs at the bottom of the web, but now flat infrared heat panels will be installed along the length of the dryer above the sheet . Calculate the dryer length needed to dry the material from the inlet at 40 percent wet basis to the outlet at 10 percent dry basis without infrared and with the infrared on with panel temperatures at 300, 500, and 700°C . Assume the emissivity and view factors are unity . We will use the energy and mass balance equations as before, except we will include the infrared term . We will assume that the web is thin enough that we can neglect temperature gradients through its thickness . (C p ,solids + C p ,water ⋅wavg,dry-basis ) ⋅

msheet dTsheet ⋅ = h ⋅ (Tair − Tsheet ) A dt 4 − T 4 )  − F ⋅ ∆H vap        + FView αε (Tsource (12-121)

We also write a mass balance:

dmw 1 = kc ⋅(Cwsurface − Cwbulk ) dt A

(12-122)

Results are shown in Table 12-51 . The calculation indicates that the drying rate can be greatly accelerated by the infrared . However, there are some idealizations such as the view factor and emissivity value . Running infrared panels can introduce problems since they apply heat to anything they

TABLE 12-50 Frequency Designation by the International Telecommunication Union (Schiffmann, 1995) Center frequency (MHz)

Frequency range (MHz)

Maximum radiation limit∗

6 .780

6 .765–6 .795

13 .560

13 .553–13 .567

Unrestricted

27 .120

26 .957–27 .283

Unrestricted

40 .680

40 .660–40 .700

Unrestricted

433 .920

433 .050–434 .790

915 .000

Under consideration

OPERATION AND TROUBLESHOOTING Troubleshooting Dryer troubleshooting is not extensively covered in the literature, but a systematic approach has been proposed in Kemp and Gardiner, “An Outline Method for Troubleshooting and Problem-Solving in Dryers,” Drying Technol . 19(8): 1875–1890 (2001) . The main steps of the algorithm are as follows: • Problem definition—definition of the dryer problem to be solved • Data gathering—collection of relevant information, e .g ., plant operating data • Data analysis, e .g ., heat and mass balance, and identification of the cause of the problem • Conclusions and actions—selection and implementation of a solution in terms of changes to process conditions, equipment, or operating procedures • Performance auditing—monitoring to ensure that the problem was permanently solved The algorithm might also be considered as a “plant doctor .” The doctor collects data, or symptoms, and makes a diagnosis of the cause(s) of the problem . Then alternative solutions, or treatments, are considered and a suitable choice is made . The results of the treatment are reviewed (i .e ., the process is monitored) to ensure that the “patient” has returned to full health . See Fig . 12-115 . The algorithm is an excellent example of the “divergent-convergent” (brainstorming) method of problem solving . It is important to list all possible causes and solutions, no matter how ridiculous they may initially seem; there may actually be some truth in them, or they may lead to a new and better idea . Problem Categorization In the problem definition stage, it is extremely useful to categorize the problem, as the different broad groups require different types of solution . Five main categories of dryer problems can be identified: 1 . Drying process performance (outlet moisture content too high, throughput too low) 2 . Materials handling (dried material too sticky to get out of dryer, causing blockage) 3 . Product quality (too many fines in product, bulk density too low/high, discoloration, etc .) 4 . Mechanical breakdown (catastrophic sudden failure) 5 . Safety, health, and environmental issues (drying air temperature too high, buildup of material in dryer, etc .)

Under consideration

902–928

Unrestricted

2450

2400–2500

Unrestricted

5800

5725–5875

Unrestricted

24,125

24,000–24,250

Under consideration

61,250

61,000–61,500

Under consideration

122,500

122,000–123,000

Under consideration

245,000

240,000–246,000

Under consideration

∗The term unrestricted applies to the fundamental and all other frequency components falling within the designated band . Special measures to achieve compatibility may be necessary where other equipment satisfying immunity requirements is placed close to ISM equipment .

FIG. 12-115

Schematic diagram of algorithm for dryer troubleshooting .

SOLIDS-DRYING FUNDAMENTALS Experience suggests that the majority of problems are of the first three types, and these are about equally split over a range of industries and dryer types . Ideally, unforeseen safety, health, and environmental issues will be rare, as these will have been identified in the safety case before the dryer is installed or during commissioning . Likewise, major breakdowns should be largely avoided by a planned maintenance program . Drying Performance Problems Performance problems can be further categorized as 1 . Heat and mass balance deficiencies (not enough heat input to do the evaporation) 2 . Drying kinetics (drying too slowly, or solids residence time in dryer is too short) 3 . Equilibrium moisture limitations (reaching a limiting value, or regaining moisture in storage) For the heat and mass balance, the main factors are • Solids throughput • Inlet and outlet moisture content • Temperatures and heat supply rate • Leaks and heat losses As well as problem-solving, these techniques can be used for performance improvement and debottlenecking . Drying kinetics, which are affected by temperature, particle size, and structure, are limited by external heat and mass transfer to and from the particle surface in the early stages; but internal moisture transport is the main parameter at lower moisture . Equilibrium moisture content increases with higher relative humidity, or with lower temperature . Problems that depend on the season of the year, or vary between day and night (both suggesting a dependence on ambient temperature and humidity), are often related to equilibrium moisture content . Materials Handling Problems The vast majority of handling problems in a dryer concern sticky feedstocks . Blockages can be worse than performance problems as they can close down a plant completely, without warning . Most stickiness, adhesion, caking, and agglomeration problems are due to mobile liquid bridges (surface moisture holding particles together) . These are extensively described in particle technology textbooks . Unfortunately, these forces tend to be at a maximum when the solid forms the continuous phases and surface moisture is present, which is the situation for most filter and centrifuge cakes at discharge . By comparison, slurries (where the liquid forms the continuous phase) and dry solids (where all surface moisture has been eliminated) are relatively free-flowing and incur fewer problems . Other sources of problems include electrostatics (most marked with fine and dry powders) and immobile liquid bridges, the so-called “sticky-point phenomenon .” This latter is sharply temperature-dependent, with only a weak dependence on moisture content, in contrast to mobile liquid bridges . It occurs for only a small proportion of materials, but is particularly noticeable in amorphous powders and foods and is often linked to the glass transition temperature . Product Quality Problems (These do not include the moisture level of the main solvent .) Many dryer problems either concern product quality or cannot be solved without considering the effect of any changes on product quality . Thus it is a primary consideration in most troubleshooting, although product quality measurements are specific to the particular product, and it is difficult to generalize . However, typical properties may include color, taste (not easily quantifiable), bulk density, viscosity of a paste or dispersion, dispersibility, or rate of solution . Others are more concerned with particle size, size distribution (e .g ., coarse or fine fraction), or powder handling properties such as rate of flow through a standard orifice . These property measurements are nearly always made off-line, either by the operator or by the laboratory, and many are very difficult to characterize in a rigorous quantitative manner . (See also the Fundamentals subsection .) Storage problems, very common in industry, result if the product from a dryer is free-flowing when packaged, but has caked and formed solid lumps by the time it is received by the customer . Sometimes the entire internal contents of a bag or drum have welded together into a huge lump, making it impossible to discharge . Depending on the situation, there are at least three different possible causes: 1 . Equilibrium moisture content: hygroscopic material is absorbing moisture from the air on cooling . 2 . Incomplete drying: product is continuing to lose moisture in storage . 3 . Psychrometry: humid air is cooling and reaching its dew point . The three types of problem have some similarities and common features, but the solution to each one is different . Therefore, it is essential to understand which mechanism is actually in play . Option 1: The material is hygroscopic and is absorbing moisture back from the air in storage, where the cool air has a higher relative humidity than the hot dryer exhaust . Solution: Pack and seal the solids immediately

12-87

on discharge in tough impermeable bags (usually double- or triple-lined to reduce the possibility of tears and pinholes), and minimize the ullage (airspace above the solids in the bags) so that the amount of moisture that can be absorbed is too low to cause any significant problem . Dehumidifying the air to the storage area is also possible, but often very expensive . Option 2: The particles are emerging with some residual moisture, and they continue to dry after being stored or bagged . As the air and solids cool, the moisture in the air comes out as dew and condenses on the surface of the solids, causing caking by mobile liquid bridges . Solution: If the material is meeting its moisture content specification, cool the product more effectively before storage, to stop the drying process . If the outlet material is wetter than stated in the specification, alter dryer operating conditions or install a postdryer . Option 3: Warm, wet air is getting into the storage area or the bags, either because the atmosphere is warm with a high relative humidity (especially in the tropics) or because dryer exhaust air has been allowed to enter . As in option 2, when the temperature falls, the air goes below its dew point and condensation occurs on the walls of the storage area or inside the bags, or on the surface of the solids, leading to caking . Solution: Avoid high-humidity air in the storage area . Ensure the dryer exhaust is discharged a long way away . If the ambient air humidity is high, consider cooling the air supply to storage to bring it below its dew point and reduce its absolute humidity . Dryer Operation Start-Up Considerations It is important to start up the heating system before introducing product into the dryer . This will minimize condensation and subsequent product buildup on dryer walls . It is also important to minimize off-quality production by not overdrying or underdrying during the start-up period . Proper control system design can aid in this regard . The dryer turndown ratio is also an important consideration during start-up . Normally the dryer is started up at the lowest end of the turndown ratio, and it is necessary to match heat input with capacity load . Shutdown Considerations The sequence for dryer shutdown is also very important and depends on the type of dryer . The sequence must be thoroughly thought through to prevent significant off-quality product or a safety hazard . The outlet temperature during shutdown is a key operating variable to follow . Energy Considerations The first consideration is to minimize the moisture content of the dryer feed, e .g ., with dewatering equipment, and to establish as high an outlet product moisture target as possible . Other energy considerations vary widely by dryer type . In general, heating with gas, fuel oil, and steam is significantly more economical than heating with electricity . Hence radiofrequency (RF), microwave, and infrared drying is energyintensive . Direct heating is more efficient than indirect in most situations . Sometimes air recycle (direct or indirect) can be effective in reducing energy consumption . And generally operating at high inlet temperatures is more economical . Recycle In almost all situations, the process system must be able to accommodate product recycle . The question is how to handle it most effectively, considering the product quality, equipment size, and energy . Improvement Considerations The first consideration is to evaluate mass and energy balances to identify problem areas. See the Experimental Methods part of this subsection for guidance on how to conduct a mass and energy balance on an industrial dryer . This will identify air leaks and excessive equipment heat losses and will enable determination of overall energy efficiency . A simplified heat balance will show what might need to be done to debottleneck a convective (hot gas) dryer, i .e ., increase its production rate F . F(XI - XO)levap ≈ GCPG(TGI - TGO) - Qwl Before proceeding along this line, however, it is necessary to establish that the dryer is genuinely heat and mass balance–limited . If the system is controlled by kinetics or equilibria, changing the parameters may have undesirable side effects, e .g ., increasing the product moisture content . The major alternatives are then as follows (assuming gas specific heat capacity CPG and latent heat of evaporation levap are fixed): 1 . Increase the gas flow rate G, as it usually increases pressure drop, so new fans and gas cleaning equipment may be required . 2 . Increase the inlet gas temperature TGI which is usually limited by risk of thermal damage to product . 3 . Decrease the outlet gas temperature TGO . But note that this increases NTUs, outlet humidity, and relative humidity and reduces both the temperature and humidity driving forces . Hence it may require a longer drying time and a larger dryer, and it may also increase equilibrium and outlet moistures . 4 . Reduce inlet moisture content XI, say, by dewatering by gas blowing, centrifuging, vacuum or pressure filtration, or a predryer . 5 . Reduce heat losses Qwl by insulation, removing leaks, etc .

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PSYCHROMETRY, EVAPORATIVE COOLING, AND SOLIDS DRYING

Dryer Safety This subsection discusses some of the key considerations in dryer safety . General safety considerations are discussed in Sec . 23, Process Safety, and should be referred to for additional guidance . Fires, explosions, and, to a lesser extent, runaway decompositions are the primary hazards associated with drying operations . The outbreak of fire is a result of ignition which may or may not be followed by an explosion . A hazardous situation is possible if 1 . The product is combustible . 2 . The product is wetted by a flammable solvent . 3 . The dryer is direct-fired . An explosion can be caused by dust or flammable vapors, both of which are fires that rapidly propagate, causing a pressure rise in a confined space . Dust Explosions Dispersion dryers can be more hazardous than layertype dryers if one is drying a solid combustible material which is then dispersed in air, particularly if the product is a fine particle size . If this finely dispersed product is then exposed to an ignition source, an explosion can result . The following conditions (van’t Land, Industrial Drying Equipment, Marcel Dekker, New York, 1991) will be conducive to fire and explosion hazard: 1 . Small particle sizes, generally less than 75 mm, which are capable of propagating a flame 2 . Dust concentrations within explosive limits, generally 10 to 60 g/m3 3 . Ignition source energy of 10 to 1000 mJ or as low as 5 mJ for highly explosive dust sources 4 . Atmosphere supporting combustion Since most product and hence dust compositions vary widely, it is generally necessary to do quantitative testing in approved test equipment . Flammable Vapor Explosions This can be a problem for products wetted by flammable solvents if the solvent concentration exceeds 0 .2 percent v/v in the vapor phase . The ignition energy of vapor-air mixtures is lower (< 1 mJ) than that of dust-air suspensions . Many of these values are available in the literature, but testing may sometimes be required . Ignition Sources There are many possible sources of an ignition, and they need to be identified and addressed by both designers and operators . A few of the most common ignition sources are 1 . Spontaneous combustion 2 . Electrostatic discharge 3 . Electric or frictional sparks 4 . Incandescent solid particles from heating system Safety hazards must be addressed with proper dryer design specifications . The following are a few key considerations in dryer design . Inert system design The dryer atmosphere is commonly made inert with nitrogen, but superheated steam or self-inertized systems are also possible . Self-inertized systems are not feasible for flammable solvent systems . These systems must be operated with a small overpressure to ensure no oxygen ingress . And continuous on-line oxygen concentration monitoring is required to ensure that oxygen levels remain well below the explosion hazard limit . Relief venting Relief vents that are properly sized relieve and direct dryer explosions to protect the dryer and personnel if an explosion does occur . Normally they are simple pop-out panels with a minimum length of ducting to direct the explosion away from personnel or other equipment . Suppression systems Suppression systems typically use an inert gas such as carbon dioxide to minimize the explosive peak pressure rise and fire damage . The dryer operating pressure must be properly monitored to detect the initial pressure rise followed by shutdown of the dryer operating systems and activation of the suppression system . Clean design Care should be taken in the design of both the dryer and dryer ancillary equipment (cyclones, filters, etc .) to eliminate ledges, crevices, and other obstructions that can lead to dust and product buildup . Smooth drying equipment walls will minimize deposits . This can go a long way in prevention . No system is perfect, of course, and a routine cleaning schedule is also recommended . Start-up and shutdown Start-up and shutdown situations must be carefully considered in designing a dryer system . These situations can create higher than normal dust and solvent concentrations . This coupled with elevated temperatures can create a hazard well beyond that of normal continuous operation . Environmental Considerations Environmental considerations are continuing to be an increasingly important aspect of dryer design and operation as environmental regulations are tightened . The primary environmental problems associated with drying are particulate and volatile organic compound (VOC) emissions . Noise can be an issue with certain dryer types . Environmental Regulations These vary by country, and it is necessary to know the specific regulations in the country in which the dryer will be installed . It is also useful to have some knowledge of the direction of regulations so that the environmental control system is not obsolete by the time it becomes operational .

Particulate emission problems can span a wide range of hazards . Generally, there are limits on both toxic and nontoxic particles in terms of annual and peak emissions limits . Particles can present toxic, bacterial, viral, and other hazards to human, animal, and plant life . Likewise, VOC emissions can span a wide range of hazards and issues from toxic gases to smelly gases . Environmental Control Systems We should consider environmental hazards before the drying operation is even addressed . The focus should be on minimizing the hazards created in the upstream processing operations . After potential emissions are minimized, these hazards must be dealt with during dryer system design and then subsequently with proper operational and maintenance procedures . Particle Emission Control Equipment The four most common methods of particulate emissions control are as follows: 1 . Cyclone separators The advantage of cyclones is they have relatively low capital and operating costs . The primary disadvantage is that they become increasingly ineffective as the particle size decreases . As a general rule of thumb, we can say that they are 100 percent efficient with particles larger than 20 mm and 0 percent efficient with particles smaller than 1 mm . Cyclones can also be effective precleaning devices to reduce the load on downstream bag filters . 2 . Scrubbers The more general classification is wet dedusters, the most common of which is the wet scrubber . The advantage of wet scrubbers is that they can remove fine particles that the cyclone does not collect . The disadvantages are that they are more costly than cyclones and they can turn air contamination into water contamination, which may then require additional cleanup before the cleaning water is put into the sewer . 3 . Bag filters The advantages of filters are that they can remove very fine particles; and bag technologies continue to improve and enable eversmaller particles to be removed without excessive pressure drops or buildup . The primary disadvantages are higher cost relative to cyclones and greater maintenance costs, especially if frequent bag replacement is necessary . 4 . Electrostatic precipitators The capital cost of these systems is relatively high, and maintenance is critical to effective operation . VOC Control Equipment The four most prevalent equipment controls are 1 . Scrubbers Similar considerations as above apply . 2 . Absorbers These systems use a high-surface-area absorbent, such as activated carbon, to remove the VOC absorbate . 3 . Condensers These systems are generally only feasible for recovering solvents from nonaqueous wetted products . 4 . Thermal and catalytic incinerators These can be quite effective and are generally a low capital and operating cost solution, except in countries with high energy costs . Noise Noise analysis and abatement is a very specialized area . Generally, the issue with dryers is associated with the fans, particularly for systems requiring fans that develop very high pressures . Noise is a very big issue that needs to be addressed with pulse combustion dryers, and it can be an issue with very large dryers such as rotary dryers and kilns . Additional considerations regarding environmental control and waste management are addressed in Sec . 22, Waste Management, and Sec . 23, Process Safety . Control and Instrumentation The purpose of the control and instrumentation system is to provide a system that enables the process to produce the product at the desired moisture target and to meet other quality control targets discussed earlier (density, particle size, color, solubility, etc .) . This segment discusses key considerations for dryer control and instrumentation . Additional more-detailed information can be found in Sec . 8, Process Control . Proper control of product quality starts with the dryer selection and design . Sometimes two-stage or multistage systems are required to meet product quality targets . Multistage systems enable us to better control temperature and moisture profiles during drying . Assuming the proper dryer design has been selected, we must then design the control and instrumentation system to meet all product quality targets . Manual versus Automatic Control Dryers can be controlled either manually or automatically . Generally, lab-, pilot-, and small-scale production units are controlled manually . These operations are usually batch systems, and manual operation provides lower cost and greater flexibility . The preferred mode for large-scale, continuous dryers is automatic . Key Control Variables Product moisture and product temperature are key control variables . Ideally both moisture and temperature measurement are done on-line, but frequently moisture measurement is done off-line and temperature (or exhaust air temperature) becomes the primary control variable . And generally the inlet temperature will control the rate of production, and the outlet temperature will control the product moisture and other product quality targets .

SOLIDS-DRYING FUNDAMENTALS Common Control Schemes Two relatively simple, but common control schemes in many dryer systems (Fig . 12-116) are as follows: 1 . The outlet air temperature is controlled by feed rate regulation with the inlet temperature controlled by gas heater regulation . 2 . The outlet air temperature is controlled by heater regulation with the feed rate held constant . Alternatively, product temperatures can replace air temperatures with the advantage of better control and the disadvantage of greater maintenance of the product temperature sensors . Other Instrumentation and Control Pressure Pressure and equipment pressure drops are important to proper dryer operation . Most dryers are operated under vacuum . This prevents dusting to the environment, but excess leakage in decreases dryer efficiency . Pressure drops are especially important for stable fluid-bed operation . Air (gas) flow rate Obviously gas flows are another important parameter for proper dryer operation . Pitot tubes are useful when a system has

Air Heater Inlet Air Temperature Product Feeder

Dryer

Product Discharge

Outlet Air Temperature FIG. 12-116 Typical dryer system .

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no permanent gas flow sensors . Averaging pitot tubes work well in permanent installations . The devices work best in straight sections of ductwork which are sometimes difficult to find and make accurate measurement a challenge . Product feed rate It’s important to know that product feed rates and feed rate changes are sometimes used to control finished-product moistures . Weigh belt feeders are common for powdered products, and there is a wide variety of equipment available for liquid feeds . Momentum devices are inexpensive but less accurate . Humidity The simplest method is sometimes the best . Wet- and drybulb temperature measurement to get air humidity is simple and works well for the occasional gas humidity measurement . The problem with permanent humidity measurement equipment is the difficulty of getting sensors robust enough to cope with a hot, humid, and sometimes dusty environment . If these are used, be careful about placement and inspection to ensure that product does not accumulate on the sensor . Interlocks Interlocks are another important feature of a well-designed control and instrumentation system . Interlocks are intended to prevent damage to the dryer system or to personnel, especially during the critical periods of start-up and shutdown . The following are a few key interlocks to consider in a typical dryer system . Drying chamber damage This type of damage can occur when the chamber is subjected to significant vacuum when the exhaust fans are started up before the supply fans . Personnel injury This interlock is to prevent injury due to entering the dryer during operation, but more typically to prevent dryer start-up with personnel in the main chamber or inlet or exhaust air ductwork on large dryers . This typically involves microswitches on access doors coupled with proper door lock devices and tags . Assurance of proper start-up and shutdown These interlocks ensure, e .g ., that the hot air system is started up before the product feed system and that the feed system is shut down before the hot air system . Heater system There are a host of important heater system interlocks to prevent major damage to the entire drying system . Additional details can be found in Sec . 23, Process Safety .

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Section 13

Distillation

Michael F. Doherty, Ph.D. (Section Editor)

Professor of Chemical Engineering, Un